Answer:
Step-by-step explanation:
The parent function here is y = x^2, whose graph is that of a parabola that opens up and has its vertex at the origin, (0, 0).
Translating this parent graph 3 units to the right and then up by 2 units will produce the desired graph of y = f(x) = (x - 3)^2 + 2.
There are no stretches or symmetry.
y-intercept: let x = 0 and find y: 9 + 2 = 11. y-intercept is (0, 11).
x-intercept: let y = 0 and find x: (x - 3)^2 + 2 = 0 => (x - 3)^2 = -2. This has no real roots. Thus, there are no x-intercepts.
Answer:
the answer is two because the absolute value delete the negative in result not in question
Answer:
A(t) = 27.86 in²
Dimensions of the paper:
L = 3.73 in
w = 7.47 in
Step-by-step explanation:
The total area of a rectangular page A = ( x + 2)* (y + 4 ) x is the length and y the wide. x and y are the dimensions of the print area
The print area of the paper is A = 6 in² 6 = x*y y = 6/x
Then print area as a function of x is
A(x) = ( x + 2 ) * ( 6/x + 4 ) ⇒ A(x) = 6 + 4*x + 12/x + 8
Taking derivatives on both sides of the equation:
A´(x) = 4 - 12/x² A´(x) = 0 4 = 12 /x²
x² = 12/4 x =√3 x = 1.73 in and y = 6 / 1.73
y = 3.47 in
Then the dimensions of the paper are.
Length L = x + 2 = 3.73 in and w = 3.47 + 4 = 7.47 in
And the least amount of paper is
A(t) = 3.73* 7.47 = 27.86 in²
To find out if x = 1.73 is an x coordinate for a minimum we get the second derivative
A´´(x) = 24/x³ is always positive A´´(x) > 0 then we have a minimum for A at x = 1.73
Answer:
40
Step-by-step explanation:
11x+13=90
11x=77
x=7
49-9=40
