So the picture below shows what the slant height is. It also shows that the pyramid can form a right triangle, in which we can use the pythagorean theorem, which is
.
But first, we have to find the height of this pyramid. The volume formula for a square pyramid is
. Since we know its a square pyramid, the length and width are going to be the same (12 ft), and we know that the volume is 432 ft^3. Using this info, we can solve for the height:

So now we can use the pythagorean theorem (remember to split the 12 by 2, since the right triangle has only half the length of the base). Our equation will be solved as such:

In short, the slant height is 10.8 ft.
<span>There are 5 boxes, where we have to put given numbers. Addition of 5 odd numbers always gives an odd number result. 30 is an even number. So there is no combination of given numbers which can give you 30 as a result.
</span>
Simplify the following:
(3 sqrt(2) - 4)/(sqrt(3) - 2)
Multiply numerator and denominator of (3 sqrt(2) - 4)/(sqrt(3) - 2) by -1:
-(3 sqrt(2) - 4)/(2 - sqrt(3))
-(3 sqrt(2) - 4) = 4 - 3 sqrt(2):
(4 - 3 sqrt(2))/(2 - sqrt(3))
Multiply numerator and denominator of (4 - 3 sqrt(2))/(2 - sqrt(3)) by sqrt(3) + 2:
((4 - 3 sqrt(2)) (sqrt(3) + 2))/((2 - sqrt(3)) (sqrt(3) + 2))
(2 - sqrt(3)) (sqrt(3) + 2) = 2×2 + 2 sqrt(3) - sqrt(3)×2 - sqrt(3) sqrt(3) = 4 + 2 sqrt(3) - 2 sqrt(3) - 3 = 1:
((4 - 3 sqrt(2)) (sqrt(3) + 2))/1
((4 - 3 sqrt(2)) (sqrt(3) + 2))/1 = (4 - 3 sqrt(2)) (sqrt(3) + 2):
Answer: (4 - 3 sqrt(2)) (sqrt(3) + 2)
X^2 + 3x - 6
This is because x^2 and 3x have nothing they can combine with, leaving them as their own number. 1 + - 6 will give you -5 as adding to a negative only reduces not adds entirely.
Hope this helps!
Answer:
The solutions to the system of equations are:

Thus, option C is true because the point satisfies BOTH equations.
Step-by-step explanation:
Given the system of the equations

Arrange equation variables for elimination






solve for x

Divide both sides by -2






The solutions to the system of equations are:

Thus, option C is true because the point satisfies BOTH equations.