SAT (Heart of Algebra)

A builder uses the function g defined by g (x) = 80x + 10,000 to estimate the cost g(x), in dollars, to build a one-story home of planned floor area of x square feet. If the builder estimates that the cost to build a certain one-story home is $106,000, what is the planned floor area, in square feet, of the home?

(a)  

  $$\frac{x}{2}=2+\frac{1}{2}y$$  

$$y-8\ =\ 24$$  

Based on the system of equations above, what is the value of

$$x^{2\ }-y^{2\ }$$  ?

A small raindrop measuring 1.2 mm in diameter has a terminal velocity of 10.22 miles per hour. A large raindrop measuring 5.0 mm in diameter has a terminal velocity of 20.1 miles per hour. If there is a linear relationship between the diameter of a raindrop and its terminal velocity, what is the terminal velocity (in miles per hour) of a raindrop measuring 3.0 mm in diameter?

If $$\frac{3}{8}\ \le\frac{m}{-2}+8\le7\$$   what is a possible value of 4m-2 ?

2y + 6x = 3

y + 3x = 2

How many solutions (x, y) does the given system of equations have?

A printing company charges $0.20 per page printed with black ink and $0.50 per page printed in color. The company also charges an additional fixed price for the

cost of printing the title and cover pages. The cost of printing a book, P, can be expressed as P = 3.5 + 0.5x + 0.2y . If a discount of m% is applied to the entire order, which equation represents the total cost of the order?

3s - 2t = a

-15s + bt = -7

n the system of equations above, a and b are constants. If the system has infinitely many solutions, what is the value of a?

A voter registration drive was held in Town Y. The number of voters, V, registered T days after the drive began can be estimated by the equation V = 3,450 + 65T. What is the best interpretation of the number 65 in this context?

Maizah bought a pair of pants and a briefcase at a department store. The sum of the prices of the pants and the briefcase before sales tax was $130.00. There was no sales tax on the pants and a 9% sales tax on the briefcase. The total Maizah paid, including the sales tax, was $136.75. What was the price, in dollars, of the pants?

(a)  

The graph above displays the total cost, C, in dollars, of renting a beach chair for h hours. Which of the following show the relationship between h and C?