We included HMH Into Math Grade 7 Answer Key PDFModule 7 Review to make students experts in learning maths.
Vocabulary
adjacent angles
complementary angles
supplementary angles
vertical angles
Choose the correct term from the Vocabulary box.
Question 1.
a pair of angles with measures that add to 90°
______________
Answer:
Complementary angles.
Explanation:
A pair of angles with measures that add to 90° is called Complementary angles.
Question 2.
a pair of angles with measures that add to 180°
______________
Answer:
Supplementary angles.
Explanation:
A pair of angles with measures that add to 180° is called Supplementary angles.
Question 3.
a pair of opposite angles formed by two intersecting lines
______________
Answer:
Vertical angles.
Explanation:
A pair of opposite angles formed by two intersecting lines is called Vertical angles.
Question 4.
a pair of angles that share a vertex and a ray but have no interior points in common ______________
Answer:
Adjacent angles.
Explanation:
A pair of angles that share a vertex and a ray but have no interior points in common is called Adjacent angles.
Concepts and Skills
Question 5.
To fence a rectangular cornfield, a farmer uses 2,600 meters of fencing. The length of the field is 800 meters. Complete the equation that can be used to determine the width w of the field in meters. Use values from the box to complete the equation.
Answer:
Question 6.
Use Tools The regular price r of a sweater was marked down by $5. Then the marked-down price was reduced by 20%. Write two expressions that represents the final reduced price of the sweater. State what strategy and tool you will use to answer the question, explain your choice, and then find the answer.
Answer:
Question 7.
The McCray family ate at a restaurant. The expression shown represents the amount of tip they left, where b is the amount of the bill.
0.15b
Write two different expressions in terms of b to represent the total amount that the family spent for the meal, including the tip.
Expression 1: ____ Expression 2: ______________
Answer:
Expression 1: b + 0.15b
Expression 2 : 1.15b
Explanation:
Total amount spent = b + 0.15b this is expression 1
Let b as common
b (1 + 0.15)
= 1.15 b Expression 2.
Determine the measure in degrees of the angle indicated with an arc.
Question 8.
Answer:
x = 19.5°, 2x = 39°, 3x = 58.5°
Explanation:
The Sum of angles in a triangle is 180°
Now add the all given angles
82.5° + 2x° + 3x° = 180
5x° = 180 °- 82.5°
5x° = 97.5
x° = 97.5 ÷ 5
x = 19.5°
2x = 2 × 19.5 = 39
3x = 3 × 19.5 = 58.5
Question 9.
Answer:
x° = 54°
7x° = 7 × 54 = 378°
8x° = 8 × 54 = 432°
Explanation:
Sum of angles in a traingle is 180°
Now add all the angles given
7x° + 8x° + 90° = 360
15x° + 90° = 360°
15x° = 360° – 90°
15x° = 270°
x° = 270° ÷ 15
x° = 54°
7x° = 7 × 54 = 378°
8x° = 8 × 54 = 432°
Question 10.
Simplify the expression.
(\(\frac{7}{8}\)x – 4) – 3(\(\frac{1}{4}\)x + 6) ____________
Answer:
x = 176
Explanation:
The given expression is (\(\frac{7}{8}\)x – 4) – 3(\(\frac{1}{4}\)x + 6)
(\(\frac{7}{8}\)x – 4) – \(\frac{3}{4}\)x + 18
\(\frac{7}{8}\)x – 4 – \(\frac{3}{4}\)x – 18
\(\frac{7}{8}\)x – \(\frac{3}{4}\)x -18 – 4
\(\frac{7}{8}\)x – \(\frac{6}{8}\)x – 22
\(\frac{x}{8}\) – 22
\(\frac{x}{8}\) = 22
x = 22 × 8
x = 176
Question 11.
A website designer charges $200 plus $49 per hour to make a website. The designer charges a bakery a total of $1,204.50 to make its website.
A. Write an equation that models this situation, where h represents the number of hours the designer worked on the bakery’s website.
Answer:
200 + 49h = $1204.50
Explanation:
h represents the number of hours
200 + 49h = $1204.50
49h = 1204.50 – 200
49h = 1004.5
h = 1004.5 ÷ 49
h = 20.5 hours
B. How many hours did it take the designer to make the bakery’s website? ____ hours
Answer:
20.5 hours.
Explanation:
It took 20.5 hours to make the bakery’s website.
Question 12.
A coach buys 5 identical baseball bats for a total of $327.45. The bats are on sale for $14.50 off the regular price. Darius tried to determine the regular price r of each bat, but his work contains an error.
