We included HMH Into Math Grade 8 Answer Key PDF Module 5 Proportional Relationships to make students experts in learning maths.

## HMH Into Math Grade 8 Module 5 Answer Key Proportional Relationships

Auto Engineer
Auto engineers design new vehicles and improve existing vehicles. Some auto engineers work on improving a car’s performance, fuel efficiency, or safety. Others specialize in certain components, such as brakes or electrical systems. Auto engineers must understand how some quantities, such as a car’s braking distance, depend on other quantities, such as the car’s speed.

Three quantities related to a car engine’s performance are torque, horsepower, and revolutions per minute (RPM). These quantities are related by the equation

where torque is measured in pound-feet. How much torque is required to produce 300 horsepower at
2500 RPM? At 5000 RPM? How are the two torques related?

Learning Mindset!
Challenge-Seeking Defines Own Challenges

As you grow, you discover the pleasure of setting your own goals and challenges, and designing ways to meet them. Maybe you want to learn a new language, write a book, or become more successful academically. Here are some things to keep in mind as you seek and define new challenges.

• Believe in your ability to improve skills which are challenges for you now. Use positive self-talk to address any fixed-mindset voices telling you that you can’t reach your goal. Believe in the power of “yet.”
• Think about how you will handle unexpected difficulties. Don’t become discouraged. Every failure can help you get closer the next time.
• Be flexible. You may find it necessary to adjust your plan or even redefine the end goal.
• Don’t be afraid to ask for advice and assistance from content resources or people with more experience than you have currently.

Reflect

Question.
How do you know whether a task is the right level of challenge for you?

Question.
Was the STEM Task an appropriate challenge for you? If not, what reasonable challenge would you set for yourself?

Proportional Smoothies

The owners of a smoothie shop want the price of each size of smoothie to be proportional to the amount of liquid it contains. A small smoothie will be 16 fluid ounces and sell for $3.52. Complete the shop’s price chart by deciding how many fluid ounces the other smoothie sizes will have and then determine the price of each smoothie. Turn and Talk • Explain how you know that the prices of the smoothies are proportional to their volumes. • The shop owners decide to charge$0.99 for each smoothie add-in. For smoothies with a single add-in, is the total price proportional to the fluid ounces? Explain.

Complete these problems to review prior concepts and skills you will need for this module.

Tables and Graphs of Equivalent Ratios

Complete each table to represent the relationship.

Question 1.
Collette runs 6.5 kilometers each week. Let d represent the total distance, in kilometers, she runs in w weeks.

Given,
Collette runs 6.5 kilometers each week. Let d represent the total distance, in kilometers, she runs in w weeks.
1 week = 6.5 km
2 week = 2 × 6.5 = 13 km
19.5 km = x week
6.5 km = 1 week
19.5 = 6.5
19.5/6.5 = 3 weeks
5 weeks = 5 × 6.5 = 32.5 km

Question 2.
A theater charges a service fee of $0.95 per ticket bought online. Let t represent the total fee paid for ordering n tickets. Answer: A theater charges a service fee of$0.95 per ticket bought online. Let t represent the total fee paid for ordering n tickets.
t = 0.95n
t = 0.95 × 3 = 2.85
5.70/0.95 = 6

Identify Proportional Relationships

Tell whether each relationship is proportional. Explain your reasoning.

Question 3.

6:48 = 1:8
8:64 = 1:8
12:96 = 1:8
15:120 = 180
The given table is proportional.

Question 4.

9:18 = 1:2
15:24 = 5:3
18:27 = 2:3
36:45 = 4:5
The given table is not proportional.

Similar Triangles

Tell whether each pair of triangles is similar. Explain your reasoning.

Question 5.

No, both the triangles are not similar.
Sum of angles = 180°
90° + 48° + x° = 180°
138° + x = 180°
x = 180° – 138°
x = 42°

Question 6.