Dog food selling for $0.50 per pound is to be mixed with a high protein blend selling for $1.50 per pound. How many pounds of the high protein blend are needed to produce a 50 pound mixture that sells for $1.25 per pound?

The number of high protein feeds needed is 37.5 pounds

Step-by-step explanation:

Firstly we define variables. Let the number of pounds of dog food be d and the number of pounds of protein feeds be p.

We have 50 pounds in total, this means :

d + p = 50(I)

The total cost here would be 50 * $1.25 since it’s $1.25 per pound: 1.25 * 50 = $62.5

Now, we multiply each feed by their cost to arrive at the total cost

This means that :

0.5d + 1.5p = 62.5(ii)

We can rewrite i as d =50 - p

We substitute this in ii

0.5(50-p) + 1.5p = 62.5

25 - 0.5p + 1.5p = 62.5

P= 62.5 -25 = 37.5 pounds

the monthly balance will be $75,000

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