The Standard form of the equation of circle is (x+21)² + (y+19)² = 849
<h3>What is Standard form of circle?</h3>
To transform general form to a standard form, you can use completing the square method or you can convert this equation
x² + y² + Dx + Ey + F = 0 to x² + y² + (-2h)x + (-2k)y + (h²+k²-r²) = 0
Here, Given: x² + y² + 42x + 38y − 47 = 0
Required: Find the values of h, k, and r using this formula
x² + y² + (-2h)x + (-2k)y + (h²+k²-r²) = 0
On comparing we get,
-2h = 42
h = 21
-2k = 38
k = 19
-47 = h² + k² - r²
-47 = 21² + 19² - r²
r² = 849
r = √849
Thus, the Standard form of the equation of circle is (x+21)² + (y+19)² = 849
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Answer:
The multiplicative rate of change is 3/4
Step-by-step explanation:
Here, we want to get the multiplicative rate of change
In this case, by dividing the succeeding term by the preceding term, we will get the multiplicative rate of change
mathematically, we have this as;
81/128 divided 27/32
= 81/128 * 32/27
= 3/4
Answer: 
Step-by-step explanation:
For this exercise it is important to know the definition of "Dilation".
A Dilation is defined as a transformation in which the Image (The figure obtained after the transformation) and the Pre-Image (The original figure before the transformation) have the same shape but have different sizes.
If the Dilation is centered at the origin, and knowing the scale factor of 
, you need to multiply each coordinate of the point T by the scale factor in order to find the coordinates of the Image T'.
Knowing that the point T has the following coordinates:
You get that the coordinates of the Image T' are the shown below:
Answer:
4.7 :)
Step-by-step explanation:
Answer:
It is a worthwhile investment for both one year and for the long term.
Step-by-step explanation:
While the investment will obtain in the first half of the year gains of 30%, and in the second half of the year losses by 20%, at the end of the year the benefit obtained by the investment will be greater than 0%. Therefore, both within a year and in the long term, it is a viable and favorable investment, since it will yield positive results at the end of the cycle.
So, for example, an initial investment of $ 100 would operate in the following way:
-First half of the year: 100 x 1.3 = 130
-Second half of the year: 130 - (130 x 0.2) = 104
Thus, at the end of the year a profit of 4% of the initial investment will be obtained.
