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1 year ago

Question 5 of 10

Mathematics

1 answer:

Harman [31]1 year ago

5 0

Answer:

Step-by-step explanation:

6x + c = k ( isolate the term in x by subtracting c from both sides )

6x = k - c ( isolate x by dividing both sides by 6 )

x = $\frac{k-c}{6}$

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Emilio's family volunteers at the local soup kitchen every 30 days. Emilio has swimming lessons every 9 days. He has both activi

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Tyresha bought an outfit for 25% off. Before the discount , the items totalled $64. how much did she pay with the discount and 6

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ANSWER:

50.88

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3 years ago

A tornado traveled 260 miles in 4 hours. if the average rate at which the tornado is moving slows by 20%, how many miles will th

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3 years ago

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In the following pair of polynomials, the second polynomial is a factor of the first. Factor completely x^3+3x^2-18x , x-4

OLga [1]

Answer:

The required factors are: x, (x + 6) and (x - 3).

Step-by-step explanation:

As per the question,

The given polynomial is:

$x^{3}+3x^{2}-18x$

Now,

BY factorization, we get

$x^{3}+3x^{2}-18x$

$=x(x^{2}+3x-18)$

By splitting the mid-term, that is split 3x like:

3x = 6x - 3x

Therefore,

$x(x^{2}+6x-3x-18)$

Now on further solving by taking common factor out, we get

$=x[x(x+6)-3(x+6)]$

$=x(x+6)(x-3)$

Therefore, the given second polynomial (x - 4), is not a factor of given polynomial $x^{3}+3x^{2}-18x$ .

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4 years ago

Sec^6x (secxtanx) - sec^4x (secxtanx) = sec^5x tan^3x

Olegator [25]

Let E the expression of the left side of the equation:

$E=\sec^6(x) (\sec (x)\tan (x)) - \sec^4(x) (\sec (x)\tan (x))\\\\
E=\sec^7(x)\tan(x)-\sec^5(x)\tan(x)\\\\
E=\sec^5(x)\tan(x)(\sec^2(x)-1)$

We must know that $\tan^2(x)+1=\sec^2(x)\iff \sec^2(x)-1=\tan^2(x)$ . So, using in the equation above:

$E=\sec^5(x)\tan(x)(\underbrace{\sec^2(x)-1}_{\tan^2(x)})\\\\
E=\sec^5(x)\tan(x)(\tan^2(x))\\\\
\boxed{E=\sec^5(x)\tan^3(x)}$

Then, the equation is true.

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4 years ago