American Public University MATH 110 Complete Course

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MATH 110 Week 1 Homework Test 1 1. Find the slope of the line passing through the points given below or state that the slope is

undefined. Then indicates whether the line through the points rises, fall is horizontal, or is vertical.(4,3)

and (5,7)

2. Find the slope of the line passing through the pair of points or state that the slope is undefined

.then indicates whether the line through the points rises, falls, is horizontal, or vertical.

3. For the equation y=8-4x, answer parts (a) and (b)

4. Find the slope and the y intercept

5. Graph the line y=mx+b for the given values.

6. Solve for y 6x+y= 18

7. Complete the ordered pairs so that each is a solution of the given linear equation. Then graph

the equation.

8. Find the slope of the line that goes through the following pairs of points. (5, 4) and (6, 2)

9. Find the missing coordinates to complete the following ordered –pairs solutions to the given

linear equation. Y+2x=5

10. Find the slope and the y – intercept.

11. Find the slope of the line passing through the pair of points that the slope is undefined. Then

indicates whether the line through the point rises, falls, is horizontal, or is vertical. (-2,8) and (-2,-4)

12. Find the slope and the y-intercept y=9x+6

13. Find the slope of the line passing through the pair of points or state that the slope is undefined.

Then indicate whether the line through the point rises, falls, is horizontal, or is vertical. (7, 9) and (-4, 9)

14. Find the slope and the y-intercept of the line given by the following equation.

15. Solve the following equation for y. 5x+6y=30 find the missing coordinates to complete the

ordered pair (6,)

16. Plot each point in the xy plane. Tell in which quadrant or what coordinates axis each point lies.

17. Use the following to write the equation of the line in slope-intercept form. M=-5,y-intercept(0,-

16).

18. Solve for y. Y-3 = -1/4x

19. Solve for y. 8x-4y=12

20. Graph the equation 5x-6y=0

21. Determine the coordinates of each of the points plotted. Tell in which quadrant or on what

coordinate axis each point lies.

22. Find the missing coordinates to complete the ordered pair solution to the given linear equation.

23. Graph the equation. Be sure to simplify the equation before graphing it. 20+6y=2y

24. Determine whether the given points are on the graph of the equation. 4x+3y= 15

25. Use the slope- intercept form to graph the equation y=5/3x+2

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MATH 110 Week 1 Homework 3.1 1. Plot each point in the xy plane. Tell in which quadrant or on what coordinate axis each point lies.

2. Determine the coordinates of each of the points plotted. Tell in which quadrant or on what

coordinate or on what coordinate axis each point lies.

3. Solve for y 3x+y=9

4. Solve for y 8x-4y=20

5. Solve the equation for y.

4x+6y= 24

6. Determine whether the given points are on the graph of the equation.

7. Solve for y. Y-8 = -2/3x

8. Solve the equation for y

8x+y=15

9. solve the following equation for y.

5x+6y=30

10. find the missing coordinate to complete the ordered pair solution to the given linear equation.

11. find the missing coordinates to complete the following ordered pair solutions to the given linear

equation.

12. find the missing coordinate to complete the ordered-pair solution to the given linear equation.

13. find the missing coordinate to complete the ordered-pair solution to the given linear equation

14. the map to the right shows the layout of towns in particular county .like many maps used in driving

or flying , it has horizontal and vertical grid makers for ease of use. Use the grid labels to indicates the

location of town 6.

15. the map to the right shows the layouts of towns in a particular county. Like many maps used in

driving or flying . it has horizontal and vertical grid makers for ease of use. Use the grid labels to indicate

the location of town 8.

16. the map to the right shows the layouts of towns in a particular county. Like many maps used in

driving or flying . it has horizontal and vertical grid makers for ease of use. Use the grid labels to indicate

the location of town 8.

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MATH 110 Week 1 Homework 3.2 1. Is the point (4,8) a solution to the equation 3x+7y=68? Why or why not?

2. Fill the blank so that the resulting statement is true.

3. Complete the ordered pairs so that each is a solution of the given linear equation. Then graph

the equation.

4. Complete the ordered pairs so that each is a solution of the given linear equation. The graph the

equation.

5. Complete the ordered pairs (0,-),(2,-) and (-1,-) so that each is a solution of the given linear

equation. Then graph the equation.

6. Complete the ordered pairs so that each is a solution of the given linear equation then graph the

equation.

7. Graph the following equation by plotting three points and connecting them. Use a tables of

values to organize the ordered pairs.

8. Graph the following equation by plotting three points and connecting them. Use a tables to

value to organize the ordered pairs.

9. Graph the equation 9x-5y=0

10. For the equation y =6-2x, answer parts (a) and (b).

11. Graph the equation. Be sure to simplify the equation before graphing it. 3x+5y= -18

12. Graph the linear equation by any method. Y=2x-3

13. Graph the linear equation by any method y=-2x+5

14. Graph the linear equation by any method 4x=-12y+8

15. Graph the equation x=5

16. Graph the equation. Be sure to simplify the equation before graphing it. 18+3y= -3y

17. Graph the equation. Be sure to simplify the equation before graphing it. 8+6x=4x

18. The number of foreign students enrolled in a certain college is approximated by the equation

S=16t+270, where is the number of years since 1980,and S is the number of foreign students. Graph the

equations for t=0, 15.

