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Gnom [1K]
3 years ago
13

What is the value of x?

Mathematics
2 answers:
valkas [14]3 years ago
6 0

We are given the values of two angles along two parallel lines.

The relationship of these angles tells us that if we add these two angles, they should equal 180°. So then we can set that equation up:

(2x+24)+x=180

And then we solve for x:

(2x+24)+x=180

3x+24=180

3x=156

x=52

So now that we know the value of x is 52, we know that the angle whose value is x, is 52°.

To solve for the other angle, we must plug in 52 for x:

2x+24

2(52)+24

104+24=128

And now we know that the value of the other angle is 128°.

andrey2020 [161]3 years ago
3 0

Since this is a parallelogram and the angles are adjacent to one another, a theorem will prove that the sum of these two angles would equal 180°

Therefore, we can set up this equation:

(2x + 24) + x = 180 ⇒ Remove parentheses

2x + 24 + x = 180 ⇒ Combine like terms

3x + 24 = 180 ⇒ Subtract 24 from both sides

3x = 156 ⇒ Divide both sides by 3

x = 52°


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The combination formula is expressed as

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\begin{gathered} P^8_6=\frac{8!}{(8-6)!} \\ =\frac{8!}{2!}=\frac{8\times7\times6\times5\times4\times3\times2!}{2!} \\ 2!\text{ cancel out, thus we have} \\ \begin{equation*} 8\times7\times6\times5\times4\times3 \end{equation*} \\ \Rightarrow P_6^8=20160 \end{gathered}

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\begin{gathered} C^8_6=\frac{8!}{(8-6)!6!} \\ =\frac{8!}{2!\times6!}=\frac{8\times7\times6!}{6!\times2\times1} \\ 6!\text{ cancel out, thus we have} \\ \frac{8\times7}{2} \\ \Rightarrow C_6^8=28 \end{gathered}

Hence, there are 28 combinations and 20160 permutations.

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