Answer:
Step-by-step explanation:
By the Pythagorean Theorem
17^2=8^2+h^2
h^2=17^2-8^2
h^2=289-64
h^2=225
h=15 meters
For this case we must simplify the following expression:![(5a^ 2 + 6a + 2) - (7a^ 2-7a-5) =](https://tex.z-dn.net/?f=%285a%5E%202%20%2B%206a%20%2B%202%29%20-%20%287a%5E%202-7a-5%29%20%3D)
We eliminate the parentheses taking into account that:
![- * + = -\\- * - = +](https://tex.z-dn.net/?f=-%20%2A%20%2B%20%3D%20-%5C%5C-%20%2A%20-%20%3D%20%2B)
So:
![5a ^ 2 + 6a + 2-7a ^ 2 + 7a + 5 =](https://tex.z-dn.net/?f=5a%20%5E%202%20%2B%206a%20%2B%202-7a%20%5E%202%20%2B%207a%20%2B%205%20%3D)
We add similar terms taking into account that:
Equal signs are added and the same sign is placed.
Different signs are subtracted and the major sign is placed.
![5a ^ 2-7a^2 + 6a + 7a +2 +5 =\\-2a ^ 2 + 13a + 7](https://tex.z-dn.net/?f=5a%20%5E%202-7a%5E2%20%2B%206a%20%2B%207a%20%2B2%20%2B5%20%3D%5C%5C-2a%20%5E%202%20%2B%2013a%20%2B%207)
Answer:
![-2a ^ 2 + 13a + 7](https://tex.z-dn.net/?f=-2a%20%5E%202%20%2B%2013a%20%2B%207)
Answer:
Length:8 m
Width:3 m
Step-by-step explanation:
<u><em>The complete question is</em></u>
If the perimeter of a rectangle is 22 meters, and the perimeter of a right triangle is 12 meters (the sides of the triangle are half the length of the rectangle, the width of the rectangle, and the hypotenuse is 5 meters). How do you solve for L and W, the dimensions of the rectangle.
step 1
<em>Perimeter of rectangle</em>
we know that
The perimeter of rectangle is equal to
![P=2(L+W)](https://tex.z-dn.net/?f=P%3D2%28L%2BW%29)
we have
![P=22\ m](https://tex.z-dn.net/?f=P%3D22%5C%20m)
so
![22=2(L+W)](https://tex.z-dn.net/?f=22%3D2%28L%2BW%29)
Simplify
-----> equation A
step 2
Perimeter of triangle
The perimeter of triangle is equal to
![P=\frac{L}{2}+W+5](https://tex.z-dn.net/?f=P%3D%5Cfrac%7BL%7D%7B2%7D%2BW%2B5)
![P=12\ m](https://tex.z-dn.net/?f=P%3D12%5C%20m)
so
![12=\frac{L}{2}+W+5](https://tex.z-dn.net/?f=12%3D%5Cfrac%7BL%7D%7B2%7D%2BW%2B5)
Multiply by 2 both sides
![24=L+2W+10](https://tex.z-dn.net/?f=24%3DL%2B2W%2B10)
----> equation B
Solve the system of equations by graphing
Remember that the solution is the intersection point both graphs
using a graphing tool
The solution is the point (8,3)
see the attached figure
therefore
The dimensions of the rectangle are
Length:8 m
Width:3 m
Answer:whole numbers
Step-by-step explanation: