CPhill

0   isn't positive

[ 8(a) + b ] + 5[ a + b]  =  13a + 6b

13a + 6b  =  8b + a

12a = 2b

6a = b

a  cannot be an integer > 1   because this would make b at least 12....which is impossible in base 8

So...

a = 1        and b = 6

Proof

16₈  + 5 [ 1 + 6]   =  [  (1)*8  + 6]  + 5*7   =  [ 14 ] + 35  =  49

And

61₈   =  6(8) + 1   =  49

So

N  =  16₈

OK.....

I think you might have

y = -4x^2 + 22x + 12

In the form     Ax^2 + Bx + C.....the x coordinate of vertex is given by  -B / [2A]

So...here the x coordinate of the vertex is  -22/ {2 * - 4)  =  -22/-8  =  11/4  = 2.75

And to find the y coordinate we have   -4(11/4)^2 + 22(11/4) + 12   = 42.25

So....the vertex is (2.75, 42.25 )

y intercept.....let x = 0   and we have   -4(0)^2 + 22(0) + 12  =    12

x  intercept ......let y = 0  and solve for x

0 = - 4x^2 + 22x + 12      divide through by - 2

0 = 2x^2 - 11x - 6       factor

(2x + 1 ) ( x -6)  = 0      set  each factor to 0 and solve for x  and we have  x = -1/2  and x = 6

And those are the x intercepts

The axis of symmetry  is just    x =  the x cooordinate of the vertex =  2.75

We have the angle bisector theorem .......we have that

45 /50  = z / 20

9/10 = z / 20       multiply both sides by 20

20 * (9/10) = z

(20/10) * 9  = z

2 * 9 = z

18 = z

(2a)

We have that   triangle ADC  is similar to triangle  CDB

Thus   AD /DC = DC/ BD

or

y / h  =  h / x    cross-multiply

xy = h^2

(2b )   angle A = angle C

        angle D = angle D

So....by AA congruency.....triangle ADC  is similar to triangle CDB

Since the y coordinates are the same.....the length  is just  absolute value difference of the x  coordinates =   l - 4 - 1 l =

l - 5 l    =  5 units

No, Nickolas....I just figured it out from the info given....

Can you not upload pics  ????

Surface area of the base  = (2)^2 =  4in^2

Area of each triangle =  (1/2) (side length of base)(height) = (1/2) (2)(5) = 5in^2

So...surface area =   base area +  area of 4 triangles =  4 + 4(5)  =  24 in ^2

f(x) = 2x^2 +3x and g(x) = 5x^2 -2x-6 

(f + g) (x)  means   f(x) + g(x)  =  [ 2x^2 + 3x ] + [ 5x^2 - 2x - 6 ]  =  7x^2 + x - 6