lesson 5-1
one day, a veterinarian saw 20 cats and 30 dogs. write each ratio in all three forms. make sure each ratio is in simplest form.
1. cats to dogs
2. dogs to cats
3. cats to animals
4. a compact car gets 135 miles per 5 gallons of gas. a midsize car gets 210 miles per 10 gallons of gas. which car gets more miles per gallon?
lesson 5-2
5. jamie’s family drives 350 miles to her grandparents’ house in 7 hours. what is their average speed in miles per hour?
6. a store sells milk in 3 sizes. the 128 fl oz container costs $4.59, the 64 fl oz container costs $3.29, and the 32 fl oz container costs $1.99. which size milk has the lowest price per fluid ounce?
lesson 5-3
tell whether the slope is positive or negative. then find the slope.
7.
image of a coordinate plane with points (-2, -2) and (1, 1)
8.
image of a coordinate plane with points (-3, 1) and (1, 0)

Question

Accepted Answer

### Question 1: cats to dogs
# Explanation:
## Step1: Identify the number of cats and dogs
Number of cats = 20, Number of dogs = 30
## Step2: Write the ratio of cats to dogs
The ratio of cats to dogs is $ \frac{20}{30} $
## Step3: Simplify the ratio
Divide numerator and denominator by their greatest common divisor, which is 10. So, $ \frac{20\div10}{30\div10} = \frac{2}{3} $
The three forms of the ratio are: $ 2:3 $, $ \frac{2}{3} $, and "2 to 3".
# Answer:
The ratio of cats to dogs in simplest form is $ 2:3 $ (or $ \frac{2}{3} $, or "2 to 3").

### Question 2: dogs to cats
# Explanation:
## Step1: Identify the number of dogs and cats
Number of dogs = 30, Number of cats = 20
## Step2: Write the ratio of dogs to cats
The ratio of dogs to cats is $ \frac{30}{20} $
## Step3: Simplify the ratio
Divide numerator and denominator by their greatest common divisor, which is 10. So, $ \frac{30\div10}{20\div10} = \frac{3}{2} $
The three forms of the ratio are: $ 3:2 $, $ \frac{3}{2} $, and "3 to 2".
# Answer:
The ratio of dogs to cats in simplest form is $ 3:2 $ (or $ \frac{3}{2} $, or "3 to 2").

### Question 3: cats to animals
# Explanation:
## Step1: Calculate the total number of animals
Total number of animals = Number of cats + Number of dogs = $ 20 + 30 = 50 $
## Step2: Write the ratio of cats to animals
The ratio of cats to animals is $ \frac{20}{50} $
## Step3: Simplify the ratio
Divide numerator and denominator by their greatest common divisor, which is 10. So, $ \frac{20\div10}{50\div10} = \frac{2}{5} $
The three forms of the ratio are: $ 2:5 $, $ \frac{2}{5} $, and "2 to 5".
# Answer:
The ratio of cats to animals in simplest form is $ 2:5 $ (or $ \frac{2}{5} $, or "2 to 5").

### Question 4: Which car gets more miles per gallon?
# Explanation:
## Step1: Calculate miles per gallon for compact car
Miles per gallon for compact car = $ \frac{135}{5} = 27 $ miles per gallon
## Step2: Calculate miles per gallon for midsize car
Miles per gallon for midsize car = $ \frac{210}{10} = 21 $ miles per gallon
## Step3: Compare the two values
Since $ 27 > 21 $, the compact car gets more miles per gallon.
# Answer:
The compact car gets more miles per gallon.

### Question 5: What is their average speed in miles per hour?
# Explanation:
## Step1: Recall the formula for average speed
Average speed = $ \frac{\text{Total Distance}}{\text{Total Time}} $
## Step2: Substitute the given values
Total distance = 350 miles, Total time = 7 hours. So, average speed = $ \frac{350}{7} = 50 $ miles per hour
# Answer:
Their average speed is 50 miles per hour.

### Question 6: Which size milk has the lowest price per fluid ounce?
# Explanation:
## Step1: Calculate price per fluid ounce for 128 fl oz container
Price per fluid ounce = $ \frac{4.59}{128} \approx 0.0359 $ dollars per fluid ounce
## Step2: Calculate price per fluid ounce for 64 fl oz container
Price per fluid ounce = $ \frac{3.29}{64} \approx 0.0514 $ dollars per fluid ounce
## Step3: Calculate price per fluid ounce for 32 fl oz container
Price per fluid ounce = $ \frac{1.99}{32} \approx 0.0622 $ dollars per fluid ounce
## Step4: Compare the three values
Since $ 0.0359 < 0.0514 < 0.0622 $, the 128 fl oz container has the lowest price per fluid ounce.
# Answer:
The 128 fl oz container of milk has the lowest price per fluid ounce.

### Question 7: Tell whether the slope is positive or negative. Then find the slope. (For the line passing through $(-2, -2)$ and $(1, 1)$)
# Explanation:
## Step1: Determine the sign of the slope
As we move from left to right (from $ x = -2 $ to $ x = 1 $), the $ y $-value increases from -2 to 1. So, the slope is positive.
## Step2: Use the slope formula
The slope $ m $ between two points $ (x_1, y_1) $ and $ (x_2, y_2) $ is given by $ m = \frac{y_2 - y_1}{x_2 - x_1} $
Substitute $ (x_1, y_1) = (-2, -2) $ and $ (x_2, y_2) = (1, 1) $
$ m = \frac{1 - (-2)}{1 - (-2)} = \frac{1 + 2}{1 + 2} = \frac{3}{3} = 1 $
# Answer:
The slope is positive, and the slope is 1.

### Question 8: Tell whether the slope is positive or negative. Then find the slope. (For the line passing through $(-3, 1)$ and $(1, 0)$)
# Explanation:
## Step1: Determine the sign of the slope
As we move from left to right (from $ x = -3 $ to $ x = 1 $), the $ y $-value decreases from 1 to 0. So, the slope is negative.
## Step2: Use the slope formula
The slope $ m $ between two points $ (x_1, y_1) $ and $ (x_2, y_2) $ is given by $ m = \frac{y_2 - y_1}{x_2 - x_1} $
Substitute $ (x_1, y_1) = (-3, 1) $ and $ (x_2, y_2) = (1, 0) $
$ m = \frac{0 - 1}{1 - (-3)} = \frac{-1}{1 + 3} = \frac{-1}{4} = -\frac{1}{4} $
# Answer:
The slope is negative, and the slope is $ -\frac{1}{4} $.

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QUESTION IMAGE

Question

Explanation:

Question 1: cats to dogs

Step1: Identify the number of cats and dogs

Step2: Write the ratio of cats to dogs

Step3: Simplify the ratio

Step1: Identify the number of dogs and cats

Step2: Write the ratio of dogs to cats

Step3: Simplify the ratio

Step1: Calculate the total number of animals

Step2: Write the ratio of cats to animals

Step3: Simplify the ratio

Answer:

Question 2: dogs to cats