Quiz about SAT Math-Kate

Question 1

Line k is defined by y=-17/3x+5. Line j is perpendicular to line k in the xy-plane. What is the slope of line j?

Accepted Answer

3/17

Answer

-17/3

Answer

-3/17

Answer

17/3

Question 2

A cargo helicopter delivers only 100-pound packages and 120-pound packages. For each delivery trip, the helicopter must carry at least 10 packages, and the total weight of the packages can be at most 1,100 pounds. What is the maximum number of 120-pound packages that the helicopter can carry per trip?

Accepted Answer

5

Answer

2

Answer

4

Answer

6

Question 3

The table gives the coordinates of two points on a line in the xy-plane. The y-intercept of the line is (k-5,b), where k and b are constants. What is the value of b?

x y

k 13

k+7 -15

Accepted Answer

33

Answer

45

Answer

8

Answer

13

Question 4

-x + y =-3.5, and x + 3y, = 9.5 If (x,y) satisfies the system of equations above, what is the value of y

Accepted Answer

3/2

Answer

1

Answer

2/3

Answer

2

Question 5

(1/2y = 4) (x-1/2y =2) The system of equations above has solution (x, y). What is the value of x?

Accepted Answer

6

Answer

3

Answer

7/2

Answer

4

Question 6

The total cost f(x), in dollars, to lease a car for 36 months from a particular car dealership is given by f(x)=36x+1000, where x is the monthly payment, in dollars. What is the total cost to lease a car when the monthly payment is $400?

Accepted Answer

$15,400

Answer

$13,400

Answer

$13,000

Answer

$37,400

Question 7

The graph of the equation ax+ky=6 is a line in the xy-plane, where a and k are constants. If the line contains the points (-2,6) and (0,-3), what is the value of k

Accepted Answer

-2

Answer

-1

Answer

2

Answer

3

Question 8

$$\left(\frac{3}{2}y-\frac{1}{4}x=\frac{2}{3}-\frac{3}{2}y\right)\left(\frac{1}{2}x+\frac{3}{2}=py+\frac{9}{2}\right)$$ In the given system of equations, p is a constant. If the system has no solution, what is the value of p?

Accepted Answer

6

Answer

4

Answer

2

Answer

12

Question 9

A window repair specialist charges $220 for the first two hours of repair plus an hourly fee for each additional hour. The total cost for 5 hours of repair is $400. Which function f gives the total cost, in dollars, for x hours of repair, where x $$\ge$$ 2?

Accepted Answer

f(x)=60x+100

Answer

f(x)=60x+220

Answer

f(x)=80x

Answer

f(x)=80x+220

Question 10

Hector used a tool called an auger to remove corn from a storage bin at a constant rate. The bin contained 24,000 bushels of corn when Hector began to use the auger. After 5 hours of using the auger, 19,350 bushels of corn remained in the bin. If the auger continues to remove corn at this rate, what is the total number of hours Hector will have been using the auger when 12,840 bushels of corn remain in the bin?

Accepted Answer

12

Answer

3

Answer

7

Answer

8

Question 11

The function h is defined by h(x)=4x+28. The graph of y=h(x) in the xy-plane has an x-intercept at a,0 and a y intercept at 0,b , where a and b are constants. What is the value of a+b?

Accepted Answer

21

Answer

28

Answer

32

Answer

35

Question 12

For line h, the table shows three values of x and their corresponding values of y. Line k is the result of translating line h down 5 units in the xy-plane. What is the x-intercept of line k?

x y

18 130

23 160

26 178

Accepted Answer

-17/6, 0

Answer

-26/3, 0

Answer

-9/2, 0

Answer

-11/3, 0

Question 13

An economist modeled the demand Q for a certain product as a linear function of the selling price P. The demand was 20,000 units when the selling price was $40 per unit, and the demand was 15,000 units when the selling price was $60 per unit. Based on the model, what is the demand, in units, when the selling price is $55 per unit?

Accepted Answer

16,250

Answer

16, 500

Answer

16, 750

Answer

17,500

Question 14

A certain apprentice has enrolled in 85 hours of training courses. The equation 10x+15y=85 represents this situation, where x is the number of on-site training courses and y is the number of online training courses this apprentice has enrolled in. How many more hours does each online training course take than each on-site training course?

Accepted Answer

5

Answer

3

Answer

2

Answer

8

Question 15

Hiro and Sofia purchased shirts and pants from a store. The price of each shirt purchased was the same and the price of each pair of pants purchased was the same. Hiro purchased 4 shirts and 2 pairs of pants for $86, and Sofia purchased 3 shirts and 5 pairs of pants for $166. Which of the following systems of linear equations represents the situation, if x represents the price, in dollars, of each shirt and y represents the price, in dollars, of each pair of pants?

Accepted Answer

4x + 2y = 86, and, 3x + 5y = 166

Answer

4x + 3y = 86, and, 2x + 5y = 16

Answer

4x + 2y = 166, and, 3x + 5y = 86

Answer

4x + 3y = 166, and, 2x + 5y = 86

Question 16

Line k is defined by y=3x+15. Line j is perpendicular to line k in the xy-plane. What is the slope of line j?

Accepted Answer

-1/3

Answer

-1/12

Answer

-1/18

Answer

-1/45

Question 17

The point (8,2) in the xy-plane is a solution to which of the following systems of inequalities?

Accepted Answer

$$x>0,\ y>0$$

Answer

x>0, y $$<0$$

Answer

x $$<$$ 0, y>0

Answer

$$x<0,\ y<0$$

Question 18

5x=15

-4x+y=-2

The solution to the given system of equations is x,y. What is the value of x+y?

Accepted Answer

13

Answer

-17

Answer

-13

Answer

17

Question 19

The cost of renting a backhoe for up to 10 days is $270 for the first day and $135 for each additional day. Which of the following equations gives the cost y, in dollars, of renting the backhoe for x days, where x is a positive integer and $$x\le10$$ ?

Accepted Answer

y=135x+135

Answer

y=270x-135

Answer

y=270x+135

Answer

y=135x+270

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