CPhill

Here's 4

24  18  29  21 16  23 13  11

First step...order the data  from lowest to highest

11 13 16  18     21  23  24  29

Find the median of the data  =  (18 + 21)/2     =  39/2  =  19.5    = Q2

Find Q1 =    (13+16) / 2 = 29/2  =  14.5

Find Q3  =   (23 + 24)/2 = 47/2 = 23.5

The first answer is correct

For the second one...using this tool : 

https://www.graphpad.com/quickcalcs/linear2/

The line fo best fit has the equation 

Y = 1.040*X + 5.210

The slope is  1.040

Third one...this is ust the graph of y   = -3x^2  shifted down 6 units

The vertex  of    y  = -3x^2  is at (0,0)

So...the vertex of this function is  (0,-6)

So...the y value of the vertx is  -6

27....We could find the inverse of the function...but....the easier method is to just solve this :

-10 = (x - 1)  / 4    multiply both sides by 4

-40  = x - 1    add 1 to  both sides

-39  = x  = f^-1 (-10)

29  We have this form

y  = a (x - h)^2 + k       where h, k   are the coordinates of the vertex

So we have

y = a (x - -3 )^2  + 5

y = a (x + 3)^2  + 5

Since the point (2, -10)  is on the graph, we can solve for  "a"

-10 = a ( 2 + 3)^2 + 5    subtract 5 from both sides

-15 = a (5)^2

-15 = 25a    divide both sides by 25

-15/25 =a

-3/5  = a

So...the function is      y  = (-3/5)(x + 3)^2 + 5

The y intercept occurs where x   =   0  ....so....

y = (-3/5)(0 + 3^^2 + 5

y = (-3/5)(3)^2 + 5

y = (-3/5)*9  + 5

y = -27/5  + 25/5

y = - 2/5  

Here's a grpah to  confirm this  : https://www.desmos.com/calculator/ecloqpgull 

Lst one.... we can always divide a polygon of n sides  into (n -2) triangles.....since each triangle has 180 degrees of measure, then  the sum of the interior angles is just  180 (n - 2)

So....we can solve this

900  = 180 (n - 2)   divide both sides by 180

5  = n - 2    add 2 to  both sides

7  = n     (7 sides)

First one -  The first term will determine the end behavoir on both sides....

As x  becomes more and more negative  and positive, "y"  will become more negative in each direction

So  A  is correct

Second one -

No

Yes ⇒   (5x - 4) (5x + 4)

No

Yes  ⇒  (5x^2  - 4x)  (5x^2 + 4x)

Last one   ...the rate of change  (slope) of the function  in the table is  [ 8 - 3 ] /  [ 3 - 2 ]  =  5 / 1   =  5

So...we are looking for all slopes > 5.....we want to put each line in the form  y  = mx + b    where m is the slope

First one

y = (11/2 ) x  +  5       m = 11/2.....   this is  >  5

Second one

-3x + 1/2y  =3     add 3x to both sides

(1/2)y  = 3x + 3      multiply both sides by  2

y = 6x + 6      m = 6 ....  this is > 5 

Third  one 

(1/9)y = (2/3) x     multiply both sids by 9

y = 9 (2/3)x

y = 6x         m  = 6  .... this is > 5 

Last one

We can see right off that 4.5  < 5.......

So...the answers are "Yes" to all but the last one

Can't help you with the first unless I can see the y values....these deal with  the range

Second one

8^2  - 27^(2/3)   =

64   -  [27^(1/3) ] ^2                   note..... {27^(1/3)  is the cube root of 27  = 3 }

64  - [ 3 ]^2  =

64 - 9 =

55

Last one 

Angle 2  = 55

Angle 3 is a right angle  = 90

Angles  2 + 3 + 4  = 180  ....so.....