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MATH 110 Week 2 Homework Test 2 1. Choose which represents the following inequality. 2x- 5y> -5

2. Graph the following inequality. Y>=1

3. Graph the equation y=5x2

4. Write an equation of the line in the figure below.

5. How can you tell whether a graph is the graph of a function?

6. Find an equation of the line that has the given slope and passes through the given point. M= -

5,(4,5)

7. Graph the inequality. X<=6

8. Use the vertical line test to determine whether the given graph is the graph of a function.

9. A line has a slope of 10. What is the slope of the line parallel to it?

10. Graph the region described by the following inequality.2x-y<=6

11. Write an equation of the line passing through the points(4,7) and (-2,-17).

12. Graph the following inequality. Y>-1

13. Write an equation of the line in the figure.

14. Determine if the ordered pairs (-1,5) and (2,-5) are solutions of the following linear inequality in

two variables. -5x+ 4y<= -5

15. Given the following functions, find the indicated values.

16. Find an equation of the line that passes through (0,7) and is parallel to y= 1/3x+6

17. Find an equation of the line that passes through (2,4) and is perpendicular to y =2x-8

18. Determine whether the relation is a function.

19. Find the domain and range of the relation. Determine whether the relation is a function.

20. During a recent population growth period in a certain state, from 1995 to 2005, the approximate

population of the state measured in millions could be predicted by the function f(x)= 0.02x2+0.06x+30.8,

where x is the number of years since 1995. Find f(0), f(6), and f(10). Graph the function

21. Graph the equation x= y2+5

22. Graph the region described by the inequality. Y<2x-4

23. Graph the following inequality. x>=4

24. Find the domain and range of the relation. Determine whether the relation is a function.

25. Find the equation of the line that fits the description. Passes through (4,6) and has zero slope.

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MATH 110 Week 2 Homework 3.4 1. Write an equation for the line described. Give the answer in slope – intercept form

2. Use the slope and the y-intercept to graph the line.

3. Find the slope and y-intercept of the line with equation 4x-y=3. Then graph the line.

4. Find the slope and y intercept of the line with equation x+8y=-8. Then graph the line.

5. Give the slope and y intercept of the line, and graph it.

6. The graph of a linear function f is shown. A. Identify the slope, y – intercept, and x-intercept.

7. Find an equation of the line that has the given slope and passes through the given point.

8. Find an equation of the line that has the given slope and passes through the given point.

9. Find an equation of the line that has the given slope and passes through the given point.

10. Find an equation of the line that has the slope m=1/3 and passes through the point(3,8).

11. Find the equation of the line that fits the description. Passes through (4,-9) and has zero slope.

12. Write an equation of the line passing through the points (1,-7) and (-4,3).

13. Write an equation of line passing through the given points.(4,-10) and (-1,5)

14. Write an equation of the line passing through the points(3,9) and (-1,-15).

15. Write an equation of the line in the figure below.

16. Write an equation of the line in the figure below.

17. Write an equation of the line in the figure below.

18. Write an equation of the line in the figure below.

19. A line has a slope of -9.

20. The equation of a line is y =3/4x+2.

21. Find an equation of the line that passes through (0,7) and is parallel to y =1/4x+5

22. Find an equation of the line that passes through (4,5) and is perpendicular to y=4x-7

23. Suppose the growth of population during the period from 1980 to 2008 can be approximated by

an equation of the form y=mx+b , where x is the number of years since 1980 and y is the population

measured in millions. Find the equations if two ordered pairs that satisfy it are(0,227) and (10,250).

MATH 110 Week 2 Homework 3.5 1. Determine whether the ordered pairs given are solutions of the linear inequality in two

variables.

2. Determine if the ordered pairs (-1,-1) and (0,-3) are solutions of the following linear inequality in

two variables.

3. Determine if the ordered pairs (-4,2) and(3,1) are solutions of the following linear inequality in

two variables. X< -y

4. Choose which graph represents the following inequality. -3x+3y>-3

5. Choose which graph represents the following inequality.

6. Choose which graph represents the following inequality.

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MATH 110 Week 2 Homework 3.6 1. Fill in the blanks.

a. The domain of a function is the set of______ of the ______variable.

2. How can you tell whether a graph is the graph of a function?

3. a. Find the domain and range of relation.

b. determine whether the relation is a function.

4. a. find the domain and range of the relation.

b. determine whether the relation is a function.

5. graph the equation y =x2-2

6. graph the equation y =4x2

7. graph the equation. x = -5y2

8. graph the equation x = y2-2

9. graph the equation. x= (y-2)2

10. use the vertical line test to determine whether the given graph is the graph of a function.

11. determine whether the relation is a function.

12. given the following functions, find the indicated values.

13. given the following functions, find the indicated values.

14. during a recent population growth period in a certain state, from 1995 to 2005, the

approximate population of the state measured in millions could be predicted by the function f(x)=

0.04x2+ 0.08x+30.6, where X is the numbers of years since 1995. Find f(0), f(6), and f(10). Graph the

function.

