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3 years ago

Three added to 4 times a number is equal to 5 less than 6 times the number.

Mathematics

1 answer:

GenaCL600 [577]3 years ago

7 0

In numbers only:
4x + 3 = 6x - 5

C)x = 4

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What is 4 1/2 divided by 2 3/8

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Answer:

36/19 or 1 17/19

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3 years ago

An investment of $500 increases at a rate of 12.5% per year. What is the value of the investment after 30 years? Round to the ne

NemiM [27]

Here's the equation:
0.125(500) + 500
But because it is 30 years:
30(0.125(500)) + 500
3.75(500) + 500
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4.75(500)
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3 years ago

What is n - 18 = -6 in equation

Arte-miy333 [17]

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3 years ago

Find M angle DEG and M angle GEF

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5 0

3 years ago

Read 2 more answers

Verify the identity. cotangent of x divided by quantity one plus cosecant of x equals quantity cosecant of x minus one divided b

Elenna [48]

Answer:

$\frac{\cot x}{1+\csc x}=\frac{\csc x-1}{\cot x}$

Step-by-step explanation:

We want to verify the identity:

$\frac{\cot x}{1+\csc x}=\frac{\csc x-1}{\cot x}$

Let us take the LHS and simplify to get the LHS.

Express everything in terms of the cosine and sine function.

$\frac{\cot x}{1+\csc x}=\frac{\frac{\cos x}{\sin x} }{1+\frac{1}{\sin x} }$

Collect LCM

$\frac{\cot x}{1+\csc x}=\frac{\frac{\cos x}{\sin x} }{\frac{\sin x+1}{\sin x} }$

We simplify the RHS to get:

$\frac{\cot x}{1+\csc x}=\frac{\cos x}{\sin x+1}$

We rationalize to get:

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

We expand to get:

$\frac{\cot x}{1+\csc x}=\frac{\cos x(\sin x-1)}{\sin^2 x-1}$

Factor negative one in the denominator:

$\frac{\cot x}{1+\csc x}=\frac{\cos x(\sin x-1)}{-(1-\sin^2 x)}$

Apply the Pythagoras Property to get:

$\frac{\cot x}{1+\csc x}=\frac{\cos x(\sin x-1)}{-\cos^2 x}$

Simplify to get:

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

$\frac{\cot x}{1+\csc x}=\frac{1-\sin x}{\cos x}$

Divide both the numerator and denominator by sin x

$\frac{\cot x}{1+\csc x}=\frac{\frac{1}{\sin x}-\frac{\sin x}{\sin x}}{\frac{\cos x}{\sin x}}$

This finally gives:

$\frac{\cot x}{1+\csc x}=\frac{\csc x-1}{\cot x}$

8 0

3 years ago