The volume of a rectangular prism is represented by the function x3 + 9x2 + 6x - 16. The length of the box is x + 2 while the height is x + 8. Find the expression representing the width of the box. (2 points) . Answer: A. x - 4 B. x - 1 C. x + 1 D. x + 4

Answers

Answer 1

Answer: easy
V=LWH
V=x³+9x²+6x-16
L=x+2
H=x+8
W=?
so
x³+9x²+6x-16=(x+2)(?)(x+8)
x³+9x²+6x-16=(x+2)(x+8)(?)
x³+9x²+6x-16=(x²+10x+16)(?)
divide both sides by (x²+10x+16) or guess what ? is
(x-1)=?

width=x-1

B is answer

or you could have trial and erroed it, since you know they multiply to get the volume

Answer 2

Answer:

Your answer is either B or x - 4.

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Alana bought some cans of paint and 1/2 of a liter of special paint additive formulated to reduce mildew. Before painting her house, she used all of the additive to put 1/8 of a liter of additive in each can. How many cans of paint did Alana buy?

Answers

Answer:

Alana bought 4 cans of paint additive

Step-by-step explanation:

Proportions

If a proportional amount of x is to be distributed between y elements, each one of them gets x/y portions.

For example, if we have 100 coins and distribute evenly between 20 boxes, each box will receive 100/20=5 coins.

Alana bought 1/2 of a liter of the special paint additive and evenly distributed it between an unknown number of cans, let's call it C. We also know each can received 1/8 of a liter of the additive. That is the proportion of the 1/2 liter of additive.

We can establish the following condition:

$\displaystyle (1/2)/(x)=(1)/(8)$

Solving for x:

$\displaystyle (1/2)/((1)/(8))=x$

Transform the division into a product:

$\displaystyle x=(1)/(2)\cdot(8)/(1)=4$

Alana bought 4 cans of paint additive

Please help I got 20mins

Answers

Answer/Step-by-step explanation:

Scale factor: 1/4

AC = DF and 10 ÷ 2.5 = 4

10 x 1/4 = 2.5

DE length: 5

AB = DE

20 x 1/4 = 5

BC length: 30

EF = BC

(Because EF is the dilation) 7.5 x 4 = 30

A rectangle has an area of 8 square centimmetres and a perimeter of 12 cm. What are the width and breath?

Answers

Let the Length be L and the Width be W

The area is 8 cm²
LW = 8

The perimeter is 12
2(L + W) = 12
L + W = 6

Solve L and W:
LW = 8 --------------- (1)
L + W = 6------------ (2)

Equation (2):
L + W = 6
L = 6 - W -------------- Sub into (1)
(6 - W) W = 8
6W - W² = 8
W² - 6W + 8 =0
(W -2 )(W - 4) = 0
W = 2 or 4

When W =2, L = 6 - 2 = 4
When W = 4, L = 6 - 4 = 2

Answer: The Width is 2 cm and the Length is 4 cm

The function f(x) = x2 – 9 is shifted 2 units up and 3 units to the left. Select the new function. A) g(x) = 2x2 – 6 B) g(x) = (x – 3)2 + 7 C) g(x) = 3x2 – 7 D) g(x) = (x + 3)2 – 7

Answers

We have the following function:
f (x) = x ^ 2 - 9
Applying the transformations we have:
Vertical translations
Suppose that k> 0
To graph y = f (x) + k, move the graph of k units up.
h (x) = x ^ 2 - 9 + 2
h (x) = x ^ 2 - 7
Horizontal translations
Suppose that h> 0
To graph y = f (x + h), move the graph of h units to the left.
g (x) = (x + 3) ^ 2 - 7
Answer:
D) g (x) = (x + 3) ^ 2 - 7

Given log 2 = 0.3010, log 3 = 0.4771. Find the value of a) log 12 b) log 5.

Answers

a) log 12
= log3*4
= log3 + log4
=log3 + log 2^2
=log3 + 2log2
= 0.4771 +2*0.3010
=1.0791

b) log5
= log10/2
= log10 - log2
=1 - 0.3110
= 0.6989

$a)\ \ \ log12=log(4\cdot3)=log4+log3=log2^2+log3=2log2+log3\approx\n\n\approx2\cdot0.3010+0.4771=0.602+0.4771=1.0791\n\n2)\ \ \ log5=log (10)/(2) =log10-log2\approx1-0.3010=0.699$

Over twenty years, it was found that the number of doctors of medicine, MD (in thousands), in the United States can be approximated by MD=(28,390+693t)/(85-t) where t=0 represents 1980. The number of doctors of osteopathy, DO (in thousands), can be approximated by DO=(776-12t)/(65-2t) .Write an expression for the total number I of doctors of medicine (MD) and doctors of osteopathy (DO). Simplify the result.

How many MDs did the United States have in 2010? How many MDs did the United States have in 2010?