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MATH 110 Week 3 Homework 4.1 1. Explain what happens when a system of two linear equation is inconsistent. What effect does it

have in obtaining a solution? What would the graph of such a system look like/

2. How many solutions can a system of two linear equations in two unknown have?

3. Determine whether the given ordered pair is a solution to the system of equations.

4. Solve the system equations by graphing. Check your solution.

5. Solve the system of equations by graphing. Check your solution.

6. Solve the system of equations by graphing. Check your solution.

7. Solve the system of equations by substitution. 5x+y = 18 y=4x

8. Solve the system by substitution. –x-6y= -13 y=3x-1

9. Solve the following system by substitution x=8y+35 x=4/3y

10. Solve the system by substitution. Y =3x 12x-4y=0

11. Solve the system by substitution. X=3y 5x-15y=5

12. Find the solutions to the system by the addition method. Check your answers.

13. Find the solution to the system by the addition method. Check your answers.

14. Find the solutions to the system by the substitution method. Check your answers.

15. If possible, solve the system of equations. Use any method. if there is not a unique solution to

the system , state a reason.

16. If possible, solve the system of equations. Use any method

17. If possible, solve the system of equations. Use any method. if there is not a unique solution to

the system , state a reason.

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MATH 110 Week 3 Homework 4.3 1. The sum of two numbers is 63. If three times the smaller number is subtracted from the larger

number, the result is 7. Find the two numbers.

2. An employment agency specializing in temporary construction help pays heavy equipment

operators $137 per day and general labourers $92 per day. If thirty-nine people were hired and the

payroll was $4398, how many heavy equipments operators were employed? How many labourers?

3. Ninety passengers rode in a train from city a to city b. Tickets for regular coach seats costs $111.

Tickets for sleeper cars seats cost $284. The receipts for the trip totalled $18,640. How many passengers

purchased each type of tickets?

4. Jen butler has been pricing speed-pass train fares for a group trip to New York. These adults and

four children must pay $110. Two adults and three children must pay $78. Find the price of the adult’s

tickets and the price of a child’s tickets.

5. On Monday, Harold picked up three donuts and four large coffees for the office staffs. He paid

$4.69. on Tuesday, Melinda picked up six donuts and six large coffees for the office staff.

6. Against the wind a small plane flew 210 miles in 1 hour and 10 minutes. The return trip took

only 50 minutes. What was the speed of the wind? What was the speed of the plane in still air?

7. Basketball players scored 17 times during one game. She scored a total 29 points, two for each

two-point shot and one free throw. How many two-point shot did she make? How many free throws?

8. Nick’s telephone company charges $0.08 per minute for weekend calls and $0.09 per minute for

calls made on weekdays. This month nick was billed for 587 minutes. The charge for these minutes was

$47.28. How many minutes did he talk on weekends and how many minutes did he talk on weekdays?

9. A basketball team played 70 games. They won 20 more than they lost.

10. The perimeter of a standard sized rectangular rug is 28 ft. The length is 2 ft longer than the

width. Find the dimensions.

11. At a concession stand, three hot dogs and four hamburgers cost $11.25; four hot dogs and three

hamburgers cost $11.50. find the cost of one hot dog and the cost of one hamburger.

12. A lab technician mixed a 610 ml solution of water and alcohol. If 3% of the solution is alcohol,

how many millilitres of water were used?

13. One canned juice drink is 20% orange juice, another is 10% orange juice. How many litters of

each should be mixed together juice?

14. $5400 is invested, part of it at 10 % and part of it at 9%. For a certain year, the total yields is

$516.00. how much was invested at each rate?

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MATH 110 Week 3 Homework 4.4 1. In the graph of the system y>=9x+5 and y<=-4x+8, would the boundry lines be solid or dashed?

Why?

2. Stephanie wanted to know if the point (3, -4) lies in the region that is a solution for y<-2x+3 and

y> 5x - 3.?

3. Graph the solution of the following system y>=3x-5 x+y<=2

4. Graph the solution of the following system y>= -3x y>= 4x+5

5. Graph the solution of the following system. Y>=2x-5 y<=3/5x

6. Graph the solution of the following system. X-y>=-1 -3x-y<=6

7. Graph the solution of the following system.x+2y<10 y<5

8. Graph the solution of the following system. y<1 x> -5

9. Graph the solution of the following system. X-2y>= -4 3x+y<=6

10. Graph the solution of the following system. 6x+5y<30 6x+5y>-30

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MATH 110 Week 3 Homework Test 3 1. Explain what happens when a system of two linear equations is inconsistent. What effect does

it have in obtaining a solution? What would the graph of such a system look like?

2. Solve the system using elimination. State whether the system is inconsistent, or consistent and

dependent.

3. Graph the solution of the following system. X-y>=-5 -4x-y<= 2.

4. Ninety-right passengers rode in a train from city A to city B. Tickets for regular coach seats cost

$112. Tickets for sleeper cars seats cost $290. The receipts for the trip totaled $20,232. How many

passengers purchased each type of ticket?

5. An employment agency specializing in temporary construction help pays heavy equipment

operators $128 per day and general labourers $95 per day. If 30 people were hired and the payroll was

$3609, how many heavy equipment operators were employed? How many labourers?

6. In the graph of the system y>=5x+6 and y<= - 3x+2, would the boundary lines be solid or

dashed? Why?

7. Stephanie wanted to know if the point (3,-4) lies in the region that is a solution for y<-2x+3 and

y>5x-3. How could she determine if this is true?

