Answer:
x = - 5
Step-by-step explanation:
Given
f(x) = 
The denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the value that x cannot be.
solve : 3x + 15 = 0 ⇒ 3x = - 15 ⇒ x = - 5 ← excluded value
Domain x ∈ R , x ≠ - 5
Answer:
A = 120 cm^2
Step-by-step explanation:
The formula for surface area of a rectangular prism is:
A = 2(area of the top) + 2(area of the front) + 2(area of one side)
Substituting the values:
A = 2(20) + 2(16) + 2(24)
First, distributing:
A = 40 + 32 + 48
Then adding, giving your final answer
A = 120 cm^2
Hope this helps you :)
Answer:
Length = 5p + 3
Perimeter = 26p + 6
Step-by-step explanation:
Given
Area = 40p² + 24p
Width = 8p
Solving for the length of deck
Given that the deck is rectangular in shape.
The area will be calculated as thus;
Area = Length * Width
Substitute 40p² + 24p and 8p for Area and Width respectively
The formula becomes
40p² + 24p = Length * 8p
Factorize both sides
p(40p + 24) = Length * 8 * p
Divide both sides by P
40p + 24 = Length * 8
Factorize both sides, again
8(5p + 3) = Length * 8
Multiply both sides by ⅛
⅛ * 8(5p + 3) = Length * 8 * ⅛
5p + 3 = Length
Length = 5p + 3
Solving for the perimeter of the deck
The perimeter of the deck is calculated as thus
Perimeter = 2(Length + Width)
Substitute 5p + 3 and 8p for Length and Width, respectively.
Perimeter = 2(5p + 3 + 8p)
Perimeter = 2(5p + 8p + 3)
Perimeter = 2(13p + 3)
Open bracket
Perimeter = 2 * 13p + 2 * 3
Perimeter = 26p + 6
