Question

1. a rectangle has a length that is 15 times its width. the function y=(15w)(w) represents this situation, where y is the area, in square feet, of the rectangle and y > 0. which of the following is the best interpretation of 15w in this context? a) the length of the rectangle, in feet b) the area of the rectangle, in square feet c) the difference between the length and the width of the rectangle, in feet d) the width of the rectangle, in feet 19. x + 2y = 6 x - 2y = 4 the solution to the given system of equations is (x, y). what is the value of x? a) 2.5 b) 5 c) 6 d) 10

Explanation:

18.

The area formula for a rectangle is $y = \text{length}\times\text{width}$. Given length is 15 times the width and width is $w$, so length is $15w$.

Step1: Add the two equations

Adding $x + 2y=6$ and $x - 2y = 4$ eliminates $y$.
$(x + 2y)+(x - 2y)=6 + 4$

Step2: Simplify the left - hand side and solve for $x$

$x+2y+x - 2y=2x$, and $6 + 4 = 10$. So $2x=10$, then $x = 5$.

Answer:

A. The length of the rectangle, in feet

19.