The Pythagorean's Theorem for our situation would look like this:
So let's call the short leg s, the long leg l and the hypotenuse h. It appears that all our measurements are based on the measurement of the short leg. The long leg is 4 more than twice the short leg, so that expression is l=2s+4; the hypotenuse measure is 6 more than twice the short leg, so that expression is h=2s+6. And the short leg is just s. Now we can rewrite our formula accordingly:
And of course we have to expand. Doing that will leave us with
Combining like terms we have
Our job now is to get everything on one side of the equals sign and solve for s
That is now a second degree polynomial, a quadratic to be exact, and it can be factored several different ways. The easiest is to figure what 2 numbers add to be -8 and multiply to be -20. Those numbers would be 10 and -2. Since we are figuring out the length of the sides, AND we know that the two things in math that will never EVER be negative are time and distance/length, -2 is not an option. That means that the short side, s, measures 10. The longer side, 2s+4, measures 2(10)+4 which is 24, and the hypotenuse, 2s+6, measures 2(10)+6 which is 26. So there you go!
Answer:
coefficient of x: 2
coefficient of y: 3
coefficient of z: -7
Step-by-step explanation:
To solve this problem, first we need to sum the polynomials A and B, then we need to check the coefficients of x, y and z.
The sum of the polynomials is:
A + B = 5z + 4x^2 - 6y + 2 + 2x + 9y - 12z - 2
A + B = 4x^2 + 2x + 3y - 7z
So, the coefficients are:
coefficient of x^2: 4
coefficient of x: 2
coefficient of y: 3
coefficient of z: -7
Answer:
12 a. 4605 feet 12 b. 1,459,063 square feet
Step-by-step explanation:
For the perimeter, we simply add the lengths of each of the 5 sides together (or multiply 5 times one side length).
P = 5(921)
P = 4605 feet
For the area, we will use composition...add the area of the triangle to the area of the trapezoid.
For the area of the triangle, the formula is
.
Filling in our values gives us
and
A = 403,045 square feet.
Now for the trapezoid. The formula for a trapezoid is
where the b's represent the bases and the h represents the height. Filling in our values gives us
Work inside the parenthesis first:
and
A = 1,056,018
Now we add those together to get that area of the Pentagon is 1,459,063 square feet
let length of the rectangle be l
length is 6 cm longer than the width, w
l = w + 6
perimeter of rectangle is 72 cm
= 2l + 2w
substitute l = w + 6
2(w+6) + 2w = 72
4w + 12 = 72
4w = 60
x = 15
ans is C. 15 cm
