Answer:
Step-by-step explanation:
x² + 2x - 3 + y² = 5
Strategy:
Convert the equation to the centre-radius form:
(x - h)² + (y - k)² = r²
The centre of the circle is at (h, k) and the radius is r
.
Solution:
Move the number to the right-hand side.
x² + 2x + y² = 8
Complete the square for x
(Take half the coefficient of x, square it, and add to each side of the equation)
(x² + 2x + 1) + y² = 9
Complete the square for y
The coefficient of y is zero.
(x² + 2x + 1) + y² = 9
Express the result as the sum of squares
(x + 1)² + y² = 3²
h = -1; k = 0; r = 3
The centre of the circle is at 
The graph of the circle below has its centre at (-1,0) and radius 3.
Answer:
51x
Step-by-step explanation:
3x^3 - 7x + 3x^3 + 4x
27x - 7x + 27x + 4x
20x + 31x
51x
Answer:
322.24 meters
Step-by-step explanation:
The scale is 4 meter per centimeter. Multiply 5.3 by 4 to get 21.2 meters. Multiply 5.3 by 4 to get 15.2 meters. Multiply 21.2 by 15.2 to get 322.24
Answer:
Dilation followed by Translation.
Step-by-step explanation:
We have the function 
.
The new transformed function is 
Now, the transformation applied to f(x) to obtain g(x) are:
1. Dilation - it is the transformation that changes the size/shape of the figure. It is generally of the form kf(x) where k is constant.
Since, we are dilating the given function by 2 units, the new dilated function becomes 
.
2. Translation - it is the transformation that shifts the figure in any direction. When the function is shifted vertically, the general form becomes f(x)+k.
As, we see that the new dilated function is shifted 3 units upwards, the final translated function becomes .
Hence, the transformations applied to obtain g(x) from f(x) are Dilation followed by Translation.
