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2 years ago

Given the graphs of f(x) =x -7 and g(x) =-5x-1, what is the solution to the equation f() = g(x)?

Mathematics

1 answer:

lions [1.4K]2 years ago

8 0

Answer:

Step-by-step explanation:

x-7=-5x-1

x-(-5x)-7=-1

x+5x-7=-1

6x-7=-1

6x=-1+7

6x=6

x=6/6

x=1

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2 years ago

If tan ⁡x=12/5, and 0°

Charra [1.4K]

The value of sin(2x) is $\frac{120}{169}$

Explanation:

Given that $tan x =\frac{12}{5}$

The formula for $sin(2x)$ is $\sin (2 x)=2 \sin x \cos x$

Since, $\tan x=\frac{o p p}{a d j}$

Also, it is given that $tan x =\frac{12}{5}$

Thus, $opp=12$ and $adj=5$

To find the hypotenuse, let us use the pythagoras theorem,

$\begin{aligned}h y p &=\sqrt{12^{2}+5^{2}} \\&=\sqrt{144+25} \\&=\sqrt{169} \\&=13\end{aligned}$

Now, we can find the value of sin x and cos x.

$\sin x=\frac{\text { opp }}{h y p}=\frac{12}{13}$

$\cos x=\frac{a d j}{h y p}=\frac{5}{13}$

Now, substituting these values in the formula for sin 2x, we get,

$\begin{aligned}\sin (2 x) &=2 \sin x \cos x \\&=2\left(\frac{12}{13}\right)\left(\frac{5}{13}\right) \\&=\frac{120}{169}\end{aligned}$

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