Which are the solutions of x^2=-11x+4

1 answer:

5 0

<span>Simplifying X2 + -4 = 0 Reorder the terms: -4 + X2 = 0 Solving -4 + X2 = 0 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + X2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + X2 = 0 + 4 X2 = 0 + 4 Combine like terms: 0 + 4 = 4 X2 = 4 Simplifying X2 = 4 Take the square root of each side: X = {-2, 2}</span>

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1. A movie theater designs two bags to hold 96 cubic inches of popcorn. a. Find the height of each bag b. Which bag should the t

MrRissso [65]

I have attached a screenshot with the images of the two popcorn bags used by the theater.

Part (a):
Bag A:
Volume of bag = area of base * height
Volume of bag = length * width * height
We have:
volume = 96 in³
length = 3 in
width = 4 in
Therefore:
96 = 3 * 4 * height
96 = 12 * height
height of bag A = 8 in
Bag B:
Volume of bag = area of base * height
Volume of bag = length * width * height
We have:
volume = 96 in³
length = 4 in
width = 4 in
Therefore:
96 = 4 * 4 * height
96 = 16 * height
height of bag B = 6 in

Part (b):
To determine the amount of paper needed, we will need to calculate the surface of each bag. Excluding the top base, each bag will have 5 faces. Four side faces (each two opposite are equal) and the base.
Bag A:
Surface area = area of base + 2*area of front face + 2*area of side face
Surface area = (3*4) + 2(8*4) + 2(8*3)
Surface area = 12 + 64 + 48
Surface area of bag A = 124 in²
Bag B:
Surface area = area of base + 2*area of front face + 2*area of side face
Surface area = (4*4) + 2(6*4) + 2(6*4)
Surface area = 16 + 48 + 48
Surface area of bag B = 112 in²
From the above calculations, we can deduce that the theater should choose bag B in order to reduce the amount of paper needed.

Hope this helps :)