Answer: 6 large frames and 12 small frames
Step-by-step explanation:
We define the following:
x = number of large frames
y = number of small frames
Make the following equations:
x + y = 18
19x + 9y = 222
Use system of equations to solve. We find the value of x first.
y = 18 - x
⇒ 19x + 9(18 - x) = 222
⇒ 19x + 162 - 9x = 222
⇒ 10x + 162 = 222
⇒ 10x = 60
⇒ x = 6
Find value of y:
6 + y = 18
y = 12
∴ 6 large frames and 12 small frames were purchased.
Answer:
a
Step-by-step explanation:
slope= rise/run
y-intercept= where the slope intersects with the y-axis
have a great day! :)
The question is asking for you to plug in each number in the brackets into x and solve for y, or f(x), g(x), etc. I will do no. 19 as an example:
f(x) = -3x + 1
This problem has the domains -2, -1, and 0. First, we'll start with -2:
f(x) = -3(-2) + 1
f(x) = 6 + 1
f(x) = 7
Now -1:
f(x) = -3(-1) + 1
f(x) = 3 + 1
f(x) = 4
Lastly, 0:
f(x) = -3(0) + 1
f(x) = 0 + 1
f(x) = 1
For question 23, we can use the distance formula, which is ratextime. The domain in this case is time (t). You can set up a function like this: d(t) = 60t
I do believe it would be a 2.2
We'll use the following properties of sine and cosine to prove this:



Then it's just a matter of filling it in...
sin20sin40 * sin60sin80 = 1/2(cos20 - cos60) * 1/2 (cos20 - cos140) =
1/8( cos40 + 1 - cos160 - cos120 - cos40 - cos80 + cos80 + cos200) =
1/8(1 - cos160 - cos120 + cos200) =
1/8(1 - cos160 - cos120 + cos160) =
1/8(1 - cos120 ) = 1/8( 1 + 1/2 ) = 3/16