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**1. A store is offering a 15% discount on all items.**

a. Write a linear equation giving the sale price, S for an item with a list price, L. b. Find the sale price of an item originally priced at $39.

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**2. Find the value of 𝑥 for the triangle**

2. Find the value of 𝑥 for the triangle. The perimeter of the triangle is 24ft.

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**3. A manufacturer pays its assembly line workers $11. 50 per hour**

3. A manufacturer pays its assembly line workers $11.50 per hour. In addition, workers receive a piecework rate of $0.75 per unit produced. a. Write a linear equation for the weekly wages W in terms of the number of units x produced per hour. b. Find the wages of a worker who works a 40-hour week and produces 350 units.

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4. solve

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5. Your school is sponsoring a pancake dinner to raise money for a field trip. You estimate that 200 adults and 250 children will attend. Let x represent the cost of an adult’s ticket and y represent the cost of a child’s ticket. A)Write an equation that can be used to find out what ticket prices could be set in order to raise $3800. B)If the school sets the child’s ticket price at $4.80, what would the adult’s tickets price be?

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**6. Which of the following is a true statement regarding domain, range, relations, and functions?**

a. In a relation, domain values can be repeated. b. In a function, range values can be repeated. c. Both statements are true.

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**7.Find the value of x so that the line passing through that two points has the given slope.**

(−1, 4) (x , 3 ) m= 1 5

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**8. Find the value of y so that the line passing through that two points has the given slope.**

(8, 1) (1 , y ) m= 1

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**9. Find the value of y so that the line passing through that two points has the given slope.**

(9, y) (3 , 2 ) m= 2 3

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**10. You find a coat that you love, it sells for $145.98.**

a. When you go to the register to buy the coat the sales person charges you sales tax at a rate of 8.25%. How much did you pay for the coat? b. When you go to another store later that day you find that same jacket is on sale at a 28% discount! How much would you have saved by buying the coat at the 2nd store? (Remember that every store must charge sales tax. It is the same rate if you are in the same city)

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**a) Write the equation for this function.. **

11. The cost of renting a 26-foot U-Haul truck is $39.95 per day and $0.59 per mile. Let f(x) represent the cost of renting a truck for a day and driving it “x” miles.. a) Write the equation for this function.. b) How much will it cost to rent a truck for a day if the driver goes a total of 32 miles? c) How far did you drive if you spent $93.05? D) What is dependent in the situation? E)What is independent in this situation?

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**a) Find the equation of the line. **

12. A certain long distance company charges $5 a month for their service plus an additional $0.05 per minute on calls. If “x” represents the total number of minutes of long distance used during any given month and “f(x)” represents the cost of the bill for that month, find the following: a) Find the equation of the line. b) How long did you talk if your bill was $10.15? c) If no long distance calls were made during a particular month, how much is the bill? d) Find the cost of a bill during a month where 250 minutes of long distance were used. e) What does f(50) represent?

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**a) What is the rate of change of the altitude per minute?**

13. After 8 minutes, the altitude of an airplane above the runway is 6 thousand feet. After 12 minutes, the altitude of the same airplane is 9 thousand feet. a) What is the rate of change of the altitude per minute? b) What is the altitude of the airplane after 15 minutes?

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**a) What is the rate of change of the population per year?**

14. According to the Census, the population of the Metro-Augusta area in 1990 was 415,184 and in 2000 was 477,441. Let “x” represent the year after 1990 and “f(x)” represent the number of people in Augusta “x” years after 1990. a) What is the rate of change of the population per year? b) If the rate of change remains the same, what is the expected population in 2010?

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**15. If k(x) = 5 x + 3, then k(2 a – 1) = a. 2 ak – k b. 10 a – 2**

c. 10 a + 2

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**16. A SQUARE has side lengths of (2 – 11 + 13x) and (11 – x + 4x).**

What is the perimeter of the square?

