The length of an australian flag is twice its width and the diagonal length is 45cm.
a. if x cm is the width of the flag, find the length in terms of x.
b. draw a diagram of the flag marking in the diagonal. mark the length and the width in terms of x.
c. use pythagoras’ theorem to write an equation relating the lengths of the sides to the length of the diagonal.
d. solve the equation to find the dimensions of the australian flag. around your answer to the nearest cm.

7

step-by-step explanation:

you ignore the remainder, therefore the answer is y = x+2

step-by-step explanation:

you have to divide the denominator by the numerator. you can use synthetic division or long division.

[-5] .     1 .     7 .     11

x + 2 + 1/x+5

let's call the solutions x₁ = (5 - 2√7)/3 and x₂ = (5 + 2√7)/3

then the equation is (x-x₁)(x-x₂) = 0

if you fill that in you get a lot of numbers which you can recognize as ax²+bx+c=0.

step-by-step explanation:

you can see that a=1 (there is just an x²)

b = (-5 -2√7 + 2√7 - 5)/3 = -10/3

c = -2√7)/3 ) * (-5+2√7)/3) = -1/3

so your answer is 3x^2 – 10x – 1 = 0