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3 years ago

What is the result of adding these two equations? 6x+2y=-2 3x-2y=-5

Mathematics

1 answer:

Kryger [21]3 years ago

8 0

Answer:

x+-7/9,y+4/3

Step-by-step explanation: Here's the answer ^^

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[tex]cos {}^{4} α+sin {}^{4} α= \frac{1}{4} (3+cos4α)<br>Prove:<br>

asambeis [7]

Given:

$\cos^4 \alpha+\sin^4\alpha=\dfrac{1}{4}(3+\cos 4 \alpha)$

To prove:

The given statement.

Proof:

We have,

$\cos^4 \alpha+\sin^4\alpha=\dfrac{1}{4}(3+\cos 4 \alpha)$

$LHS=\cos^4 \alpha+\sin^4\alpha$

$LHS=(\cos^2 \alpha)^2+(\sin^2 \alpha)^2$

$LHS=(\cos^2 \alpha+\sin^2\alpha)^2-2\sin ^2\alpha\cos^2 \alpha$ $[\because a^2+b^2=(a+b)^2-2ab]$

$LHS=(1)^2-2(1-\cos^2 \alpha)\cos^2 \alpha$ $[\because \cos^2 \alpha+\sin^2\alpha=1]$

$LHS=1-2\cos^2 \alpha+2\cos^4 \alpha$

Now,

$RHS=\dfrac{1}{4}(3+\cos 4 \alpha)$

$RHS=\dfrac{1}{4}[3+(2\cos^2 2\alpha-1)]$ $[\because \cos 2\theta=2\cos^2\theta -1]$

$RHS=\dfrac{1}{4}[2+2\cos^2 2\alpha]$

$RHS=\dfrac{1}{4}[2+2(2\cos^2 \alpha-1)^2]$ $[\because \cos 2\theta=2\cos^2\theta -1]$

$RHS=\dfrac{1}{4}[2+2(4\cos^4 \alpha-4\cos \alpha+1)]$ $[\because (a-b)^2=a^2-2ab+b^2]$

$RHS=\dfrac{1}{4}[2+8\cos^4 \alpha-8\cos \alpha+2]$

$RHS=\dfrac{1}{4}[4+8\cos^4 \alpha-8\cos \alpha]$

$RHS=1+2\cos^4 \alpha-2\cos \alpha$

$RHS=1-2\cos^2 \alpha+2\cos^4 \alpha$

$LHS=RHS$

Hence proved.

8 0

3 years ago

Find the volume of a cylinder whose height is 10 cm. and circumference of the base is 16π cm.

aksik [14]

Answer:

203.71832715763

7 0

3 years ago

5 oranges cost $2. Find the cost of 20 oranges.

Sonja [21]

<h3>Answer: $8</h3>

===================================================

Work Shown:

(5 oranges)/(2 dollars) = (20 oranges)/(x dollars)

5/2 = 20/x

5x = 2*20 .... cross multiply

5x = 40

x = 40/5 .... dividing both sides by 5

x = 8

20 oranges cost $8

--------------

Another way to approach the problem is to note that the jump from "5 oranges" to "20 oranges" is "times 4".

5*4 = 20

So we'll apply the "times 4" operation to the old cost of $2 to get the new cost being 2*4 = 8 dollars

4 0

3 years ago

Read 2 more answers

Which of the division expressions below has a remainder? Select all that apply.

gavmur [86]

Answer:

A, B, C, & E

Step-by-step explanation:

A) 19,456 ÷ 6 = 3,242 $\frac{2}{3}$

(2/3 is 0.666666666 etc)

B) 28,765 ÷ 13 = 2,212.692308...

C) 4,145 ÷ 3 = 1,381 $\frac{2}{3}$

(2/3 is 0.666666666 etc)

D) 4,165 ÷ 17 = 245

(Not bolded because it is not an answer)

E) 44,312 ÷ 16 = 2,769.5

C -> When dividing by three, if the first number's values do not add up to a multiple of 3 there will be a remainder. Example from your problem,

4,145 -> 4 + 1 + 4 + 5 = 14 -> 14 is not a multiple of 3, so there is a reminder

D -> No decimal / fraction, no remainder!

Have a nice day!

I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

8 0

3 years ago

Which relation represents a proportional function?

Advocard [28]

The answer is A, this is because as the amount of toppings increases so does the price increase proportionally.

4 0

3 years ago