3) The sum of two numbers is 17. The difference between five times the first number and three times the second number is 13. Find the two numbers.

8 and 9.

Step-by-step explanation:

Let the two unknown numbers be a and b.

When added together, they equal 17. In other words:

a + b = 17.

The difference between five times the first number and three times the second number is 13. In other words:

5a - 3b = 13.

We have a system of equations. We can use substitution. From the first equation, we can derive a = 17 - b. Let's substitute this in:

5(17 - b) - 3b = 13

85 - 5b - 3b = 13

-8b = -72

b = 9

a = 17 - b.

a = 17 - 9 = 8.

Thus, the two numbers are 8 and 9.

step-by-step explanation: h: (- 3, 6)

m: (1, - 2)

o: (7, 6)

r: (- 9, - 2)

midpoint of hm: (- 1, 2)

midpoint of or: (- 1, 2)

therefore, b is the midpoint of both diagonals bisect each other !

to prove the diagonals are perpendicular, show that the product of the slopes = - 1