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17. You are running a concession stand at the basketball game. You sell hot dogs for $1 and sodas for $.50. At the end of the night, you made $200. Let x represent the number of hot dogs sold and y represent the number of sodas sold. A)Write an equation that represents this situtation.

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18. John is an insurance salesman who works on commission. Each time he gets a new client who purchases car insurance, he earns $100 in commission. Each time he gets a client who purchases homeowners insurance, he earns $50 in commission. Let x represent the number of clients who purchase car insurance and let y represent the number of clients who purchase homeowners insurance. Write an equation that you could use to find out how many clients, for each type of insurance, John would need to earn $3000 in commission. A)Write an equation that represents this situtation.

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19. solve

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**a) What x-value represents 1987?**

20. Assume that the sales of a certain appliance dealer are approximated by a linear function. Suppose that sales were $13,500 in 1982 and $65,500 in Let x = 0 represent 1982 a) What x-value represents 1987? b) Find the equation giving yearly sales.

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21.Green Glass Recycling uses the function given by F(t) = -5000t + 90,000 to determine the salvage value in dollars of a waste removal truck t years after it has been put into use. a) What does F(T) mean? b) What does t mean? c) What does 90,000 mean? d) What does mean? e) What is the salvage value of the truck after it has been in operation for 6 years? f) How many years can the truck be used before the salvage value of the truck is $25,000? g) When is the value of the truck $0? h) What is the value of the truck at time of purchase?

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22. The mathematical model C(x) = 450x + 25,000 represents the cost in dollars a company has in manufacturing “x” computers during a month. Based on this: a) How much does it cost the company if no computers are made a certain month? b) How many computers can be made for $115,000 in a certain month? c) How much will it cost the company during a month where 350 computers are made? d) What does the 25,000 represent? e) What does the 450 represent? f) What does x and C(x) represent?

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**a) What value of “x” represents 2000? **

23. It is estimated that there were C(x) = 2.4x + 24 million homes in the U.S. with computers from 1991 to If “x” represents the years after 1991, find the following: a) What value of “x” represents 2000? b) Find the estimated number of computers in U.S. homes in the year 2000. c) In what year is it estimated that there are 50 million computers in U.S. homes?

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**24. Determine the domain and range for the following equation**

24. Determine the domain and range for the following equation. 2 x+ 3 y = 6 a. domain = {2} and range = {3} b. domain = {all real numbers} and range = {all real numbers} c. domain and rage cannot be determined

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25. solve

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**a. f(1) = 3 b. domain of f = {1, 2, 3, 4} c. f(1) = 2**

26. If f = {(1, 3),(2, 1),(3, 2),(4, 0)}, then which of the following statements is false? a. f(1) = 3 b. domain of f = {1, 2, 3, 4} c. f(1) = 2

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28.Which is true? a. domain = { x: x ≤ 5} and range = { y: y ≥ –5} b. range = { y: y ≤ 5} and domain = { x: x ≥ –5} c. domain = {all real numbers} and range = {all real numbers}

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**29. Slope and Rate of Change (m), …**

Special Cases Vertical lines like x = 4 A. What is the SLOPE? Horizontal lines line y = 4 B. What is the SLOPE? 3, Ac2A

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**Changes to b, the y intercept of a line, effect its__________**

30.m and b in a Linear Function- Fill in the blank (then….taks_tutorial - A Very Good Teacher\9th Grade\9th Grade\Objective 3\Objective 3 Powerpoint.ppt Changes to m, the slope of a line, effect its_________ Changes to b, the y intercept of a line, effect its__________ y = 1 - 4 3, Ac2C

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**The quotient of x and a number 12 is negative sixty.**

31. What is x? The quotient of x and a number 12 is negative sixty.

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**32. How big is the shadow of the tree?**

A tree is 6 feet tall and casts a shadow that is x feet long. A light pole is 14 feet tall casts a shadow that is x+20 feet long.

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**33. Translate the statement**

Four less than the quotient of ten and x is twenty.

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**The perimeter of a rectangle is 120 cm and the width is 28 cm.**

34. Find the length. The perimeter of a rectangle is 120 cm and the width is 28 cm.

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35. Find the Dimensions. The length of a rectangle is 5 cm more than its width. The perimeter of the rectangle is 26.

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**Jack drove 62 miles per hour for 8 hours.**

36. How fast did Jack drive? Jack drove 62 miles per hour for 8 hours.

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**Rachel drove 378 miles for 7 hours.**

37. How far did RAchel go? Rachel drove 378 miles for 7 hours.

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38. Solve for y 2𝑥−𝑦=8.

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39. Solve for x 2𝑥−𝑦=8.

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40. Solve for l 𝑃=2𝑙+2𝑤.

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41. Solve for w 𝐴=𝑙𝑤.

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**42. In the equation 𝑎 𝑏 +5=12, what is the value of 𝑎 𝑏 ?**

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**43. What is the x and y intercepts?**

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**44. Vertical lines Draw it. Identify the slope.**

What does the equation look like? Is it a function

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**45. Horizontal lines Draw it. Identify the slope.**

What does the equation look like? Is it a function

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**46. What will happen if the slope is doubled?**

It will move up 2 units. It will move down 2 units. It will become steeper. It will become less steep.

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**47. What will happen if the slope is halved?**

It will move up 2 units. It will move down 2 units. It will become steeper. It will become less steep.

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**48. What will happen if the yintercept is changed -1?**

It will move up 2 units. It will move down 2 units. It will become steeper. It will become less steep.

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**49. What will happen if the yintercept is changed -5?**

It will move up 2 units. It will move down 2 units. It will become steeper. It will become less steep.

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**50. What is the value of y when 𝑥=2?**

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**50. What is the value of x when 𝑦=1?**

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51. Solve 5−𝑥=12

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**52.Are the following sets of expressions equivalent or not equivalent and explain your reasoning.**

A πr2 and 2πr B. 2(l + w) and 2l + 2w lwh and hwl D 𝑏ℎ 𝑎𝑛𝑑 𝑏ℎ 2 E. d = rt and 𝑟= 𝑡 𝑑

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**53. Circle all statements that can be represented by the expression a + b.**

the difference of a and b B. b more than a C. sum of a and b D. a is more than b E. a more than b the product of a and b G. b is more than a H. a plus b

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**54. Who did it correctly? . Carl solved it this way… **

Billy solved it this way… 2 3𝑥+8 −𝑥=7𝑥+4 Step 1 2 3𝑥+8 =8𝑥+4 Step 2 3𝑥+8=4𝑥+2 Step 3 8=𝑥+2 Step 4 6=𝑥 6𝑥+16−𝑥=7𝑥+4 5𝑥+16=7𝑥+4 −2𝑥+16=4 −2𝑥=−12 Step 5 𝑥=6

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**𝑚= 1 𝑥+2 (A) -2 (B) -1 (C) 0 (D) 1 (E) 2**

58. Given the slope above, which of the following values for x would result in an undefined slope? 𝑚= 1 𝑥+2 (A) -2 (B) -1 (C) 0 (D) 1 (E) 2

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**(A) 𝑚=2𝑛−250 (B) 𝑛=250−2 (C) 𝑛=250−2𝑚 (D) 𝑚=250−2𝑛 (E) m=2𝑛+250**

59. Joseph began with $250 in his account. He is spending an average of $2 per week. Which of the following equations describes the realtionship between the amount of money in his account, m , and the number of months, n, she has been spending? (A) 𝑚=2𝑛−250 (B) 𝑛=250−2 (C) 𝑛=250−2𝑚 (D) 𝑚=250−2𝑛 (E) m=2𝑛+250

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**60. Which of the following equations has y-intercept of 4 and x-intercept of 4?**

(B) 4𝑥+4𝑦=−4 (C) −𝑥+𝑦=4 (D) 𝑥−𝑦=4 (E) 𝑥+𝑦=4

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**61. If −16,𝑦 is the solution to the equation 3𝑥−8𝑦−24=0,what is the value of y?**

