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3 years ago

Simplify: 3(2x - 6) + 2

Mathematics

1 answer:

Oksi-84 [34.3K]3 years ago

7 0

Answer:

6x-16

Step-by-step explanation:

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Someone knows this ??

Dima020 [189]

Answer: A (1)

Explanation:

a(11) means column 1, row 1. Therefore, the answer would be the top left value.

8 0

3 years ago

Suppose cos(x)= -1/3, where π/2 ≤ x ≤ π. What is the value of tan(2x). EDGE

AVprozaik [17]

Answer:

Step-by-step explanation:

We are given that:

$\displaystyle \cos x = -\frac{1}{3}\text{ where } \pi /2 \leq x \leq \pi$

And we want to find the value of tan(2<em>x</em>).

Note that since <em>x</em> is between π/2 and π, it is in QII.

In QII, cosine and tangent are negative and only sine is positive.

We can rewrite our expression as:

$\displaystyle \tan(2x)=\frac{\sin(2x)}{\cos(2x)}$

Using double angle identities:

$\displaystyle \tan(2x)=\frac{2\sin x\cos x}{\cos^2 x-\sin^2 x}$

Since cosine relates the ratio of the adjacent side to the hypotenuse and we are given that cos(<em>x</em>) = -1/3, this means that our adjacent side is one and our hypotenuse is three (we can ignore the negative). Using this information, find the opposite side:

$\displaystyle o=\sqrt{3^2-1^2}=\sqrt{8}=2\sqrt{2}$

So, our adjacent side is 1, our opposite side is 2√2, and our hypotenuse is 3.

From the above information, substitute in appropriate values. And since <em>x</em> is in QII, cosine and tangent will be negative while sine will be positive. Hence:

<h2> $\displaystyle \tan(2x)=\frac{2(2\sqrt{2}/3)(-1/3)}{(-1/3)^2-(2\sqrt{2}/3)^2}$ </h2>

Simplify:

$\displaystyle \tan(2x)=\frac{-4\sqrt{2}/9}{(1/9)-(8/9)}$

Evaluate:

$\displaystyle \tan(2x)=\frac{-4\sqrt{2}/9}{-7/9} = \frac{4\sqrt{2}}{7}$

The final answer is positive, so we can eliminate A and B.

We can simplify D to:

$\displaystyle \frac{2\sqrt{8}}{7}=\frac{2(2\sqrt{2}}{7}=\frac{4\sqrt{2}}{7}$

So, our answer is D.

7 0

3 years ago

For (x - 1)(x - 7) to equal 0, either (x - 1) or (x - 7) must equal what?

Kisachek [45]

$(x - 1)(x - 7) = 0$

${x}^{2} - 8x + 7 = 0$

${x}^{2} - 8x = - 7$

$- 7x = \frac{ - 7}{x}$

$x = \frac{ - 7}{ \frac{x}{ - 7} } \implies x = x \implies x \in \mathbb{R}$

x is true for any number in real domain.

8 0

3 years ago

A hot air balloon descends from an altitude of 2,000 feet at a constant rate of 90 feet per minute. The graph shows the altitude

SSSSS [86.1K]

Y=90x+2,000

90 is the rate of change because the hot air balloon descends 90 feet per minute.
And 2,000 is the starting point because the hot air balloon started the descent at 2,000 feet.

3 0

2 years ago

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lina2011 [118]

I don’t understand. lol

5 0

3 years ago