Vanessa draws one side of equilateral ΔABC on the coordinate plane at points A(–2, 1) and B(4,1). What are the possible coordina
1 answer:
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Answer:
3,750 cars.
Step-by-step explanation:
We are given that the equation:
Models the relationsip between <em>y</em>, the number of unfilled seats in the stadium, and <em>x</em>, the number of cars in the parking lot.
We want to determine the number of cars in the parking lot when there are no unfilled seats in the stadium.
When there are no unfilled seats in the stadium, <em>y</em> = 0. Thus:
Solve for <em>x</em>. Subtract 9000 from both sides:
Divide both sides by -2.4:
So, there will be 3,750 cars in the parking lot when there are no unfilled seats in the stadium.
Answer:
Step-by-step explanation:
The directrix of the parabola is the horizontal line with the eqaution The focus of the parabola is at point (-4,10), than the axis of symmetry of the parabola is the perpendicular line to the directrix passing through the focus. Its equation is
The distance between the directrix and the focus is so
and the vertex is at point
Parabola goes in positive y-direction, hence its equation is
where is the vertex, so the equation of this parabola is
Answer:
{-1, 1/2, 2/3, 1}
Step-by-step explanation:
I find a graphing calculator to be a most useful tool for problems like this. (See attached.)
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First of all, observe that the constant is -2, so 0 is not a zero.
It is often useful to look at the sum of coefficients. Here, that is 0, indicating 1 is a zero.
You can divide that out, or simply continue by looking at the sum of coefficients with odd-degree terms negated. Then you have 6 +7 -4 -7 -2 = 0, indicating -1 is also a zero.
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At this point, it can be useful to divide out the factors you know. The synthetic division tableaus attached show that work. First is division by (x+1), then by (x -1).
The result of doing that is the quadratic ...
6x^2 -7x +2 = 0
This can be factored ...
(6x^2 -3x) -(4x -2) = 0 . . . . . . rewrite -7x and group term pairs
3x(2x -1) -2(2x -1) = 0 . . . . . . . factor each pair
(3x -2)(2x -1) = 0 . . . . . . the factorization of the remaining quadratic
The zeros of this are the values of x that make the factors zero: 2/3 and 1/2.
The zeros of the given function f(x) are x ∈ {-1, 1/2, 2/3, 1}.
