Answer:
For the first question(B)
x=-2
x=5
For part C, the question is not clear
For the last question, the approximated value is -5/4
Answer:
- w = 8
- x = 8√2
- y = 8√2
- z = 16
Step-by-step explanation:
A 45-45-90 right triangle is isosceles. That means both legs are the same length, and its hypotenuse is √2 times the leg length. You can figure these facts using trigonometry or the Pythagorean theorem, or you can rely on your memory of them.
w = 8 . . . . . . . . . . . same as the leg length shown
x = y = 8√2 . . . . . hypotenuse of smaller triangle; both legs are the same
z = (8√2)√2 = 16 . . . . hypotenuse of larger triangle
I used similarities in triangles
3
2
+
3
−
7
Distribute
(
6
2
−
4
−
5
)
−
1
(
3
2
−
7
+
2
)
(
6
x
2
−
4
x
−
5
)
−
1
(
3
x
2
−
7
x
+
2
)
(6x2−4x−5)−1(3x2−7x+2)
(
6
2
−
4
−
5
)
−
3
2
+
7
−
2
Answer:
Second choice:
![x=2t](https://tex.z-dn.net/?f=x%3D2t)
![y=4t^2+4t-3](https://tex.z-dn.net/?f=y%3D4t%5E2%2B4t-3)
Fifth choice:
![x=t+1](https://tex.z-dn.net/?f=x%3Dt%2B1)
![y=t^2+4t](https://tex.z-dn.net/?f=y%3Dt%5E2%2B4t)
Step-by-step explanation:
Let's look at choice 1.
![x=t+1](https://tex.z-dn.net/?f=x%3Dt%2B1)
![y=t^2+2t](https://tex.z-dn.net/?f=y%3Dt%5E2%2B2t)
I'm going to subtract 1 on both sides for the first equation giving me
. I will replace the
in the second equation with this substitution from equation 1.
![y=(x-1)^2+2(x-1)](https://tex.z-dn.net/?f=y%3D%28x-1%29%5E2%2B2%28x-1%29)
Expand using the distributive property and the identity
:
![y=(x^2-2x+1)+(2x-2)](https://tex.z-dn.net/?f=y%3D%28x%5E2-2x%2B1%29%2B%282x-2%29)
![y=x^2+(-2x+2x)+(1-2)](https://tex.z-dn.net/?f=y%3Dx%5E2%2B%28-2x%2B2x%29%2B%281-2%29)
![y=x^2+0+-1](https://tex.z-dn.net/?f=y%3Dx%5E2%2B0%2B-1)
![y=x^2](https://tex.z-dn.net/?f=y%3Dx%5E2)
So this not the desired result.
Let's look at choice 2.
![x=2t](https://tex.z-dn.net/?f=x%3D2t)
![y=4t^2+4t-3](https://tex.z-dn.net/?f=y%3D4t%5E2%2B4t-3)
Solve the first equation for
by dividing both sides by 2:
.
Let's plug this into equation 2:
![y=4(\frac{x}{2})^2+4(\frac{x}{2})-3](https://tex.z-dn.net/?f=y%3D4%28%5Cfrac%7Bx%7D%7B2%7D%29%5E2%2B4%28%5Cfrac%7Bx%7D%7B2%7D%29-3)
![y=4(\frac{x^2}{4})+2x-3](https://tex.z-dn.net/?f=y%3D4%28%5Cfrac%7Bx%5E2%7D%7B4%7D%29%2B2x-3)
![y=x^2+2x-3](https://tex.z-dn.net/?f=y%3Dx%5E2%2B2x-3)
This is the desired result.
Choice 3:
![x=t-3](https://tex.z-dn.net/?f=x%3Dt-3)
![y=t^2+2t](https://tex.z-dn.net/?f=y%3Dt%5E2%2B2t)
Solve the first equation for
by adding 3 on both sides:
.
Plug into second equation:
![y=(x+3)^2+2(x+3)](https://tex.z-dn.net/?f=y%3D%28x%2B3%29%5E2%2B2%28x%2B3%29)
Expanding using the distributive property and the earlier identity mentioned to expand the binomial square:
![y=(x^2+6x+9)+(2x+6)](https://tex.z-dn.net/?f=y%3D%28x%5E2%2B6x%2B9%29%2B%282x%2B6%29)
![y=(x^2)+(6x+2x)+(9+6)](https://tex.z-dn.net/?f=y%3D%28x%5E2%29%2B%286x%2B2x%29%2B%289%2B6%29)
![y=x^2+8x+15](https://tex.z-dn.net/?f=y%3Dx%5E2%2B8x%2B15)
Not the desired result.
Choice 4:
![x=t^2](https://tex.z-dn.net/?f=x%3Dt%5E2)
![y=2t-3](https://tex.z-dn.net/?f=y%3D2t-3)
I'm going to solve the bottom equation for
since I don't want to deal with square roots.
Add 3 on both sides:
![y+3=2t](https://tex.z-dn.net/?f=y%2B3%3D2t)
Divide both sides by 2:
![\frac{y+3}{2}=t](https://tex.z-dn.net/?f=%5Cfrac%7By%2B3%7D%7B2%7D%3Dt)
Plug into equation 1:
![x=(\frac{y+3}{2})^2](https://tex.z-dn.net/?f=x%3D%28%5Cfrac%7By%2B3%7D%7B2%7D%29%5E2)
This is not the desired result because the
variable will be squared now instead of the
variable.
Choice 5:
![x=t+1](https://tex.z-dn.net/?f=x%3Dt%2B1)
![y=t^2+4t](https://tex.z-dn.net/?f=y%3Dt%5E2%2B4t)
Solve the first equation for
by subtracting 1 on both sides:
.
Plug into equation 2:
![y=(x-1)^2+4(x-1)](https://tex.z-dn.net/?f=y%3D%28x-1%29%5E2%2B4%28x-1%29)
Distribute and use the binomial square identity used earlier:
![y=(x^2-2x+1)+(4x-4)](https://tex.z-dn.net/?f=y%3D%28x%5E2-2x%2B1%29%2B%284x-4%29)
![y=(x^2)+(-2x+4x)+(1-4)](https://tex.z-dn.net/?f=y%3D%28x%5E2%29%2B%28-2x%2B4x%29%2B%281-4%29)
![y=x^2+2x+-3](https://tex.z-dn.net/?f=y%3Dx%5E2%2B2x%2B-3)
.
This is the desired result.