If you earned up to $113,700 in 2013 from an employer, your social security tax rate was 6.2% of your income. if
you earned over $113,700, you paid a fixed amount of $7,049.40.
a. write a piecewise linear function to represent the 2013 social security taxes for incomes between $0 and
$500,000.

where f(x) is the the social security taxes in dollars and x is the amount earned in 2013

Step-by-step explanation:

The problem states that for the first $113,700 you will pay a tax rate of 6.2% for your income. When taking 6.2% of an amount you can turn the percentage into a decimal number and multiply it by the total income which will be represented by the letter x:

0.062x

for an interval of

this is the first part of the piecewise defined function. For the next part, the problem states tht the social security tax will be a fixed amoun of $7,049.40, so the second part of the piecewise defined function would be just:

7,049.40

for an interval of

according to the specifications of the problem.

So the whole piecewise defined function will be

where f(x) is the the social security taxes in dollars and x is the amount earned in 2013

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°