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2 years ago

What is the smallest number by which 864 must be multiplied with to make the quotient a perfect cube?

Mathematics

1 answer:

In-s [12.5K]2 years ago

3 0

Answer:

Number is two

Step-by-step explanation:

First of all we find the closest factors of 864 which are 32 x 27

Simply them we have

32 x 27 = 2^5 x 3³

Next we know that to be aperfect cube, each exponent needs to be equally divided by divisible by 3.

So If we multiply 864 x 2 we get

Then

1728 = 2^6 x 3³

So if we finally

Take the cube root of that is 2²* 3^1 = 4 x 3= 12

So 2² x 3^1

So if we equate the powers we have the answer as 2.

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Which one of the following reasons does NOT explain why 4x+5y≠9xy?

viva [34]

<h3>The terms 4x and 5y has different variable present in it. $4x + 5y \neq 9xy$ </h3>

<em><u>Solution:</u></em>

Given that,

$4x + 5y \neq 9xy$

<em><u>The reason is:</u></em>

When we are adding terms which has exactly the same variables, we must add the constants and let the result stand with variable

Which means,

4x + 10x = 14x

But,

We cannot add terms that has different variable

Which means,

4x + 5y

Here, both the terms 4x and 5y has different variable present in it. Hence they cannot be added together

$4x+5y\neq 9xy$

6 0

2 years ago

Leah makes an origami photo frame to showcase her favorite family picture. The size

Andreyy89

Answer:

28 feet

Step-by-step explanation:

3.5 x 8 = 28

trust me

6 0

2 years ago

What is AE ? Enter your answer in the box. units Two segments A D and B C intersect at point E to form two triangles A B E and D

spin [16.1K]

Answer:

The length of AE is 20 units.

Step-by-step explanation:

Given two segments AD and BC intersect at point E to form two triangles ABE and DCE. Side AB is parallel to side DC. A E is labeled 2x+10. ED is labeled x+3. AB is 10 units long and DC is 4 units long.

we have to find the length of AE

AB||CD ⇒ ∠EAB=∠EDC and ∠EBA=∠ECD

In ΔABE and ΔDCE

∠EAB=∠EDC (∵Alternate angles)

∠EBA=∠ECD (∵Alternate angles)

By AA similarity, ΔABE ≈ ΔDCE

therefore, $\frac{AE}{ED}=\frac{AB}{CD}$

⇒ $\frac{2x+10}{x+3}=\frac{10}{4}$

⇒ $8x+40=10x+30$

⇒ $x=5$

Hence, AE=2x+10=2(5)+10=20 units

The length of AE is 20 units.

5 0

3 years ago

I NEED HELP IMMEDIATELY

stepan [7]

Answer:

Between 80 and 160

Step-by-step explanation:

this is such a bad graph i honestly could not give you an exact answer

6 0

2 years ago

Movies Tonight is a typical video and DVD movie rental outlet for home-viewing customers. During the weeknight evenings, custome

stepladder [879]

Answer:

the probability having no customers are in the system is 0.375

Step-by-step explanation:

The computation of the probability having no customers are in the system is as follows;

Given that the arrival rate is 1.25 customers per minute

The Service rate is 2 customers per minute

Based on the above information, the probability is

$=P_0\\\\=(1-\frac{\lambda }{\mu })\\\\=(1-\frac{1.25}{2})\\\\=1-0.625\\\\= 0.375$

Hence, the probability having no customers are in the system is 0.375

6 0

2 years ago