4.021> A. 4.201 B. 4.12 C. 4.012 D. 4.211 E. None

s344n2d4d5 [400]

30+5=5+30 with commutative property or 30+5=35

6 0

3 years ago

A baker is building a rectangular solid box from cardboard to be able to safely deliver a birthday cake. The baker wants the vol

k0ka [10]

The length of the rectangular delivery box must be equal to 4 inches.

Let the length of the box be L.

Let the width of the box be W.

Let the height of the box be H.

Given the following data:

Volume of box = 224 cubic inches.

Translating the word problem into an algebraic expression;

$W = 3 + L$ ......equation 1

$H = 4 + L$ ......equation 2.

Mathematically, the volume of a rectangular solid is given by the formula;

$Volume = length * width * height$ .....equation 3.

Substituting the values into equation, we have;

$224 = L * (3 + L) * (4 + L)\\\\224 = (3L + L^{2})* (4 + L)\\\\224 = 12L + 3L^{2} + 4L^{2} + L^{3} \\\\224 = 12L + 7L^{2} + L^{3}$

Rearranging the polynomial, we have;

$L^{3} + 7L^{2} + 12L - 224 = 0$

We would apply the remainder theorem to solve the polynomial.

According to the remainder theorem, if a polynomial P(x) is divided by (x - r) and there is a remainder R; then P(r) = R.

When x = 3

$(x - 3) = 0\\x = 3$

$P(3) = 3^{3} + 7(3^{2}) + 12(3) - 224\\\\P(3) = 27 + 7(9) + 36 - 224\\\\P(3) = 27 + 63 + 36 - 224 = -98 \neq 0$

We would try with 4;

$P(4) = 4^{3} + 7(4^{2}) + 12(4) - 224\\\\P(4) = 64 + 7(16) + 48 - 224\\\\P(4) = 64 + 112 + 48 - 224\\\\P(4) = 224 - 224 = 0$

Therefore, 4 is one of its roots.

Hence, the length of the rectangular delivery box must be equal to 4 inches.

Find more information on polynomial here: brainly.com/question/10689855

3 0

2 years ago

Given the parent function of y = | x |, list the values that would fill in the table of the transformed function y = | x - 4 |.

NeTakaya

I believe it is answer letter D.

3 0

3 years ago

Read 2 more answers

What is the greatest common factor of 45x^3, 24x^2, and 16x?

Phoenix [80]

Answer:

$\huge\boxed{\sf GCF = x}$

Step-by-step explanation:

Firstly we'll factorize the terms:

45x³ = 3 * 3 * 5 * x * x * x

24x² = 2 * 2 * 2 * 3 * x * x

16x = 2 * 2 * 2 * 2 * x

The factor which is common in all three terms is:

= x

Hence GCF = x

$\rule[225]{225}{2}$

Hope this helped!

8 0

2 years ago

The linear inequality y<-2/3x+2 is graphed. Determine a solution for the inequality. A) (0,2) B) (3,0) C) (0,0) D) (0,3)

jenyasd209 [6]

Hello!

The graph y < -2/3x + 2 has a dotted line. That means that any points on the dotted line or not shaded, is not a solution to this inequality. Since we are given 4 choices, we can substitute those values into the given inequality to see if it is true.

A) (0, 2)

2 < -2/3(0) + 2

2 < 2, this is false.

B) (3, 0)

0 < -2/3(3) + 2

0 < -2 + 2

0 < 0, this is false.

C) (0, 0)

0 < -2/3(0) + 2

0 < 2, this is true.

D). (0, 3)

3 < -2/3(0) + 2

3 < 2, this is false.

To check if choice C) (0, 0) is true, we should look at the given graph.

Since (0, 0) is in the shaded area, and is not graphed on the dotted line, therefore, a solution to this linear inequality is C, (0, 0).

5 0

3 years ago