8. If possible, solve the system of equations. Use any method.

9. Solve the system using elimination.

10. Graph the solution of the following system.

11. How many possible solutions can a system of two linear equations in two unknowns have?

12. Graph the solution of the following system.

13. Against the wind a commercial airline in South America flew 630 miles in 3.5 hours. With a

tailwind the return trip took 3 hours. What was the speed of the plane in the air? What was the speed of

the wind?

14. Solve by the substitution method 8x+3y= 10 X=16-9y

15. Graph the solution of the following system x+3y<15 y<5

16. Kevin and Randy Muise have a jar containing 63 coins, all of which are either quarters or nickels.

The total value of the coins in the jar is $11.55. How many of each type of coin do they have?

17. If possible, solve the system of equations. Use any method. if there is not a unique solution to

the system, state a reason.

18. Determine whether (a) (2,5) , (b) (-2,2) and (c) (2,-2) are the solutions of the system.

19. Solve the system of equations using elimination.

20. Solve the system of equations using substitution. Then classify the system of equations.

21. Solve the system by the substitution method. x+2y = 3 y = 2x+14

22. Determine whether the given set of ordered pairs (a) (3,5),(b)(-1,-5) and (2,1) are solutions of

the system of equations.

23. The Jurassic Zoo charges $9 for adult admission and $2 for each child. the total bill for the 94

people from a school trip was $356. how many adults and how many children went to the zoo.

24. The sum of two numbers is 81. If twice the smaller number is subtracted from the larger

number, the result is 6. Find the two numbers.

25. If possible, solve the system of equations. Use any method. if there is not a unique solution to

the system , state a reason.

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MATH 110 Week 4 Homework 8.1 1. Write in simplest exponent form. (-7)(x)(y)(z)(y)(z)(y)(x)

2. Multiply and simplify.(a4.a9).

3. Use the product rule to simplify.(-4x5)(5x9)

4. Multiply. (13x3)(4x)

5. Multiply.(8ab5)(4a5b4)

6. Multiply.( 9w)(3w6z)(0)

7. Divide. Assume that the variable in the denominator is nonzero.

8. Divide. Assume that all variables in any denominator are nonzero. Y2/y5

9. Divide assume that are variables in the denominator are nonzero. a17 /2a9.

10. Divide assume that all variables in the denominator are nonzero. 16a6b/-64a3b5.

11. Simplify (c6)2

12. Simplify(3x3y6z)2

13. Simplify(-3x2)4

14. Simplify (2x/3y5)3

15. Simplify (-2x2y0z2)4

16. Simplify. Assume that variables a is nonzero. a-6

17. Simplify. Assume that variables a is nonzero. 1/ a-3

18. Simplify. Express your answer with positive exponents. Assume that all variables are nonzero. x-

6y-4/ z-3.

19. Simplify. Assume that variable x is non zero.b5x-4.

20. Simplify .assume that variables z is non zero. 6z-8

21. Simplify. Express the answer with positive exponents. (6xy-2/z3)2.

22. Evaluate (125)2/3.

23. Evaluate (4)3/2.

24. Simplify the given expression 225 -1/2

25. Simplify the following expression and express the answer with positive exponents. Evaluate or

simplify the numerical expressions. (64)-2/3

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MATH 110 Week 4 Homework 8.2 Explain why the cube root of a negative number is a negative number.

Find the square root. √16

Evaluate if possible. √100+√225

Evaluate if possible -√1/25

Evaluate if possible√-169

For the given function, find the indicated function values. Find the domain of the

function.√3x+18

Find the root 3√216

Find the root that is a real number. 3√-125

Evaluate if possible 8√(3)8

Rewrite with a rational exponent. 3√y

Assume the variable responsible a positive real number. Replace the radical with a rational

exponent. 5√a4.

Simply assume that all variables represent positive numbers. 3√p9q24

Simplify assume that the variables represents positive real numbers. √16x8y24

Write the expression in radical form. Assume that the variables represent a positive real

numbers. C5/5.

Write the expression in radical form and then evaluate. 363/2.

Simplify (32x10) -1/5

Simplify assume that the variables represents positive and negative real numbers. 4√a32b8

Assume the variable responsible a positive real number. √144 x20 y28

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MATH 110 Week 4 Homework Test 4 1. Simplify the following expression and express the answer with positive exponents. Evaluate or

simplify the numerical expressions. (64) -2/3

2. Simplify .assume that the variables represent positive real numbers. √169x14y18

3. Evaluate if possible √-64

4. Simplify. Assume that variables b is nonzero. 5b-8

5. Simplify .assume that the variables represent any positive or negative real number. 6√a36b12

6. Write the expression in radical form. Assume that the variable represents a positive real number

c7/5.

7. Simplify. (32x10) -1/5

8. Write is simplest exponent form (-3)(a)(b)(c)(a)(b)(c)(c).

9. Evaluate if possible √36+√196

10. Write the expression in radical form and then evaluate. 36-3/2.

11. Rewrite with a rational exponent 5√z.

12. Evaluate if possible 5√(6)5.

13. Simplify the expression. Assume that all variables are nonnegative real numbers. √96x3yz8

14. Find the root that is a real number. 3√-64

15. Combine 5√27 -√3

16. Simplify. Express your answer with positive exponents. Assume that all variables are nonzero. x-

3y-9/z-6

17. Use the product rule to simplify. (-3x8)(8x7)

18. Simplify √96

19. Simplify. Assume that all variables represent positive numbers. 3√s9t18

20. Evaluate (25)3/2.

21. Multiply (9w)(6w5z)(0)

22. Simplify (b9)5

23. Divide. Assume that all variables in any denominator are nonzero.

24. Combine 3√2+√11-7√11

25. For the given function, find the indicated function values. Find the domain of the function.

F(x)=√5x+15, find (0) f(1) f(4),f(-1)

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MATH 110 Week 5 Homework 8.4 1. Multiply and simplify. √2√5

2. Multiply (3√7)(-7√2)

3. Multiply (9√27)(-7√3)

4. Multiply (3-√2)(5+√2)

5. Multiply and simplify. Assume that all variables represent nonnegative numbers.(3√5+√11)(√5-

2√11)

6. Multiply and simplify. (√2+4√7)(√3+√2).

7. Multiply and simplify (√3-3√5)2

8. Multiply and simplify. Assume that the variable represents a nonnegative number.(8-5√b)2

9. Multiply and simplify. Assume that all variables represents nonnegative numbers.(√3x-1-2)2

10. Divide and simplify.√64/25.

11. Divide and simplify. Assume that all variables represent positive numbers.

12. Divide and simplify. Assume that all variables represent nonnegative numbers.

3√216x11y12/125

13. Divide and simplify. Assume that all variables represent nonnegative numbers.3√5y8/3√64x9

14. Simplify by rationalizing the denominator. 6/√7.

15. Simplify by rationalizing the denominator √81/7.

16. Rationalize the following denominator and simplify. 1/√5y

17. Simplify by rationalizing the denominator. √25a/√5y.

18. Simplify by rationalizing the denominator √3/√15x.

19. Simplify by rationalizing the denominator 7/√3x

20. Simplify by rationalizing the denominator x/√13-√3

21. Simplify by rationalizing the denominator. 5y/√11+√10

22. Simplify by rationalizing the denominator. √7+√3/√7-√3

23. The cost of fertilizing a lawn is $0.25 per square foot. Find the cost to fertilize the triangular

lawn whose base is (8+√11) feet and attitude is √44 feet.

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MATH 110 Week 5 Homework 8.5 1. Before squaring each side of a radical equation, what step should be taken first?

2. Solve. If the equation has no real solution, so state.√3x+7= 4.

3. Solve the radical equation √9x-5-7 =0

4. Solve the radical equation y+1=√11y-17

5. Solve the radical equation 2x=√19x+5

6. Solve the radical equation 3= 8+√9x+7

7. Solve the radical equation y-√y-5 =7

8. Solve the radical equation √y+4-4=y

9. Solve the radical equation x-3√x-2=2

10. Solve the radical equation √3x2-x =x

11. Solve the radical equation √x+8=1+√x-7

12. Solve the radical equation √14x+1 =1+√12x

13. Solve the radical equation √x+7 =1+√x+1

14. Solve the radical equation √2x+16-√x+1=3

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MATH 110 Week 5 Homework Test 5 1. Last summer the price of gasoline changed frequently. One station owner noticed that the

number of gallons he sold each day seemed to vary inversely with the price per gallon. If he sold 2500

gallons when the price was $4.10, how many gallons could he expect to sell if the price fell to $3.80?

2. Solve the radical equation 2x= √3x+1

3. Multiply and simplify (7√3)(-9√7)

4. If y varies directly as x, and y=6 when X=5 find y when x=15

5. Solve the radical equation. Check your solutions.√x+13=1+√x+2

6. Divide and simplify. Assume that all variables represent nonnegative numbers. 3√27x5x6/125

7. Solve the radical equation. Check your solutions √11x+1= 1+√9x

8. Solve the radical equation. Check your solutions y+1 = √15y-41

9. Divide and simplify √81/16

10. Find an equation of variation where y varies inversely as x and y=1 when x=14

11. Simplify by rationalizing the denominator. √2/√14x

12. Multiply and simplify.(5-√3)(3+√3)

13. Simplify by rationalizing the denominator √13+√11/√13-√11

14. Divide and simplify Assume that all variables represent nonnegative numbers.

3√12y11/3√125x12

15. Solve if the equation has no real solution, so state. √3x+22= 7

16. Solve the radical equation. Check your solution(s).√3x2-x=x

17. Multiply and simplify. Assume that all variables represent nonnegative numbers. (4-3√b)2

18. Solve the radical equation. Check your solution 3=10+ √5x+4.

19. Solve the radical equation. Check your solution √7x-6-8=0

20. Multiply and simplify. Assume that all variables represent nonnegative numbers.(5√3+√2)(√3-

2√2)

21. Solve the radical equation. Check your solution √x+7=1+√x-2

22. Multiply and simplify. √7√10.

23. Simplify by rationalizing the denominator √36/2

24. Solve the radical equation. Check your solution(s)√2x+16-√x+1=3

25. Divide and simplify Assume that all variables represent positive numbers. √75x/16y10

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MATH 110 Week 5 Homework 8.7 1. Give an example in everyday life of direct variation and write an equation as a mathematical

model.

2. If y varies inversely with X, we write the equation _____

3. If y varies directly as x, and y=7 when x=4, find y when x=12

4. The pressure exerted by a certain liquid at a given point varies directly as the depth of the point

beneath the surface of the liquid. The pressure at 50 feet is 19 pounds per square inch. What is the

pressure at 160 feet?

