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3 years ago

8

Derek has 12 shirts in his closet. if 2 out of every 3 of these shirts are striped, how many striped shirts does derek have in h

is closet

1 answer:

Mila [183]3 years ago

6 0

There would be 8 striped shirts.

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Verify the identity (tan x + 1)^2 + (tan x-1)^2= 2 sec^2 x

Elina [12.6K]

$(\tan x+1)^2+(\tan x-1)^2=2\sec^2x\\\\\text{use}\ \tan x=\dfrac{\sin x}{\cos x}\\\\L_s=\left(\dfrac{\sin x}{\cos x}+\dfrac{\cos x}{\cos x}\right)^2+\left(\dfrac{\sin x}{\cos x}-\dfrac{\cos x}{\cos x}\right)^2\\\\=\left(\dfrac{\sin x+\cos x}{\cos x}\right)^2+\left(\dfrac{\sin x-\cos x}{\cos x}\right)^2\\\\=\dfrac{(\sin x+\cos x)^2}{\cos^2x}+\dfrac{(\sin x-\cos x)^2}{\cos^2x}\\\\\text{use}\ (a\pm b)^2=a^2\pm2ab+b^2$

$=\dfrac{\sin^2x+2\sin x\cos x+\cos^2}{\cos^2x}+\dfrac{\sin^2x-2\sin x\cos x+\cos^2}{\cos^2x}\\\\=\dfrac{\sin^2x+2\sin x\cos x+\cos^2+\sin^2x-2\sin x\cos x+\cos^2}{\cos^2x}\\\\=\dfrac{2\sin^2x+2\cos^2x}{\cos^2x}=\dfrac{2(\sin^2x+\cos^2x)}{\cos^2x}\\\\\text{use}\ \sin^2x+\cos^2x=1\\\\=\dfrac{2(1)}{\cos^2x}=2\cdot\dfrac{1}{\cos^2x}=2\left(\dfrac{1}{\cos x}\right)^2\\\\\text{use}\ \sec x=\dfrac{1}{\cos x}\\\\=2(\sec^2x)=2\sec^2x=R_s\\\\L_s=R_s\Rightarrow The\ identity$

4 0

3 years ago

What does x equal 7(2x+5)=4x -9 -x <br> PLEASEEEE HELPPPP ME

Gennadij [26K]

Answer: x=-4

Step-by-step explanation:

Given

7(2x+5)=4x-9-x

Expand parenthesis

14x+35=4x-9-x

Combine like terms

14x+35=3x-9

Subtract 35 on both sides

14x+35-35=3x-9-35

14x=3x-44

Subtract 3x on both sides

14x-3x=3x-44-3x

11x=-44

Divide 11 on both sides

11x/11=-44/11

x=-4

Hope this helps!! :)

Please let me know if you have any questions

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3 years ago

Find the first four terms of this geometric sequence A1= 3 and r=-3

timama [110]

A(n)=-1(-3^n)

3, -9, 27, -81

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3 years ago

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What is 7500×5643 ÷3

just olya [345]

Answer:

<h2>14107500</h2>

Step-by-step explanation:

$7500 \times 5643 \\ = \frac{42322500}{3} \\ = 14107500$

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3 years ago

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Which is the most accurate way to estimate 26% of 91?

notka56 [123]

Answer:

B

Step-by-step explanation:

26% is close to 25%, which is equal to 1/4th.

You're adding to the number and removing from the percentage so it balances it out.

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3 years ago