1. solve.
-15 ÷ (-5)
2. rewrite using the
distributive property.
8(b + 7)
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?
3. find the missing side
length of the similar shapes.
15 18
9
25 30
?
4. find the measure of
angle r.
75° r 30°

Question

Accepted Answer

### 1. Solve $-15 \div (-5)$
# Explanation:
## Step1: Recall division of negatives
Dividing two negative numbers gives a positive result. So, $-15 \div (-5)$ is the same as $15 \div 5$.
## Step2: Perform the division
$15 \div 5 = 3$
# Answer: $3$

### 2. Rewrite $8(b + 7)$ using the distributive property
# Explanation:
## Step1: Apply distributive property
The distributive property states that $a(b + c)=ab + ac$. Here, $a = 8$, $b = b$, and $c = 7$.
## Step2: Multiply out
$8\times b+8\times7 = 8b + 56$
# Answer: $8b + 56$

### 3. Find the missing side length of the similar shapes
# Explanation:
## Step1: Identify the ratio of corresponding sides
For the first triangle, sides are $15$, $9$, $18$. For the second triangle, corresponding sides are $25$, $\text{?}$, $30$. Let's find the ratio of the first pair of corresponding sides: $\frac{25}{15}=\frac{5}{3}$. We can also check with the hypotenuse: $\frac{30}{18}=\frac{5}{3}$. So the scale factor is $\frac{5}{3}$.
## Step2: Find the missing side
The side corresponding to $9$ in the first triangle. Let the missing side be $x$. Then $\frac{x}{9}=\frac{5}{3}$. Cross - multiply: $3x = 9\times5$.
## Step3: Solve for $x$
$3x=45$, divide both sides by $3$: $x = 15$
# Answer: $15$

### 4. Find the measure of angle $r$
# Explanation:
## Step1: Recall straight - line angle
A straight line is $180^{\circ}$. So the sum of the angles $75^{\circ}$, $r$, and $30^{\circ}$ is $180^{\circ}$.
## Step2: Set up the equation
$75^{\circ}+r + 30^{\circ}=180^{\circ}$
## Step3: Solve for $r$
First, add $75^{\circ}$ and $30^{\circ}$: $105^{\circ}+r=180^{\circ}$. Then subtract $105^{\circ}$ from both sides: $r = 180^{\circ}- 105^{\circ}=75^{\circ}$
# Answer: $75^{\circ}$

### 5. Find the equation to find the number of cups of flour for 36 cookies
# Explanation:
## Step1: Determine the number of dozens in 36 cookies
A dozen is 12 cookies. So, $36\div12 = 3$ dozens.
## Step2: Set up the proportion
Let $x$ be the number of cups of flour. Since 1 dozen (12 cookies) uses 2 cups of flour, the ratio of cookies to flour should be constant. So, $\frac{12}{2}=\frac{36}{x}$ (or we can think in terms of dozens: 1 dozen needs 2 cups, 3 dozens need $x$ cups, so $x=\frac{36}{12}\times2$ or the equation can be set up as $\frac{2}{12}=\frac{x}{36}$ (where $x$ is the number of cups of flour). Cross - multiplying gives $12x=2\times36$, or we can also write it as $x=\frac{36}{12}\times2$)
# Answer: $\frac{2}{12}=\frac{x}{36}$ (or equivalent like $12x = 72$ or $x=\frac{36}{12}\times2$)

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QUESTION IMAGE

Question

Explanation:

1. Solve \(-15 \div (-5)\)

Step1: Recall division of negatives

Step2: Perform the division

Step1: Apply distributive property

Step2: Multiply out

Step1: Identify the ratio of corresponding sides

Step2: Find the missing side

Step3: Solve for \(x\)

Answer:

2. Rewrite \(8(b + 7)\) using the distributive property