Which of the following is the correct factorization of the polynomial below?

Help me answer the question

Nastasia [14]

$\huge \boxed{\mathbb{QUESTION} \downarrow}$

Revathi's age is 1/3 of her mother's age. If their difference in age is 24 years, find Revathi's age.

$\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}$

Given,

Mother's age = x
Revathi's age = 1/3 x = ?
Difference in their age = 24 years ⇨ x - 1/3 x = 24.

Now, let's solve this question using the above equation which we just formed.

$\sf \: x - \frac{1}{3}x = 24 \\$

Combine x and $\sf\:-\frac{1}{3}x$ to get $\sf\frac{2}{3}x$ .

$\sf\frac{2}{3}x=24 \\$

Multiply both sides by $\sf\frac{3}{2}$ , the reciprocal of $\sf\frac{2}{3}$ .

$\sf \: x=24\times \left(\frac{3}{2}\right)$

Express $\sf24\times \left(\frac{3}{2}\right)$ as a single fraction.

$\sf \: x=\frac{24\times 3}{2} \\$

Multiply 24 and 3 to get 72.

$\sf \: x=\frac{72}{2} \\$

Divide 72 by 2 to get 36.

$\boxed{ \bf \: x=36 }$

We now have the age of Revathi's mother (x) = 36 years. Now, let's find Revathi's age ⇨ $\sf\:(\frac{1}{3}x)$

$\rightarrow \sf \: \frac{1}{3} x \\ \rightarrow \sf \: \frac{1}{3} \times 36 \\ \rightarrow \sf \: \frac{1}{ \bcancel 3} \times \bcancel{36} \\ \rightarrow \sf \:1 \times 12 \\ = \boxed{\boxed{\bf \: 12}}$

So, Revathi is 12 years old.

6 0

2 years ago

Read 2 more answers

The perimeter of one of the rectangular playrooms at Miss Pittypat's Day Care is 72 feet. It's width is 10 feet.

Alex17521 [72]

Answer:

The area of the rectangular playroom is 260 feet² .

Step-by-step explanation:

Given:

The perimeter of the rectangular playroom is 72 feet and it's width is 10 feet.

Now, to find its area we need the length .

So, putting the formula of perimeter we get it's length:

Let the length be l .

Perimeter = 2( length + width)

$72=2(l+10)$

$72=2l+20$

subtracting both sides from 20:

$72-20=2l+20-20$

$52=2l$

Dividing both sides by 2:

$52\div2=2l\div2$

$26=l$

Length is 26 feet.

And, to get the area we put the formula of finding the area:

$Area=length\times width$

$Area=26\times 10$

$Area=260$

Therefore, the area of the rectangular playroom is 260 feet² .

3 0

3 years ago

Can somebody plz help on this homework?

exis [7]

Basically, if the words in the word bank are similar or opposing or cause and effect add them to the bank

3 0

2 years ago

Need help with this?

Scilla [17]

Answer:

Measurements.

Step-by-step explanation:

Measurements are important because they help us in our every day lives such as cooking and baking, construction and many other things but measurements also help us find out our weight and height, or even what size shoe we have. So basically measurements are important in every part of our every day lives.

Hope it helps!

OwO

3 0

2 years ago

I give you a tricky one Express 108 ×125as a product of prime factors in exponential form

lana [24]

Answer:

$108 \times 125=2^2 \times 3^3 \times 5^3$

Step-by-step explanation:

To express the given product (108 X 125) as a product of prime factors

Step 1: Express each of the numbers as a product of its prime factors.

$108=2^2 \times 3^3\\125=5^3$

Step 2: Write the product together, and combine any like terms if any

Therefore,

$108 \times 125=2^2 \times 3^3 \times 5^3$

8 0

3 years ago