I WILL GIVE BRAINIEST Go to your math tools and open the Graph tool to graph Gwen’s and Keith’s equations. Be sure to remove Tristan’s equation before adding Keith’s equation.

Do the two lines intersect? Why or why not? What does this mean in terms of the situation? If they intersect, at what point do they intersect and what does this point mean in terms of the situation?

gwen’s: y = 100 + 10x

keith's: y = 10x

Gwen, Tristan, and Keith like to work out at the gym. They each have an app on their phone that estimates the calories they burn. By the time Tristan and Keith started exercising, Gwen had already burned 100 calories. Gwen burns 10 calories every minute, Tristan burns 125 every 10 minutes, and Keith burns 300 calories every 30 minutes. Let x represent the number of minutes since Tristan and Keith started exercising and y represent the number of app-estimated calories burned.

y = Ax + B

Gwen has already burned 100 calories at time x = 0 so the y intercept is 100

Gwen burns 10 calories / minute so the slope is 10 cal/min

y = 10x + 100

Keith has burned no calories at x = 0 so y intercept is 0

Keith burns (300 / 30) = 10 calories / min so the slope is 10 cal/min

y = 10x + 0

The lines do NOT intersect as the both have the same slope (10 cal/min).

It means that Gwen will have burnt 100 more calories than Keith if they stop at the same time, or Keith will have to work out 10 minutes after Gwen stops to burn as many calories as she did. Or they can both work towards their OWN goals rather than someone else's goal and quit when they're satisfied.

Step-by-step explanation:

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°