Answer:
Step-by-step explanation:
We can use either angle, but I'm going to use the one on the bottom. So, in order to find x, we need to use tangent. One side we know is the adjacent, and the side we don't know is the opposite, therefore we need tangent. Here's the equation:
Obviously, we can't have a root in our denominator, so we need to get rid of it somehow. Here's how:
We multiply the denominator of the fraction by . multiplied by itself is simply 2. Try it! We also want to multiply the numerator by , but there isn't really a number we can use with that, so we'll just add it to the side. The equation you have now is:
Let's try to work this out now. Since the denominator is 2, we have to multiply both sides by it to find x.
We can plug 2 in for the x in the numerator now:
2 and 2 cancel out, so you get 1 in both the numerator and denominator. That's how we get our answer of 
Also, because this is a 45-45-90 triangle, you don't really have to do all that work. If it's a 45-45-90 triangle, both legs should be the same length. :)
Answer: <em>10 + 9 </em>
Step-by-step explanation:
<em>1. Distribute: 3(6+3) - (8-x) = 18 + 9 - (8)</em>
<em>2. Eliminate redundant parentheses: 18 + 9 - (8) = 18 + 9 - 1 ⋅ 8</em>
<em>3. Multiply the numbers: 18 + 9 - 1 ⋅ 8 = 18 + 9 - 8 </em>
4. Combine like terms: 18 + 9 - 8 = 10 + 9
<em>⋅</em>
<em />
16 red cars and 12 black cars. He put half of each colour in each box. Therefore he would put 8 red and 6 black in each box. 8 red + 6 black is 14. Therefore he would have 14 cars in each box.
14.
Answer:
a. 73; b. 48.9; c. 2; d. 33.8; e. 73
Step-by-step explanation:
Assume the function was
S(t)= 73 - 15 ln(t + 1), t ≥ 0
a. Average score at t = 0
S(0) = 73 - 15 ln(0 + 1) = 73 - 15 ln(1) = 73 - 15(0) =73 - 0 = 73
b. Average score at t = 4
S(4) = 73 - 15 ln(4 + 1) = 73 - 15 ln(5) = 73 - 15(1.61) =73 - 24.14 = 48.9
c. Average score at t =24
S(24) = 73 - 15 ln(24 + 1) = 73 - 15 ln(25) = 73 - 15(3.22) =73 - 48.28 = 24.7
d. Percent of answers retained
At t = 0. the students retained 73 % of the answers.
At t = 24, they retained 24.7 % of the answers.
e. Maximum of the function
The maximum of the function is at t= 0.
Max = 73 %
The graph below shows your knowledge decay curve. Knowledge decays rapidly at first but slows as time goes on.
If we multiply the top equation by -4 we can get rid of the x so:
-4x+20y=-12
4x-4y=12
Add these up
16y=0
Y=0
X=3
