Vera's piggy bank contained $10.90 in quarters, dimes, and nickels. There were six more than two times as many nickels as quarters and four less than two times as many dimes as quarters.
Create an equation to represent the situation.

Step-by-step explanation:

We have to convert everything to the same value. For example, 8$ would be 8 cents. And 1 Nickle would be 5 cents.

n = number of nickles

d = the number of dimes

q = number of quarters

1 nickle = 5 cents

1 dime = 10 cents

1 quarter = 25 cents

Step 1: Convert the total amount from dollars to cents.

There were $10.90 in total. Since there are 100 Cents in 1 Dollar, there would be 1090 cents in 10.90 dollars. (Tip you can easily find how many cents there are in dollars if you simply remove the decimal ".")

We are converting this because we need to have every value in the same term.

Step 2: Convert all of the amounts to cents.

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°