-1/4 + (-5/3)
When there is no number between a grouping symbol and a + or - sign, by default you can multiply the contents in the group by 1 to get rid of the grouping symbols.
3/15 reduces to 1/5
1/5 = 0.2....0.2 * 100 = 20%
The volume of the first cube is (5h^2)^3, while the volume of the second cube is (3k)^3, so their total volume is (5h^2)^3 + (3k)^3. We can use the special formula for factoring a sum of two cubes:
x^3 + y^3 = (x + y)(x^2 - xy + y^2)
(5h^2)^3 + (3k)^3 = (5h^2 + 3k)((5h^2)^2 - (5h^2)(3k) + (3k)^2)
= (5h^2 + 3k)(25h^4 - 15(h^2)(k) + 9k^2)
This is the second of the given choices.
Answer:
7√2 or approx. 9.89949
Step-by-step explanation:
distance between two points is
d=√(∆x^2+∆y^2)
where...
d is distance
∆x is change in x value
and ∆y is change in y value
In this problem ∆x=(-3)-4=(-7)
∆y=5-(-2)=7
plugging in those values gives us
d=√((-7)^2+7^2)
Solving this expression gives us
d=√(49+49)=√98
After simplifying the radical we are left with 7√2 or about 9.89949.
We can solve by figuring the area of the rectangle then add it to the area of the semicircle.
Area of the rectangle: length · width = 6 · 10 = 60 ft²
Area of the semicircle: (πd²)/8 = (3.14 · 6²)/8 = (3.14 · 36)/8 = 14.13 ft²
Total area of the figure: 60 + 14.13 = 74.13 ft² ≈ 74 ft²
