Answer:
see below
Step-by-step explanation:
8 can be factored from each of the terms of the sum. (It's the distributive property.)
8·0 + 8·1 + 8·2 + ... + 8·26 + 8·27
= 8·(0 +1 +2 + ... +26 +27)
Area of square = s^2
Area of Rectangle = lw
l = 2s
w+3 = s
solve for w, w=s-3
Now we have l and w.
Plug both into area of rectangle formula so: (2s)(s-3)
Since both areas are equal set both equations equal to each other:
(2s)(s-3)=s^2
Now simplify
2s^2-6s=s^2
s^2-6s=0, Solve for s.
Factor polynomial. s(s-6)=0 , s can be equal to 0 or 6. HOWEVER, you cannot have a side length of 0 therefore the side length has to be 6.
Now plug in s for the length formula for the rectangle:
l = 2s so... l = 2(6) so length of rectangle = 12.
Now plug in s for the width formula for the rectangle:
w+3=s so... w+3=6 so width of rectangle = 3.
Now the dimensions of the rectangle are 12 by 3. 12 being length and 3 width.
To CHECK:
Find area of rectangle:
A=lw so A=3 times 12 so A=36
Find area of square:
We know the side is equal to 6 so
A=s^2 so 6^2 = 36
The areas are equal that verifies the answer of 12 by 3.
Because 12 + 3 is not equal to 16...
Answer:
in triangle MNO
relationship between perpendicular and hypotenuse is given by sin angle
sin64°=p/h=70/x
x=70/sin64°=77.88foot
length of MN to the nearest tenth of a foot.
=78ft