(B) 16 (C) −16 (D) −9 (E) 3 8

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62. The original function 𝑦=− 3 5 𝑥+8 is graphed on the same grid as the new function 𝑦= 2 5 𝑥+8. Which of the following statements about these graphs is true? (A)𝐓𝐡𝐞 𝐠𝐫𝐚𝐩𝐡 𝐨𝐟 𝐭𝐡𝐞 𝐨𝐫𝐢𝐠𝐢𝐧𝐚𝐥 𝐟𝐮𝐜𝐧𝐧𝐢𝐨𝐧 𝐢𝐬 𝐥𝐞𝐬𝐬 𝐬𝐭𝐞𝐞𝐩 𝐭𝐡𝐚𝐧 𝐭𝐡𝐞 𝐭𝐡𝐞 𝐠𝐫𝐚𝐩𝐡 𝐨𝐟 𝐭𝐡𝐞 𝐧𝐞𝐰 𝐟𝐮𝐧𝐜𝐭𝐢𝐨𝐧 (B) 𝐓𝐡𝐞 𝐠𝐫𝐚𝐩𝐡 𝐨𝐟 𝐭𝐡𝐞 𝐨𝐫𝐢𝐠𝐢𝐧𝐚𝐥 𝐟𝐮𝐜𝐧𝐧𝐢𝐨𝐧 𝐢𝐬 𝐩𝐚𝐫𝐚𝐥𝐥𝐞𝐥 𝐭𝐡𝐚𝐧 𝐭𝐡𝐞 𝐭𝐡𝐞 𝐠𝐫𝐚𝐩𝐡 𝐨𝐟 𝐭𝐡𝐞 𝐧𝐞𝐰 𝐟𝐮𝐧𝐜𝐭𝐢𝐨𝐧 (C)The graphs intersect at (𝟖,𝟎) (D)The graphs intersect at (𝟎,𝟖)

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**A) Positive B) Negative C) 0 D) Undefined**

63.. When the dependent variable increases when the independent variable increases, the rate of change is A) Positive B) Negative C) 0 D) Undefined

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**A) Positive B) Negative C) 0 D) Undefined**

64.When the dependent variable stays the same as the independent variable increases, the rate of change is A) Positive B) Negative C) 0 D) Undefined

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**A) Positive B) Negative C) 0 D) Undefined**

65.When the dependent variable decreases as the independent variable increase, the rate of change is A) Positive B) Negative C) 0 D) Undefined

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**A) Positive B) Negative C) 0 D) Undefined**

66.When the dependent variable increase as the independent variable stays the same, the rate of change is A) Positive B) Negative C) 0 D) Undefined

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**A) Positive B) Negative C) 0 D) Undefined**

67.When the dependent variable increase as the independent variable stays the same, the rate of change is A) Positive B) Negative C) 0 D) Undefined

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**68. Who is driving the slowest?**

Purple Red Orange

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**69. Who is driving the Fastest?**

Purple Red Orange

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**70. If 𝑥,−5 is the solution to the equation 𝑥−𝑦=12,what is the value of x?**

(B) 17 (C) −17 (D) −7 (E) 7 (F) 1 (G) −1

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71. solve Rebecca bought some apples for $0.50 per pound and some oranges for $0.75 per pound. She bought a total of 10 pounds of fruit and spent a total of $ How many pounds of apples and oranges did she buy?

