CPhill

We have to know how many tests you have taken before you made the 28......  

I'm not great at Physics.....but I think we need this equation :

V_f   = V₀  +  at

Where

V_f  = final velocity

V₀  = initial velocity  

a  =  acceleration

So we have

44km / hr  =   0  + (5km / hr^2) * a

44km / hr   =  (5km / hr^2) * a          divide both sides  by  (5km / hr^2)

[ 44km / hr ]  

__________       =    a    =   [44/5] hr   =   8.8 hrs

[ 5km / hr^2 ]  

3x  + 2y  >  - 5

Let's first graph  3x +  2y    = -5

To do this   let    x  be any value ......  I 'll let it   = 1   .......  then  to find y

3(1)  + 2y  = -5

3  +  2y   = -5     subtract  3 from both sides

2y  = -8     divide both sides by 2

y = -4       so     ...     (1,-4)  is on the graph

Now   let x  be any other value.......I'll choose 0  ....find y again

3(0)  + 2y  = -5

0  +  2y  = -5

2y  = -5     divide both sides by  2

y  = -5/2     so.......  (0, -5/2)   is on the graph

Plot these two points and draw a line through them

Here's what the graph should look like :       https://www.desmos.com/calculator/dx8dnbgefp

Now......pick  a point on either side of this line  - I'll choose (0,0)   -       and  put it into the original function

So we have

3(0)  + 2(0)  >  -5    

0  >  - 5       

Since this is true.....we shade the side of the line which  contains (0,0)...also....since we have a ">"  symbol......the line should be a dashed one......

Putting ths all together , here's the final  graph   :  https://www.desmos.com/calculator/dx8dnbgefp

Let's just write an equation for the line itself

We have two points on the line (-6,0)  and (0,5)

Slope  =  [   5 - 0]  /  [  0 - -6 ] =    5 / 6

So....the equation becomes

y  = (5/6) (x  - 0 ) + 5

y =  (5/6)x  + 5      multiply through by 6

6y  =  5x  +  30     subtract   5x from both sides

-5x  + 6y   =  30     we want this to look similar to one of the given equations ....so .... multiply through by  -1

5x  - 6y   =  -30

Now....using either ≤  or  ≥    one of the following equations will be correct

5x  - 6y  ≤  -30   or

5x - 6y  ≥  -30  

We can pick any point in the shaded area to test  - (0,0)  seems easiest -  and see what  equation is the correct one

5(0)  - 6(0)  ≤  -30 

0  ≤  -30      nope!!!

5(0) - 6(0)  ≥  -30

0 ≥  30     yes  !!!

So....the correct answer is the last one...here's the graph : https://www.desmos.com/calculator/yl7kt7chbh

2. C

3. B

4. A

5. D

You don't want the "negative" tangent.....you want the "tangent inverse".....just press the "2nd"  key  and find the  "atan" (arctangent or tangent inverse)) function.....

So.....I assume you want to know the current price???

If so  ....after the first two years, the price was  34 (.98)^2  ≈  32.65  per m^3

[ each successive year the price was 98% = .98  of the year before]

And in the next five years   it increased  to  its current price of    32.65 (1.06)^5  ≈  43.69 per m^3

[each successive  year after the second one,  the price rose by 6%   = 1 + .06 =    1.06 ]

Thanks to the guest for spotting my earlier error....I'm not with it today....LOL!!!!!

Look at    -7x^2       and   -35x^2

Note that for each  x value  we put in the first function, the second function is 5 times as much  

For instance if x  = 1.......    -7(1)^2  = -7

But     -35(1)^2   = -35 * 1    =   -35    ......five times as much as the first one.....

So.....

g(x)  "stretches" f(x)  by a factor of 5

The  " +5"   at the end of the second function just translates  -35x^2  up   5 units

So

g(x)   stretches  f(x)  vertically by a factor of 5 and translates this up 5 units

y  = x  ...if we have a vertical stretch of 6 units......x  must become  6x

So       y =  6x

Look at the graph here : https://www.desmos.com/calculator/lsp6ddool2

Note that when x  = 2  in y = x....then  y = 2

But....when  x  = 2  in 6x........then y  = 12.......six times as much  !!!!

Look at the other answers

y  = x/6   =  y = (1/6) x      so this one actually vertically  "compresses"   the original function.....

y  = x + 6     just translates y = x  up 6 units

y  = x - 6     translates y  = x  down 6 units

Hang in there, NSS.....these are sometimes difficult for me, too.....!!!!!

10 + 16 /25

Note that 

16 / 25       can be converted to      64 / 100      if we multiply both numerator and denominator by 4

So we have

10  +   64 / 100   =     10   +  .64    =      10.64

The correct answer for the first one is   ⇒ f (x + 1)

A reflection across the x axis changes  f(x)  to  -f(x)  = g(x) 

So.....

Multiplying  f(x)   by -1 on  both sides, we have that

-f(x)  =  - ( x^2 + 5)

-f(x)  = -x^2  - 5

And for  -f(x), we can write g(x)

so

g(x)  = -x^2 - 5

Look  at the graph here, NSS :  https://www.desmos.com/calculator/zq0ozrsd5b

Notice if we "flipped" the  red graph - f(x) -    across the x axis.....it would coincide perfectly with the blue graph, g(x)