As the earth rotates, it travels a distance of 80 miles in 5 minutes. At this constant rate, which equation best represents y, the total distance the earth travels in x minutes?

y=16x

Step-by-step explanation:

So, you are given the equation as if y=total distance the earth travels in x minutes. If you are given that you travel 80 miles in 5 minutes, you can plug  these value into the variables they are representing and solve for the constant.

Visual:

y=xk          y=miles        x=minutes         k=constant

Plug in your values and you get:

80=5k

Now, you solve for k by diving 5 on both sides, which leaves you with k=16.

Now you plug your value for k into the original equation, leaving you with y=16x

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°

sine

step-by-step explanation: