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zimovet [89]
2 years ago
12

Use the coordinates of the labeled point to find the point slope equation of the line

Mathematics
1 answer:
Karo-lina-s [1.5K]2 years ago
4 0

Answer:

D. y + 1 = -2(x - 2)

Step-by-step explanation:

Point-slope form equation is given as y - b = m(x - a), where,

(a, b) = a point of the graph.

m = slope of the graph

Find the slope of the graph:

Slope = \frac{rise}{run} = \frac{-4}{2} = -2

Using the point (2, -1) and the slope, m, = -2, we can derive the equation in point-slope form by substituting a = 2, b = -1, and m = -2 into y - b = m(x - a).

✅The equation would be:

y - (-1) = -2(x - 2)

y + 1 = -2(x - 2)

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Could you help me to solve the problem below the cost for producing x items is 50x+300 and the revenue for selling x items is 90
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Answer:

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Step-by-step explanation:

(Assuming the correct revenue function is 90x−0.5x^2)

The cost function is given by:

C(x) = 50x + 300

And the revenue function is given by:

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The profit function is given by the revenue minus the cost, so we have:

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To find the points where the profit is $50, we use P(x) = 50 and then find the values of x:

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-0.5x^2 + 40x - 350 = 0

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Using Bhaskara's formula, we have:

\Delta = b^2 - 4ac = (-80)^2 - 4*700 = 3600

x_1 = (-b + \sqrt{\Delta})/2a = (80 + 60)/2 = 70

x_2 = (-b - \sqrt{\Delta})/2a = (80 - 60)/2 = 10

So the values of x that give a profit of $50 are x = 10 and x = 70

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The maximum value of P(x) is in the vertex. The x-coordinate of the vertex is given by:

x_v = -b/2a = 80/2 = 40

Using this value of x, we can find the maximum profit:

P(40) = -0.5(40)^2 + 40*40 - 300 = $500

The maximum profit is $500, so it is NOT possible to make a profit of $2,500.

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