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4 years ago

9

A rectangular prism has a volume of 729 ft'. The length, width, and height are all the same. What is the length of each side of

the prism?

2 answers:

elena55 [62]4 years ago

5 0

Answer:

9

Step-by-step explanation:

german4 years ago

3 0

Answer:

9

Step-by-step explanation:

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Help me out please I'm not sure what goes where and I always get frustrated with these

Hunter-Best [27]

yes:x+7=18

no:2x+7=36

x+14=36

not enough info:(2×x)+(2×7)=36

2 (x+7)=72

6 0

3 years ago

If AC = 14, what is the measure of AD? Round your answer to the nearest hundredth.

nikklg [1K]

Part A

Answer: Choice D) $\text{AD} = \sqrt{(2n+5)^2+(4n-3)^2}$

-----------------------------------------------

Explanation:

Let E be the intersection point of the diagonals. For any parallelogram, the diagonals bisect each other. This means that AE = EC = 2n+5 and it also means EB = DE = 4n-3

Focus on triangle AED. This triangle is a right triangle with angle AED as a 90 degree angle (any rhombus has its diagonals that are perpendicular to one another). The legs of this triangle are AE = 2n+5 and ED = 4n-3

Apply the pythagorean theorem to find hypotenuse AD

$(\text{leg1})^2+(\text{leg2})^2 = (\text{hypotenuse})^2\\\\(\text{AE})^2+(\text{ED})^2 = (\text{AD})^2\\\\(\text{AD})^2 = (\text{AE})^2+(\text{ED})^2\\\\\text{AD} = \sqrt{(\text{AE})^2+(\text{ED})^2}\\\\\text{AD} = \sqrt{(2n+5)^2+(4n-3)^2}\\\\$

This points to choice D as the final answer.

===========================================================

Part B

<h3>Answer: 7.07</h3>

-----------------------------------------------

Explanation:

If AC = 14, then half of this is AE = 7. The diagonals bisect each other, so they cut each other in half with E at the midpoint.

Since AE = 2n+5, we can solve for n like so

2n+5 = 7

2n = 7-5

2n = 2

n = 2/2

n = 1

Then we can find the length of AD

$\text{AD} = \sqrt{(2n+5)^2+(4n-3)^2}\\\\\text{AD} = \sqrt{(2*1+5)^2+(4*1-3)^2}\\\\\text{AD} = \sqrt{(2+5)^2+(4-3)^2}\\\\\text{AD} = \sqrt{7^2+1^2}\\\\\text{AD} = \sqrt{49+1}\\\\\text{AD} = \sqrt{50}\\\\\text{AD} \approx 7.0710678\\\\\text{AD} \approx 7.07\\\\$

Segment AD is roughly 7.07 units long. The other external sides of the rhombus (AB, BC and CD) are also this length because the four sides of any rhombus are the same length.

7 0

3 years ago

F(x) = 8cos(2x) on (0,2π)

Leviafan [203]

Answer:

Step-by-step explanation:

First put the lower limit, i.e., x=0,

F(x)=8cos[2(0)]=8cos(0)=8(1)=8

;cos(0)=1

Now,put the upper limit of given interval, i.e., x = π,

F(x)=8cos[2(π)]=8cos(2π)=8(1)=8

;cos(2π)=1

7 0

4 years ago

A box of oatmeal must contain 16 oz. The machine that fills the oatmeal boxes is set so that, on the average, a box contains 16.

Rudiy27

Answer:

0.1587

Step-by-step explanation:

Use this website : https://www.numerade.com/questions/a-box-of-oatmeal-must-contain-16-oz-the-machine-that-fills-the-oatmeal-boxes-is-set-so-that-on-the-2/

7 0

3 years ago

I really need help guys can some one plz help me it's for 10 points

11111nata11111 [884]

Answer:

$\sqrt{8}----- 2units,2units$

$\sqrt{7} ------\sqrt{5}units,\sqrt{2}units$

$\sqrt{5}-------1unit,2units$

$3------2units, \sqrt{5}units$

Step-by-step explanation:

Use pythagorean's theorem to solve each pair individually.

The instructions say that you have the two sides (a and b) and you have to match it with their hypothenuse.

$Formula: c^2=a^2+b^2$

1. $a=\sqrt{5}, b=\sqrt{2}$

Plug this into the formula.

$c=\sqrt{(\sqrt{5} )^2+(\sqrt{2})^2 }$

The square here eliminates the roots.

$c=\sqrt{5+2}\\ c=\sqrt{7}$

2. $a=\sqrt{3}, b=4$

$c=\sqrt{(\sqrt{3} )^2+(4)^2}\\ c=\sqrt{3+16}\\ c=\sqrt{19}$

3. $a=2, b=\sqrt{5}$

$c=\sqrt{(2)^2+(\sqrt{5})^2 }\\ c=\sqrt{4+5}\\ c=\sqrt{9}\\ c=3$

4. $a=2, b=2$

$c=\sqrt{(2)^2+(2)^2}\\ c=\sqrt{4+4}\\ c=\sqrt{8}$

5. $a=1, b=2$

$c=\sqrt{(1)^2+(2)^2}\\ c=\sqrt{1+4}\\ c=\sqrt{5}$

7 0

3 years ago