James and Bethany Morrison are celebrating their 10th anniversary by having a reception at a local reception hall. They have budgeted $3500 for the reception. If the reception hall charges a $50 cleanup fee plus $34 per person find the greatest number of people that they may invite and still have within their budget.

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Step-by-step explanation:

Create the equation:

$34 times the number of people plus the $50 cleaning fee has to be less than or equal to $3500

Or

34p + 50 <= 3500

34p <= 3450

p <= 101.470588

We can have a part of a person attending the reception so we have to drop the remainder/decimal. Therefore the most amount of people that can attend the party and stay within budget is 101.

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°