Follow order of operations.
Distribute what is in the parentheses.
4[6a^2 -2ab +3ab] + 5[3ab + 6b^2 -4ab]
Combine like terms in the brackets.
4[6a^2 + 3ab] + 5[-1ab + 6b^2]
Distribute the 4 and the 5.
24a^2 + 12ab -5ab + 30b^2
Combine like terms.
24a^2 +7ab + 30b^2
That's your final answer:
24a^2 +7ab + 30b^2
I hope this helps you
f (x)=(x+2)^3/2
f'(x)=3/2. (x+2)^3/2-1
f'(x)=3/2 (x+2)^1/2
f'(x)=3/2.square root of (x+2)
1/4 goes into 2 2 /4
Means 2 2/4 divided by 1/4
Change 2 2 /4 to improper fraction. = (2*2 + 4)/4 = 10/4
10/4 ÷ 1/4
10/4 × 4/1
= 10
So it is 10.
The volume of a prism is area of the base times height.
This is a triangular prism. The base is a triangle.
The volume is area of the base times height, and the base is a triangle.
Find the area of the triangle and multiply by the height of the prism.
V = volume of the prism
A = area of the base
H = height of the prism
h = height of the triangle
b = base of the triangle
V = AH
V = (1/2)bhH
V = (1/2) * 9 ft * 7 ft * 15 ft
V = 472.5 ft^3
Did you notice the little box with corners marked in the angle down at the bottom ?
That angle is a right angle, and <em>this triangle is a right triangle</em> !
This piece of information is a big help. It breaks the problem wide open.
You know that in order to find the longest side of a right triangle . . .
-- Square the length of one short side.
-- Square the length of the other short side.
-- Add the two squares together.
-- Take the square root of the sum.
One short side=48. Its square = 2,304.
The other short side=48. Its square = 2,304.
Add the two squares: 2,304 + 2,304 = 4,608
The square root of the sum = √4,608 = <em><u>67.88</u></em> (rounded)
