Tara is shown a picture of a dart board along with some dimensions. She knows that each triangular section in the dartboard is congruent. What is the approximate length of arc x?

The approximated length of arc x is 4 inches ⇒ C

Step-by-step explanation:

That means the diameter of the inner circle is less than the diameter of the outer circle by 4 inches (2 in from each side)

The circumference of the inner circles formed from 20 congruent arcs of length x inches

Now let us find x

The formula of the circumference of a circle is C = π d, where d is the diameter of the circle

∵ The diameter of the inner circle is 24 inches

∴ d = 24

∴ C = 24 π

∵ C = 20 x

- Equate 20 x by 24 π

∴ 20 x = 24 π

- Divide both sides by 20

∴ x = 3.769911184

- Round it to the nearest unit

∴ x ≅ 4

The approximated length of arc x is 4 inches

14 1/8 inches of molding

Step-by-step explanation:

In order to find the solution, we'll have to do 2 fractions subtractions.

To be able to subtract fractions, we have to make sure they are placed in the same denominator.  So, the first thing we'll do is to convert all the numbers in 8th, because that's the greatest denominator.

For the last one, we'll first convert the 2 feet into 24 inches.

Now, we'll subtract each of the two pieces cut from the original molding's length, first the 10 1/4 inches piece

then the 2 feet 1/8 piece

So,  the contractor is left with 14 1/8 inches of molding.