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rewona [7]
3 years ago
5

Factor the expression completely.

Mathematics
1 answer:
evablogger [386]3 years ago
6 0

Answer:

Factoring the expression xy^4+x^4y^4 completely we get \mathbf{xy^4(x+1)(x^2-x+1)}

Step-by-step explanation:

We need to factor the expression xy^4+x^4y^4 completely

We need to find common terms in the expression.

Looking at the expression, we get xy^4 is common in both terms, so we can write:

xy^4+x^4y^4\\=xy^4(1+x^3)

So, taking out the common expression we get: xy^4(1+x^3)

Now, we can factor the term (1+x^3) or we can write (x^3+1) by using formula:

a^3+b^3=(a+b)(a^2-ab+b^2)

So, we get:

xy^4(1+x^3)\\=xy^4(x^3+1)\\Applying\:the\:formula\;of\:a^3+b^3\\=xy^4(x+1)(x^2-x+1)

Therefor factoring the expression xy^4+x^4y^4 completely we get \mathbf{xy^4(x+1)(x^2-x+1)}

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The area of a rectangular wall of a barn is 85 square feet. Its length is 12 feet longer than the width. Find the length and wid
MaRussiya [10]

Answer:

Length = 17 feet, Width = 5 feet

Step-by-step explanation:

Given:

The area of a rectangular wall of a barn is 85 square feet.

Its length is 12 feet longer than the width.

Question asked:

Find the length and width of the wall of the barn.

Solution:

Let width of a rectangular wall of a barn = x

<u>As length is 12 feet longer than the width.</u>

Length of a rectangular wall of a barn = 12+x

As we know:

Area\ of\ rectangle=length\times breadth

85=(12+x)x\\\\85=12x+x^{2} \\

Subtracting both sides by 85

x^{2} +12x-85=0\\x^{2} +17x-5x-85=0\\Taking\ common\\x+(x+17)-5x(x+17)=0\\(x+17)(x-5)=0\\x+17=0, x-5=0\\x=-17,x=5

As width can never be in negative, hence  width of a rectangular wall of a barn = x = 5 feet

Length of a rectangular wall of a barn = 12+x=12+5=17\ feet

Therefore, length and width of the wall of the barn is 17 feet and 5 feet respectively.

                 

4 0
3 years ago
A statement can help you organize the numbers to answer a question about percents
Semenov [28]

Answer:

<u> $50</u> is <u>27.02%</u> of <u>$185</u>.

Step-by-step explanation:

Money spent on clothing = $50

Money spent on Groceries = $100

Money spent on Gas = $35

Total money spent = $185

Our question is to find the percentage of total money that is spent on clothing.

Percentage money on clothing = \frac{Money spent on clothing}{Total money} × 100

                                                   = \frac{50}{185} × 100

                                                   = 27.02% (approx)

Hence,<u> $50</u> is <u>27.02%</u> of <u>$185</u>.  

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Evaluate each expression if f = –4, g = 2, and h = 7.<br><br><br> h – f
skelet666 [1.2K]

Answer:

11

Step-by-step explanation:

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he books in a private library are classified as fiction and nonfiction. There are 400 books in the library. There are 40 more fi
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