# intermediate algebra

Math 125 : Exam 4 Chapter 12Student ID : ______________

SHOW WORK FOR CREDIT . Box Answers

1 . Graph the function x y

-5 0 .02

-4 0 .03

-3 0 .06

-2 0 .13

-1 0 .25

0 0 .50

1 1 .00

2 2 .00

3 4 .00

4 8 .00

5 16 .00

Solution

Substitute to (x 2×2 1 , for all x , g (x ?[g (x )] 2 (g (x )2 1 ?[g (x )] 2 (3x-2 )2 1 ?[g (x )] 2 (9×2-12x [banner_entry_middle]

4 1 ?[g (x )] (18×2-24x 8 1 ?[g (x )] 18×2-24x 9

Solution Solution

Transform 27 into 33

36-3x (1 /33 3-3

Therefore

6-3x -3

Add 3x 3 to both sides of the equation

6 3 3x

Divide both sides by 3

x 9 /3 3 Solution

Raise both sides of the equations to 3 exponents 81 34

6 . Find the exact solution of each equation Solution : Solution

Transfrom 32 to 25 Raise both sides to x exponents log2 (2-5 x 16 x4

-5 log2 (2 x since log2 (2 1 24 x4

X -5 x 2 Solution

logan8 logam3 – loga l from log xn n log x

from log (AB log A log B and log (A /B log A – log B 8 . Express as the sum or difference of logarithms , move exponents , etc Simplify Solution : Solution 9 . Biff plans to invest 2500 for three years at 8 compounded quarterly . Find the number of years until there is 9500 in the account . Round to the nearest tenth of a year

f (x 9500

x number of years

rate 8 / 4 0 .02 becomes quarterly rate

f (x 2500 (1 0 .02 )4x

9500 2500 (1 .02 )4x (1 .02 )4x (9500 /2500

log (1 .02 )4x log (9500 /2500

4xlog (1 .02 log 9500 – log 2500 x 16 .8 years

10 . Solve the equation Solution : Solution

where ln is the natural logarithm

x 1 .04

10 .40 find

The direction the parabola opens

a -1

Since a 0 so opens downward

The coordinates of the vertex

h -1

k – 3

vertex is at (-1 ,-3

The equation of the axis of symmetry

x -1

Graph

Solution

Transform into the equation by dividing both sides by 144 this an ellipse with vertices (0 ,0 ) and a 4 , b 3 By completing the square (x2-10x 25 (y2-8y 16 ) -23 – 41 0 (x-5 ) 2 (y-4 )2 64 (x-5 ) 2 (y-4 )2 82 This is circle with center at (5 ,4 ) and radius of 8 . Find the distance between the points whose coordinates are (- 2 , 3 and (4 , – 5

Solution

Solution

Add

y 7x – x2

2x- y -6

2x- 0 7x – x2 – 6

x2 2x-7x 6 0

x2-5x 6 0 (x-3 (x-2 0

x1 3

x2 2… [banner_entry_footer]

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