55 + 90  + Angle 4  = 180

145 + Angle 4  = 180      subtract 145 from both sides

Angle 4 =  180 - 145  =    35  (degrees)

First one....a coefficient can only be  "attached" to a variable....."10"  has no variable attached to it...so...it is not a coefficient

Second one

      -x^2  - 5x   -    6

+ (  2x^2  - 7x   +  8 )

________________

     x^2    - 12x  +  2

Third one  -  9x^2 - 60x + 100

This is a perfect square trinomial....take the square root of the first term  = 3x

Take the square root of the last term  = 10

Since we have a  " - "   on the second term....that's the sign we use in factoring....so we have

(3x^2  - 10) (3x^2 - 10 )  = (3x - 10 )^2

Fourth one -

(x - 3)^2  + 8  = 12     subtract 8 from both sides

(x - 3)^2   = 4             take both square roots on the right side

x - 3  = ±√4

x - 3  =  ±2          add 3 to both sides

x  = ±2  + 3.....so we have

x  = 2 + 3  = 5      or

x  = -2 + 3   = 1

So...the two solutions are   x = 1  and x  = 5

Last one

x^2 + 14x  =- 48     add 48 to both sides

x^2 + 14x  + 48  = 0

We are looking for two  numbers to factor with that multiply to 48  and sum to -14....note....-8  and -6  fit the bill  !!!

So....factor this as

(x - 8) (x - 6)  =  0

Set each factor to 0 and solve for x  and we have

x  - 8  =  0                              x  - 6  = 0

add 8 to both sides              add 6 to both sides

x  = 8                                        x  = 6                  are the two solutions

Mmmm....don't see how they get that....here is  Wolframalpha's answer :  http://www.wolframalpha.com/input/?i=(x%5E2)+%5E(1%2F7)

It seems to match mine......

First one  - 3%  = .03   .....so    the value each year  is   100%  - 3%  = 97%  of what is was the year before  = .97

So...after 9 years, we have

14000(.97)^9   ≈  $ 10,643   = $10,650

Second  one  - exponential form  is   y   = ab^x

Not A.....this looks to be the quadratic  y  = x^2     this is not exponential

Not B .....this looks to be something like the absoluite value graph  y  = -  l  x + 4  l  + 1

C is correct.....we have a common geometric ratio of   1/4  between the successive term to the previous term..... the function is

y  = 1024(1/4)^x     where  x is an integer ≥ 2

Third  one.....

A   -  yes  ...we add the exponents on x and y in the first term and get 6

B - yes   - -x^6     is a sixth power term

C - no.....no exponents sum to 6

D - no.....same reason as C

Fourth one  -   g(x) shfits the graph of  f(x)  = ³√x    1  unit to the right and 3 units up  ⇒  "B"

Here's a graph  :  https://www.desmos.com/calculator/g1lhumawur

Whenever we have an angle bisected like this...it sets up this relationship  :

BD / BC  =  AD / AC

So

x / 4   = 2.25 / 3        multiply both sides by  4

x = 4 (2.25)  / 3  =     9  / 3      =  3

First one  - None are equal to x^7

A  = x^(7/2)

B = x^(-5)

C =x^(2/7)

D  = X^(-5)

Second one - Range = what y values are covered by the relation ??...these are  B = {-5, -3, 2, 4 }

Third one  - (2x - 1) (3x + 1)  = 2x(3x + 1)  - 1(3x + 1)  =  6x^2 + 2x  -3x - 1   =  6x^2 - x - 1

Fourth one  - let's rearrange  "C"

5x  =  y  - 8      add 8 to both sides

5x + 8  =  0

Note that when x  = 0, y  = 8

This must be the correct one since the point   (0,8)  is in the table

Fifth one  -   4 + x

                   _____     

                      12

The only thing that would make this undefined is if the denominator could be made to  = 0...however...nothing makes the denominator   = 0.....so we can put any real number into the function for x .....so..... "A"

Last one - this isn't srtictly linear.....my best guess ??   B = 89...reason....the function always increases by  more than 1 from  year-to-year but never by as much as 10