h(x)= 4/x-5 What is the domain of h? A: All real values of x such that x ≠ 4 B:All real values of x such that x ≥ 4 C: All real values of x such that x ≠5 D: All real values of x such that x ≤ 5 E: All real values of x

C. All real values of x such that x ≠ 5

Step-by-step explanation:

Given

h(x) = 4/(x - 5)

Required

Determine the domain of the function

To get the domain of the function, we start by writing out the denominator in the following format:

x - 5 ≠ 0

Add 5 to both sides

x - 5 + 5 ≠ 0 + 5

x ≠ 5

The domain can be written in builder notation as follows

x = { x ∈ R: x≠ 5}

The above expression implies that the domain of the function is all real values of x but x ≠ 5

From the list of options, the correct answer is C.

Expression gives the perimeter = 4x√17

Step-by-step explanation:

∵ The diagonals of the rhombus ⊥ to each other and

  bisects each other

∴ Half the longest diagonal = 8x/2 = 4x

∴ Half the shortest diagonal = 2x/2 = x

Use Pythagoras theorem to find the length of the side of the rhombus

∴ The length of the side = √[(4x)² + (x)²] = √[16x² + x²] = √(17x²)

∴ S = x√17

∵ Perimeter of the rhombus = 4 × S

∴ P = 4 × x√17 = 4x√17