Given:
The height of the given trapezoid = 6 in
The area of the trapezoid = 72 in²
Also given, one base of the trapezoid is 6 inches longer than the other base
To find the lengths of the bases.
Formula
The area of the trapezoid is
where, h be the height of the trapezoid
be the shorter base
be the longer base
As per the given problem,
Now,
Putting, A=72, and h=6 we get,
or,
or,
or,
or,
or,
So,
The shorter base is 9 in and the other base is = (6+9) = 15 in
Hence,
One base is 9 inches for one of the bases and 15 inches for the other base.
Let
L-------> the length of the rectangle
W------> the width of the rectangle
we know that
the perimeter of the rectangle is equal to
-----> because Tamara's using the whole ribbon
so
-------> equation A
-------> equation B
Substitute equation B in equation A
find the value of L
therefore
the answer is
The system of equations is
Complete the squares to get
which is the equation of a circle centered at (1, -3) with radius 4, and thus with area 16π.
No, you do not have to line up the decimals.
B°a means that we plug a into the x value of b and go from there. In this case, we get
(using the distributive property) and we have to figure out what the domain is. The domain is what x can equal, and since you can't have a square root of a negative number, 3(x-1) has to be greater than or equal to 0. Solving for that, we get 3(x-1)≥0. Dividing both sides by 3, we get x-1≥0. Next, we can add 1 to both sides to get x≥1. In interval notation, [1 encompasses 1 while (1 is everything above 1. In addition, it doesn't have to be less than anything, so we have ∞) at the end, making it [1, ∞). We have the parenthesis at the end because it doesn't include infinity, but everything less than it