ElectricPavlov

4.  

Since the triangles are similar, set up as ratios

130/60 = (42x+1) /78     now solver for x    multiply both sides by 78

130/60 * 78 = 42x +1

169 = 42x+1

168=42x

x=4

5.

Similarly  

18/30 =  (x+19)/55

18/30  * 55 = x+19

33= x+19

x=14

6.   Now.....do you think you can do this one?

OK.....another way...

AFTER you get to

-2x^2 +12x -8                arrange into vertex form  y=a(x-h)^2 +k    the vertex is h,k

-2{ x^2 -6x +4}

-2{(x-3)^2 +4 -9}

-2 {(x-3)^2 -5}

-2 (x-3)^2 +10             so  h,k is the vertex   =   3,10

There MIGHT (probably) be an easier way, but here is ONE way:

(x+(-3-sqrt5))(x+(-3+sqrt5))   is given in the question for the roots

   if you multiply these two term out you will get

x^2-6x+4    now multiply by -2

-2x^2 +12x-8 =0     (a parabola)

to find vertex take derivative and set equal to zero

-4x+12 = 0     x = 3    substitue this into the equation

        to get      y=10     for the vertex    3,10

(100)^1/4  / 2 sqrt(5)

(10^2)^1/4 / 2 sqrt5

10^2/4  / 2 sqrt 5

sqrt 10  / 2 sqrt 5

sqrt (5) sqrt (2) / 2 sqrt5

sqrt(2) / 2

.707

Is THIS what you mean...or can you provide a sample of what you are asking?

7   expan  

     contra

    expan

   contra

8   -5 -2 = -7     1/2 of -7 is -3.5      -5 -(-3.5) = -1.5 = x

     3-(-2) = 5    1/2 of 5 is 2.5      3-2.5  = .5   = y

9 3-10 = -7    divided by 5   (3:2 ratio....3+2=5)    -7/5  x 3 =  -  21/5      3-(-21/5) = 36/5 =x

    2-12 = -10   divided by 5  = -2                           -2     x 3 = -6              2-(-6) = 8  = y

(there is ANOTHER point which will divide this line 3:2 ratio...can you find it?)

10  similar to 9

The degree is the highest power of the exponents with nonzero coefficients.

This polynomial has a degree of 7   (a^7)

Note that if it had   a^7b^4   as a term it would be a 11th degree polynomial (7+4)   

OOps.....you left the scale factor off of this question too !

Since you only have ONE equation with TWO unknowns , the possible answers are infinite.

scale factor of what?