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.) $$ \frac{3}{5^{2}}=12 $$ 41.) $$ \frac{2}{3} c=8 $$ 35.) $$ \frac{4}{6^{2}}=71 / 3 $$ 42.) $$ \frac{3}{4} c=51 / 4 $$

Question

UpStudy AI · Accepted Answer

Solve the equation by following steps:
- step0: Solve for $$d$$:
  $$7d=56$$
- step1: Divide both sides:
  $$\frac{7d}{7}=\frac{56}{7}$$
- step2: Divide the numbers:
  $$d=8$$
Solve the equation $$ 9 y=63 $$.
Solve the equation by following steps:
- step0: Solve for $$y$$:
  $$9y=63$$
- step1: Divide both sides:
  $$\frac{9y}{9}=\frac{63}{9}$$
- step2: Divide the numbers:
  $$y=7$$
Solve the equation $$ \frac{3}{4} c=51 / 4 $$.
Solve the equation by following steps:
- step0: Solve for $$c$$:
  $$\frac{3}{4}c=\frac{51}{4}$$
- step1: Multiply by the reciprocal:
  $$\frac{3}{4}c\times \frac{4}{3}=\frac{51}{4}\times \frac{4}{3}$$
- step2: Multiply:
  $$c=17$$
Solve the equation $$ 15 m=45 $$.
Solve the equation by following steps:
- step0: Solve for $$m$$:
  $$15m=45$$
- step1: Divide both sides:
  $$\frac{15m}{15}=\frac{45}{15}$$
- step2: Divide the numbers:
  $$m=3$$
Solve the equation $$ \frac{1}{2} v=10 $$.
Solve the equation by following steps:
- step0: Solve for $$v$$:
  $$\frac{1}{2}v=10$$
- step1: Multiply by the reciprocal:
  $$\frac{1}{2}v\times 2=10\times 2$$
- step2: Multiply:
  $$v=20$$
Solve the equation $$ 9 x=143 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$9x=143$$
- step1: Divide both sides:
  $$\frac{9x}{9}=\frac{143}{9}$$
- step2: Divide the numbers:
  $$x=\frac{143}{9}$$
Solve the equation $$ \frac{2}{7} x=8 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\frac{2}{7}x=8$$
- step1: Multiply by the reciprocal:
  $$\frac{2}{7}x\times \frac{7}{2}=8\times \frac{7}{2}$$
- step2: Multiply:
  $$x=28$$
Solve the equation $$ 21 x=84 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$21x=84$$
- step1: Divide both sides:
  $$\frac{21x}{21}=\frac{84}{21}$$
- step2: Divide the numbers:
  $$x=4$$
Solve the equation $$ 14 r=42 $$.
Solve the equation by following steps:
- step0: Solve for $$r$$:
  $$14r=42$$
- step1: Divide both sides:
  $$\frac{14r}{14}=\frac{42}{14}$$
- step2: Divide the numbers:
  $$r=3$$
Solve the equation $$ 2 m=124 $$.
Solve the equation by following steps:
- step0: Solve for $$m$$:
  $$2m=124$$
- step1: Divide both sides:
  $$\frac{2m}{2}=\frac{124}{2}$$
- step2: Divide the numbers:
  $$m=62$$
Solve the equation $$ 29 t=77 $$.
Solve the equation by following steps:
- step0: Solve for $$t$$:
  $$29t=77$$
- step1: Divide both sides:
  $$\frac{29t}{29}=\frac{77}{29}$$
- step2: Divide the numbers:
  $$t=\frac{77}{29}$$
Solve the equation $$ \frac{2}{3} c=8 $$.
Solve the equation by following steps:
- step0: Solve for $$c$$:
  $$\frac{2}{3}c=8$$
- step1: Multiply by the reciprocal:
  $$\frac{2}{3}c\times \frac{3}{2}=8\times \frac{3}{2}$$
- step2: Multiply:
  $$c=12$$
Solve the equation $$ \frac{3}{5^{2}}=12 $$.
Check the equality by following steps:
- step0: Check the equality is true or false:
  $$\frac{3}{5^{2}}=12$$
- step1: Multiply both sides of the equation by LCD:
  $$\frac{3}{5^{2}}\times 5^{2}=12\times 5^{2}$$
- step2: Simplify the equation:
  $$3=300$$
- step3: Check the equality:
  $$\textrm{false}$$
Solve the equation $$ \frac{4}{6^{2}}=71 / 3 $$.
Check the equality by following steps:
- step0: Check the equality is true or false:
  $$\frac{4}{6^{2}}=\frac{71}{3}$$
- step1: Divide the terms:
  $$\frac{1}{3^{2}}=\frac{71}{3}$$
- step2: Calculate:
  $$0.\dot{1}=\frac{71}{3}$$
- step3: Calculate:
  $$0.\dot{1}=23.\dot{6}$$
- step4: Check the equality:
  $$\textrm{false}$$
Here are the solutions to the equations provided:

