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Algebra help

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1. What is the exact solution to the equation e2x+1 = 7?

• x=2/1+ln7
• x=1+ln7/2
• x=ln7-1/2
• x=2/ln7-1

2. The parent function is f(x)=2x+3-3 and the new function g(x)=2x+2-1

How does the grah change from f(x) to g(x)

select each correct answer

• The graph is shifted 1 unit right

• The graph is shifted 2 units down

• The graph is shifted 1 unit left

• The graph is shifted 2 units up

3. Solve the sytem of equations using the substitution method

y=2+5/6x

4x-3y=3

thankies

Dec 15, 2018

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1.     e^(2x + 1) = 7        take the Ln of both sides

Ln e^(2x + 1)  = Ln 7       and by a log property, we can write

(2x + 1) Ln e  =  Ln 7      since Ln e  = 1, we can drop this

2x + 1  =  Ln 7             subtract 1 from both sides

2x  = Ln (7)  - 1          divide both sides by 2

x  =   [ Ln (7) - 1 ] / 2      { third answer }

2.

The graph is shifted 1 unit right

The graph is shifted 2 units up

3.

y=2+5/6x

4x-3y=3

Sub the first equation into the second for y   and we have

4x - 3 [ 2 + 5/6 x ]  = 3        simplify

4x - 6 - 15/6 x  =  3

4x - 6 -  5/2 x  = 3     multiply through by 2 to clear the fraction

8x - 12 - 5x  = 6

3x - 12 = 6         add 12 to both sides

3x  =  18       divide both sides by  3

x = 6

And using  y = 2 + 5/6 x    .....  we can find  y    as

y =  2 + 5/6 (6)   =   2  + 5    = 7   Dec 15, 2018