Set up a proportion that looks like 5/12 = 13/x with X being the actual distance between the cities if they are 13 inches apart on the map.

Then cross-multiply to get 5x = 156. Divide by 5 to isolate the X and get X = 31.2

The cities are a distance of 31.2 miles apart.

I'm guessing your question cut off where you put to the nearest... and you mean to round to the nearest whole number in which case your answer would be just 31 miles apart.

8 0

3 years ago

Solve the equation. Then check your solution.4- 3/5(3a+4)=7A. -7.4B. -6C. 3D. -3

Evgesh-ka [11]

Answer: a = -3

Explanations:

The given equation is:

$4\text{ - }\frac{3}{5}(3a+4)\text{ = 7}$

This can be re-written as:

$4-\frac{3(3a+4)}{5}=7$

Collect like terms:

$\begin{gathered} -\frac{3(3a+4)}{5}=\text{ 7 - 4} \\ -\frac{3(3a+4)}{5}=\text{ 3} \end{gathered}$

Cross multiply:

$\begin{gathered} -3(3a+4)\text{ = 3}\times5 \\ -3(3a+4)=\text{ 15} \\ \text{Expand the bracket} \\ -9a\text{ - 12 = 15} \\ \text{Collect like terms} \\ -9a\text{ = 15 + 12} \\ -9a\text{ = 27} \\ \text{Divide both sides by -9} \\ \frac{-9a}{-9}=\frac{27}{-9} \\ a\text{ = -3} \end{gathered}$

To verify if the solution is correct, substitute a = -3 into the question given. If the Right Hand Side equals the Left Hand Side, then the solution is correct.

$\begin{gathered} 4-\frac{3(3a+4)}{5}=\text{ 7} \\ \text{Substitute a = }-3 \\ 4\text{ - }\frac{3(3(-3)+4)}{5}\text{ = 7} \\ 4\text{ - }\frac{3(-9+4)}{5}\text{ = 7} \\ 4\text{ - }\frac{3(-5)}{5}\text{ = 7} \\ 4\text{ - }\frac{-15}{5}=\text{ 7} \\ 4-(-3)=7 \\ 4+3=7 \\ 7=7 \end{gathered}$

Since the Left Hand Side = Right Hand Side = 7, the solution a = -3 is correct

5 0

6 months ago