Find the measure of a. A. 20 B. 70 C. 80 D. 40

The width of a container is 5 feet less than its height. Its length is 1 foot longer than its height. The volume of the containe

juin [17]

The height of container is 8 feet

Solution:

Let "w" be the width of container

Let "l" be the length of container

Let "h" be the height of container

The width of a container is 5 feet less than its height

Therefore,

width = height - 5

w = h - 5 ------ eqn 1

Its length is 1 foot longer than its height

length = 1 + height

l = 1 + h ---------- eqn 2

The volume of container is given as:

$v = length \times width \times height$

Given that volume of the container is 216 cubic feet

$216 = l \times w \times h$

Substitute eqn 1 and eqn 2 in above formula

$216 = (1 + h) \times (h-5) \times h\\\\216 = (h+h^2)(h-5)\\\\216 = h^2-5h+h^3-5h^2\\\\216 = h^3-4h^2-5h\\\\h^3-4h^2-5h-216 = 0$

Solve by factoring

$(h-8)(h^2+4h+27) = 0$

Use the zero factor principle

If ab = 0 then a = 0 or b = 0 ( or both a = 0 and b = 0)

Therefore,

$h - 8 = 0\\\\h = 8$

Also,

$h^2+4h+27 = 0$

Solve by quadratic equation formula

$\text {For a quadratic equation } a x^{2}+b x+c=0, \text { where } a \neq 0\\\\x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

$\mathrm{For\:} a=1,\:b=4,\:c=27:\quad h=\frac{-4\pm \sqrt{4^2-4\cdot \:1\cdot \:27}}{2\cdot \:1}$

$h = \frac{-4+\sqrt{4^2-4\cdot \:1\cdot \:27}}{2}=\frac{-4+\sqrt{92}i}{2}$

Therefore, on solving we get,

$h=-2+\sqrt{23}i,\:h=-2-\sqrt{23}i$

Thus solutions of "h" are:

h = 8

$h=-2+\sqrt{23}i,\:h=-2-\sqrt{23}i$

"h" cannot be a imaginary value

Thus the solution is h = 8

Thus the height of container is 8 feet

8 0

3 years ago

Question 3 (Multiple Choice Worth 1 points)

Evgen [1.6K]

Answer:

$g(x) = x + 6$

Step-by-step explanation:

The parent function is given as:

$f(x) = x + 8$

We want to find a new function that results after shifting f(x), 2 units to the right.

Let that function be g(x), then

$g(x) = f(x - 2)$

We replace x by x-2 in f(x) to get:

$g(x) = x - 2 + 8$

When we simplify, we obtain:

$g(x) = x + 6$

8 0

3 years ago

Juan rents a car for $29.00 a week. He pays $17.00 per week for the insurance and spends $13.50 weekly on gas. What will his cos

Goryan [66]

$29+$17+$13 = $59 weekly spending
So 1 month gonna be $59 times 4 = $236 per month

5 0

2 years ago

Read 2 more answers

Solve asap! this is for a grade -14 + x + 6 = -14

tino4ka555 [31]

Answer:

= −6

Step-by-step explanation:

6 0

2 years ago

A pizza has 8 slices and papa gino's sells the whole pizza for $16. What is the unit rate for a slice of pizza?

BabaBlast [244]

Answer:

It would be $2 per piece, because 16 divided by 8 is two.

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers