Mathematics, 30.01.2020 01:00 anna8352

The function f(x) = −x2 + 50x − 264 models the profit, in dollars, a yoga studio makes for selling monthly memberships, where x is the number of memberships sold and f(x) is the amount of profit.

part a: determine the vertex. what does this calculation mean in the context of the problem? (5 points)

part b: determine the x-intercepts. what do these values mean in the context of the problem? (5 points)

Answers: 3

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Answer from: shariaharper

The given function is f(x) = -x^2 + 50x - 264

. This is a quadratic function because the degree of the polynomial, the variable with the highest exponent, is 2.

All quadratic functions can be expressed in the form f(x) = ax^2 + bx + c

.
In your equation,
a = -1
b = 50
c = -264

The equation for the x-coordinate vertex of a quadratic function is $x = \frac{-b}{2a}$ .
Applying this to the given function,
$x = \frac{-(50)}{2(-1)} = \frac{50}{2} = 25$ .

Now plug the value of x into f(x) to find f(x) (aka the y-coordinate).
$f(x) = -x^2 + 50x - 264 \\
f(25) = -(25)^2 + 50(25) - 264 \\
f(25) = 361$

The vertex is (25, 361)

Part B
The x-intercept is where the graph crosses the x-axis. Therefore, f(x) (aka the y-coordinate) will be 0. So the x-intercept will be in the form of (x, 0).

To find the x-intercept, set f(x) = 0.
$0 = -x^2 + 50x - 264 \\
0 = (x-6)(x-44) \\
x = 6, x = 44$ .

Therefore the x-intercepts will be at (6, 0) and (44, 0)

Answer from: jfleming733

The vertex is (25,361), the x intercepts are (6,0) and (44,0).

Step-by-step explanation:

Consider the provided function,

f(x) = -x^2 + 50x - 264

The standard equation of the quadratic equation is f(x) = ax^2 + bx + c

And the vertex of the quadratic equation can be calculated as:

$h=\frac{-b}{2a}$ and k = f(h)

Part A:

By comparing the provided equation with the standard equation we can concluded that a = -1, b = 50 and c = -264

Now use the vertex formula and substitute the respective value in the formula that will give us the x coordinate of the vertex.

$h=\frac{-50}{2(-1)}$

$h=\frac{50}{2}$

h=25

Now substitute h = 25 in the provided equation as shown:

f(h) = -(25)^2 + 50(25) - 264

f(h) = -625 + 1250 - 264

f(h) =361

Hence, the vertex is (25,361).

The provided equation has a negative x² coefficient that means it is a downward parabola having maximum at vertex (25,361) but there exist no minimum point.

In context of the problem: The profit will be maximum when the number of membership sold is 25.

Part B:

To determine the x intercept simply substitute f(x)=0 and solve for x.

-x^2 + 50x - 264=0

x^2 -50x + 264=0

x^2 -6x-44x +264=0

x(x-6)-44(x-6)=0

(x-6)(x-44)=0

$x=6\ or\ x=44$

Hence, the x intercepts are (6,0) and (44,0).

That means, there will be zero profit when the number of memberships sold are 6 or 44.

Answer from: Quest

its 4 because 2 times 2 is 4, if you double the number two you get four

Answer from: Quest

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.