Question

1. in the standard (x,y) coordinate plane, what is the slope of the line given by the equation 4x = 7y + 5?

a. -\frac{4}{7}
b. \frac{4}{7}
c. \frac{7}{4}
d. 4
e. 7

1. for which of the following conditions will the sum of integers m and n always be an odd integer?

f. m is an odd integer.
g. n is an odd integer.
h. m and n are both odd integers.
j. m and n are both even integers.
k. m is an odd integer and n is an even integer.

1. the lengths of the 2 legs of right triangle \triangle abc shown below are given in inches. the midpoint of \overline{ab} is how many inches from a?

a. 16
b. 20
c. 21
d. 28
e. 40

1. in \triangle def, the length of \overline{de} is \sqrt{30} inches, and the length of \overline{ef} is 3 inches. if it can be determined, what is the length, in inches, of \overline{df}?

f. 3
g. \sqrt{30}
h. \sqrt{33}
j. \sqrt{39}
k. cannot be determined from the given information

1. laura plans to paint the 8 - foot - high rectangular walls of her room, and before she buys paint she needs to know the area of the wall surface to be painted. two walls are 10 feet wide, and the other 2 walls are 15 feet wide. the combined area of the 1 window and the 1 door in her room is 60 square feet. what is the area, in square feet, of the wall surface laura plans to paint?

a. 200
b. 340
c. 360
d. 390
e. 400

Explanation:

Step1: Calculate the area of all walls

The area of a rectangle is \(A = length\times width\).
For the two walls of width \(10\) feet and height \(8\) feet, the combined area is \(2\times(10\times8)=160\) square feet.
For the two walls of width \(15\) feet and height \(8\) feet, the combined area is \(2\times(15\times8) = 240\) square feet.
The total area of all four walls is \(160 + 240=400\) square feet.

Step2: Subtract the area of the window and door

The combined area of the window and door is \(60\) square feet.
The area to be painted is \(400-60 = 340\) square feet.

Answer:

B. 340