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Katyanochek1 [597]
2 years ago
14

The sum of two numbers is eighteen. The total of three times the smaller and twice the larger is forty-four. Find the two number

s.
Mathematics
1 answer:
sashaice [31]2 years ago
6 0

Answer:

  • The numbers are 8 and 10.

Step-by-step explanation:

Let the numbers be x and y.

The sum of two numbers is eighteen:

  • x + y = 18

The total of three times the smaller and twice the larger is forty-four:

  • 3x + 2y = 44

Solve the system by substitution:

  • x = 18 - y

Substitute x and solve for y:

  • 3(18 - y) + 2y = 44
  • 54- 3y + 2y = 44
  • 54 - y = 44
  • y = 54 - 44
  • y = 10

Find x:

  • x = 18 - 10
  • x = 8
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A bookstore marks up the price of a book by 25% of the cost from the publisher. Therefore, the
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3 years ago
Find the coordinates of the other endpoint when you are given the midpoint (point M) and one of the endpoints (point P)
satela [25.4K]
The known endpoint is P = (-16,0)

Let Q = (x,y) be the other endpoint. It is unknown for now.

Looking at the x coordinates of P and Q, we see that they are -16 and x respectively. Adding these values up gives -16+x. Dividing that result by 2 gives (-16+x)/2. This result is exactly equal to the midpoint x coordinate, which is the x coordinate of M (0). 

So we have this equation (-16+x)/2 = 0. Let's solve for x

(-16+x)/2 = 0
2*(-16+x)/2 = 2*0
-16+x = 0
x-16 = 0
x-16+16 = 0+16
x = 16

Therefore the x coordinate of point Q is 16.

------------------------------------

Let's do something similar for the y coordinates.

The y coordinates of P and Q are 0 and y respectively. Add them up and divided by 2, then set the result equal to -16 (y coordinate of midpoint M) getting this equation (0+y)/2 = -16

Solve for y

(0+y)/2 = -16
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y = -32

The y coordinate of point Q is -32

------------------------------------

The point Q goes from (x,y) to (16, -32)

Final Answer: (16, -32)
3 0
3 years ago
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