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**A) 𝑏+𝑝=9 2𝑏+1𝑝=14 C) 𝑏+𝑝=14 𝑏+2𝑝=9 𝑏+𝑝=14 2𝑏+1𝑝=9 D) 𝑏+𝑝=9 𝑏+2𝑝=14**

72. Alexis purchased two colors of wild flowers. The blue flowers cost $1 for each package and the pink flowers cost $2 for each package. How many packages of each flower did Alexis buy if she paid $14 for a total of 9 packages of wildflowers. Which system of linear equations can be used to find b, the number of blue flowers sold and p, the number of pink flowers sold? A) 𝑏+𝑝=9 2𝑏+1𝑝=14 C) 𝑏+𝑝=14 𝑏+2𝑝=9 𝑏+𝑝=14 2𝑏+1𝑝=9 D) 𝑏+𝑝=9 𝑏+2𝑝=14

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73. solve You are in charge of buying the hamburger and chicken for a party. You have $60 to spend. The hamburger costs $2 per pound and chicken is $3 per pound. If you buy 15 pounds of hamburger, how many pounds of chicken can you buy?

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74. What is the domain? 𝑦≥2 𝑥≥2 𝑦≥0 𝑥≥0

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75. What is the Range? 𝑦≥2 𝑥≥2 𝑦≥0 𝑥≥0

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76. What is the Range? 𝑦≥2 𝑥≥2 𝑦≥0 𝑥≥0 All reals

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**77. What is the Range? 4≥𝑥≥0 4≥𝑦≥0 −1≤𝑥≤6 -1≤𝑦≤6 4≤𝑥≤0 4≤𝑦≤0 −1≥𝑥≥6**

−1≥𝑦≥6 All reals

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**78. What is the Domain? 4≥𝑥≥0 4≥𝑦≥0 −1≤𝑥≤6 -1≤𝑦≤6 4≤𝑥≤0 4≤𝑦≤0 −1≥𝑥≥6**

−1≥𝑦≥6 All reals

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**79. What is the Domain? 4≥𝑥≥0 4≥𝑦≥0 −1≤𝑥≤6 -1≤𝑦≤6 4≤𝑥≤0 4≤𝑦≤0 −1≥𝑥≥6**

−1≥𝑦≥6 All reals

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80. If 𝟓𝒌,𝟔𝒌 𝒂𝒏𝒅 (𝟗𝒌,𝟐𝒌)are two points on the graph of a line and k is not equal to 0, what is the slope of the line?

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**81The sales tax rate at a gas store is 9. 25 %**

81The sales tax rate at a gas store is 9.25 %. Sales tax on an item is a function of its price. Which of the following is the independent and dependent quantity in this function. A. Dependent: The sales tax rate on the item Independent: The items price B. Not here C. Dependent: The items price Independent: The sales tax rate on the item D. Dependent: The amount of sales tax on the item Independent: The items price E. Dependent: The items price Independent: The amount of sales tax on the item

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**82Which of the following are functions?.**

{(-2,7), (-1,7), (0,3), (1,1), (2,1)} {(-3,7), (-5,7), (-3,3), (6,1), (8,1)} Domain 2 3 6 Range 5 7 9 11

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83. If −𝒌, 𝒌 𝟐 𝒂𝒏𝒅 (−𝟔𝒌,𝟒 𝒌 𝟐 ) are two points on the graph of a line and k is not equal to 0, what is the slope of the line?

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84. In the quadratic equation 𝒙 𝟐 −𝒙+𝒄=𝟎, c represents an unknown constant. If 𝒙=−𝟒 is one of the solutions to this equation, what is the value of c?

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85. A phone company is promoting a new cell phone service plan: a customer can make up to 600 minute of calls each month for If the number of minutes used in a month exceeds 600, then the function 𝒄=𝟎.𝟑𝟎 𝒎−𝟔𝟎𝟎 +𝟒𝟗.𝟗𝟗. a. If the total number of minutes used is more than 600, then every minute used costs 30cents. b. The first 600 minutes used cost 40 cents each, after which there is an additional charge of $49.99. c. Not here d. If the total number of minutes used is more than 600, then every minute beyond 600 costs 30 cents. e. Every minute used costs 30 cents each, regardless of the total number of minutes used.

