6. Jayden does 2 sit-ups on the first day of the month, 4 the next day, 8 the
next day, and so on. If she continues with the pattern, how many total sit-
ups will she have done after 30 days?

I believe Jayden will have done 1,073,741,824 sit-ups after 30 days.

Step-by-step explanation:

Each day of the month Jayden does double the amount of sit-ups as before. The days would add to be 2, 4, 8, 16, 32, 64 134,217,728 for the 27th day, 268,435,456 for the 28th, and then skipping to the 30th day you would get a total of 1,073,741,824 sit-ups.

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°