Linear Equations and Systems of Equations: 700068RR (pennfoster exam answers)

What's the slope of a line that passes through (-4,-13) and (19,11)?

24/23

Joshua is going to mow lawns during his summer break. The graph in the figure shows a linear relationship between the number of weeks he will be mowing and the number of lawns he will mow. If he earns $25 for each lawn he mows, how much money will he earn after mowing lawns for 5 weeks? O A. $1,500 O B. $125 O C. $750 O D. $3,000

A. $1,500

Subtract (4x - 1) from 4(5x + 7). O A. 16x + 29 O B. 16x + 27 O C. 24x +27 O D. 24x + 29

A. 16x + 29

Solve the equation 3(x - 7) = 42. O A. 21 O B. 49 O C.7 O D. 36

A. 21

Suppose a crew at an unloading dock can unload 3 trucks per hour, and they've already unloaded 17 trucks. Which expression can be used to model the number of trucks the crew unloads after h hours? O A. 3h + 17 O B. 17h -3 O C.3h = 17 O D. 17h + 3

A. 3h + 17

Subtract (5x + 3) from (9x - 7) O A. 4x - 10 O B.4x-4 O C.-4x + 10 O D. 4x + 10

A. 4x - 10

Triangles ABC and DEF are similar triangles. What are the lengths of the unknown sides? © A. DE = 24 yd.; EF = 10 yd. O B. DE = 24 yd.; EF = 15 yd. O C. DE = 18 yd.; EF = 15 yd O D. DE = 18 yd.; EF = 10 yd.

A. DE = 24 yd.; EF = 10 yd.

Find the possible values for s in the inequality 12s - 20 ≤50 - 3s - 25. OA.s≤3 O B.s≤⅓ O C.s≤ 5/9 O D.s≤9

A. s≤3

Solve -4(6x + 3) =-12(x + 10). O A. x = 9 O B. x=2 OC.x=-5 O D.x=5

A. x = 9

Solve the inequality -1 > -2(x - 4) - 5(4x - 7). O A. x>2 O B.x<2 OC.x>-23 O D.x>8

A. x>2

The sum of two numbers is 13. Two times the first number minus three times the second number is 1. If you let x stand for the first number and y for the second number, what are the two numbers? O A.x =8, y = 5 O B. x=5,y=8 O C.x=-5,y=-8 O D.x=-8,y=-5

A.x =8, y = 5

The figure above graphs the system of equations below y=4x+3 y=-x-2 What's the solution of the system? O A. (1,-1) O B. (-1,-1) O C. (-1,1) O D. (0,-2)

B. (-1,-1)

Solve the system below using subtraction. 7x + 2y = 13 -x+2y=-11 What's the solution of the system? O A. (-3,4) © B. (3,-4) O C. (4,-3) O D. (-4,3)

B. (3,-4)

There are three groups of elderly residents at Bayside Residential Home, one with 14 members, the next with 23 members, and the third with 17 members. The management is selecting a trip for all of the residents, and each trip choice will cost a certain amount per resident. Write an expression to represent the total cost, letting c represent the cost of the trip per resident. O A.37c^2+17c O B. 54C O C. 54c^3 O D. 14C + 40c^2

B. 54C

A line in the Cartesian plane passes through the points (5,8) and (9,15). What's the slope of the line? A. 4/7 B. 7/4 C. -4/7 D. -7/4

B. 7/4

A contractor is setting up new accounts for the local cable company. She earns $75 for each customer account she sets up. Which expression models this situation, and how much will she profit if she sets up 8 customers? (The variable c represents the number of customers.) O A. 75/c; $9.78 O B. 75c; $600 O C.C + 75; $600 O D.C-75; $9.78

B. 75c; $600

Solve the equation 4(x - 2) = 3x + 1 O A. 8 O B. 9 O C.3 O D.2

B. 9

The system of equations 3x - 6y = 20 and 2x - 4y = 3 is O A. independent. O B. inconsistent. O C. dependent. O D. consistent.

B. inconsistent.

One number is equal to two times a second number. Two times the first number plus two times the second number is 24. If you let x stand for the first number and y for the second, what are the two numbers? O A.x=-24, y=-12 O B. x=8, y = 4 O C.x = 12, y = 6 O D. x = 24, y = 12

B. x=8, y = 4

Solve the system of equations 2r + 2s = 50 and 2r -S = 17. OA.r=-8,s=33 O B.r= 14, s= 11 O C.r= 3, s= 11 O D.r=25,S= 33

B.r= 14, s= 11

Solve 9 = 1 + 8x - 8. O A.x=10 O B.x=2 O C.x=8 O D.x = all real numbers

B.x=2

Jake is shopping for a new toaster oven. He wishes to calculate the total cost of his purchase before going to the register, including the 9% sales tax. What's the total cost of the toaster oven that Jake wants to buy if its price is marked at $39.99? O A. $43.19 O B. $4.99 © C. $43.59 O D. $36.39

C. $43.59

Solve the following system by any method, -3x + 5y = -9 4x + 8y = 12 O A. (0,-4) O B. (4,0) © C. (3,0) O D. (0,-3)

C. (3,0)

Which point is a solution to the inequality y ≤ 8x - 3? O A. (3,22) O B. (-2,-18) O C. (4,29) O D. (-3,-17)

C. (4,29)

Lori rented a car for one day. The daily rental rate was $12.50 plus 25 cents per mile. The total cost of her rental was $46. How many miles did she drive that day? O A. 96 O B. 46 © C. 134 O D. 50

C. 134

The graph of the distance a car travels at a constant speed passes through points (0,0) and (2,136). The x scale is hours, and the y scale is miles. How fast is the car traveling? O A. 134 miles per hour O B. 34 miles per hour O C. 68 miles per hour O D. 136 miles per hour

C. 68 miles per hour

Find the value of x in the equation 9 - 4x = 57. O A.-16.5 O B. 16.5 O C.-12 O D. 12

C.-12

The expression 148 - 24d gives the number of pizzas a store has in stock, where d is the number of days. How many pizzas will the store have in stock after five days? O A. 76 O B. 120 © C.28 O D. 124

C.28

Solve the equation 4(x - 3) = 16. O A. 19 O B. 13 O C.7 O D. 67

C.7

Jack intends to purchase a shirt that was originally marked $35 but is now 30% off. Write a linear expression for the new cost of the shirt. Then, calculate the sale price of it. O A.c-3.5c; $22.75 O B. c-0.35c; $22.75 © C.C-0.30c; $24.50 O D. C-0.30c; $22.75

C.C-0.30c; $24.50

Solve the inequality 7a + 13 < 48. O A.a =5 O B.a> 5 O C.a<5 O D.as5

C.a<5

Solve 10 + 6(-9 - 4x) = 10(x - 12) + 8. O A.x=-6 O B. x= 17 OC.x=2 O D.x=-18

C.x=2

What's the slope-intercept form of the equation of the line graphed in this figure? points: (-5,-2) (5,4) O A.y=-⅗x+1 O B.y=-5/3x-1 O C.y=⅗x + 1 O D.y= 5/3x + 1

C.y= ⅗x + 1

When Sharon began shopping this morning, she had $40.00. She purchased five paperback books and had lunch. The books were all the same price, and lunch cost $3.25. She now has $7.00 left. What was the price of each of the books? O A. $6.60 O B. $7.35 O C. $8.75 O D. $5.95

D. $5.95

What are the coordinates of the point where the two lines intersect? O A. (-2,3) O B. (-3,3) O C. (3,0) © D. (3,3)

D. (3,3)

Solve the system of equations below using substitution. 2x - 3y =-1 X=y+1 What's the solution of the system? O A. (-3,-4) O B. (-4,-3) O C. (3,4) O D. (4,3)

D. (4,3)

Find the value of x in the equation 2(x - 3) + 5x = 5(2x + 6). O A.-2 O B.2 O C. 12 O D. -12

D. -12

What's the slope of a line that passes through (-8,-16) and (18,5)? A. 26/21 B. -21/26 C. -26/21 D. 21/26

D. 21/26

The sum of two numbers is 12, and their difference is 4. Write and solve a system of equations to find the value of the two numbers. O A. -4,-8 O B. -5,-9 O C. 6,10 © D. 4,8

D. 4,8

A television that was originally marked $199.95 is now 25% off. Write a linear expression for the new cost of the television. Then, calculate the sale price of it. O A.c-0.25c; $49.99 O B. c + 0.25c; $249.94 O C.C + 0.25c; $149.96 O D. C-0.25c; $149.96

D. C-0.25c; $149.96

A line in the Cartesian plane passes through the points (1,3) and (5,4). What's the slope of the line? O A. -1/4 O B. 4/1 O C.-4/1 O D. ¼

D. ¼

Solve the equation 32 - 5y = 87, O A. 23.8 O B.-23.8 O C.11 O D.-11

D.-11

Find the slope of the line graphed on the Cartesian plane in the figure. the one which points are (0,-2) & like (5,-5) O A. 7/2 O B. -7/2 O c.¾ O D.-¾

D.-¾

Rewrite the equation 2x + 4y + 2 = 3y + 5 in general form. OA.2x+74+7=0 O B. 2x+y =3 O C.y=-2x+3 OD.2x+y-3=0

D.2x+y-3=0

Solve the system of equations 3r- 4s = 0 and 2r + 5s = 23. O A.r=-12, S = 9 O B.r= 12, s=0 O C.r=-1,s=-3 O D.r= 4, S = 3

D.r= 4, S = 3

Solve 1- 2X -1= -10. O A. No solution O B. x=-g O C.x=9 O D.x=5

D.x=5

Solve 7x - 5x - 3 = X + 4. O A.x=-10 O B. x=-8 O C.x=6 O D.x=7

D.x=7

Y= 1/4x - 2 y= 7/4x +4 Which of the following graphs shows the solution to the system of equations seen above?

The one where the lines intersect at ( -4, -3 ).

A group of friends ate a meal in a restaurant, and the cost of their bill is m. Which expression represents the total amount that they'll pay if they tip 20%? O A. 0.2 +m O B. 1.2 + m © C. 0.2m (WRONG) O D.1.2m

not sure but i think it's D. 1.2m