The sum of four times a first number and eight times a second number is 64. if the second number is subtracted from four times the first number, the result is 19. find the numbers.

First number is 6, second is 5

Step-by-step explanation:

What you have to do here is make a system of equations. X will be the first number, and y will be the second. With the first sentence, we can make the equation 4x + 8y = 64. The second sentence gives us 4x - y = 19. We can subtract these two equations to get 9y = 45. Quickly solving this we get y = 5. If we plug that in to the second equation, then we get 4x - 5 = 19. 4x = 24, then we solve that and get 6.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

to find the total number of combinations, multiply the quantity of each item by each other:

2 pairs of shoes x 3 pairs of shorts = 6 different combinations.