CPhill

Here's a simple reason :

Note :    6  / 3   =  2       because 2 * 3  = 6        [ quotient *  divisor  = dividend  ]

But

3 / 0   =  ?         because.....  ?  *  0     cannot posssibly return a value of 3  ....  in other words,  quotient * divisor  is undefined

Britney is correct....!!!!

Using the quadratic formula, we obtain two solutions :

alpha =   [ - b + √[ b^2 - 4ac] ] / {2a]       and   beta  =  [ - b - √[ b^2 - 4ac] ] / {2a]

So

alpha + beta   =      [ - b + √[ b^2 - 4ac] ] / {2a]   +   [ - b -√[ b^2 - 4ac] ] / {2a]   =  [ - 2b] / [2a]  =   -b/a

And  alpha * beta    =

[ - b + √[ b^2 - 4ac] ] / {2a]   *   [ - b + √[ b^2 - 4ac] ] / {2a]  =  [   b^2  - [b^2 - 4ac] ]  / [ 4a^2]  =

[ 4ac ] / [ 4a^2]  =   c / a

(5x^3)/ (3x^2y)   simplifies to  (5x) / ( 3y)

So we have

 [(5x) / (3y) ]   ÷  [ (25)/ (3y^9) ]       invert the second fraction and multiply

[ (5x)/ ( 3y) ]  * [ (3y^9)/ ( 25) ]        swap denominators

[(5x) / (25)]  * [ (3y^9) / (3y) ] =

(x / 5)   *  ( y^8)  =

( x * y^8) / 5

x^4 - 3x^3 - x^2 - 27x - 90 = 0

It's not easily factored, but let's guess, initially, that either 2, or -2 is one of the roots

Let's check - 2, first

(-2)^4 - 3(-2)^3 - (-2)^2 - 27(-2) - 90  =

16 + 24 - 4 + 54 - 90  =

94 - 94  =   0

So......-2 is a root

Two answers  include -2, but one of them has only 5 as the other possible root....then the possible factorization of the polynomial is either :

(x + 2)^2 ( x - 5)^2   but the ending constant will = 100 so this is no good

(x + 2)^3 (x - 5)       but the ending constant  = -40....no good either

(x +2) (x - 5)^3       but the ending constant is -250.....nope

So.......the only possible solution is  5, -2, 3i, -3i

Check

(x - 5) (x + 2) (x - 3i) (x + 3i)  =

( x^2 - 3x -10) ( x^2 - 9i^2) =

(x^2 - 3x -10) (x^2 + 9) =

x^4 + 9x^2 - 3x^3 - 27x - 10x^2 - 90  =

x^4 - 3x^3 - x^2 - 27x - 90   !!!!

Note  that they are only asking us to sketch the graphs

Here's the solution for  48    [ intersection points of a circle and a line ]  :  https://www.desmos.com/calculator/iipiffr3er

Here's 52 :  https://www.desmos.com/calculator/wqgjvkt18q

 And 53 :  https://www.desmos.com/calculator/zvh42ht4u5

The last two are tangent lines to circles

6t  -  (2/3) + (1/5)t  = 4 +  (2 - t) / 3      and we can write

6t  - (2/3) + (1/5)t   =  4 + 2/3  -  (1/3)t        multiply through by 15 to clear the fractions

90t  -  10  +  3t  =  60  + 10  -  5t        simplify

93t  - 10    =  70  -  5t         add 10, 5t  to both sides

98t   =  80            divide both sides by 92

t  =  80 / 98   =    40/ 49

1. Payment per person =   Total Debt / Population  =  1,000,000,000/ 18,700,000 ≈ $53.48 = $53

2.  Number of Bills in One Classroom  =  Volume of classroom / Volume of Bills  =

24 ft  =  288 in     ......    25 ft  =  300 in   ....... 10 ft =  120 in

So

[ 288 * 300 * 120 ]  /  [ 6.14 *   2.61 * 0.0043 ]   ≈ 150,458,821  would fit in one room

And

Number of Classrooms Needed for one billion bills =

1,000,000,000 / 150,458,821   ≈ 6.6 Classrooms

The slope of any horizontal line  = 0