What are the solutions of the quadratic equation (x – 8)2 – 13(x – 8) + 30 = 0? use u substitution to solve.

x= 18 or x=11

Step-by-step explanation:

Given the equation as

(x-8)² -13(x-8)+30=01

Let x-8 to be substituted by u

So x-8=u2

Use equation 2 in equation 1

(u)² -13(u) +30 =0

u²-13u+30=0factorize

u²-3u-10u+30=0

u(u-3)-10(u-3)=0

(u-10) (u-3) =0find value of u

u-10=0

u=10 or

u-3=0

u=3

Use values of u in equation  2

when u=10

but u=x-8

hence 10=x-8

x=10+8=18

or

when u=3

hence 3=x-8

x=3+8=11

x= 18 or x=11

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)

5/12, or 5: 12

step-by-step explanation: