#5- [Multiple answer] Why would no ecosystem exist without energy conversion?

Norma's retirement party will cost $24 if she invites 12 guests. If there are 13 guests, how much will Norma's retirement party

blagie [28]

Answer:

If there are 13 guests, it would cost Norma $26

Step-by-step explanation:

Since 12 guest equals 24 dollars all you have to do is divide 24/12 which would give you 2dollars. this means that she has to pay 2 dollars per guest. Multiply 13 becuase you want to know how much money it would cost with 13 guests and you get 26 dollars. Hope this helps.

8 0

3 years ago

Read 2 more answers

Rewrite with only sin x and cos x.

Annette [7]

Option A

$\cos 3 x=\cos x-4 \cos x \sin ^{2} x$

Solution:

Given that we have to rewrite with only sin x and cos x

Given is cos 3x

$cos 3x = cos(x + 2x)$

We know that,

$\cos (a+b)=\cos a \cos b-\sin a \sin b$

Therefore,

$\cos (x+2 x)=\cos x \cos 2 x-\sin x \sin 2 x$ ---- eqn 1

We know that,

$\sin 2 x=2 \sin x \cos x$

$\cos 2 x=\cos ^{2} x-\sin ^{2} x$

Substituting these values in eqn 1

$\cos (x+2 x)=\cos x\left(\cos ^{2} x-\sin ^{2} x\right)-\sin x(2 \sin x \cos x)$ -------- eqn 2

We know that,

$\cos ^{2} x-\sin ^{2} x=1-2 \sin ^{2} x$

Applying this in above eqn 2, we get

$\cos (x+2 x)=\cos x\left(1-2 \sin ^{2} x\right)-\sin x(2 \sin x \cos x)$

$\begin{aligned}&\cos (x+2 x)=\cos x-2 \sin ^{2} x \cos x-2 \sin ^{2} x \cos x\\\\&\cos (x+2 x)=\cos x-4 \sin ^{2} x \cos x\end{aligned}$

$\cos (x+2 x)=\cos x-4 \cos x \sin ^{2} x$

Therefore,

$\cos 3 x=\cos x-4 \cos x \sin ^{2} x$

Option A is correct

7 0

3 years ago

What stays the same no matter what location your in

nikitadnepr [17]

The mass of an object

5 0

3 years ago

Y = 3/5x + 1, 5y = 3x - 2, 10x - 6y = -4 is it perpendicular, parallel, neither

Ber [7]

Answer:

$y=\frac{3}{5} x+1$ and $5y=3x-2$ are parallel.

$10x-6y=-4$ is neither parallel nor perpendicular.

Step-by-step explanation:

First, you have to simplify each equation in terms of y.

$y=\frac{3}{5} x+1\\5y=3x-2\\10x-6y=-4$

Your first equation is already in terms of x, so simplify your second equation.

$5y=3x-2\\y=\frac{3}{5} x-\frac{2}{5}$

Now you can simplify your third equation.

$10x-6y=-4\\-6y=-10x-4\\y=\frac{5}{3} x+\frac{2}{3}$

These are your three equations in terms of y:

$y=\frac{3}{5} x+1\\\\y=\frac{3}{5} x-\frac{2}{5} \\\\y=\frac{5}{3} x+\frac{2}{3}$

Now, all you have to know is how to tell using your slope if a line is parallel or perpendicular to another.

Two parallel lines will have the exact same slope.

Two perpendicular lines will have slopes which are opposite reciprocals. For example, a line with a slope of 2 is perpendicular to a line with a slope of $-\frac{1}{2}$ , as they have opposite signs and are reciprocal (2/1 versus 1/2) to each other.

Your first two equations have the same slope and are therefore parallel.

Your third equation is a reciprocal, but it is not opposite, and is therefore not parallel nor perpendicular.

5 0

3 years ago

I NEED HELP ASAP PLS Select the correct graphed line for the equation below.

ddd [48]

2. Sorry if I’m wrong but that’s what I just put

4 0

3 years ago