The given question seem incomplete
Rewrite the expression as a simplified expression containing one term
cos (α + β)cos(β) + sin( α + β)sin(β)
Answer:
The simplified form of the given expression is cos(α)
Step-by-step explanation:
We are given the expression
cos (alpha + beta)cos(beta) + sin( alpha + beta)sin(beta)
we will proceed by expanding the given expression as
(cos(alpha)cos(beta) - sin(alpha)sin(beta))cos(beta) + (sin(alpha)cos(beta)+cos(alpha)sin(beta))sin(beta)
cos(alpha)cos^2(beta) -sin(alpha)sin(beta)cos(beta) + sin(alpha)cos(beta)sin(beta) + cos(alpha)sin^2(beta)
The two middle terms will cancel each other so we are left with
cos(alpha)cos^2(beta) + cos(alpha)sin^2(beta)
cos(alpha)[cos^2(beta) + sin^2(beta)]
cos(alpha) (1) = cos(alpha) [cos^2(beta) + sin^2(beta) = 1]
Therefore the simplified form of the given expression is cos(α)
When dividing fractions, theres this thing you do call "keep, change, flip"
You keep the first fraction the same, change the division to a multiplication, and change the fraction to have the numbers flipped.
4 = 4/1
1 1/8 = 9/8
4/1 * 8/9 = 32/9
32/9 = 3 5/9
3 5/9 is the final answer
Okay, to work out the original price, all you have to do is get the sale price ($146.54) and then divide it by 1 - 0.[whatever the percentage is]. In this case, the percentage is 15%, so you do 1 - 0.15 = 0.85.
So to work out the original price, you do:
146.54 ÷ 0.85 = $172.40
The original price is $172.40. :)
<h3>
Answer: $65.25</h3>
Explanation:
A markup of 45% means we involve the multiplier 1.45
100% + 45% = 1.00 + 0.45 = 1.45
The selling price is 1.45*45 = 65.25
This is the price before tax.
Answer:
48 inches
Step-by-step explanation:
12 in=1
24 in = 2
36 in = 3
48 in = 4
Add 12 everytime