A. vertical angles are congruent
b. alternate interior angles are congruent
c. if alternate interior angles are congruent, lines are parallel <span />
Hence, the correct answer is: C) (x - 6)^2 = 45
Further explanation:
Given equation is:

We will move the constant term on other side of the equation

To complete the square, we will take the coefficient of x and divide it by 2, as we already know that one term is x.

So, adding (6)^2 on both sides

Hence, the correct answer is: C) (x - 6)^2 = 45
Keywords: Quadratic Equation, Solution of equation
Learn more about quadratic equation at:
#LearnwithBrainly
3)The original rational number was 17/12.
4)The age of Ruby and Reshma are 20 and 28 years respectively.
Explanation:
3)Let the numerator be x.
So denominator will be (x - 5)
If we add 5 to numberator then it will be (x + 5)
New number is (x + 5)/(x - 5)=11/6
Solve for X by cross multiplying
6(x + 5)=11(x - 5)
6x + 30=11x - 55
5x=85
x=17
So original rational number was 17/12.
4)The ages of Ruby and Reshma are in the ratio 5:7
So, let the present ages of Ruby and Reshma be 5x and 7x respectively.
Also, it is given that four years from now the ratio of their ages will be 3:4
So, the equation - 5x + 4 / 7x + 3 = 3/4
⇒4(5x+4)=3(7x+4)
⇒20x+16=21x+12
⇒21x−20x=16−12
⇒x=4
⇒5x=20 and 7x=28
The age of Ruby and Reshma are 20 and 28 years respectively.
Answer:
h = 19.6 ft
Step-by-step explanation:
Given that,
A 20 ft ladder 4ft from the base of the wall.
The height of the ladder, H = 20 ft
The base distance, b = 4 ft
We need to find the height of the reach. Let it is P.
Using Pythagoras theorem,

or
P = 19.6 ft
So, the height is 19.6 ft.