A. Describe the error that Darius made.
Answer:
The error that Darius made
5r = 327.45 + 72.50
5r = 399.95
Explanation:
Coach bought baseball bats for a total of $327.45.
Darius’s Work
5(r – 14.50) = 327.45
5r – 72.50 = 327.45
5r = 327.45 + 72.50
5r = 399.95 (Here is the error that Darius made)
r = 399.95 ÷ 5
r = $79.99
B. What is the correct regular price of each bat? $____
Answer:
The correct regular price of each bat is $79.99.
Question 13.
Which expression is equivalent to (8x + 6) + (10x – 30)?
A. 6(3x – 4)
B. 9(2x – 24)
C. 18(x – 24)
D. 18x – 36
Answer:
The expression is equivalent to (8x + 6) + (10x – 30) is 6(3x – 4).
Explanation:
Given equation is (8x + 6) + (10x – 30)
Let us solve the given expression
8x + 6 + 10x – 30
8x + 10x + 6 – 30
18x – 24
Let us take 6 as a common
6 (3x – 4).
Determine the measure in degrees of the angle indicated with an arc.
Question 8.
Answer:
x = 19.5°, 2x = 39°, 3x = 58.5°
Explanation:
The Sum of angles in a triangle is 180°
Now add the all given angles
82.5° + 2x° + 3x° = 180
5x° = 180 °- 82.5°
5x° = 97.5
x° = 97.5 ÷ 5
x = 19.5°
2x = 2 × 19.5 = 39
3x = 3 × 19.5 = 58.5
Question 9.
Answer:
x° = 54°
7x° = 7 × 54 = 378°
8x° = 8 × 54 = 432°
Explanation:
Sum of angles in a traingle is 180°
Now add all the angles given
7x° + 8x° + 90° = 360
15x° + 90° = 360°
15x° = 360° – 90°
15x° = 270°
x° = 270° ÷ 15
x° = 54°
7x° = 7 × 54 = 378°
8x° = 8 × 54 = 432°
Question 10.
Simplify the expression.
(\(\frac{7}{8}\)x – 4) – 3(\(\frac{1}{4}\)x + 6) ____________
Answer:
x = 176
Explanation:
The given expression is (\(\frac{7}{8}\)x – 4) – 3(\(\frac{1}{4}\)x + 6)
(\(\frac{7}{8}\)x – 4) – \(\frac{3}{4}\)x + 18
\(\frac{7}{8}\)x – 4 – \(\frac{3}{4}\)x – 18
\(\frac{7}{8}\)x – \(\frac{3}{4}\)x -18 – 4
\(\frac{7}{8}\)x – \(\frac{6}{8}\)x – 22
\(\frac{x}{8}\) – 22
\(\frac{x}{8}\) = 22
x = 22 × 8
x = 176
Question 11.
A website designer charges $200 plus $49 per hour to make a website. The designer charges a bakery a total of $1,204.50 to make its website.
A. Write an equation that models this situation, where h represents the number of hours the designer worked on the bakery’s website.
Answer:
200 + 49h = $1204.50
Explanation:
h represents the number of hours
200 + 49h = $1204.50
49h = 1204.50 – 200
49h = 1004.5
h = 1004.5 ÷ 49
h = 20.5 hours
B. How many hours did it take the designer to make the bakery’s website? ____ hours
Answer:
20.5 hours.
Explanation:
It took 20.5 hours to make the bakery’s website.
Question 12.
A coach buys 5 identical baseball bats for a total of $327.45. The bats are on sale for $14.50 off the regular price. Darius tried to determine the regular price r of each bat, but his work contains an error.
A. Describe the error that Darius made.
___________________
___________________
___________________
___________________
Answer:
The error that Darius made
5r = 327.45 + 72.50
5r = 399.95
Explanation:
Coach bought baseball bats for a total of $327.45.
Darius’s Work
5(r – 14.50) = 327.45
5r – 72.50 = 327.45
5r = 327.45 + 72.50
5r = 399.95 (Here is the error that Darius made)
r = 399.95 ÷ 5
r = $79.99
B. What is the correct regular price of each bat? $ ___________________
Answer:
The correct regular price of each bat is $79.99.
Question 13.
Which expression is equivalent to (8x + 6) + (10x – 30)?
A. 6(3x – 4)
B. 9(2x – 24)
C. 18(x – 24)
D. 18x – 36
Answer:
The expression is equivalent to (8x + 6) + (10x – 30) is 6 (3x – 4).
Explanation:
Given equation is (8x + 6) + (10x – 30)
Let us solve the given expression
8x + 6 + 10x – 30
8x + 10x + 6 – 30
18x – 24
Let us take 6 as a common
6 (3x – 4).
