Answer:
Initially, you have 2573 pieces.
You use 5 pieces each minute.
Right when you start, you have 2573 pieces.
One minute after that, you have 2573 - 5 pieces.
Another minute after, you have 2573 - 2*5 pieces.
Another minute after, you have 2573 - 3*5 pieces.
And so on.
You can see the pattern here, and with this, we can find the linear equation that represents the number of pieces that you have as a function of time.
Then, if the variable t represents the number of minutes that passed since you started, we can write the equation:
f(t) = 2573 - 5*t
That represents the number of pieces that you have after t minutes.
After you cut off 6 pieces, the rope is 18.25 inches long
Answer: 70 degrees 35 times 2
Answer:
See below.
Step-by-step explanation:
f(x) = -25x2 + 30x − 9
This is a parabola which opens downwards.
Part A.
The discriminant b^2 - 4ac = 30^2 - 4*(-25) * -9
= 900 - 900
= 0
This indicates that the graph of the function just touches the x-axis. So there is one root of multiplicity 2.
Factoring:
-25x2 + 30x − 9
= -(25x^2 - 30x + 9)
= -(5x - 3)(5x - 3)
so the roots are x = 3/5 multiplicity 2.
The x -intercept is at (0.6, 0).
Part B.
The y intercept is when x = 0 so here it is
y = -25(0)^2 + 30(0) -9
= -9
The constant at the end of the function (-9) indicates the y-intercept.
The y intercept is at (0, -9).
Part C.
The end behaviour of f(x):
The negative coefficient (-25) of x^2 indicates that the graph increases from negative infinity from the left.
Since it is a parabola that opens downwards ( because of the -25) it decreases to negative infinity on the right.
Answer:
x = -1, 3.
Step-by-step explanation:
x2 - 2x = 3
Completing the square:
We use the identity: a^2 - bx = (a - b/2)^2 - (b/2)^2:
(x - 1)^2 - 1^2 = 3
(x - 1)^2 = 3 + 1
(x - 1)^2 = 4
Taking square roots of both sides
x - 1 = +/- 2
x = 2 + 1 , -2 + 1
x = -1, 3.
