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:
A.) 1/49
B.) 1/512
Step-by-step explanation:
Answer:
- zeros are {-2, 3, 7} as verified by graphing
- end behavior: f(x) tends toward infinity with the same sign as x
Step-by-step explanation:
A graphing calculator makes finding or verifying the zeros of a polynomial function as simple as typing the function into the input box.
<h3>Zeros</h3>
The attachment shows the function zeros to be x ∈ {-2, 3, 7}, as required.
<h3>End behavior</h3>
The leading coefficient of this odd-degree polynomial is positive, so the value of f(x) tends toward infinity of the same sign as x when the magnitude of x tends toward infinity.
- x → -∞; f(x) → -∞
- x → ∞; f(x) → ∞
__
<em>Additional comment</em>
The function is entered in the graphing calculator input box in "Horner form," which is also a convenient form for hand-evaluation of the function.
We know the x^2 coefficient is the opposite of the sum of the zeros:
-(7 +(-2) +3) = -8 . . . . x^2 coefficient
And we know the constant is the opposite of the product of the zeros:
-(7)(-2)(3) = 42 . . . . . constant
These checks lend further confidence that the zeros are those given.
(The constant is the opposite of the product of zeros only for odd-degree polynomials. For even-degree polynomials. the constant is the product of zeros.)
We are given original selling price of book = $b.
Price is marked down by 46%.
46% can be written as 46/100 in decimals it would be 0.46.
Therefore, markdown as a decimal is 0.46
Now, markdown is 0.46 of original price = 0.46b
Therefore, new price after marked down can be written by expression =
b - 0.46b = 0.56b.
<h3>Therefore, the expression for the sale price of the hardcover book is 0.56b.</h3>
If original retail price was = $29.00.
The sale price would be 0.56b = 29*0.56 = $15.66.
Total saving = 29-15.66 = $13.34.
Therefore, you save $13.34 by paying the sale price $15.66.
<span>y = -1/2x +2 1/2</span>
General equation;
y = mx + c
Calculating the slope;
Change in y/ (change in x) = gradient m
(2-1)/(1-3) = - 1/2
Replacing m gives;
y= -1/2x + c
Calculating the value of c
take point (1,2) above and replace y with 2 and x with 1
2=-1/2 *1 +c
c = 2 1/2
Equation then is
y = -1/2x +2 1/2
