Answer:
FD≈25.94.. rounded = 26
Step-by-step explanation:
FD²=12²+(4x+11)²
FD²=144+16x²+88x+121
FD²=265+16x²+88x
also
FD²=12²+(13x-16)²
FD²=144+169x²-416x+256
FD²=400+169x²-416x
thus
265+16x²+88x = 400+169x²-416x
16x²-169x²+88x+416x+265-400 = 0
-153x²+504x-135 = 0
we will solve this quadratic equation by suing the quadratic formula to find x
x=(-504±sqrt(504²-4(-153)(-135)))/2(-153)
x=(-504±
)/2(-153)
x=(-504±
)/-306
x=(-504±
)/-306
x=(-504±414)/-306
x=(-504+414)/-306 and x=(-504-414)/-306
x=-90/-306 and x=-918/-306
x= 5/17 , 3
substituting x by the roots we found
check for 5/17:
4x+11 = 4×(5/17)+11 = (20/17)+11 = (20+187)/17 = 207/17 ≈ 12.17..
13x-16 = 13×(5/17)-16 = (65/17)-16 = (65-272)/17 = -207/17 ≈ -12.17..
check for 3:
4x+11 = 4×3+11 = 12+11 = 23
13x-16 = 13×3-16 = 23
thus 3 is the right root
therfore
ED=23 and CD=23
FD²=FE²+ED² or FD²=FC²+CD²
FD²=12²+23²
FD²=144+529
FD²=673
FD=√673
FD≈25.94.. rounded = 26
a. The average value of 
on the given interval is
b. Solve for 
:
I am not quite sure what the choices are, but the answer
to that problem is:
If p is a positive integer, then p(p+1)(p-1) is always
divisible by “an even number”.
The explanation to this is that whatever number you input
to that equation, the answer will always be an even number. This is due to the
expression p(p+1)(p-1) which always result in a even product.
For example if p=3, then (p+1)(p-1) becomes (4)(2) giving
you a even number.
And if for example if p=2, then (p+1)(p-1) becomes (3)(1)
which gives an odd product, but we still have to multiply this with p therefore
2*3 = 6 which is even product. The outcome is always even number.
<span>Answer: From the choices, select the even number</span>
Answer:
<em>797.0ft²</em>
Step-by-step explanation:
<u>Find a related diagram attached</u>
Area of the gate = Area of the semicircle + Area of the Rectangle
Area of the semicircle = πr²/2
r is the radius
From the diagram, radius r = 20/2 = 10ft
Area of the semicircle = 3.14(10)²/2
Area of the semicircle = 3.14(100)/2
Area of the semicircle = 314/2
Area of the semicircle = 157ft²
Area of the rectangle = Length * Width
Area of the rectangle = 20*32
Area of the rectangle = 640ft²
Area of the gate = 157 + 640
Area of the gate = 797ft²
<em>Hence the area of the gate is 797.0ft²</em>
each term is negative and 1/4 of previous term so the nth term is the n-1 term times -1/4 so f(n)= -1/4 f(n-1)
