Answer:
A positive relationship between the inputs and the outputs is one wherein more of one input leads to more of an output. This is also known as a direct relationship. On the other hand a negative relationship is one where more of one input leads to less of another output.
Step-by-step explanation:
Hope this helps
<h2>
Answer:</h2>
<em> The side of the triangle is either 38.63ft or 10.35ft</em>
<h2>
Step-by-step explanation:</h2>
This problem can be translated as an image as shown in the Figure below. We know that:
- The side of the square is 10 ft.
- One of the vertices of an equilateral triangle is on the vertex of a square.
- Two other vertices are on the not adjacent sides of the same square.
Let's call:
Since the given triangle is equilateral, each side measures the same length. So:
x: The side of the equilateral triangle (Triangle 1)
y: A side of another triangle called Triangle 2.
That length is the hypotenuse of other triangle called Triangle 2. Therefore, by Pythagorean theorem:
![\mathbf{(1)} \ x^2=100+y^2](https://tex.z-dn.net/?f=%5Cmathbf%7B%281%29%7D%20%5C%20x%5E2%3D100%2By%5E2)
We have another triangle, called Triangle 3, and given that the side of the square is 10ft, then it is true that:
![y+(10-y)=10](https://tex.z-dn.net/?f=y%2B%2810-y%29%3D10)
Therefore, for Triangle 3, we have that by Pythagorean theorem:
![(10-y)^2+(10-y)^2=x^2 \\ \\ 2(10-y)^2=x^2 \\ \\ \\ \mathbf{(2)} \ x^2=2(10-y)^2](https://tex.z-dn.net/?f=%2810-y%29%5E2%2B%2810-y%29%5E2%3Dx%5E2%20%5C%5C%20%5C%5C%202%2810-y%29%5E2%3Dx%5E2%20%5C%5C%20%5C%5C%20%5C%5C%20%5Cmathbf%7B%282%29%7D%20%5C%20x%5E2%3D2%2810-y%29%5E2)
Matching equations (1) and (2):
![2(10-y)^2=100+y^2 \\ \\ 2(100-20y+y^2)=100+y^2 \\ \\ 200-40y+2y^2=100+y^2 \\ \\ (2y^2-y^2)-40y+(200-100)=0 \\ \\ y^2-40y+100=0](https://tex.z-dn.net/?f=2%2810-y%29%5E2%3D100%2By%5E2%20%5C%5C%20%5C%5C%202%28100-20y%2By%5E2%29%3D100%2By%5E2%20%5C%5C%20%5C%5C%20200-40y%2B2y%5E2%3D100%2By%5E2%20%5C%5C%20%5C%5C%20%282y%5E2-y%5E2%29-40y%2B%28200-100%29%3D0%20%5C%5C%20%5C%5C%20y%5E2-40y%2B100%3D0)
Using quadratic formula:
![y_{1,2}=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \\ \\ y_{1,2}=\frac{-(-40) \pm \sqrt{(-40)^2-4(1)(100)}}{2(1)} \\ \\ \\ y_{1}=37.32 \\ \\ y_{2}=2.68](https://tex.z-dn.net/?f=y_%7B1%2C2%7D%3D%5Cfrac%7B-b%20%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D%20%5C%5C%20%5C%5C%20y_%7B1%2C2%7D%3D%5Cfrac%7B-%28-40%29%20%5Cpm%20%5Csqrt%7B%28-40%29%5E2-4%281%29%28100%29%7D%7D%7B2%281%29%7D%20%5C%5C%20%5C%5C%20%5C%5C%20y_%7B1%7D%3D37.32%20%5C%5C%20%5C%5C%20y_%7B2%7D%3D2.68)
Finding x from (1):
![x^2=100+y^2 \\ \\ x_{1}=\sqrt{100+37.32^2} \\ \\ x_{1}=38.63ft \\ \\ \\ x_{2}=\sqrt{100+2.68^2} \\ \\ x_{2}=10.35ft](https://tex.z-dn.net/?f=x%5E2%3D100%2By%5E2%20%5C%5C%20%5C%5C%20x_%7B1%7D%3D%5Csqrt%7B100%2B37.32%5E2%7D%20%5C%5C%20%5C%5C%20x_%7B1%7D%3D38.63ft%20%5C%5C%20%5C%5C%20%5C%5C%20x_%7B2%7D%3D%5Csqrt%7B100%2B2.68%5E2%7D%20%5C%5C%20%5C%5C%20x_%7B2%7D%3D10.35ft)
<em>Finally, the side of the triangle is either 38.63ft or 10.35ft</em>
Answer:
An axiom in Euclidean geometry states that in space, there are at least two three four five lies in the same plane not lie in the same plane lie on the same line
Answer:
D.16
Step-by-step explanation:
Answer:
-1 > -2
Step-by-step explanation:
-9 ÷ (3(3) > -2
-9 ÷ 9= -1
-1 > -2
this is true