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3 years ago

Eight times a number is the same as thirty five more than three times a number

Mathematics

1 answer:

serg [7]3 years ago

8 0

Times - multiply same as - = more than - subtract
$8x=35+3x$

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Is x^2+3x+8 a monomial, binomial, or trinomial

torisob [31]

Answer:

A trinomial

Step-by-step explanation:

Since there are three terms, x^2, 3x, and 8, it is a trinomial

6 0

4 years ago

Cos^2 x+4sin^2 x/2=1

lana [24]

$Let\ \dfrac{x}{2}=a,\ therefore\ x=2a.\\\\\cos^2x+4\sin^2\dfrac{x}{2}=\cos^22a+4\sin^2a\\\\\text{use}\ \cos2x=\sin^2x-\cos^2x\\\\=(\sin^2a-\cos^2a)^2+4\sin^2a\\\\\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\=(\sin^2a)^2-2(\sin^2a)(\cos^2a)+(\cos^2a)^2+4\sin^2a\\\\=\sin^4a-2\sin^2a\cos^2a+\cos^4a+4\sin^2a\\\\=\underbrace{\sin^4a+2\sin^2a\cos^2a+\cos^4a}_{(*)}-4\sin^2a\cos^2a+4\sin^2a\\\\\text{use}\ (*)\qquad(a+b)^2=a^2+2ab+b^2$

$=\underbrace{(\sin^2a)^2+2\sin^2a\cos^2a+(\cos^2a)^2}_{(*)}-4\sin^2a(\cos^2a-1)\\\\=(\sin^2a+\cos^2a)^2-4\sin^2a(\cos^2a-1)\\\\\text{use}\ \sin^2a+\cos^2a=1\to\sin^2a=\cos^2a-1\\\\=1^2-4\sin^2a(\sin^2a)=1-4\sin^4a=1-(2\sin^2a)^2$

$\cos^22a+4\sin^2a=1\\\\1-(2\sin^2a)^2=1\qquad\text{subtract 1 from both sides}\\\\-(2\sin^2a)^2=0\to2\sin^2a=0\qquad\text{divide both sides by 2}\\\\\sin^2a=0\to\sin a=0\\\\a=k\pi\ for\ k\in\mathbb{Z}\\\\\dfrac{x}{2}=k\pi\qquad\text{multiply both sides by 2}\\\\\boxed{x=2k\pi\ for\ k\in\mathbb{Z}}$

6 0

3 years ago

Help me, I am not sure of the operations.

Hoochie [10]

61.) First you have to think there are 36 packs, 12 cards in 1 pack and 2 stickers in one pack. SO you have to multiply 36 by 12 and 2 by 36. Your answer for 61 will be (36 x 12) + (36 x 2)

Hopefully this helps.

5 0

4 years ago

Help Me, Will give 100 points.

Damm [24]

Answer:

The total monthly cost would be $214

Step-by-step explanation:

This is rather simple. They gave us 1,250, which is half of 2,500. Simple multiplication:

1,250 = 2,500

107 = x

2 × 1,250 = 2,500

2 × 107 = 214

Therefore, the total monthly cost if the cell phone is used for 2,500 minutes is $214.

4 0

3 years ago

Read 2 more answers

If you deposit $5,000 into an account that pays 4.75% annual interest how much money will be in the account after 7 years if the

victus00 [196]

$6662.50

4.75% = $237.50
$237.50 x 7 = $1662.50

$5000 + $1662.50 = $6662.50

Answer = $6,662.50

4 0

3 years ago