College Algebra Help?

Question

Under College Level Questions: Could someone show me how to do #25, #28, #30, #31(any), #37, and #39. The answers are @ the end of the document so I don't want just the answer, I need an explanation. Check to make sure your answer matches their's. Thanks!

http://www.rlc.dcccd.edu/testcenter/accureview.pdf

Answer 1

#25) Solve (3x-9)/[2x+1)(x-7)] ≤ 0
When is a fraction nonnegative?
When the numerator is ≥ 0 and the denominator is ≤ 0 (1)
or
when the numerator is ≤ 0 and the denominator is ≥ 0. (2)
Let's consider each case separately.
Case (1):
Here 3x -9 ≥ 0, so x ≥ 3.
To make the bottom nonpositive, we can't
have 2x + 1 ≤ 0, because x ≥ 3. So we must have
2x +1 > 0 and x < 7.
Solution for case (1): [3,7).

Case (2): Now x ≤ 3.
We want the denominator positive.
So both factors must be positive or both must be negative.
Both factors can't be positive, since x > 7 contradicts
x ≤ 3.
So both are negative and 2x +1 < 0 overrides x ≤ 3.
So the answer for this case is (- ∞ , -1/2).
The answer, then is the union of the 2 intervals
from (1) and (2).

28.The given line, L, can be written as
y = 3x -7.
Its slope is 3.
The slope of a line perpendicular to L is
therefore -1/3.
So the wanted line has equation
y = -1/3 x + b.
Now plug in (-1,2) to find b.
2 = 1/3 + b
b = 5/3
So y = -1/3 x + 5/3.
Or, multiplying by 3 and simplifying,
x + 3y = 5.

30). Let me give you a hint here.
First, find the slope of the line.
Then y = mx + b.
You know m,so plug in either point to find b.
To help a bit more, the slope turns out to be 10/3.
You can carry on from here.

31). a). is a circle, because the coefficients of x² and y²
are equal and positive.
b). is an ellipse because the coefficients of x² and y²
are both positive and unequal.
c). is a hyperbola because the coefficients of x² and
y² have opposite signs.
d). is a parabola, because only 1 of x, y is squared.
e) There's no such curve because if we complete
the squares in x and y, we will get a negative sum
of 2 squares, which is impossible. I'll let you work out
the details!

37). The graph of y = √-x is the same as the graph
of y = √x reflected about the y axis. In other
words, Change every x coordinate on y = √x
to its negative and plot the same graph.

39. It's just like the graph of y = e^x except steeper.
Plot many points with the aid of a calculator!

Hope that helps!!

Answer 2

2+2=4

Answer 3

Your placement try would not qualify you to get into an more advantageous lever of Math so which you will could desire to take the pre-algebra in the past you are able to examine in for a Math that's tranferable to a school. See a councelor.

Answer 4

http://www.algebra.com/