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3 years ago

7

Which equivalent expression will be generated by applying the Distributive Property and combining like terms in the expression 1

1 + 4(x + 2y + 4)?
4x + 2y + 27
4x + 8y + 11
4x + 8y + 27
4x + 8y + 10

2 answers:

bazaltina [42]3 years ago

8 0

$11+4(x+2y+4)$ , expanding the bracket gives
$11+4x+8y+16$ , collecting like terms give
$4x+8y+27$

faust18 [17]3 years ago

6 0

Answer: the answer is c

Step-by-step explanation:

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Hi there!

<u>What we need to know:</u>

The three main trigonometric ratios are sine, cosine and tangent:

$\displaystyle sin\theta=\frac{opposite}{hypotenuse}$ $\displaystyle cos\theta=\frac{adjacent}{hypotenuse}$ $\displaystyle tan\theta=\frac{opposite}{adjacent}$

"Opposite" refers to the side opposite the angle that is not the hypotenuse.

"Hypotenuse" refers to the side opposite the right angle of a right triangle.

"Adjacent" refers to the side next to the angle that is not the hypotenuse.

"θ" is read as "theta". It just represents the angle.

Keep in mind that these three ratios only apply to right triangles.

You can use the mnemonic "soh-cah-toa" to help you remember these ratios.

<u>First question</u>

For the first question, we're given the angle with a measure of 56 degrees and the length of the <em>hypotenuse</em>. We must calculate <em>a</em>, which represents the side <em>adjacent </em>to the given angle.

Given the hypotenuse and the adjacent side, we know that we must use the cosine ratio:

$\displaystyle cos\theta=\frac{adjacent}{hypotenuse}$

Plug in the given information:

$\displaystyle cos56=\frac{a}{13}$

Isolate <em>a</em> by multiplying both sides by 13:

$13\displaystyle cos56=a$

Solve using a calculator:

$a=7.3$

Therefore, <em>a</em> is equal to 7.3 when rounded to 1 decimal place.

<u>Other information you will need to know:</u>

In the above question, we needed to solve for a side. But what if we were given two sides and we needed to solve for an angle? For example:

$\displaystyle sin\theta=\frac{5}{8}$

In this case, we will use the inverse sine ratio:

$\displaystyle \theta=sin^-^1(\frac{5}{8})$

Solve using a calculator:

$\displaystyle \theta=39$

Therefore, the angle would equal approximately 39 degrees.

I hope this helps!

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