1. **Equation:** $$ 15 m = 45 $$  
   **Solution:**  
   $$
   m = \frac{45}{15} = 3
   $$

2. **Equation:** $$ 2 m = 124 $$  
   **Solution:**  
   $$
   m = \frac{124}{2} = 62
   $$

3. **Equation:** $$ 7 d = 56 $$  
   **Solution:**  
   $$
   d = \frac{56}{7} = 8
   $$

4. **Equation:** $$ 14 r = 42 $$  
   **Solution:**  
   $$
   r = \frac{42}{14} = 3
   $$

5. **Equation:** $$ 21 x = 84 $$  
   **Solution:**  
   $$
   x = \frac{84}{21} = 4
   $$

6. **Equation:** $$ 29 t = 77 $$  
   **Solution:**  
   $$
   t = \frac{77}{29}
   $$

7. **Equation:** $$ 9 y = 63 $$  
   **Solution:**  
   $$
   y = \frac{63}{9} = 7
   $$

8. **Equation:** $$ 9 x = 143 $$  
   **Solution:**  
   $$
   x = \frac{143}{9} \approx 15.8
   $$

9. **Equation:** $$ \frac{2}{7} x = 8 $$  
   **Solution:**  
   $$
   x = 8 \cdot \frac{7}{2} = 28
   $$

10. **Equation:** $$ \frac{1}{2} v = 10 $$  
    **Solution:**  
    $$
    v = 10 \cdot 2 = 20
    $$

11. **Equation:** $$ \frac{3}{5^{2}} = 12 $$  
    **Solution:**  
    This equation is false since $$ \frac{3}{25} \neq 12 $$.

12. **Equation:** $$ \frac{2}{3} c = 8 $$  
    **Solution:**  
    $$
    c = 8 \cdot \frac{3}{2} = 12
    $$

13. **Equation:** $$ \frac{4}{6^{2}} = \frac{71}{3} $$  
    **Solution:**  
    This equation is false since $$ \frac{4}{36} \neq \frac{71}{3} $$.

14. **Equation:** $$ \frac{3}{4} c = \frac{51}{4} $$  
    **Solution:**  
    $$
    c = \frac{51}{4} \cdot \frac{4}{3} = 17
    $$

If you have any further questions or need additional assistance, feel free to ask!
Here are the solutions to the equations: 1. $$ m = 3 $$ 2. $$ m = 62 $$ 3. $$ d = 8 $$ 4. $$ r = 3 $$ 5. $$ x = 4 $$ 6. $$ t = \frac{77}{29} $$ 7. $$ y = 7 $$ 8. $$ x \approx 15.8 $$ 9. $$ x = 28 $$ 10. $$ v = 20 $$ 11. The equation is false. 12. $$ c = 12 $$ 13. The equation is false. 14. $$ c = 17 $$

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