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Mariana [72]
4 years ago
13

What is five times the difference of twice a number and fourteen is negative ten. Find the number

Mathematics
1 answer:
Mariana [72]4 years ago
5 0
We can write the equation:

5(2x-14)=-10
10x-70=-10 (distribute the 5)
10x=60 (add 70 to both sides)
x=6 (divide both sides by 10)

Hope this helps!
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Write the trigonometric expression in terms of sine and cosine, and then simplify. cot()/sin()-csc()
OLEGan [10]

Answer:

First, we know that:

cot(x) = cos(x)/sin(x)

csc(x) = 1/sin(x)

I can't know for sure what is the exact equation, so I will assume two cases.

The first case is if the equation is:

\frac{cot(x)}{sin(x)} - csc(x)

if we replace cot(x) and csc(x) we get:

\frac{cot(x)}{sin(x)} - csc(x) = \frac{cos(x)}{sin(x)} \frac{1}{sin(x)}  - \frac{1}{sin(x)}

Now let's we can rewrite this as:

\frac{cos(x)}{sin(x)} \frac{1}{sin(x)}  - \frac{1}{sin(x)} =\frac{cos(x)}{sin^2(x)} - \frac{1}{sin(x)}

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

We can't simplify it more.

Second case:

If the initial equation was

\frac{cot(x)}{sin(x) - csc(x)}

Then if we replace cot(x) and csc(x)

\frac{cos(x)}{sin(x)}*\frac{1}{sin(x) - 1/sin(x)} = \frac{cos(x)}{sin(x)}*\frac{1}{sin^2(x)/sin(x) - 1/sin(x)}

This is equal to:

\frac{cos(x)}{sin(x)}*\frac{sin(x)}{sin^2(x) - 1}

And we know that:

sin^2(x) + cos^2(x) = 1

Then:

sin^2(x) - 1 = -cos^2(x)

So we can replace that in our equation:

\frac{cos(x)}{sin(x)}*\frac{sin(x)}{sin^2(x) - 1} = \frac{cos(x)}{sin(x)}*\frac{sin(x)}{-cos^2(x)} = -\frac{cos(x)}{cos^2(x)}*\frac{sin(x)}{sin(x)}  = - \frac{1}{cos(x)}

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3 years ago
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viva [34]

Answer:

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Step-by-step explanation:

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