SAT math Linear&Parabola

x=y−3

x/2+ 2y=6

Which ordered pair (x, y) satisfies the system of equations shown above?

• (−3,0)

• (0, 3)

• (6, −3)

• (36,−6)

A software company is selling a new game in a standard edition and a collector’s edition. The box for the standard edition has a volume of 20 cubic inches, and the box for the collector’s edition has a volume of 30 cubic inches. The company receives an order for 75 copies of the game, and the total volume of the order to be shipped is 1,870 cubic inches. Which of the following systems of equations can be used to determine the number of standard edition games, s, and collector’s edition games, c, that were ordered?

• 75 − s = c

  20s + 30c = 1,870

• 75 − s = c

  30s + 20c = 1,870

• s − c = 75

  25(s + c) = 1,870

• s − c = 75

  30s + 20c = 1,870

y = 19.99 + 1.50x

The equation above models the total cost y, in dollars, that a company charges a customer to rent a truck for one day and drive the truck x miles. The total cost consists of a flat fee plus a charge per mile driven. When the equation is graphed in the xy-plane, what does the y-intercept of the graph represent in terms of the model?

• A flat fee of $19.99

• A charge per mile of $1.50

• A charge per mile of $19.99

• Total daily charges of $21.49

The scatterplot above shows the numbers of grams of both total protein and total fat for eight sandwiches on a restaurant menu. The line of best fit for the data is also shown. According to the line of best fit, which of the following is closest to the predicted increase in total fat, in grams, for every increase of 1 gram in total protein?

• 2.5

• 2.0

• 1.5

• 1.0

In the xy‐plane above, a point (not shown) with coordinates (s, t) lies on the graph of the linear function f. If s and t are positive integers, what is the ratio of t to s ?

• 1 to 3

• 1 to 2

• 2 to 1

• 3 to 1

2x+3y = 5

4x + cy = 8

In the system of equations above, c is a constant. For what value of c will there be no solution (x, y) to the system of equations?

• 3

• 4

• 5

• 6

On its opening day, a car dealership had an inventory of 29 cars. During the first 6 months, 18 additional cars were purchased by the dealership each week, and the sales team sold an average of 15 cars per week. During the first six months, which of the following equations best models the car inventory, c, at the dealership t weeks after opening day?

• c=−t+29

• c=t+29

• c=(3/2)t+29

• c=3t+29

A pool initially contains 1,385 cubic feet of water. A pump begins emptying the water at a constant rate of 20 cubic feet per minute. Which of the following functions best approximates the volume v(t), in cubic feet, of the water in the pool t minutes after pumping begins, for 0≤t≤69 ?

• v(t) = 1,385 − 20t

• v(t) = 1,385 − 69t

• v(t) = 1,385 + 20t

• v(t) = 1,385 + 69t

Juliet rented a car for one day from a company that charges $80 per day plus $0.15 per mile driven. If she was charged a total of $98 for the rental and mileage, for how many miles of driving was Juliet charged? (Assume there is no tax.)

• 15

• 120

• 533

• 633

For a ride,a taxi driver charges an initial fare of $3.00 plus $0.40 for each 15 of a mile driven. If the total charge for a ride is $27.00, what is the distance traveled, in miles?

• 3

• 8

• 12

• 15