This is a classic example of a 45-45-90 triangle: it's a right triangle (one angle of 90) & two other sides of the same length, which means two angles of the same length (and 45 is the only number that will work). With a 45-45-90 triangle, the lengths of the legs are easy to determine:
45-45-90
1-1-sqrt2
Where the hypotenuse corresponds to sqrt2.
Now, your hypotenuse is 10.
To figure out what each leg is, divide 10/sqrt2 (because sqrt2/sqrt2 = 1, which is a leg length in the explanation above).
Problem: you can't divide by radicals. So, we'll have to rationalize the denominator:
(10•sqrt2)/(sqrt2•sqrt2)
This can be rewritten:
10sqrt2/sqrt(2•2)
=10sqrt2/sqrt4
=10sqrt2/2
=5sqrt2
Hope this helps!!
Answer:
$ 199.56 per sq ft
Step-by-step explanation:
price / ft^2 = 450 000 / 2255 = 199.56
Rewrite the boundary lines <em>y</em> = -1 - <em>x</em> and <em>y</em> = <em>x</em> - 1 as functions of <em>y </em>:
<em>y</em> = -1 - <em>x</em> ==> <em>x</em> = -1 - <em>y</em>
<em>y</em> = <em>x</em> - 1 ==> <em>x</em> = 1 + <em>y</em>
So if we let <em>x</em> range between these two lines, we need to let <em>y</em> vary between the point where these lines intersect, and the line <em>y</em> = 1.
This means the area is given by the integral,

The integral with respect to <em>x</em> is trivial:

For the remaining integral, integrate term-by-term to get

Alternatively, the triangle can be said to have a base of length 4 (the distance from (-2, 1) to (2, 1)) and a height of length 2 (the distance from the line <em>y</em> = 1 and (0, -1)), so its area is 1/2*4*2 = 4.
3z-4=6z-17
-3z-4=-17 (subtracted the 6z from both sides)
-3z=-13 (added the 4 to both sides)
z=

(divided both sides by -3z)
z=
Answer: (28/37) - (48/37)*i
Step-by-step explanation:
We want to solve the quotient:

To solve it, we need to multiply the whole quotient by the complex conjugate of the denominator.
Remember that for a complex number:
a + b*i
the complex conjugate is:
a - b*i
Then if the denominatoris:
6 + i
the complex conjugate is:
6 - i
Then to solve the quotient we have:

This is equal to:

Then the initial quotient is equal to:
(28/37) - (48/37)*i