Chapter 1 Algebra: Understand Numerical And Algebraic Expressions
Guided Practice 7
Page 57 Exercise 1 Answer
Formulas are useful because it generalize a relationship between two or more quantitites.
Result
Because it generalize a relationship between quantities
Page 57 Exercise 2 Answer
It is important to define each variable used in formulas because a formula uses symbols to relate between quantities.
Result
Because formula uses symbols to relate between quantities
Read And Learn More: enVisionmath 2.0 Grade 6 Volume 1 Solutions
Page 57 Exercise 3 Answer
Step 1 → Identify the values in the formulas
d = distance
r = rate = 400 miles per hour
t = time = 5 hours
Step 2 → Substitute the values in the formula and evaluate
d = rt
d = 400 × 5
d = 2000
The plane will travel 2000 miles in 5 hours.
Result
2000 miles
Page 57 Exercise 4 Answer
Step 1 → Identify the values in the formulas
d = distance = 510 miles
r = rate = 68 miles per hour
t = time
Step 2 → Substitute the values in the formula and evaluate
d = rt
510 = (68)t Substitute the value
510 = 68t Simplify
\(\frac{510}{68}=\frac{68 t}{68}\) Divide both sides by 68
t = 7.5
It will take 7.5 hours for a car travelling at a rate of 68 miles per hour to go 510 miles.
Result
7.5 hours
Page 57 Exercise 5 Answer
Step 1 → Identify the values in the formulas
V = volume
s = length = width = height = 8 cm
Step 2 → Substitute the values in the formula and evaluate
V = \(s^3\)
V = \((8)^3\) Substitute the value
V = 512
The Volume of the cube is 512\(cm^3\)
Result
512\(cm^3\)
Page 57 Exercise 6 Answer
Step 1 → Identify the values in the formulas
A = Total surface area
s = length = width = height = 8 cm
Step 2 → Substitute the values in the formula and evaluate
A = \(6s^2\)
A = \(6(8)^2\) Substitute the value
A = 6 × 64 Simplify
A = 384\(cm^2\)
The Total surface area of the cube is 384\(cm^2\)
Result
384 \(cm^2\)
Page 57 Exercise 7 Answer
Step 1 → Identify the values in the formulas
g = number of gallons of gasoline used
m = miles per gallon = 16
d = distance traveled = 296
Step 2 → Substitute the values in the formula and evaluate
g = \(\frac{d}{m}\)
g = \(\frac{296}{16}\) Substitute the value
g = 18.5
Myra will need 18.5 gallons of gasoline to travel 296 miles.
Result
18.5 gallons
Page 58 Exercise 8 Answer
Step 1 → Identify the values in the formulas
F = Fahrenheit
C = Celsius = 26°
Step 2 → Substitute the values in the formula and evaluate
F = (C × 1.8) + 32
F = (26 × 1.8) + 32 Substitute the value
F = 46.8 + 32 Simplify
F = 78.8°
The temperature in Fahrenheit is 78.8°
Result
78.8°
Page 58 Exercise 9 Answer
Step 1 → Identify the values in the formulas
F = Fahrenheit = 45°F
C = Celsius = 13°C
Step 2 → Substitute the values in the formula and evaluate
F = (C × 1.8) + 32
45 = (13 × 1.8) + 32 Substitute the value
45 = 23.4 + 32 Simplify
45 ≠ 55.4
Since Left hand side is not equal to Right hand side.
So, the thermometer cannot show as both 45°F and 13°C
Result
NO
Page 58 Exercise 10 Answer
Step 1 → Identify the values in the formulas
A = Average grade
X = test score = 78
Y = test score = 90
Z = test score = 81
Step 2 → Substitute the values in the formula and evaluate
A = \(\frac{X+Y+Z}{3}\)
A = \(\frac{78+90+81}{3}\) Substitute the value
A = \(\frac{249}{3}\) Simplify
A = 83
Jules average test grade is 83
Result
83
Page 58 Exercise 11 Answer
Step 1 → Identify the values in the formulas
d = density
m = mass of the object = 65 grams
v = volume = 8 cubic meters
Step 2 → Substitute the values in the formula and evaluate
d = \(\frac{m}{v}\)
d = \(\frac{65}{8}\) Substitute the value
d = 8.125 gram per cubic meter
Density of the object is 8.125 gram per cubic meter
Result
8.125 gram per cubic meter
Page 58 Exercise 12 Answer
\(7\left(3^2+5\right)-\left(\frac{81}{9}\right)\) Evaluate
= \(7(9+5)-\left(\frac{81}{9}\right)\) \(3^2\) = 9
= 7(14) − 9 Evaluate inside the parentheses
= 98 − 9 Multiply
= 89 Subtract
Result
89
Page 58 Exercise 13 Answer
Step 1→Identify the values in the formulas
I = Interest = $696
p = Principal loan amount = $5800
r = rate = 4% = 0.04
t = time
Step 2 → Substitute the values in the formula and evaluate
I = prt
696 = 5800 ⋅ 0.04 ⋅ t Substitute the value
696 = 232t Simplify
\(\frac{696}{232}=\frac{232 t}{232}\) Divide both sides by 232
t = 3
Janie will take 3 years to pay off the loan
Result
3 years
Page 58 Exercise 14 Answer
Option 1 → 4.50 for each hour worked.
Option 2 → Final payment of $350
Step 1 → Identify the values in the formulas
p = total payment after 15 days
h = hours worked each day=6 hours
Step 2 → Substitute the values in the formula and evaluate
p = 15 × 4.50h
p = 15 × 4.50(6) Substitute the value
p = 15 × 27 Simplify
p = 405
Jeremiah should choose Option 1 as that he will get more payment than Option 2.
Result
Option 1