The value of y varies jointly with the values of x and z When x = 4 and z = 10, the value of y is 360. What is the value of y when x 5 and z = 12?
A. 540
B. 9
C. 153
D. 450

A

Step-by-step explanation:

Joint variation is given by:

Where k is some constant.

We are given that y = 360 when x = 4 and z = 10. Therefore:

Solving for k:

Therefore, our equation is:

Then when x = 5 and z = 12:

The answer is A.

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°

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