5. The stopping distance d of a car after the brakes are applied varies directly as the speed r. If a

car travelling 30 mph can stop in 40 ft, how many feet will it take the same car to sto when it is travelling

120 mph?

6. If y varies inversely with the square of x, and y =14 when x=4,find when x=0.2

7. Last summer he price of gasoline changed frequently. One station owner noticed that the

number of gallons he sold each day seemed to vary inversely with the price per gallon. If he sold 2400

gallons when the price was $4.30, how many gallons could he expect to sell if the price fell to $4.10?

8. Every year on earth last day, a group of volunteers pick up garbage at hidden falls park. The time

it takes to clean the beach varies inversely with the number of people picking up garbage last year, 36

volunteers took 4 hours to clean the park. If 59 volunteers come to pick up garbage this year, how long

will it take to clean the park?

9. The weight that can be safely supported by a 2-by 6 inch support beam varies inversely with its

length. A builder finds that a support beam that is 8 feet long will support 800 pounds. Find the weight

can be safely supported by abeam that is 16 feet long.

10. The amount of time it take to fill a whirlpool tub is inversely proportional to the square of the

radius of the pipe used to fill it. If a pipe of radius 1.5 inches can fill the tub in 5 minutes, how long will it

take the tub to fill if a pipe of 3 inches is used?

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MATH 110 Week 6 Homework 9.1 1. Solve the equation by using the square root properly x2=64

2. Solve the equation by using the square root properly 3x2-45=0

3. Solve the equation by using the square root properly (x-5)2=18

4. Solve the equation by using the square root properly(z+2)2=7

5. Solve the equation by using the square root properly(5x+1)2=7

6. Solve the equation by using the square root properly(8x-3)2=36

7. Solve the equation by using the square root properly(2x+3)2=49

8. Complete the square for the expression and then factor the resulting perfect square trinomial.

x2+ 8x

9. Complete the square for the binomial and factor the resulting perfect square trinomial.x2-10x

10. Add the proper constant to the binomial so that the resulting trinomial is a perfect square

trinomial. Then factor the trinomial. then factor the trinomial x2+19x+____

11. Find the perfect square trinomial whose first two terms are x2-1/5x, and then factor the

trinomial.

12. Determine the constant that should be added to the binomial so that it becomes a perfect

square trinomial. Then write and factor the trinomial. x2+ 5/6x

13. Solve the equation by completing the square.x2+10x+13=0

14. Solve the equation by completing the square x2-4x=26

15. Solve the equation by completing the square x2-18x=-80

16. Solve the equation by completing the square (x2/2)+(5/2)x=2

17. Solve the equation by completing the square 2y2+10y=-9

18. Solve the equation by completing the square x2+8x-13=0

19. The sides of the box shown are labelled with the dimensions in feet. What is the value of x if the

volume of the box is 64 cubic feet?

20. The time a basketball player spends in the air when shooting a basket is called "the hang time."

The vertical leap L measured in feet is related to the hang time "t" measured in seconds by the equation

L=4t^2. Suppose that a basketball player has a vertical leap of 2 feet 3 inches find the hang time for this

leap.

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MATH 110 Week 6 Homework 9.2 1. use the discriminate to find what type of solutions the equation has. Do not solve the equation.

8x2+3x=2

2. use the discriminate to find what type of solutions the equation has. Do not solve the equation

8x2+13x+5=0

3. use the discriminate to find what type of solutions the equation has. Do not solve the equation

5x2+5=-10x

4. solve by the quadratic formula and simplify. X2=5/8

5. solve by the quadratic formula and simplify 7x2-x-6=0

6. solve the equation. then solve by the quadratic formula and simplify x(x+6)-3= 6x+1

7. solve by the quadratic formula and simplify x2-x-1=0

8. solve by the quadratic formula 4x2-7x-8=0

9. solve by the quadratic formula 2x2-3x-4=0

10. solve by the quadratic formula 16x2+8=10

11. simplify the equation then solve by the quadratic formula 4x(x+2)-9=2x-8

12. simplify the equation then solve by the quadratic formula 1/30+ 1/y= 2/y+5

13. Write a quadratic equation having the given solutions. 3,13

14. Write a quadratic equation having the given solutions 7, -8

15. A company that manufactures mountain bikes makes a daily profit p according to the equation

p= -200x2+8200x- 83402, where p is measured in dollars and x is the number of mountain bikes made

per day. Find the number of mountain bikes that must be made each day to produce a zero profit for the

company.

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MATH 110 Week 6 Homework Test 6 1. Solve the equation by using the square root properly (7x-2)2=49

2. The time a basketball player spends in the air when shooting a basket is called the”hang time”.

The vertical leap l measured in feet is related to the hang time t measured in seconds by the equation

l=4t22.suppose that a basketball player has a vertical leap of 3 feet 7 inches. Find the hang time for this

leap.

3. Solve the equation by using the square root properly.(x-5)2=28

4. Find the perfect square trinomial whose first two terms are x2-1/6x, and the factor the

trinomial.

5. Write a quadratic equation having the given solutions. 13,15

6. Solve by the quadratic formula. 4x2+6=9

7. Solve the equation by completing the square. X2+14x+22=0

8. A security fence encloses a rectangular are on one side of a park in a city. Three sides of fencing

are used, since the fourth side of the area is formed by a building. The enclosed area measures 2178

square feet. Exactly 132 feet of fencing is used to fence in three sides of this rectangle. What are the

possible dimensions that could have been used to construct this area?

