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Notice that the y coordinate of both points is  0  .

So the line passing through both points is a horizontal line at  y = 0 .     

I finally figured this one out without relying on "technology"

(4x^2 + 6x + 4) ( 4y^2  - 12y + 25)  =  14    factor out a 2

2 (2x^2 + 6x + 4) (4y^2 - 12 + 25)  =  28     divide by 2 on each side

(2x^2 + 3x + 2) ( 4y^2  - 12y + 25)  =  14   

Factor 2, 4  out of each of the first two terms, respectively

(x^2 + (3/2)x + 1) (y^2 - 3y + 25/4)  = 7/4

Complete the square on  x and y  

( x^2 + (3/2)x + 9/16 +  7/16) ( y^2 - 3y + 9/4 + 4)  = 7/4

[ ( x + 3/4)^2  + 7/16 ] [ ( y - 3/2)^2 + 4 ]  = 7/4    expand

 ( x + 3/4)^2  * ( y - 3/2)^2 + 4  ( x + 3/4)^2 + (7/16)  ( y - 3/2)^2 + 7/4  =  7/4

Subtract 7/4 from each side

 ( x + 3/4)^2  * ( y - 3/2)^2 + 4  ( x + 3/4)^2 + (7/16)  ( y - 3/2)^2  =  0

Note that each term will equal 0  when x = -3/4  and y = 3/2.....!!!!

Here is the graph for  b .

Here is the graph for  d .

OK....so we have that

[8x + 2 ] + [8x + 8]  =  90       simplify

16x + 10  = 90       subtract 10 from both sides

16x  = 80    divide both sides by 16

x = 5

So...one angle is   8(5) + 2  = 42°  and the other is 90 - 42 = 48°

complementary angle 

Are these angles supposed to lie next to each other on a line ??

They definitely do Chris :)

I mean Trolls definitely collect their tolls from Troll booths!!     

Surface Area = Lateral area + Base area

Radius =Diameter/2

              =6/2 =3

Slant Height =sqrt[8^+ 3^2]

                        =8.544

Lateral area=Slant Height x Pi x Radius

                      =8.544 x 3.141592 x 3

                      =80.525 units squared

Base Area =Pi x r^2

                    =3.141592 x 3^2

                    =28.274 units squared

Surface Area =80.525 + 28.274

                        =108.8 =~109 units squared.

Note: Because I used Pi to 6 decimal places instead of 2 decimal places, I got the answer closer to 109.

Base area  = area of a square =   9^2  = 81 units^2     (1)

Area of the sides  =  area of 4 trianges each with a base of 9 and height of 5 =   

4*  (1/2)(9)(5)  = 90 units^2   (2)

Surface area  = (1)  + (2)  =  [ 81 + 90 ] =  171 units^2

Radius = Diameter/2

R =4/2 =2

Vertical Height =10

10^2 + 2^2 =Slant Height

Slant Height =10.198

Lateral Area = Slant height x Pi x Radius

                        =10.198 x 3.141592 x 2

                         =~64 units squared

962 divided by 8 is 120.5

Step 1 - Reflect across line y = x

Step 2 - Translate 6 units up

B and D

(-2i) (8i)  =

(-2 * 8 )  * ( i * i )  =

-16 * i^2   =

-16 * -1  =

16

x^2 - 7x  -  6  = 0

Let   a  =1, b =  -7   and c =  -6

The "formula" is

[ - b ±√ [ b^2 - 4ac]  ]  /  [2a]

Filling in the missing pieces, we have

[ - (-7) ±√ [ (-7)^2 - 4 (1)(-6) ] / [ 2(1) ]

[ 7 ±√ [ 49 + 24 ] ]  / 2

[ 7 ±√ 73 ] / 2

So...the two solutions are

[ 7 +√ 73 ] / 2     and  [ 7 -√ 73 ] / 2

Very nice, GA and Melody.....!!!

BTW.....if a Troll collects fares....does he do so from a "Troll" booth ??

Welcome to the forum!

Yes, school is very important. It helps you get a job and keeps you up to date with society. Those are just some of the positive effects of schools.

That bridge needs a Troll. Aside from collecting fares, he can have an occasional snack of puréed dumb dumb.  

These lil’imps often give us big chimps a bad reputation.  They never pay for their fares, but they expect on time, first-class service, and they have fits when they don’t get it.  The little monkeys are much smarter than the bridge running fool is, though. They are much less likely to become monkey mincemeat.

2x^2 + 16x + 24

First rule ⇒ take out the greatest common factor, 2

2 [ x^2 + 8x + 12 ]

We need two numbers that sum to 8 and multiply to 12

6 and 2 are the ones we need .....so factor with these and we have

2 (x + 6) (x + 2) 

y = -x^2 + 12x - 4

We need to complete the square, NSS

Factor out the negative

y = - ( x^2 - 12x + 4)

Take 1/2 of -12  = -6   square it  = 36....add it and subtract it inside the parentheses

y = - (x^2 - 12x + 36 + 4 - 36)     factor the first three terms, simplify the rest

y = - [  ( x - 6)^2  - 32 ]      apply the negative back across the terms

y =  - (x - 6)^2  + 32

In the form, y = a (x - h)^2 + k   the vertex is (h, k)  =  ( 6 , 32 )