Q - 6 = √(27 - 2q)
----------------------- each side squared by two
(q - 6)² = 27 - 2q
q² - 6q - 6q + 36 = 27 - 2q
q² - 12q + 36 = 27 - 2q
------------------------ move all terms to the left side
q² - 12q + 2q + 36 - 27 = 0
q² - 10q + 9 = 0
------------------------ factorize
(q - 9)(q - 1) = 0
q = 9 or q = 1
The solution is
q = 9
or
q = 1
Answer:
Andy is 4 years old.
Step-by-step explanation:
Given:
Ruth age = 10
We need to find Andy age.
Let the age of Andy be x.
Also given Andy is two-fifths of Ruth's age.
Expressing the above statement in expression form we get
Hence Andy is 4 years old.
1. As x approaches 1, f(x) approaches 3-1, that is 2.
If a = 2 and b = 3, f(1) = 2(1)^2 + 3(1) = 5
So there is a 'jump' in values of x at x = 1. So its not continuous at x=1.
2. For continuity at x = 1, ax^2 + bx must = 2 that is when a + b = 2.
3. for continuity at x = 2 , ax^2 + bx must be = 0 that is when a*2^2 + 2b = 0
- that is 4a + 2b = 0.
4. we have system of equations:-
a + b = 2
4a + 2b = 0
this gives a = -2 and b = 4 So f(x) is continuous when a = -2 and b = 4.
Answer:
A. Cos θ = 16/42
Step-by-step explanation:
The angle the ladder makes with the floor = θ
Hypotenuse = length of the ladder = 42 m
Adjacent = Distance from the bottom of the ladder to the wall = 16 m
Therefore to find θ, we would apply the trigonometric function, CAH:
Cos θ = adj/hyp
Which is:
Cos θ = 16/42
