Question

1. the equation shows a proportional relationship between the distance in miles, y, tommy rides his motorcycle, and the number of gallons of gas, x, he uses.

y = 38.5x
what is the constant of proportionality? enter the answer as a whole number or a decimal in the box.
constant of proportionality =

1. angles k and l are complementary angles. the measure of angle k can be represented by the expression (4x + 9)°, and the measure of angle l can be represented by the expression (2x + 3)°.

what is the measure, in degrees, of angle k?
a.13°
b.28°
c.61°
d.91°

1. for the two triangles shown in the diagram, the lengths of their corresponding sides are proportional.

diagram of two triangles with side lengths: first triangle has sides 12, 6, x; second triangle has sides 16, 8, y
based on the side lengths labeled above, which of the following equations represents the proportional relationship between x and y ?
a.y = \frac{1}{2} x
b.y = \frac{3}{4} x
c.y = \frac{4}{3} x
d.y = 2x

1. mrs. tyler’s room shares a common wall with a storage closet. the closet is 15 feet long and 25 feet wide, as shown.

diagram of mrs. tyler’s room and storage closet: room and closet are rectangles sharing a common wall, closet is 15 feet (length) and 25 feet (width)
the combined area of her room and the closet is 1,250 square feet. how long is mrs. tyler’s room?
a.35 feet
b.40 feet
c.50 feet
d.85 feet

Explanation:

Problem 4

Step1: Recall proportional form

A proportional relationship is $y=kx$, where $k$ is the constant of proportionality.

Step2: Match with given equation

Given $y=38.5x$, so $k=38.5$.

Problem 15

Step1: Define complementary angles

Complementary angles sum to $90^\circ$.
<Expression>$(4x+9)^\circ+(2x+3)^\circ=90^\circ$</Expression>

Step2: Simplify to solve for $x$

Combine like terms and isolate $x$.
<Expression>$6x+12=90 \implies 6x=78 \implies x=13$</Expression>

Step3: Calculate angle K

Substitute $x=13$ into angle K's expression.
<Expression>$(4(13)+9)^\circ=(52+9)^\circ=61^\circ$</Expression>

Problem 19

Step1: Find scale factor

Calculate ratio of corresponding sides.
<Expression>$\text{Scale factor}=\frac{16}{12}=\frac{4}{3}$ or $\frac{8}{6}=\frac{4}{3}$</Expression>

Step2: Relate $x$ and $y$

Since $y = \text{scale factor} \times x$.
<Expression>$y=\frac{4}{3}x$</Expression>

Problem 25

Step1: Define total length

Let $L$ = length of the room. Total combined length is $L+15$.

Step2: Set up area equation

Combined area = total length $\times$ width.
<Expression>$25(L+15)=1250$</Expression>

Step3: Solve for $L$

Isolate $L$ by dividing and subtracting.
<Expression>$L+15=\frac{1250}{25}=50 \implies L=50-15=35$</Expression>

Answer:

1. constant of proportionality = $38.5$
2. C. $61^\circ$
3. C. $y = \frac{4}{3}x$
4. A. 35 feet