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3 years ago

Factor 9x^2 -5 . using difference of squares

1 answer:

5 0

$\bf \textit{difference of squares}
\\ \quad \\
(a-b)(a+b) = a^2-b^2\qquad \qquad 
a^2-b^2 = (a-b)(a+b)\\\\
-------------------------------\\\\
9x^2-5\qquad 
\begin{cases}
9x^2=3^2x^2\\
\qquad (3x)^2\\
5=\sqrt{5^2}\\
\qquad (\sqrt{5})^2
\end{cases}\implies
\begin{array}{llll}
(3x)^2-(\sqrt{5})^2
\\\\\\
(3x-\sqrt{5})~(3x+\sqrt{5})
\end{array}$

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Justin wants his new treehouse to blend in with the leaves, so he decides to paint it green. He mixes some white paint and green

spayn [35]

Answer:

C. neither. the roof and walls are the same shade of green

Step-by-step explanation:

The first batch:

Some white and some green

The second batch:

Triple amount of white and triple amount of green

As we see the ratio of white to green has not changed

Therefore there won't be any difference in painting

Correct answer choice is C.

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3 years ago

The indefinite integral can be found in more than one way. First use the substitution method to find the indefinite integral. Th

Fantom [35]

Answer:

∫ $6x^5(x^6-2)\,dx$ = $\frac{1}{2}(x^6-2)^2+C$

Step-by-step explanation:

To find:

∫ $6x^5(x^6-2)\,dx$

Solution:

Method of substitution:

Let $x^6-2=t$

Differentiate both sides with respect to $t$

$6x^5\,dx=dt$

[use $(x^n)'=nx^{n-1}$ ]

So,

∫ $6x^5(x^6-2)\,dx$ = ∫ $t\,dt$ = $\frac{t^2}{2}+C_1$ where $C_1$ is a variable.

(Use ∫ $t^n\,dt=\frac{t^{n+1} }{n+1}$ )

Put $t=x^6-2$

∫ $6x^5(x^6-2)\,dx$ = $\frac{1}{2}(x^6-2)^2+C_1$

Use $(a-b)^2=a^2+b^2-2ab$

So,

∫ $6x^5(x^6-2)\,dx$ = $\frac{1}{2}(x^6-2)^2+C_1=\frac{1}{2}(x^{12}+4-4x^6)+C_1=\frac{x^{12} }{2}-2x^6+2+C_1=\frac{x^{12} }{2}-2x^6+C$

where $C=2+C_1$

Without using substitution:

∫ $6x^5(x^6-2)\,dx$ = ∫ $6x^{11}-12x^5\,dx$ = $\frac{6x^{12} }{12}-\frac{12x^6}{6}+C=\frac{x^{12} }{2}-2x^6+C$

So, same answer is obtained in both the cases.

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2 years ago

Draw a number line to divide 70÷5

defon

If you need help the answer is 14 use long division or just subtract all depending on what the numbers are.

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2 years ago

Help please!!!!!:( Solve the equation for x. Round your answer to two decimal places. Do not include "x =" in your answer.

svet-max [94.6K]

The solution to the problem is as follows:

If you use Ln you can get rid of e.

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I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!

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3 years ago

Read 2 more answers

The interior angles formed by the side of a hexagon have measures of them up to 720° what is the measure of angle a

timofeeve [1]

Answer:

n = 6

Step-by-step explanation:

the formula for interior angle is ( n-2)

but we given the measure of one angle, so solve

720 = (n - 2)180

720/180 = (n - 2)

4 = (n - 2)

combine the like terms

4 + 2 =n

6 = n

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2 years ago