Answer:
x= 3/2
Step-by-step explanation:
log3(x) + log3(2x-1) =1
We know that log a+log b = log ab
log3((x)(2x-1)) = 1
Raise each side to the base 3
3^log3((x)(2x-1)) = 3^1
x*(2x-1) = 3^1
Distribute
2x^2 -x = 3
Subtract 3 from each side
2x^2 -x-3 = 3-3
2x^2 -x-3 = 0
Factor
(2x-3) (x+1) =0
Using the zero product property
2x-3 =0 x+1 =0
2x=3 x=-1
x = 3/2 x =-1
But we cannot take logs of negatives ( as we see when we put it back in the original equation)
so x=-1 is an extraneous solution
x= 3/2
It would be C because bisectors split the angle in half
Answer:
Step-by-step explanation:
Comment and answer
ABC is similar to XBY The triangles are similar because
- B is a common angle to both
- <A = <BXY AB is a transversal cutting 2 parallel lines
- <C = <BYX BC is a transversal cutting 2 parallel lines
BX = 2 Given
XA = 3 Given
BY = 3 Given
YC = x Object of question
BX/(BX + XA) = BY / (BY + YC) Parts of two similar triangles
2/(2 + 3) = 3/(3+ x) Combine the left
2/5 = 3/(3 + x) Cross Multiply
2*(3 + x) = 3*5 Remove the brackets
6 + 2x = 15 Subtract 6 from both sides
6-6+2x = 15 - 6 Combine
2x = 9 Divide by 2
2x/2 = 9/2
x = 4.5
Answer
x = 4.5 or D
Equivalent lines for sure
Part A would be 2 lines below the surface because since he is 2 lines above the surface (represented by +10 feet).
Part B would be -50 feet because he would be BELOW the surface (represented by "-", like -45).
Part C would be 20 because DeWayne would be at the tip of the seaweeds, -20 feet. Since each line is 5 feet, then he would have to swim 20 feet up to reach the surface.
Part D would be 0 feet. Since one line above the surface is 5, and one line below the surface is -5, subtracting or adding 5 would be 0.
:)
Hope this helped,
Loafly