Answer:
25 nickle and 30 quarters
Step-by-step explanation:
30 time .25 is 7.5 and 25 times .05 is 1.25 so yea thats it
Rates are used to show how a quantity measures over another.
Andy does not read at a constant rate.
The table is given as:
![\left[\begin{array}{cccccc}x&10&20&30&40&50\\y&4&9&10&15&20\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccccc%7Dx%2610%2620%2630%2640%2650%5C%5Cy%264%269%2610%2615%2620%5Cend%7Barray%7D%5Cright%5D)
Pick any two points from the table:
![(x_1,y_1) = (10,4)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%20%3D%20%2810%2C4%29)
![(x_2,y_2) = (20,9)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29%20%3D%20%2820%2C9%29)
The rate (m) is then calculated as:
![m = \frac{y_2 - y_1}{x_2 - x_1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D)
So, we have:
![m = \frac{9-4}{20-10}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B9-4%7D%7B20-10%7D)
![m = \frac{5}{10}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B5%7D%7B10%7D)
![m = 0.5](https://tex.z-dn.net/?f=m%20%3D%200.5)
Pick another point from the table
![(x_1,y_1) = (10,4)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%20%3D%20%2810%2C4%29)
![(x_2,y_2) = (30,10)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29%20%3D%20%2830%2C10%29)
The rate (m) is then calculated as:
![m = \frac{y_2 - y_1}{x_2 - x_1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D)
![m = \frac{10 - 4}{30 - 10}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B10%20-%204%7D%7B30%20-%2010%7D)
![m = \frac{6}{20}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B6%7D%7B20%7D)
![m = 0.3](https://tex.z-dn.net/?f=m%20%3D%200.3)
The rates calculated are not equal
<em>i.e. 0.3 and 0.5 are not equal</em>
This means that;
Andy does not read at a constant rate.
Read more about rates at:
brainly.com/question/13103052
Answer=150 seats were on the plane total
54 81
____=____
100 x
cross multiply
54x=8100
x=150 seats
Answer:
![\theta=\frac{\pi}{2},\frac{3\pi}{2},\frac{2\pi}{3},\frac{4\pi}{3}](https://tex.z-dn.net/?f=%5Ctheta%3D%5Cfrac%7B%5Cpi%7D%7B2%7D%2C%5Cfrac%7B3%5Cpi%7D%7B2%7D%2C%5Cfrac%7B2%5Cpi%7D%7B3%7D%2C%5Cfrac%7B4%5Cpi%7D%7B3%7D)
Step-by-step explanation:
If I'm interpreting that correctly, you are trying to solve this equation:
![sin(\theta )+1=cos(2\theta)](https://tex.z-dn.net/?f=sin%28%5Ctheta%20%29%2B1%3Dcos%282%5Ctheta%29)
for theta. To do this, you will need a trig identity sheet (I'm assuming you got one from class) and a unit circle (ditto on the class thing).
We need to solve for theta. If I look to my trig identities, I will see a double angle one there that says:
![cos(2\theta)=1-2sin^2(\theta)](https://tex.z-dn.net/?f=cos%282%5Ctheta%29%3D1-2sin%5E2%28%5Ctheta%29)
We will make that replacement, then we will have everything in terms of sin.
![sin(\theta)+1=1-2sin^2(\theta)](https://tex.z-dn.net/?f=sin%28%5Ctheta%29%2B1%3D1-2sin%5E2%28%5Ctheta%29)
Now get everything on one side of the equals sign to solve for theta:
![2sin^2(\theta)+sin(\theta)=0](https://tex.z-dn.net/?f=2sin%5E2%28%5Ctheta%29%2Bsin%28%5Ctheta%29%3D0)
We can factor out the common sin(theta):
![sin\theta(2sin\theta+1)=0](https://tex.z-dn.net/?f=sin%5Ctheta%282sin%5Ctheta%2B1%29%3D0)
By the Zero Product Property, either
or
![2sin\theta+1=0](https://tex.z-dn.net/?f=2sin%5Ctheta%2B1%3D0)
Now look at your unit circle and find that the values of theta where the sin is 0 are located at:
![\theta=\frac{\pi }{2},\frac{3\pi}{2}](https://tex.z-dn.net/?f=%5Ctheta%3D%5Cfrac%7B%5Cpi%20%7D%7B2%7D%2C%5Cfrac%7B3%5Cpi%7D%7B2%7D)
The next one we have to solve for theta:
simplifies to
and
![sin\theta=-\frac{1}{2}](https://tex.z-dn.net/?f=sin%5Ctheta%3D-%5Cfrac%7B1%7D%7B2%7D)
Look at the unit circle again to find the values of theta where the sin is -1/2:
![\theta=\frac{2\pi}{3},\frac{4\pi}{3}](https://tex.z-dn.net/?f=%5Ctheta%3D%5Cfrac%7B2%5Cpi%7D%7B3%7D%2C%5Cfrac%7B4%5Cpi%7D%7B3%7D)
Those ar your values of theta!
Answer:
345.6
Step-by-step explanation: