You are purchasing a new refrigerator. To fit in the space, the width of the refrigerator cannot be more than 42 inches. To meet your storage requirements, the width of the refrigerator must be at least 36 inches. Write a compound inequality that represents this range

Given:

To fit in the space, the width of the refrigerator cannot be more than 42 inches.

To meet your storage requirements, the width of the refrigerator must be at least 36 inches.

To find:

The compound inequality that represents this range.

Solution:

Let w be the width of the refrigerator.

To fit in the space, the width of the refrigerator cannot be more than 42 inches.  It means width of the refrigerator must be less than or equal to 42.

        ...(i)

To meet your storage requirements, the width of the refrigerator must be at least 36 inches. It means width of the refrigerator must be greater than or equal to 36.

         ...(ii)

Using (i) and (ii), we get

Therefore, the required compound inequality is .

hi there!

the answer to this question is d: 35

step-by-step explanation:

5 to the power of 2 is 25

2 multiplied by 5 is 10

then you add the 2 numbers and you get 35

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