1. Math 123c Test 4 Show all work. (10 pt. each)
1. Solve log x(9) = –1/3 for x. .
3. Solve log4 (5) – log4 (x –1) = 3 4. Solve 92x * 32x – 1 = 27 without a calculator.
without the calculator.
5. Draw the circle x 2 + y 2 – 6x + 8y = 9. Label the center and the highest, lowest, left most and right most
points.
6. Draw the ellipse 4x2 – 16x + y2 + 4y = –4, find the center, draw the graph and label the highest, lowest, left
most and right most points.
7. Solve the following system of equations
3X + 2Y = 1
2X + 3Y = –1
8. Solve
2X + Y + 4Z = 11
X + 2Y + 2Z = 7
3X – 3Y –2Z = -4
9. We have 50 bills in $1’s, $5’s and $10’s. There are 4 more $10–bills than the $5–bills. Their total value is
$346. How many of each do we have? (Set up a system of equations and solve the system)
10. There’re three brand of fertilizers A, B, and C. Following is a table of the amount of nitrogen, phosphorus,
and potassium in a box of each brand (in lb). How many boxes of each brand are needed in order to make a
mixture that contains 6 lb of nitrogen, 6 lb of phosphorus and 7 lb of potassium?
Brand A B C
N 1 2 2
P 2 1 2
K 2 2 1
11. Horizontal parabolas
12. Hyperbolas