<span>A = 2 * (0.5ab) + b (10 - a) = ab + 10b - ab = 10b
10b = 30√2; b = 3√2
sin α = 3√2 / 6; α = 45 degrees
Small angle: 45°; Large angle: 135°</span><span>
</span>
Answer: A. divided the difference of the two quantities by the sum of the two quantities.
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Explanation:
The difference of the quantities is 20-15 = 5
The sum of the quantities is 20+15 = 35
Dividing those results leads to 5/35 = 0.142857 which rounds to 0.1429
That converts to 14.29%
This is likely the path Adam took. This path is incorrect. The correct steps are shown below
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Difference = 20-15 = 5
Divide the difference over the original quantity
5/20 = 1/4 = 0.25 = 25%
We have a 25% decrease because the new quantity (15) is smaller than the old quantity (20)
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Here's another way to approach the problem
A = old value = 20
B = new value = 15
C = percent change
C = [ (B-A)/A ] * 100%
C = [ (15-20)/20 ] * 100%
C = (-5/20)*100%
C = -0.25*100%
C = -25%
The negative C value means we have a negative percent change, ie we have a percent decrease. So this is another way to get a 25% decrease.
Answer:
The surface of the prism is 84m²
Step-by-step explanation:
You have 4 figures here (two the same triangles)
you need to determine the surface of each and then sum it to one. This will be your final surface.
rectangles:
3*6= 18m²
5*6 = 30m²
4*6 = 24m²
triangles:
You need to determine the square of the triangles from the Heron's formula.
Heron's formula states that the area of a triangle whose sides have lengths a, b, and c is
,
where s is the semi-perimeter of the triangle; that is,
.
So the permimeter of the triangle is
2p=4+5+3 = 12m
p = 6m
![S = \sqrt{p*(p-a)*(p-b)*(p-c)} = \sqrt{6*(6-3)*(6-4)*(6-5)} = \sqrt{6*3*2*1} =\sqrt{36} =6[m^{2} ]](https://tex.z-dn.net/?f=S%20%3D%20%5Csqrt%7Bp%2A%28p-a%29%2A%28p-b%29%2A%28p-c%29%7D%20%20%3D%20%5Csqrt%7B6%2A%286-3%29%2A%286-4%29%2A%286-5%29%7D%20%20%3D%20%5Csqrt%7B6%2A3%2A2%2A1%7D%20%3D%5Csqrt%7B36%7D%20%3D6%5Bm%5E%7B2%7D%20%5D)
So the surface of the prism is a total sum of all surfaces:
P = 18m²+30m²+ 24m²+2*6m² = 84m²
Answer:
A: 8
B: 96
I'm not sure on C, sorry.
