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:
Well, It is but not because..rotation symmetry, and a square has -turn (or 90-degree) rotation symmetry. As you may have already observed, many figures have 180-degree rotation symmetry but no other rotation symmetry. A figure has 180-degree rotation symmetry if it looks the same when turned halfway around...Soo yeah..I think I am right, So sorry if I'm wrong.
Step-by-step explanation:
Answer and Step-by-step explanation:
To solve for r, we need to get everything away from r. We can start off by moving five thirds, and pi.
Multiply each side by 
, then divide by 
(pi)
Now, take the cubed root of both sides.
![\sqrt[3]{\frac{3x}{5\pi } } = r](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B%5Cfrac%7B3x%7D%7B5%5Cpi%20%7D%20%7D%20%20%3D%20r)
^^ That is the answer.
<em><u>#teamtrees #PAW (Plant And Water)</u></em>
Answer:
The income that she will have left over after paying his
federal income tax = $63,775.
Step-by-step explanation:
- The amount of taxable income = $79,950
- So, the taxable income will be in the range from $33,950 to $82,250.
- It means, there will be $4675 fixed tax and additional 25% tax on the amount over $33,950.
As
The amount over $33,950 = $79,950 - $33,950 = $46,000
So
The additional tax = 46000 × 0.25 = $11,500 ∵25% = 0.25
So, the total federal income tax will be: $11500 + $4675 = $16,175
Therefore, the income that she will have left over after paying his federal income tax = $79,950 - $16,175 = $63,775.
Keywords: income, income tax
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