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Anastasy [175]
4 years ago
7

Simplify each expression 17x + 4 - 3x

Mathematics
1 answer:
Liono4ka [1.6K]4 years ago
3 0

Answer:

14x+4

Step-by-step explanation:

17x-3x=14x

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What is the slope of a line that is perpendicular to the line y=8x-12
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Perpendicular lines have slopes that are opposite reciprocals. It means that if we have 8, then its opposite reciprocal would be -1/8.

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Amy and Sarah are twins. They have a younger brother who is 3 years younger.
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3 years ago
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}

Or

\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
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