What is the distance between the points (7, -3) and (-5, 6)?

The distance between the two points is: √145≈12.04 to 2 decimal places.

Step-by-step explanation:

If using a grid it will make the answer easier to solve.

21units

12 units + 9 units

It's fun to pretend. Think of something you can count and purchase from a couple of places. That should work nicely.

I choose:

x = number of dogs adopted from an animal shelter

Now - we have to have 2 scenarios - one for each side of the equation. How about we set this up like someone adopted the same number of dogs (x) from 2 different animal shelters and the money spent at each location was the same amount (because the equations, or scenario, has to be equal.)

What can we think of where we would need to multiply 25 for the dogs at one shelter and 35 for the dogs at another. How about the cost in dollars to adopt one?

What can the 60 & 20 represent to add to the 25x and 35x? It has to be money because our other portion will be dollars. How about an additional expenses that had to be paid to cover some shots.

Okay - so here we go.

Ray adopted the same number of dogs from two animal shelters. The fee for adopting dogs at the first shelter was $25 each. The fee for adopting dogs at the second shelter was $35 each. The first shelter charged an additional fee of $60 for giving shots to some of the dogs. The second shelter charged and additional fee of $20 for providing medicine to one of the dogs. The total money spent at each shelter was the same. What was the number of dogs purchased at each shelter.

Shelter 1 ... 60 + 25x

Shelter 2 ... 35x + 20

We know the two equations have to be equal.

60+ 25x = 35x + 20

Let's move the x terms to the right and numbers to the left using subtraction.

60-20=35x-25x

40 = 10X

4 = x There were 4 dogs purchased from each shelter.

Check:

60+ 25(4) = 35(4) + 20

160 = 160

Our story checks out. He spent $160 at each shelter for 4 dogs from each shelter.