1. solve.
-15 ÷ (-5)
2. rewrite using the distributive property.
8(b + 7)
3. find the missing side length of the similar shapes.
(images of two triangles: first triangle with sides 15, 9, 18; second triangle with sides 25,?, 30)
4. find the measure of angle r.
(image of an angle with a straight line and angles 75° and 30° around angle r)
5. the cookie shop can bake a dozen cookies with 2 cups of flour. if they are planning to make 36 cookies, what equation can help the bakers find out how many scoops of flour to use?

Question

Accepted Answer

Problem 2: Rewrite $8(b + 7)$ using the distributive property.
# Explanation:
## Step 1: Recall the distributive property.
The distributive property states that $a(b + c) = ab + ac$. Here, $a = 8$, $b = b$, and $c = 7$.
## Step 2: Apply the distributive property.
$8(b + 7) = 8 \times b + 8 \times 7 = 8b + 56$
# Answer:
$8b + 56$

### Problem 3: Find the missing side length of the similar shapes.
# Explanation:
## Step 1: Recall the property of similar triangles.
In similar triangles, the ratios of corresponding sides are equal. Let's identify the corresponding sides. The first triangle has sides $15$, $9$, $18$, and the second has sides $25$, $\text{?}$, $30$. Let's find the ratio of corresponding sides. For example, the side of length $15$ in the first triangle corresponds to the side of length $25$ in the second triangle. The ratio is $\frac{25}{15}=\frac{5}{3}$. Alternatively, we can use another pair: the side of length $18$ in the first triangle corresponds to the side of length $30$ in the second triangle. The ratio is $\frac{30}{18}=\frac{5}{3}$, which confirms the scale factor is $\frac{5}{3}$. Now, the side of length $9$ in the first triangle corresponds to the missing side (let's call it $x$) in the second triangle. So we set up the proportion $\frac{x}{9}=\frac{5}{3}$ (since the scale factor is $\frac{5}{3}$, the second triangle's sides are $\frac{5}{3}$ times the first triangle's sides).
## Step 2: Solve for $x$.
Cross - multiply: $3x = 9\times5$
$3x = 45$
Divide both sides by $3$: $x=\frac{45}{3}=15$
# Answer:
$15$

### Problem 4: Find the measure of angle $r$.
# Explanation:
## Step 1: Recall the property of a straight line.
A straight line forms a $180^{\circ}$ angle. So, the sum of the angles $75^{\circ}$, $r$, and $30^{\circ}$ is $180^{\circ}$.
## Step 2: Set up the equation and solve for $r$.
$75^{\circ}+r + 30^{\circ}=180^{\circ}$
Combine like terms: $105^{\circ}+r = 180^{\circ}$
Subtract $105^{\circ}$ from both sides: $r=180^{\circ}- 105^{\circ}=75^{\circ}$
# Answer:
$75^{\circ}$

### Problem 5: The cookie shop can bake a dozen (12) cookies with 2 cups of flour. If they are planning to make 36 cookies, what equation can help the bakers find out how many cups (let's assume "scoops" is a typo and it's cups, or the logic is similar) of flour to use?
# Explanation:
## Step 1: Define the variable.
Let $x$ be the number of cups of flour needed for 36 cookies.
## Step 2: Set up the proportion.
The ratio of cookies to flour should be the same. For 12 cookies, we use 2 cups of flour. So, $\frac{12}{2}=\frac{36}{x}$ (this is a proportion equation that can be used to solve for $x$). Alternatively, we can think in terms of unit rate. The unit rate of cookies per cup of flour is $\frac{12}{2} = 6$ cookies per cup. Then, if $x$ is the number of cups, $6x=36$ (since the number of cookies is equal to the unit rate times the number of cups).
# Answer:
One possible equation is $\frac{12}{2}=\frac{36}{x}$ (or $6x = 36$ where $x$ is the number of cups of flour).

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QUESTION IMAGE

Question

Explanation:

Step 1: Recall the distributive property.

Step 2: Apply the distributive property.

Step 1: Recall the property of similar triangles.

Step 2: Solve for \(x\).

Step 1: Recall the property of a straight line.

Step 2: Set up the equation and solve for \(r\).

Answer:

Problem 3: Find the missing side length of the similar shapes.