Question

Checking for Extranuous Solutions Help Among Other Things. Will give Medals!

1.) Solve 9|9-8x|=2x+3 and check for extranous solutions
2.) Which equation defines the graph of y=x^2 after it is shifted vertically 3 units up and horizontally 2 units right?
a) y=(x+2)^2+3
b) y=(x-3)^2+2
c) y=(x-2)^2+3
d) y=(x+3)^2+2
3.) A candle is 17 in tall after burning for 3 hours. After 5 hours it is 15 inches tall. Write a linear equation to model the relationship between height (h) and the time(t). Predict the height of the candle at 8 hours.
Show all work and Explain, Please! Thank you!

Answer 1

@texaschic101

Answer 2

@carlyleukhardt

Answer 3

ill help u if you help me

Answer 4

@dan815

Answer 5

@Chillsquad

Answer 6

For number (1), we have to take in consideration the very definition of Absolute value:
\[9\left| 9-8x \right|=2x+3\]
And the definition of absolute value is:
\(\left| \alpha \right|=\) \(\alpha , x \ge 0\)
\(-\alpha , x<0\)
So, therefore, we have to consider two scenarios for the solution of the equation:
\[(1) \rightarrow 9(9-8x)=2x+3\]
\[(2) \rightarrow (-9)(9-8x)=2x+3\]
And you solve them both independantly to get the solutions.

Answer 7

Thanks!!

Answer 8

do you know what the extraneous solutions could be if any