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86. If −𝒌,𝟒𝒌 𝒂𝒏𝒅 (−𝟔𝒌,𝟒𝒌) are two points on the graph of a line and k is not equal to 0, what is the slope of the line

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**87.Which of the following is not a correct description of the graph of the function 𝒚=−𝟓𝒙−𝟐.**

a. The graph of the function contains the point −1,3 and when the value of x increases by 1 unit, the value of y decreases by 5 units. b. The graph of the function contains the points −5,23 , 2,−12 𝑎𝑛𝑑 5,−27 . c. The graph of the function is a line that passes through the point 0,−2 with a slope of −5. d. The graph of the function contains the point (2,−12) and when the value of x decreases by 5 units, y decreases by 25. e. The graph of the function contains the point (2,−12) and when the value of x decreases by 5 units, y increases by 25.

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**𝑥+𝑦=52 𝑥−𝑦=18 b. 4𝑥+4𝑦=52 4𝑥−4𝑦=18 2𝑥+2𝑦=52 2𝑦−2𝑥=18 d. 4𝑥+4𝑦=18**

88. The sum of the perimeters of two different squares is 52 centimeters, and the difference between their perimeters is 18 centimeters. If x represents the side length of the larger square and y represents the side length of the smaller square, which of the following systems of equations could be used to find the dimensions of the squares. 𝑥+𝑦=52 𝑥−𝑦=18 b. 4𝑥+4𝑦=52 4𝑥−4𝑦=18 2𝑥+2𝑦=52 2𝑦−2𝑥=18 d. 4𝑥+4𝑦=18 4𝑥−4𝑦=52

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**Some values of two linear equations are shown below**

Some values of two linear equations are shown below. What is the solution to the system of equations represented by the tables? x y -2 11 2 19 5 25 8 31 x y -4 27 -1 18 1 12 2 9 a) ,19 b) (5,25) c) 0,15 d) 𝑛𝑜 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛 e) Infinitely many solutions

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**90 The graph of a quadratic function is shown below. .**

Which statement about this graph is not true? The quadratic has two solutions and two zeros The vertex is at ( 0, -6 ) and is the shape of a parabola The y-axis is the line of symmetry The quadratic has one root and has a y-intercept at ( 0, 5 )

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**91. What is the best estimate of the positive value of x for which this function equal 2?**

3 -2 2

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92. In the quadratic equation 𝒙 𝟐 −𝒙+𝒄=𝟎, c represents an unknown constant. If 𝒙=−𝟓 is one of the solutions to this equation, what is the value of c?

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**A. 𝑦= 1400(1+.025) 𝑥 B. 𝑦= 1400(1−2.5) 𝑥 C. 𝑦= 1400(.025) 𝑥**

93. A population of 1400 deer decreases by 2.5 % per year. At the end of 15 years, there will be approximately 958 deer in the population. Which function can be used to determine the number of deer, y, in this population at the end of t years?. A. 𝑦= 1400(1+.025) 𝑥 B. 𝑦= 1400(1−2.5) 𝑥 C. 𝑦= 1400(.025) 𝑥 D. 𝑦= 1400(1−.025) 𝑥

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**Some values of two linear equations are shown below**

Some values of two linear equations are shown below. What is the solution to the system of equations represented by the tables? x y -2 - 1 2 11 5 20 8 29 x y -4 -20 -8 1 - 5 2 - 2 a) ,19 b) (5,25) c) 0,15 d) 𝑛𝑜 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛 e) Infinitely many solutions

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**Some values of two linear equations are shown below**

Some values of two linear equations are shown below. What is the solution to the system of equations represented by the tables? x y -2 - 1 2 11 5 20 8 29 x y -4 -7 5 1 8 2 11 a) ,19 b) (5,25) c) 0,15 d) 𝑛𝑜 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛 e) Infinitely many solutions

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96. In the quadratic equation 𝒙 𝟐 −𝒙+𝒄=𝟎, c represents an unknown constant. If 𝒙=𝟐 is one of the solutions to this equation, what is the value of c?

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Grade 10 Mathematics Graphs Application.

Grade 10 Mathematics Graphs Application.

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