9. Solve the equation by completing the square. X2-4x=18

10. Solve by the quadratic formula x2+x-4=0

11. Solve the equation by completing the square x2/2+5/2x=2

12. Solve the equation by using the square root properly 2x2-12=0

13. Solve by the quadratic formula. 8x2-7x-7=0

14. Solve the equation by using the square root properly. X2=49

15. Use the discriminate to find what type of solutions the equation has. Do not solve the equation.

4x2+9= -12x

16. Solve the equation by completing the square x2-8x=-12

17. Simplify the equation. Then solve by the quadratic formula.1/6+1/y= 3/y+3

18. Solve by the quadratic formula. 2x2-7x-6=0

19. Solve the equation by completing the square 2y2+10y=-11

20. Solve by the equation formula and simplify. 4x2+x-5=0

21. Solve by the equation formula and simplify x2=3/5x

22. Solve by the equation by any method. x2+10x-4=0

23. Simplify the equation. Then solve by the quadratic formula x(x+5)-7=5x+9

24. Simplify the equation. Then solve by the quadratic formula 4x(x+2)-3=6x-2

25. Solve the equation by using the square root properly (2x+5)2=49

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MATH 110 Week 7 Homework 9.5

1. Find the coordinates of the vertex and the intercepts of the following quadratic function. When

necessary, approximate the x-intercepts to the nearest tenth. F(x)=x2+6x-7

2. Find the coordinate of the vertex , the y-intercepts and the x-intercepts of the following

quadratic function. g(x)= -x2-8x+9

3. Find the vertex, the y-intercepts, and the x-intercepts, and then graph the function. P(x)=

2x2+8x+3

4. Find the vertex, the y-intercept, and the x-intercepts, and then graph the function. F(x)=x2+6x+9

5. Find the vertex, the y- intercept, and the x-intercepts, and then graph the function.

P(x)=x2+4x+3

6. Find the vertex, the y- intercept, and the x-intercept, and then graph the function. p(x)=-x2+10x-

21.

7. Find the vertex, the y- intercept, and the x-intercept, and then graph the function.

r(x)=2x2+4x+7.

8. Find the vertex, the y- intercept, and the x-intercepts , and then graph the function. f(x)= x2—49

9. Determine , without graphing, whether the given quadratic function has a maximum value or a

minimum value and then find the values. F(x)=-3x2+18x-9

10. Determine , without graphing, whether the given quadratic function has a maximum value or a

minimum value and then find the values. F(x)=2x2+12x-3

11. Determine , without graphing, whether the given quadratic function has a maximum value or a

minimum value and then find the values. F(x)= 3x2+24x-4

12. Suppose that the manufacturer of a dvd player has found that, when the unit price is p dollars,

the revenue R as a function of the price p is R(p) =-2.5p2+400p. (a) for what price will the revenue be

maximized?

13. The daily profit p in dollars of a company making tables is described by the function p(x)= -

5x2+280x-3600, where x is the number of tables that are manufactured in 1 day. Use this information to

find p(25).

14. The daily profit p in dollars of a company making tables is described by the function p(x)=-

6x2+312x-3570, where x is the number of tablets that are manufactured in 1 day. The maximum profit

of the company occurs at the vertex of the parabola. How many tables should be made per day in order

to obtain the maximum profit for the company? What is the maximum profit?

15. Susan throws a softball upward into the air at a speed of 32 feet per second from a 120-foot

platform. the distance upward that the ball travels is given by the function d(t) =-16t2+32t+120. What is

the maximum height of the softball? How many seconds does it take to reach the ground after first

being thrown upward?

16. A security fence encloses a rectangular area on one side of a park in a city. Three sides fencing

are used, since fourth side of the area is formed by a building. The enclosed area measures 242 square

feet. Exactly 44 feet of fencing is used to fence in three sides of this rectangle. What are the possible

dimensions that could have been used to construct this area?

17. Palo alto college is planning to construct a rectangular parking lot on land bordered on one side

by a highway. the plan is to use 600 feet of fencing off the other three sides. What dimensions should

the lot have if the enclosed area is to be maximum?

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MATH 110 Week 7 Homework Test 7 1. Solve for the variable specified. Assume that all other variables are nonzero. A=25r2; for r

2. Use the Pythagorean Theorem to find the missing side. C=9,a=6,find b

3. Use the Pythagorean Theorem to find the missing side. c=√40,b=√10,

4. Consider a right triangles with legs a and b hypotenuse c. Find the exact length of the missing

side.

5. Use the Pythagorean Theorem to find the missing side.

6. A brace for a shelf has the shape of a right triangle. Its hypotenuse is 6 inches long and the two

legs are equal in length. How long are the legs of the triangle?

7. The area of a rectangular wall of a brain is 32 feet. its length is 12 feet longer than twice its

width. Find the length and width of the wall of the brain.

8. The length of a rectangle is 5 meters less than twice the width. If the area of the rectangular is

493 square meters, find the dimensions.

9. Bob drove from home to work at 60 mph. After work the traffic was heavier, and he drove home

at 25 mph. His driving time to and from work was 1 hour and 8 minutes. How far does he live from his

job?

