Question
29.) \( 15 m=45 \) 36.) \( 2 m=124 \) 30.) \( 7 d=56 \) 37.) \( 14 r=42 \) 31.) \( 21 x=84 \) 38.) \( 29 t=77 \) 32.) \( 9 y=63 \) 39.) \( 9 x=143 \) 33.) \( \frac{2}{7} x=8 \) 40.) \( \frac{1}{2} v=10 \) 34.) \( \frac{3}{5} z=12 \) 41.) \( \frac{2}{3} c=8 \) 35.) \( \frac{4}{6} z=7^{1 / 3} \) 42.) \( \frac{3}{4} c=51 / 4 \)
Ask by Sandoval Little. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Here are the solutions to each equation:
29) m = 3
30) d = 8
31) x = 4
32) y = 7
33) x = 28
34) z = 20
35) z = (3/2)·7^(1/3)
36) m = 62
37) r = 3
38) t = 77/29
39) x = 143/9
40) v = 20
41) c = 12
42) c = 17
Solution
Below are the step‐by‐step solutions for each equation. (Note that even though some letters repeat, each equation is separate.)
29) 15m = 45
Divide both sides by 15:
m = 45 ÷ 15 = 3
30) 7d = 56
Divide by 7:
d = 56 ÷ 7 = 8
31) 21x = 84
Divide by 21:
x = 84 ÷ 21 = 4
32) 9y = 63
Divide by 9:
y = 63 ÷ 9 = 7
33) (2/7)x = 8
Multiply both sides by the reciprocal, 7/2:
x = 8 × (7/2) = 56/2 = 28
34) (3/5)z = 12
Multiply both sides by 5/3:
z = 12 × (5/3) = 60/3 = 20
35) (4/6)z = 7^(1/3)
First, note that 4/6 simplifies to 2/3. Then multiply by the reciprocal (3/2):
z = 7^(1/3) × (3/2) = (3/2)·7^(1/3)
36) 2m = 124
Divide by 2:
m = 124 ÷ 2 = 62
37) 14r = 42
Divide by 14:
r = 42 ÷ 14 = 3
38) 29t = 77
Divide by 29:
t = 77 ÷ 29 = 77/29
(This fraction does not simplify to an integer.)
39) 9x = 143
Divide by 9:
x = 143 ÷ 9 = 143/9
(This fraction remains as is.)
40) (1/2)v = 10
Multiply both sides by 2:
v = 10 × 2 = 20
41) (2/3)c = 8
Multiply both sides by 3/2:
c = 8 × (3/2) = 24/2 = 12
42) (3/4)c = 51/4
Multiply by the reciprocal (4/3):
c = (51/4) × (4/3) = 51/3 = 17
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To summarize:
• Equation 29: m = 3
• Equation 30: d = 8
• Equation 31: x = 4
• Equation 32: y = 7
• Equation 33: x = 28
• Equation 34: z = 20
• Equation 35: z = (3/2)·7^(1/3)
• Equation 36: m = 62
• Equation 37: r = 3
• Equation 38: t = 77/29
• Equation 39: x = 143/9
• Equation 40: v = 20
• Equation 41: c = 12
• Equation 42: c = 17
Any answer that is equivalent to the ones above is correct.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Explain 
Simplify this solution Beyond the Answer
To solve equations like these, remember that the goal is to isolate the variable. This often involves performing the same operation on both sides. For instance, if you're dealing with \( 15m = 45 \), divide both sides by 15 to find \( m \). This method allows you to systematically tackle each equation step-by-step. Don’t forget about checking your answers! After solving each equation, it’s vital to substitute your answer back into the original equation to ensure it holds true. This is a common mistake many make—assuming they got it right without verification! A simple plug-and-check can save you from error.
