CPhill

n  = 27

The divisors  are

1  3   9  27

And their product   is   1 * 3 * 9 * 27  =   27 * 27  = 27^2   =  729

6. Solve for x.

-14 < 3x + 5 or 1/2x + 5 > 7

-14 < 3x     divide both sides by 3

-14/3 < x

(1/2)x +  5 > 7     multiply through by 2

x + 10  > 14    subtract 10 from both sides

x >   4

So

x > - 14/3   or   x > 4

We must choose the  most restrictive interval that solves both equations

This  is    x > 4

5. Solve for x.

-14 < 3x -  2x < 7

-14 < x < 7

In interval notation

(-14, 7)

4. Plot the inequality on the number line

x < -2 or x > 5

3. What is the interval notation for the compound inequality?

-5 > a or a > 4

a < - 5   or   a  > 4

( -infinity, -5) or (4, infinity )

2. Heather is 6 years younger than 5 times her daughter's age. The sum of their ages is greater than 90.

What is the youngest age Heather's daughter can be?

Let her daughter's age  =  D

Heather's age  is 5D - 6

And we have that

D + 5D - 6 > 90    simplify

6D - 6 > 90     add 6 to both sides

6D  > 96       divide both sides by 6

D > 16

Her daughter  must  be at least 17

1.

2x – 5y = 14     multiply through by 6  →  12x - 30y   = 84     (1)

7x + 6y = -2      multiply through by 5 →   35x + 30y  = -10    (2)

Add  (1)  and (2)

47x  = 74

x = 74 / 47

And using  2x  - 5y  = 14     we have

2(74/47) - 5y  = 14

148 / 47  - 5y  = 14

148/47  - 14   = 5y

148 /47  - 658 / 47  =  5y

-510 / 147  = 5y    divide both sides by 5

-102 / 147  = y

Note that this function only approaches 0  from the right

lim              8√x  / x   =

x→ 0⁺

lim              8  / √x

x → 0⁺

As  x   approaches  0,  √x  is  an extremely small positive number  [but not 0 ]

So      8  /  [ an extremely small number ]  =  infinity

So.....since the limit is infinite....this  limit doesn't actually exist 

AB  = AP  + BP

CD = CP + DP

By the  intersecting chord theorem

AP *  BP  = CP * DP

3 * BP  =  8 *  DP

BP / DP  = 8 / 3

H = hardcover books

Paperback books   = twice the harcover books  = 2H

Original number in the  collection  = H + 2H  =  3H

Books  checked out  = H   + x(3H/9)   where x is the number of members checking out the paperback books

Paperbacks returned  = 2(3H /9)

Paperbacks not returned  = (x - 2)(3H/9)

So  we have this equation

Books in collection  = [ books returned ] + [ books not returned ]

3H  = [2 (3H/9)] + [ H + (x - 2)(3H/9) ]     simplify

3H =  [ H(2/3) ] + [ H + (H)(x - 2)/3 ]     divide through  by H

3  = (2/3) + 1 + (x - 2)/3

3  = (2/3) + 1 + (x - 2)/3      multiply through by 3

9 = 2 + 3 + x - 2

9 = 3 + x

9 - 3   = x

6   = x

You need to make 5 calls.....one to Member 7427  and  (x - 2)  = (6 - 2)  = 4 more to those who checked out the unreturned paperbacks