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3 years ago

How many solutions does 2(3x+8)=2x+16+4x have

Mathematics

2 answers:

Olenka [21]3 years ago

5 0

Answer: infinitely many solutions

Step-by-step explanation:

Simplify left side using distributive property to 6x+16. Combine like terms (2x and 4x) on the right side to 6x+16. Both sides simplify to the same expression (left side = right side) so there are infinitely many solutions. You can plug in any real number for x and the left side will always equal the right side.

arsen [322]3 years ago

3 0

Answer:

The equation has infinitely many solutions.

Step-by-step explanation:

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Find sin(2x), cos(2x), and tan(2x) from the given information.

larisa86 [58]

Since $\cot(x)=\frac{2}{3}$ and $\cot^{2} x+1=\csc^{2} x$ , we know that:

$\left(\frac{2}{3} \right)^{2}+1=\csc^{2} x\\\\\frac{13}{9}=\csc^{2} x\\\\\csc x=\frac{\sqrt{13}}{3}$

If $\csc x=\frac{\sqrt{13}}{3}$ , this means that $\sin x=\frac{3}{\sqrt{13}}$ and by the Pythagorean identity,

$\sin^{2} x+\cos^{2} x=1\\\left(\frac{3}{\sqrt{13}} \right)^{2}+\cos^{2} x=1\\\frac{9}{13}+\cos^{2} x=1\\\cos^{2} x=\frac{4}13}\\\cos x=\frac{2}{\sqrt{13}}$

Using the double angle formula for sine, $\sin(2x)=2\left(\frac{3}{\sqrt{13}} \right)\left(\frac{2}{\sqrt{13}} \right)=\boxed{\frac{12}{13}}$
Using the double angle formula for cosine, $\cos(2x)=1-2\left(\frac{3}{\sqrt{13}} \right)^{2}=\boxed{-\frac{5}{13}}$
So, since tan=sin/cos, $\tan (2x)=\frac{\sin(2x)}{\cos(2x)}=\frac{\frac{12}{13}}{-\frac{5}{13}}=\boxed{-\frac{12}{5}}$

7 0

2 years ago

Could someone plz help ^w^ thank you!

rosijanka [135]

Answer:

The first one:)

Step-by-step explanation:

REMEMBER TO:

1. Give me Brainliest, please... (ASAP)

2. HAVE A WONDERFUL DAY!

6 0

3 years ago

Read 2 more answers

Solve for y: 32 5yi = 16x - 40i

Ahat [919]

If you would like to solve 32 + 5yi = 16x - 40i for y, you can do this using the following steps:

<span>32 + 5yi = 16x - 40i
</span>5yi = 16x - 40i - 32 /5
yi = 16x/5 - 8i - 32/5 /i
y = 16x/5i - 8 - 32/5i

The correct result would be <span>y = 16x/5i - 8 - 32/5i.</span>

3 0

3 years ago

Find the circumference r=14m

andrew11 [14]

Answer:

There!!

Step-by-step explanation:

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