10. Palo Alto College is planning to construct a rectangular parking lot on bordered on one side by a

highway. The plan is to use 760 feet of fencing to fence off the other three sides. What dimensions

should the lot have if the enclosed area is to be a maximum?

11. A rocket is fired upward from some initial distance above ground. Its height in feet, h above the

ground, t seconds after it is given by h=-16t2+128t+2448.

12. Find the coordinates of the vertex and the intercepts of the following quadratic function. when

necessary, approximate the x – intercepts to the nearest tenth. F(x)= x2+2x-8

13. Find the coordinates of the vertex, the y-intercept, and the x-intercepts of the following

quadratic function. g(x)=-x2-4x+12

14. Find the coordinate of the vertex and the intercepts of the following quadratic function. when

necessary, approximate the x-intercepts to the nearest tenth.

15. Find the vertex, the y-intercepts, and the x-intercepts, and then graph the function. p(x)= -x2+

4x-3

16. Determine, without graphing, whether the given quadratic function has a maximum value or a

minimum value or a minimum value or a minimum value and then find the value. F(x)=2x2+16x-5

17. Suppose that the manufacturer of a dvd player has found that, when the unit price is p dollars,

the revenue R as a function of the price p is R(p)= -2.5p2+ 750p. (a) for what price will the revenue be

maximized?

18. Find the vertex, the y-intercept, and the x-intercepts, and then graph the function.

19. Two young college graduates opened a chain of print shops. The chain expanded rapidly during

the early 1990s and 2005 is given by the equation y = 2.5x2+27.5x+142 where x is the number of years

since 1990.how many print shops where there in 1995?

20. The daily profit p in dollars of a company making tables is described by the function p(x)=-

6x2+312x-3762, where x is the number of tables that are manufactured in 1 day. The maximum profit of

the company occurs at the parabola. How many tables should be made per day in order to obtain the

maximum profit for the company? What is the maximum profit?

21. Susan throws a softball upward into the air at a speed of 32 foot platform. The distance upward

that the ball travel is given by the function d(t) = - 16t2 +32t+24. What are the maximum heights of the

softball? How many seconds does it take to reach the ground after first being thrown upward?

22. A security fence encloses a rectangular area on one side of a park in a city. Three sides of fencing

are used, since the fourth side of the area is formed by a building. The enclosed are measures 800

square feet. Exactly 80 feet of fencing is used to fence in three sides of this rectangle. What are the

possible dimensions that could have been

Used to construct this area?

23. Use the Pythagorean Theorem to find the length of the sides of the triangle.

24. Determine, without graphing, whether the given quadratic function has a maximum value or a

minimum value and then find the value.

25. the revenue r received by a company selling x pairs of sunglasses per week is given by the

Function R(x)= -0.1x2+40x. (a) find the values of R(11) and R(56). (b) how many pairs of sunglasses must

be sold in order for the revenue to be $3000 per week? (c) how many pair of sunglasses must be sold in

order for revenue to be $4000 per week?

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MATH 110 Week 8 The Final Exam 1. Graph the region described by the following inequality. 3x-y>=1

2. Multiply and simplify. Assume that all variables represent nonnegative numbers. (3√5+√7)(√5-

2√7)

3. For the equation y=2=2x, answer part (a) and (b).

4. Solve the system by the substitution method. x+3y=3 y=2x+22

5. Solve the radical equation. check your solutions(s) √x+6=1 + √x-9

6. Use the discriminante to find what type of solutions the equations has. Do not solve the

equation. 2x2+7x=-2

7. Use the Pythagorean Theorem to find the missing side.

8. Find the domain and range of the relation. (b) determine whether the relation is a

function.(6.55),(7.45)(6.65)(8.50)

9. Find the slope of the straight line that passes through the following pair of points.(5,-3) and(-7,-

3)

10. On Monday, Harold picked up five donuts and six large coffees for the office staff. He paid $8.45.

on Tuesday, Melinda picked up six donuts and three large coffees?

11. Determine whether (a)(3,4), (b)(-3,3) and (c)(3,-3) are the solutions of the system. X-y =-6

3x+y=-6

12. A brace for a shelf has the shape of right triangle. Its hypotenuse is 18 inches long and the two

legs are equal in length. How long are the legs of the triangle?

13. If y varies directly as x, and y=4 when x=3, find y when x=12.

14. Write a quadratic equation having the given solutions. -6,3.

15. Check the solution x=-2+√13 in the equation x2+4x-9=0

16. How can you tell whether a graph is the graph of a function?

17. Evaluate if possible √-225

18. Simplify. Express the answer with positive exponents. ((5xy-3)/(z2))2

19. Graph the solution of the following system. Y>=5x-3 x+y<=8

20. Find the coordinates of the vertex and the intercepts of the following quadratic function. When

necessary, approximate the x-intercepts to the nearest tenth. f(x)=x2-2x-8.

21. Solve by the quadratic formula and simplify. X2= (7/8)x

22. Write an equation of the line in the figure below.

23. Find the solution to the system by the addition method. check your answer. 2s+5t=8 5s-10t=

11 what is the solution to the system?

24. The perimeter of a rectangular floor is 80 feet. Find the dimensions of the floor if the length is

three times the width.

25. If y varies inversely with the square of x , and y=11 when x=3, find y when x=0.2

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