Answer:
We know that the equation of the circle in standard form is equal to <em>(x-h)² + (y-k)² = r²</em> where (h,k) is the center of the circle and r is the radius of the circle.
We have x² + y² + 8x + 22y + 37 = 0, let's get to the standard form :
1 - We first group terms with the same variable :
(x²+8x) + (y²+22y) + 37 = 0
2 - We then move the constant to the opposite side of the equation (don't forget to change the sign !)
(x²+8x) + (y²+22y) = - 37
3 - Do you recall the quadratic identities ? (a+b)² = a² + 2ab + b². Now that's what we are trying to find. We call this process <u><em>"completing the square"</em></u>.
x²+8x = (x²+8x + 4²) - 4² = (x+4)² - 4²
y²+22y = (y²+22y+11²)-11² = (y+11)²-11²
4 - We plug the new values inside our equation :
(x+4)² - 4² + (y+22)² - 11² = -37
(x+4)² + (y+22)² = -37+4²+11²
(x+4)²+(y+22)² = 100
5 - We re-write in standard form :
(x-(-4)²)² + (y - (-22))² = 10²
And now it is easy to identify h and k, h = -4 and k = - 22 and the radius r equal 10. You can now complete the sentence :)
Answer: The total percentage loss would be 67%.
Step-by-step explanation:
Since we have given that
Rate of decline each year = 20%
Number of years = 5
We need to find the total percentage loss in value of the house at the end of 5 years.
So, Total percentage loss would be
Hence, the total percentage loss would be 67%.
slope intercept formula is y = mx + b.
Isolate the y. Note the equal sign. What you do to one side, you do to the other. Do the opposite of PEMDAS. First, subtract 2x from both sides
2x (-2x) + 3y = (-2x) + 1470
3y = -2x + 1470
Isolate the y. Divide 3 from both sides
(3y)/3 = (-2x + 1470)/3
y = (-2x + 1470)/3
Simplify
y = (-2/3)x + 490
y = (-2/3)x + 490 is your answer
hope this helps
Step-by-step explanation:
The area of the triangular base is: 19
square units
How to calculate the base area
The given parameters are:
Volume = 27.36 cubic units
Height = 2.88 unit
The volume of a triangular prism is:
V = 0.5 * B *h
Where B represents the base area.
So, we have:
27.36 = 0.5 * B * 2.88
27.36 B * 1.44 -
Solve for B
B = 19
Hence, the area of the triangular base is: 19 square units
Answer:=c
Step-by-step explanation:
