Question 9. Factor x^2 - 6x + 9.
A
(x - 3)
B
(x - 3)(x + 3)
C
(x - 3)^2
D
9x + 3)^2

C

Step-by-step explanation:

Given

x² - 6x + 9

Consider the factors of the constant term (+ 9) which sum to give the coefficient of the x- term (- 6)

The factors are - 3 and - 3, since

- 3 × - 3 = + 9 and - 3 - 3 = - 6, thus

x² - 6x + 9 = (x - 3)(x - 3) = (x - 3)² → C

a²-2*a*b+b²=(a-b)²

x²-6x+9=x²-2*x*3+3²=(x-3)²  C)

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places

70 years.

step-by-step explanation: