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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