i need some help with my pre calc. homework plzzz help me out?

Question

1.between what two consecutive intergers is the value of log(2)66


5. a line with a slope of -3 passes through the point (0;9). which of the following is another point on this line


A. (-3,9)
b. (1,8)
c. (3,1)
D. (7,-12)
e. (10,-20)


9. three circles are inscribed in a rectangle as shown. if the height of the rectangle is 30 cm. , find the area of the shaded region.


8. solve the absolute value inequality

I 2x + 7 I
------------ > 1
I 3 I



9. simplifiy and plot the result of the complex plane

(3+3i)- (-2-i)

Answer 1

Since its homework, let me just give some pointers on the first two which hopefully will help you ... for the third one (question 9), its not possible to solve it without seeing the picture in question.

1) Log (2) 66 is whatever power you need to raise 2 to so as to get 66. For instance Log(2)1024 = 10 since 2 raised to the tenth power is 1024. Based on this you should be able to answer the question.
5) A line of slope 'm' passing through a point (x1, y1) is defined by the equation
y - y1 = m (x - x1)
Use the information provided to get the equation of the line and then plug in to see which of the points satisfy the equation of the line

hope I have been partially helpful :-)

Answer 2

I only have time to do part of this for you.
In #5 You are given the slope and y-intercept.
The equation is y = -3x + 9.
Rewrite it as 3x + y = 9.
Now just plug in your choices. Only (7,-12) satisfies
the equation.

#1. The question really asks: 66 lies between what
powers of 2? I.E., 2^x <66 <2^(x+1), where x is an
integer. What is x?
By computation, 2^6 = 64 and 2^7 = 128,
so x = 6 and the value of the logarithm is between 6 and 7.

#9. Combine real and imaginary values to get 5 + 4i.
So we lay off 5 units on the real axis and 4 on
the imaginary axis and plot the point.

Answer 3

1. You want to know what log[base 2](66) falls between.

To solve this, note that you're working with base 2. All you have to do is write out powers of 2 that fall around 66. Note that

64 < 66 < 128
2^6 < 66 < 2^7

Take the log[base 2] of the inequality, to get

log[base 2](2^6) < log[base 2](66) < log[base 2](2^7)

Note that by the log property log[base b](a^c) = c*log[base b](a)

6*log[base 2](2) < log[base 2](66) < 7*log[base 2](2)

And remember that log[base 2](2) = 1, so

6 < log[base 2](66) < 7

8. Solve the inequality:

|2x + 7| / |3| > 1

|3| = 3, so

|2x + 7| / 3 > 1
|2x + 7| > 3

Absolute inequalities with a greater (or greater than) sign will consist of the disjunction of two inequalities (using the OR). This translates to:

2x + 7 > 3 OR 2x + 7 < -3
2x > -4 OR 2x < -10
x > -2 OR x < -5

If you wanted this in interval notation,

x is in (-infinity, -5) U (-2, infinity)

Answer 4

1. 6 and 7




5. Fill in the equation y = mx + b.
9 = -3(0) + b
b = 9

Your new equation would be:
y = -3x + 9

Then figure out which of your points satisfies the equation. The answer is D. (7,-12) because -12 = -3(7) + 9.




9. You haven't provided us an image to refer to..



I'm still in Algebra II so I'm not to sharp on the other two. good luck!

Answer 5

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