Answer:
The dog's running area is approximately 942 feet².
Step-by-step explanation:
The dog is leashed to a fixed point, the leash has a length of 20 ft, therefore he can rotate around that point at the maximum distance equal to the length of the leash. This pattern forms a circle, but there is an obstruction, which is the corner of the house. This obstruction takes an arc of the original circle, so the running area of the dog is the area of the whole circle minus the area of the arc formed by the corner of the house.
The dog's running area is approximately 942 feet².
Answer:
y = (x - 4)² - 25
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
To obtain this form use the method of completing the square.
Given
y = (x + 1)(x - 9) ← expand factors using FOIL, thus
y = x² - 8x - 9
To complete the square
add/subtract ( half the coefficient of the x- term )² to x² - 8x
y = x² + 2(- 4)x + 16 - 16 - 9
= (x - 4)² - 25 ← in vertex form
a) The formula for compound interest is:
Total = starting amount x (1 + interest rate)^ number of years
b)
Using the given information you have:
1200 = 500 x (1+0.045)^x where x is the length of time you want to find.
1200 = 500 (1.045)^x
Divide both sides by 500:
2.4 = 1.045^x
Use natural logarithms:
ln(1.045^x) = ln(2.4)
Solve for x:
X = ln(2.4) / ln(1.045)
X = 19.889 years ( Round the answer as needed).
When at least one of the factors still has a common factor
Answer:
I think the answer is Option D, 135 degrees.
Since the angles of all of the octagon combined is 1080, divide that by 8 to get 135 which means that all 8 angles are 135 degrees.
