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elena55 [62]
4 years ago
9

Solve the equation -6 + 6n = 42 for n

Mathematics
2 answers:
Reptile [31]4 years ago
7 0

Answer:

8

Step-by-step explanation:

-6 + 6n = 42

First move the 6 over to the other side by adding....

6n = 48

now you will divide by 6 to get n by itself

n = 8

SashulF [63]4 years ago
5 0

Answer:

n= 8

Step-by-step explanation:

What gets -6 to 42?

-6 plus 6= 0

0=42= 42

42+6= 48

48/6 = 8

N=8

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Answer:

2

Step-by-step explanation:

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3 years ago
I need help with finding the answer to a) and b). Thank you!
shtirl [24]

Answer:

\displaystyle \sin\Big(\frac{x}{2}\Big) = \frac{7\sqrt{58} }{ 58 }

\displaystyle \cos\Big(\frac{x}{2}\Big)=-\frac{3 \sqrt{58}}{58}

\displaystyle \tan\Big(\frac{x}{2}\Big)=-\frac{7}{3}

Step-by-step explanation:

We are given that:

\displaystyle \sin(x)=-\frac{21}{29}

Where x is in QIII.

First, recall that sine is the ratio of the opposite side to the hypotenuse. Therefore, the adjacent side is:

a=\sqrt{29^2-21^2}=20

So, with respect to x, the opposite side is 21, the adjacent side is 20, and the hypotenuse is 29.

Since x is in QIII, sine is negative, cosine is negative, and tangent is also negative.

And if x is in QIII, this means that:

180

So:

\displaystyle 90 < \frac{x}{2} < 135

Thus, x/2 will be in QII, where sine is positive, cosine is negative, and tangent is negative.

1)

Recall that:

\displaystyle \sin\Big(\frac{x}{2}\Big)=\pm\sqrt{\frac{1 - \cos(x)}{2}}

Since x/2 is in QII, this will be positive.

Using the above information, cos(x) is -20/29. Therefore:

\displaystyle \sin\Big(\frac{x}{2}\Big)=\sqrt{\frac{1 +  20/29}{2}

Simplify:

\displaystyle \sin\Big(\frac{x}{2}\Big)=\sqrt{\frac{49/29}{2}}=\sqrt{\frac{49}{58}}=\frac{7}{\sqrt{58}}=\frac{7\sqrt{58}}{58}

2)

Likewise:

\displaystyle  \cos \Big( \frac{x}{2} \Big) =\pm \sqrt{ \frac{1+\cos(x)}{2} }

Since x/2 is in QII, this will be negative.

Using the above information, cos(x) is -20/29. Therefore:

\displaystyle  \cos \Big( \frac{x}{2} \Big) =-\sqrt{ \frac{1- 20/29}{2} }

Simplify:

\displaystyle \cos\Big(\frac{x}{2}\Big)=-\sqrt{\frac{9/29}{2}}=-\sqrt{\frac{9}{58}}=-\frac{3}{\sqrt{58}}=-\frac{3\sqrt{58}}{58}

3)

Finally:

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

Therefore:

\displaystyle \tan\Big(\frac{x}{2}\Big)=\frac{7\sqrt{58}/58}{-3\sqrt{58}/58}=-\frac{7}{3}

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3 years ago
What is the slope of the line through (1, 0) and (3, 8)?
Troyanec [42]
The slope of the line through (1,0) and (3,8) is 4
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kenny6666 [7]

Answer:

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A solid right pyramid has a square base with an edge length of s units and a height of h units. Which expression represents the
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<span><u><em>The correct answer is not listed; it is: </em></u>
V=</span>\frac{1}{3} s^2h units³<span>.

<u><em>Explanation</em></u><span><u><em>: </em></u>
<u>The volume of a right prism is given by: </u>
the area of the base * the height.

However, this is a pyramid; since it comes to a point, the volume is:
</span></span>\frac{1}{3} <span>* the area of the base * the height.

Since the base is <u>a square</u>, the area is s*s=s</span>²<span>. The height is h.
This gives us:
V=</span>\frac{1}{3} s^2h units³.
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4 years ago
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