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noname [10]
3 years ago
13

Hey, i need help with these (image attached)

Mathematics
1 answer:
Ilya [14]3 years ago
7 0

Answer:

1. (3/5a^3b -5/6ab^3)^2

2. (x/3 +y/5)^2

Step-by-step explanation:

As you know, the square of a binomial expands like this:

(p +q)^2 = p^2 +2pq +q^2

The two "end" terms of the expansion are the squares of the terms of the binomial, and the middle term of the expansion is twice the product of the binomial terms (with the same sign as the binomial).

So, you can work this by ...

• check to see if the "end" terms are perfect squares. If they are, write the binomial as their sum, with the sign of the middle term

• check to see if the middlt term is double the product of the two binomial terms you just wrote. If it is, complete the problem by indicating the square of that binomial.

___

1. The square root of 9/25a^6b^2 is 3/5a^3b, so that will be one term of the binomial.

The square root of 25/36a^2b^6 is 5/6ab^3, so that will be the other term of the binomial. The sign of the middle term -a^4b^4 is negative, so our binomial is ...

(3/5a^3b -5/6ab^3)

The product of these two terms is (-1/2)a^4b^4, and the given middle term is twice that. The given trinomial is the square ...

9/25a^6b^2 -a^4b^4 +25/36a^2b^6 = (3/5a^3b -5/6ab^3)^2

___

2. The square root of 1/9x^2 is x/3. The square root of 1/25y^2 is y/5. The middle term, 2/15xy, is double the product of these terms, so the expression is the square ...

1/9x^2 +2/15xy +1/25y^2 = (x/3 +y/5)^2

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Factor completely 15x^5 + 12x^4-24x^3-3x^2
diamong [38]

Answer:

3x^2 (5x^3 + 4x^2 - 8x - 1)

Step-by-step explanation:

The given expression is 15x^5 + 12x^4-24x^3-3x^2

Here we have to find the GCF of all the above terms.

The GCF is 3x^2, let's take out 3x^2 and write the remaining terms in the parenthesis.

15x^5 + 12x^4-24x^3-3x^2

=3x^2 (5x^3 + 4x^2 - 8x - 1)

Therefore, the factors are 3x^2 and (5x^3 + 4x^2 -8x -1).

15x^5 + 12x^4-24x^3-3x^2 = 3x^2 (5x^3 + 4x^2 -8x -1)

Thank you.

7 0
3 years ago
A circle has an area of 314.1592. What is the diameter? (round to the nearest whole number)
ad-work [718]

Answer:

20

Step-by-step explanation:

The area of a circle is equal to pi*radius^2

We can then write this as

314.1592=π*r^2

We then divide pi to get

100=r^2

take the square root and you find that the radius equals around 10

The diameter is always equal to the radius times two which means that the diameter is 20

hope this helps

8 0
3 years ago
One-sixth the sum of eight and a number
Aleks04 [339]

Step-by-step explanation:

Let the number be x.

<u>1</u><u> </u> =8 + x

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6×<u>1</u>=6×8+6×x

6

1=48+6x

1-48=6x

<u>-</u><u>4</u><u>7</u>=<u>6</u><u>x</u>

6. 6 x = -7 <u>5</u>

6

x is equal to minus seven whole number five divided by six.

7 0
3 years ago
A line passes trough the point { 0, -3/2} and has a slope of 1/2. what is the equation of the line?
Luden [163]

Solutions: x=1.

Hope this helps!

6 0
3 years ago
Anyone wanna help please?
maria [59]

Answer:

sure

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
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