CPhill

Here's a few, BigChungus

1a)   Multiplying  a polynomial by a  constant  doesnot change its degree

So....adding two 4th power polynomial together  still produces a 4th power  polynomial

1b )  Let  b  = -1/2

So    (1/2) g(x)  produces     -x^4  - x   + 1/2

Adding  this to  f(x)  will produce    -3x^2  - x + 5/2

So....the smallest  that   f + b*g    can be is  degree  2

  2log₂(x+5)  =    log₂(x−9)   +  log₂(x+53)+  1

Note  that   log ₂ 2   = 1

So  we  have

  2log₂(x+5)  =    log₂(x−9)   +  log₂(x+53)+  log ₂ 2

And  by some log properties we  can simplify this as

log ₂ ( x + 5)^2  =  log ₂  [ (x - 9) (x + 53) * 2 ]

The logs are the same so we can solve   this

(x + 5)^2  =  (x - 9) (x + 53) * 2

x^2 + 10x + 25 =  (x^2 + 44x -477) * 2

x^2 +10x + 25  = 2x^2  + 88x  - 954   rearrange as

x^2 + 78x   -979   =  0     factor as

(x + 89)  ( x - 11)   =0

Setting  each  factor  to 0  and solving for  x produces

x  = -89   reject....it makes the logs negativein the  original problem

x =  11   =  solution

YUCK!!!!

SORRY!!!!

See my revised answer   ....!!!!

A rhombus has sides of length 10 cm and one diagonal of length 12 cm. How long is the other diagonal, in cm?

1/2  the length of the  other  diagonal = sqrt [ side^2 - (1/2 of other diagonal)^2  ]  =

sqrt  [ 10^2  - 6^2 ]  = sqrt  [100 - 36 ]  =   sqrt [64] = 8

So....the  other diagonal is twice this  =  16

Draw  a parallel  segment to the  base   from the  upper right vertex  to the left side of the figure

The  height of the  right triangle  formed =  sqrt (25^2 - 24^2 )= sqrt ( 625 - 576)= sqrt ( 49(  = 7

So...the length of the  left side  of the  figure = 13 + 7  = 20

So  the perimeter=  20  + 25 + 13 + 24 =  82

The common difference  is   7

We  can solve this

48  = -36 + 7 ( n -1)      add 36 to both sides

84  = 7 ( n - 1)    divide both sides by 7

12 =  n - 1      add 1 to both sides

13  = n  = numbers in list

An assortment of 200 pencils is sold through a catalog for $\$19.90$. Shipping is an additional $\$6.95$. Including the charges for both the pencils and the shipping, what is the average cost, in cents, for each pencil? Express your answer rounded to the nearest whole number.

Avg cost  = 

[ 19.90  +  6.95  ]  / 200 =     .13  = 13  cents

The ages  are

19,19, 20, 20, 21, 21,22,24,25,25,26,27,28,28, 30,30,30,31,32,32,34,34,35,38,39,45,48

Mean   = 29  = x

Median  = 28  = y

Mode  = 30  = z

So

x (y  - z)   =     29  ( 28 - 30)   =  29 (-2)   = -58

Here's  part (b)

It's  the  graph of  f(2x)

Now....all you  have to  do for  part (d)  is to  shift this graph over to the  right  by  8 units  and  connect the  dots

Each  point shown will have  8  added to its x coordinate and  y will not change

Let me know if you have  trouble with this

My classroom has 11 rows of chairs, with 11 chairs in each row. The chairs in each row are numbered from 1 to 11. How many chairs have odd numbers?

We  have   11 * 11  = 121 chairs

So....the number of  "odd" ones  =  120/2 + 1 =   60 + 1  =    61