Find the domain for the function f(x) = the quotient of the square root of the quantity x minus 3 and the quantity x minus 5.

The domain is (-∞, 3] and (5, ∞)

Step-by-step explanation:

The given function is

In order to find the domain, the denominator cannot be zero and quotient must not be a negative number.

Here the denominator is x - 5

Which must be greater than zero.

x - 5 > 0

x > 5

The numerator must be less than or equal to 0.

x - 3 ≤ 0

x ≤ 3

Therefore, the domain is (-∞, 3] and (5, ∞)

answer: hey there,

the answer you are looking for is a..

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m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°