Vivian is going to do some yard work, but she needs to leave her house at 1: 00 to go to a football game. she is going to mow the lawn for 1 hour and 10 minutes, trim some bushes for 30 minutes, and put down some mulch for 35 minutes. she will also need 20 minutes to shower and get dressed. what time should she start the work so she will be ready at 1: 00?

Vivian should start working by 10.25 am.

Step-by-step explanation:

Time taken to mow the lawn = 1 hour and 10 minutes

Time to trim bushes = 30 minutes

Time for putting down mulch = 35 minutes

Time to get dressed = 20 minutes.

Total time = 1 hour + (10+30+35+20) minutes

= 1 hour + 95 minutes

= 1 hour + (60+35) minutes

= 1 hour + 1 hour + 35 minutes

= 2 hours 35 minutes.

This means Vivian should start working 2 hours 35 minutes before 1:00 pm.

So, it becomes ; 10:25 am.

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°

for this case we must apply distributive property to the following expression:

the distributive property states that:

then, when applying the property we have to multiply the -2 for each term within the parenthesis: