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2 years ago

Find the GCF of the monomials: 32x^2 and 24x^2y

Mathematics

1 answer:

aev [14]2 years ago

4 0

Answer:

8x^2

Explanation:

First, do prime factorization of each of the coefficients:

32 ⇒ 2^5

24 ⇒ 2^3, 3

The greatest common factor (GCF) of the coefficients is 2^3 = 8.

Next, find the GCF of the variables:

x^2

x^2, y

The GCF of the variables is x^2.

Finally, multiply the GCF of the coefficients by the GCF of the variables to get:

8x^2

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HELP ME PLEASE!

melomori [17]

Do you mean the hypotenuse of the triangle?

If so, you can use pythagorean theorem:

a^2 + b^2 = c^2

11^2 + 8^2 = c^2

121 + 64 = 185 = c^2

c = sqrt(185) = 13.6

6 0

3 years ago

Hello , how to do 6(iii)?

Doss [256]

Answer:

$\displaystyle \frac{dS}{dt}=\frac{3}{50r}$

Step-by-step explanation:

Water is being pumped into an inflated rubber sphere at a constant rate of 0.03 cubic meters per second.

So, dV/dt = 0.03.

We want to show that dS/dt is directly proportional to 1/r.

In other words, we want to establish the relationship that dS/dt = k(1/r), where k is some constant.

First, the volume of a sphere V is given by:

$\displaystyle V=\frac{4}{3}\pi r^3$

Therefore:

$\displaystyle \frac{dV}{dt}=4\pi r^2\frac{dr}{dt}$

Next, the surface area of a sphere S is given by:

$\displaystyle S=4\pi r^2$

Therefore:

$\displaystyle \frac{dS}{dt}=8\pi r\frac{dr}{dt}$

We can divide both sides by 2:

$\displaystyle \frac{1}{2}\frac{dS}{dt}=4\pi r\frac{dr}{dt}$

We can substitute this into dV/dt. Rewriting:

$\displaystyle \frac{dV}{dt}=r\Big(4\pi r\frac{dr}{dt}\Big)$

So:

$\displaystyle \frac{dV}{dt}=\frac{1}{2}r\frac{dS}{dt}$

Since dV/dt = 0.03 or 3/100:

$\displaystyle \frac{3}{100}=\frac{1}{2}r\frac{dS}{dt}$

Therefore:

$\displaystyle \frac{dS}{dt}=\frac{3}{50r}=\frac{3}{50}\Big(\frac{1}{r}\Big)$

Where k = 3/50.

And we have shown that dS/dt is directly proportional to 1/r.

4 0

3 years ago

(I need these answered asap and with work and explanation included)

erik [133]

Answer:

blue marbles - 2/9. red marbles - 3/9 = 1/3 clear marbles - 4/9. Davis got a 2/9 chance and Tessa got a 2/8 or 1/4 chance. I don't know about the last question. it might be 5/9 but I don't know sorry.

4 0

2 years ago

If line t is a transversal of lines l and m, name the angle relationship of the given angle pairs.

Ghella [55]

Answer:

$\angle 1\ and\ \angle 3$ are corresponding angles and are congruent to each other.

$\angle 8\ and\ \angle 4$ are alternate exterior angles and thus congruent to each other.

$\angle 2\ and\ \angle 3$ are interior angles on the same side, and they are supplementary(sum=180°).

Step-by-step explanation:

Given:

Line $l\parallel m$

Line $t$ is traversal.

By angle properties we can name the angle relationship of given angle pairs.

$\angle 1\ and\ \angle 3$ are corresponding angles and are congruent to each other.

$\angle 8\ and\ \angle 4$ are alternate exterior angles and thus congruent to each other.

$\angle 2\ and\ \angle 3$ are interior angles on the same side, and thus they are supplementary.

8 0

3 years ago

A theme park charges $45 for each adult ticket and $30 for each child ticket. A family purchased 10 tickets for $345. Which syst

andrey2020 [161]

Answer:

a or b I am not for sure.

Step-by-step explanation:

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5 0

2 years ago

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