Tavon has a gift card for $110 that loses $2.50 for each​ 30-day period it is not used. He has another gift card for $90 that loses $2 for each​ 30-day period it is not used. a. Write and solve an equation for the number of​ 30-day periods until the value of the gift cards will be equal.
b. What will the value of each card be when they have equal​ value?

30 day period

The first equation is 50 - 2x (because you start with $50 and subtract 2 for each 30 day period)

The second equation is 40-1.5x

Set them equal to each other:  50 - 2x = 40 - 1.5x

Solve for x:

50 - 2x = 40 - 1.5

  +2x   +2x

50 = 40 + 0.5 x

-40   -40

10 = 0.5 x

20 = x

So there will be 20 30-day periods until the cards will be equal in value.

Check:  After 20 periods, 50 - 2(20) = $10 left

40 - 1.5(20) = also $10 left

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°