Answer:
No solutions
Step-by-step explanation:
Distribute the -1 on the left side
-1(5x+7) +1 = -5x-5
-1*5x +-1*7 +1 = -5x -5
-5x-7+1=-5x-5
Combine like terms
-5x-6=-5x-5
Add 5x on both sides
-6=-5
This statement is false, therefore there are no solutions
Hope this helps! :)
Answer:
Option B.) –6x3 + x2 – √5
Step-by-step explanation:
A is wrong because, polynomial expressions cannot have a variable as a denominator.
C is wrong because there is no constant.
D is wrong because, polynomial expressions cannot have a variable as a denominator.
Hope that helps! :-)
54x^2+208x-308=-2x-8
54x^2+208x-308+2x+8=0
54x^2+210x-300=0
9x^2+35x-50=0 (divided both sides by 6)
9x^2+45x-10x-50=0 (wrote the 35x as a difference)
9x(x+5)-10(x+5)=0
(9x-10)(x+5)=0
Now solve the equations:
9x-10=0
x=10/9
x+5=0
x=-5
Therefore, x has two solutions, 10/9 and -5!!
If you take the point on the bridge directly beneath the lowest point on the cable to be the origin, then the parabola has equation
![y = ax^2+bx+10](https://tex.z-dn.net/?f=y%20%3D%20ax%5E2%2Bbx%2B10)
300 ft to either side of the origin, the parabola reaches a value of <em>y</em> = 90, so
![a(300)^2+b(300)+10 = 90 \implies 4500a+15b = 4](https://tex.z-dn.net/?f=a%28300%29%5E2%2Bb%28300%29%2B10%20%3D%2090%20%5Cimplies%204500a%2B15b%20%3D%204)
![a(-300)^2+b(-300)+10 = 90 \implies 4500a-15b = 4](https://tex.z-dn.net/?f=a%28-300%29%5E2%2Bb%28-300%29%2B10%20%3D%2090%20%5Cimplies%204500a-15b%20%3D%204)
Adding these together eliminates <em>b</em> and lets you solve for <em>a</em> :
![(4500a+15b)+(4500a-15b)=4+4 \\\\ 9000a = 8 \\\\ a = \dfrac1{1125}](https://tex.z-dn.net/?f=%284500a%2B15b%29%2B%284500a-15b%29%3D4%2B4%20%5C%5C%5C%5C%209000a%20%3D%208%20%5C%5C%5C%5C%20a%20%3D%20%5Cdfrac1%7B1125%7D)
Solving for <em>b</em> gives
![4500\left(\dfrac1{1125}\right)+15b=4 \\\\ 4+15b = 4 \\\\ 15b=0 \\\\ b=0](https://tex.z-dn.net/?f=4500%5Cleft%28%5Cdfrac1%7B1125%7D%5Cright%29%2B15b%3D4%20%5C%5C%5C%5C%204%2B15b%20%3D%204%20%5C%5C%5C%5C%2015b%3D0%20%5C%5C%5C%5C%20b%3D0)
So the parabola's equation is
![y = \dfrac{x^2}{1125}+10](https://tex.z-dn.net/?f=y%20%3D%20%5Cdfrac%7Bx%5E2%7D%7B1125%7D%2B10)
150 ft away from the origin, the cable is at a height <em>y</em> of
![y = \dfrac{150^2}{1125}+10 = \boxed{30}](https://tex.z-dn.net/?f=y%20%3D%20%5Cdfrac%7B150%5E2%7D%7B1125%7D%2B10%20%3D%20%5Cboxed%7B30%7D)
ft above the bridge.