Mandy went rock climbing at the climbing gym for 2 1/2 hours on Thursday. On Saturday, she went to Castle Rock State Park and climbed for 1 1/2 times as long. How much time did she spend rock climbing in all?

6 1/4 hours

Step-by-step explanation:

For Mandy,

On Thursday at the climbing gym ,she spent = 2 1/2 hours rock climbing

= 5/2 hours rock climbing

On Saturday, she went to Castle Rock State Park and climbed for 1 1/2 times as long

= 3/2 times as long as she did at the climbing gym

= 3/2 × (5/2 hours)

= 15/4 hours

The time she spent rock climbing in all is calculated as:

= 5/2 hours + 15/4 hours

Find L.C.M = 4

= (2×5) + (15 × 1)/ 4

= 10 + 15/4

= 25/4 hours

= 6 1/4 hours.

Therefore, she spent 6 1/4 hours rock climbing.

22 and 22

step-by-step explanation:

10 plus 12 equals 22.

12 plus 10 also equals 22 because regardless of what order they're in, they're gonna equal the same thing.

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°