Answer:
1st option
Step-by-step explanation:
The 2 angles are alternate exterior angles and are congruent , so
3x = 2x + 20 ( subtract 2x from both sides )
x = 20
Answer:
55°
Step-by-step explanation:
The angle 305° is in the fourth quadrant
To find the related acute angle ( the reference angle ) subtract from 360°
reference angle = 360° - 305° = 55°
Applying the formula for the area of a sector and length of an arc, the value of k is calculated as: 27.
<h3>What is the Area of a Sector?</h3>
Area of a sector of a circle = ∅/360 × πr²
<h3>What is the Length of an Arc?</h3>
Length of arc = ∅/360 × 2πr
Given the following:
- Radius (r) = 9 cm
- Length of arc = 6π cm
- Area of sector = kπ cm²
Find ∅ of the sector using the formula for length of acr:
∅/360 × 2πr = 6π
Plug in the value of r
∅/360 × 2π(9) = 6π
∅/360 × 18π = 6π
Divide both sides by 18π
∅/360 = 6π/18π
∅/360 = 1/3
Multiply both sides by 360
∅ = 1/3 × 360
∅ = 120°
Find the area of the sector:
Area = ∅/360 × πr² = 120/360 × π(9²)
Area = 1/3 × π81
Area = 27π
Therefore, the value of k is 27.
Learn more about area of sector on:
brainly.com/question/22972014
Before we start answering the question, let's define the compound interest formula:
Where:
<span>'A'</span> is the amount of money in dollars
'P' is the principal amount of money in dollars
'r' is the interest rate (decimal)
'n' is the number of times interest is compounded per year
't' is the time in years
<span>
(A) Find Principal Amount</span><u /><span><u>Given:</u>
</span>A = 12,000
P = ?
r = 0.08
n = 2 (semiannually)
t = 5
Now we plug our values in and solve:



∴ You would have to deposit $8106.77 in order to have $12,000 in 5 years from now.
(B) Find Principal AmountSame given values as above, with the exception of 't' which is now 10 instead of 5.



∴ You would have to deposit $5476.64 in order to have $12,000 in 10 years from now.
Hope this helps!