CPhill

Definitely not D  !!!....the graph shows it goes higher than this

Each little  "tick"  mark on "y"  represents 4 ft

If we go to 1.5 seconds on x.....note that the that the height is about 1 tick mark past 96 ft at this time

So   ...  it reaches a height of 96 + 4  =   100 ft   at 1.5 sec

Looks like   "a"  might be the best option   !!!

Do you see this, RP??? 

2. We can  find AB  thusly

sin (60)  = AB / 24

24 * √3 /2  =  AB

12√3  = AB

And  BE  =  (1/2)  of   AE  = 12

But ABE  and  BCE form similar triangles

So....if  BE  is  (1/2) of AE

Then BC  is  (1/2)  of AB  = 6√3

And CE  is  1/2 of BE  =  6

And triangle DCE is similar to triangle CBE

So since CE  is (1/2) of BE....then...

ED  is(1/2)  of CE  = 3     and

DC  is (1/2) BC  = 3√3

So  the perimeter of   ABCD  =

AB + BC + CD  + DE + EA  =

12√3  + 6√3  + 3√3  + 3  + 24  =

 [ 21√3  +   27 ] cm  ≈  63.4 cm

If I haven't made any errors  !!!!

1.  

The side of the smaller square  = 1 cm   and the side of the larger square  = 4 cm

Let the distance from  the top right of the smaller square to the intersection of AB with the side of the larger square  = x

So  the small triangle formed above the smaller square has a hypotenuse of   √[ 1 + x^2]

And  the larger triangle formed at the "top" part  of the larger square has  legs of  4  and [ (4) - (1 + x)]  =  (3 -x)    so    the hypotenuse  of this triangle  is  √  [ 4^2  + (3 - x)^2 ]  =

√ [  16  + 9 - 6x  + x^2 ]  =  √ [ x^2 - 6x + 25 ]

And the triangles are similar  such that

1 / √[ 1 + x^2]  =  4 /  √ [ x^2 - 6x + 25 ]      cross-multiply

√ [ x^2 - 6x + 25 ]  =  4 √[ 1 + x^2]          square both sides

x^2  - 6x + 25   =  16 (x^2 + 1)

x^2  - 6x + 25  =  16x^2  + 16

15x^2 + 6x - 9  =  0

5x^2  + 2x - 3  =  0

(5x - 3) (x + 1)  =  0

Setting each factor to 0 and solving for x produces   x  = 3/5  = .6  and x  = -1

But  x  is a length so it can't be negative

So  x  =  3/5 cm = .6cm

So....the length of AB  is

√[ 1 + (.6)^2]   +   √ [ (.6)^2 - 6(.6) + 25 ]  =

√ [ 1.36]  +  √ [ 21.76 ]  ≈ 5.8  cm    

We don't need any math for the first one, NSS

We can never get a negative answer out of a positive root

Thus....all the answers that have negative x values included are no good

So....by process of elimination....the last answer is correct  !!!

Second one

We have this

0.75 ( 140)  = s^2  /  [ 30.25 ]      multiply both sides by  30.25

(30.25) ( 0.75) (140)  =  s^2

Take  the positive root of both sides

√ [ (30.25) ( 0.75) (140)  ]  =  s  ≈   56 mph 

First one

Note that the diameter forms the hypotenuse of a right triangle

So   x   is just complementary to the 71° angle =   90  - 71   =   19°

Do you see this???

Second one

Arc GEC  and  Arc GFC  sum to  360°

So

230  + arc GFC  =  360     subtract   230 from both sides

arc GFC  = 130°

And  since angle GDC is a central angle intercepting this arc, it has the same measure  = 130°

You are correct  !!!

Last one

WC  and MQ are equal chords....and equal chords in a circle intersect equal arcs

So

arc CW  is congruent to arc  MQ       the  second answer is correct

Just as in the other problem, RP....we need to find the vertex....review my other answer in how to do this....so we have

x coordinate of the vertex     =     -(28)  / (2 * 2)   =  -7

y coordinate  of the vertex =   2(-7)^2 + 28(-7)  - 2  =  98 - 196 - 2  =  -100

We have a  positive in front of the first term.....thus.....this parabola turns upward

Thus.....the lowest y value  on the graph is    - 100

When we talk about "range", we are just referring to  the y values covered by the graph

So...   the range   is   

y ≥ -100    ⇒   all y values ≥ -100  are covered by the graph

"c"  is correct  

Here's the graph  : https://www.desmos.com/calculator/qoagejrwux

y  =  ( x + 3)^2  -  3

The   " +3 "   inside the parentheses  [ contrary to intuition]   shifts the graph of y = x^2  3 units to the left

If it was  "-3",  it would shift the graph 3 units to the right

The  " - 3 "   at the end shifts this down 3 units

So....."b"  is correct

Here's the graph of the transformations : https://www.desmos.com/calculator/xruxghuvu5

In the form

y  =  ax^2  + bx + c

The x coordinate of the vertex  is  given  by      -b / [2a]

So....we have

y  = -2x^2 + 28x  -  18       ......    b  = 28     a   =  -2

So...the x coordinate of the vertex  is given by

-(28) / [ 2 * -2]   =   -28 / -4   =  7

So  to find the y coordinate of the vertex...sub this value back into the function

-2(7)^2  + 28(7)  -  18   =

-98 +  196 - 18  =

80

So....the vertex  is  ( 7, 80)

This is a  vertical parabola    ....the  axis  of symmetry  is just   

x    =  the x coordinate of the vertex

x  =  7 

Here's the graph :  https://www.desmos.com/calculator/wcucis6wzt

Thanks, tertre.....!!!

I believe that EP's answer is correct.....we are looking for the number of ways to partition 5  into 2 parts.....these are :

5  0

4  1

3  2   =      3 ways