Question

1. what is the y-intercept of the line with a slope of 2 that passes through the point (1, 2)?

a. -2
b. -\\(\frac{1}{2}\\)
c. 0
d. \\(\frac{1}{2}\\)

1. what is the surface area, in square centimeters, of a cube with each edge length of 5 cm?

a. 15
b. 25
c. 125
d. 150

page 9 of 11

1. the length of a rectangle is three times its width. if the perimeter of the rectangle is 96 inches, what is its length in inches?

a. 12
b. 24
c. 36
d. 48

mathematics formula sheet
perimeter
square \\( p = 4s \\)
rectangle \\( p = 2l + 2w \\)
triangle \\( p = s_1 + s_2 + s_3 \\)
circle (circumference) \\( c = 2\pi r \\) or \\( \pi d \\)

area
square \\( a = s^2 \\)
rectangle \\( a = lw \\)
triangle \\( a = \frac{1}{2}bh \\)
circle \\( a = \pi r^2 \\)
parallelogram \\( a = bh \\)
trapezoid \\( a = \frac{1}{2}h(b_1 + b_2) \\)

surface area and volume
rectangular/right prism \\( sa = ph + 2b \\) \\( v = bh \\)
cylinder \\( sa = 2\pi rh + 2\pi r^2 \\) \\( v = \pi r^2 h \\)
pyramid \\( sa = \frac{1}{2}ps + b \\) \\( v = \frac{1}{3}bh \\)
cone \\( sa = \pi rs + \pi r^2 \\) \\( v = \frac{1}{3}\pi r^2 h \\)
sphere \\( sa = 4\pi r^2 \\) \\( v = \frac{4}{3}\pi r^3 \\)
(\\( p \\) = perimeter of base \\( b \\); \\( \pi \approx 3.14 \\))

page 10 of 11

Explanation:

Question 48

Step1: Recall slope-intercept form

The slope - intercept form of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept. We know that \(m = 2\), so the equation of the line is \(y=2x + b\).

Step2: Substitute the point into the equation

The line passes through the point \((1,2)\). Substitute \(x = 1\) and \(y = 2\) into the equation \(y=2x + b\):

$$
LATEXBLOCK0
$$

Step3: Solve for \(b\)

Subtract 2 from both sides of the equation \(2=2 + b\):

$$
LATEXBLOCK1
$$

Step1: Recall the formula for the surface area of a cube

A cube has 6 faces, and each face is a square. The area of one square face with side length \(s\) is \(A=s^{2}\). The surface area \(SA\) of a cube is given by the formula \(SA = 6s^{2}\).

Step2: Substitute the value of \(s\)

We are given that the edge length \(s = 5\space cm\). Substitute \(s = 5\) into the formula \(SA=6s^{2}\):

$$
LATEXBLOCK0
$$

Step1: Define variables

Let the width of the rectangle be \(w\) inches. Then the length \(l\) of the rectangle is \(3w\) inches (since the length is three times the width).

Step2: Recall the formula for the perimeter of a rectangle

The perimeter \(P\) of a rectangle is given by the formula \(P = 2l+2w\). We know that \(P = 96\) inches. Substitute \(l = 3w\) and \(P = 96\) into the formula:

$$
LATEXBLOCK0
$$

Step3: Simplify and solve for \(w\)

Combine like terms: \(96=8w\). Divide both sides by 8:

$$
LATEXBLOCK1
$$

Step4: Find the length

Since \(l = 3w\) and \(w = 12\), then \(l=3\times12 = 36\) inches.

Answer:

C. 0

Question 49