CPhill

(2t + 3, 3 - 3t)   =  ( x, y)

This implies that     

2t + 3   =  x     subtract 3 from both sides

2t = x  - 3       divide both sides  by 2

t =  (x - 3) / 2          (1)

And we also have that   

y =  3 - 3t         substituting (1)   in for  t, we get that

y  =3 - 3  ( x - 3) / 2                        simplify

y= 3 - (3/2)(x - 3)

y=  3  -  (3/2) x + 9/2

y=  6/2 - (3/2)x  + 9/2

y= -(3/2)x  + 15/2

Thus...we have a line with a slope of   -3/2  and a  y intercept  of  15/2

Note that when x  = 7   y  = -(3/2)(7) + 15/2   = -21/2 + 15/2  = -6/2  = -3

And we  can verify the y intercept.....when x = 0 ...... 2t = -3   ⇒  t = -3/2

Plugging this into  3 - 3(-3/2)  =   3 + 9/2 =  6/2 + 9/2  = 15/2 

Here is a graph of the parameterized line  and the linear equation  :  https://www.desmos.com/calculator/ruklcsfe62

Note that the  graphs  coincide

3^(5x + 3) *  27^x

Note that 27^x  = (3^3)^x     =  3^(3x)   ....so we have....

3^(5x + 3) * 3^(3x)        using a property of exponents   we can write

3^( 5x + 3  + 3x)  =

3^( 8x + 3)   

So  f(x)   =  8x + 3

Between 12 and 5  we have    (5/12) * 360°   =   150°

The arc length  is given  by ;

2 pi  ( diameter/2) *  150  / 360  =

2 pi  * ( 25/2) *  5/12  =

[ 2 * 25 * 5 ] pi  / [ 2 * 12]  =

250pi / 24  ≈   32.7  cm

D. 9 + (-3)

B. distance

Although "phone numbers" is a rather interesting  choice....LOL!!!!

As long as we're not  specifying an ordered set, order does not  matter    {1,2,3}   is the same set as { 2,3,1 }

False.....whole numbers are just the  positive integers (the "counting  numbers" ) 1,2,3,4,5.....etc.

B. False

False.....2 is the only even prime...all the  rest are  odd

See here : https://web2.0calc.com/questions/is-this-statement-true-or-false_11