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Rudik [331]
3 years ago
10

SOMEONE PLEASE HELP ANSWER MY QUESTIONS!!!!!!!!!!!!

Mathematics
1 answer:
Semmy [17]3 years ago
4 0
1)
y=mx+b
where m is the slope

We know the slope is 5 and the line passes through the point (4,3).

m=5 \\
(4,3) \\
x=4 \\ y=3 \\ \\ 
3=5 \times 4 + b \\
3=20 + b \\
b=3-20 \\
b=-17

The equation of the line is:
y=5m-17

Now the second point:
(2,y) \\
x=2 \\
y \\ \\ y=5 \times 2 -17 \\ y=10-17 \\ y=-7

The answer:
The value of y is -7.

2)
The line passes through the origin, or the point (0,0), and has a slope of -32.
The slope is negative so the line goes down from left to right.
It crosses both x and y axes in the point (0,0).
Therefore, it only passes through II and IV quadrant.

You can also find the equation of the line, find one more point and draw it.
y=mx+b \\ \\
m=-32 \\
(0,0) \\
x=0 \\ y=0 \\ \\
0=-32 \times 0 + b \\
b=0 \\ \\
y=-32x

Find the y-coordinate of the point for example (1,y).
(1,y) \\
x=1 \\ y \\ \\
y=-32 \times 1 \\
y=-32

The line passes through the points (0,0) and (1,-32). Now you can draw it (see the attachment).

The answer:
The line passes through quadrants II and IV.

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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
s344n2d4d5 [400]

Answer:

Profit function: P(x) = -0.5x^2 + 40x - 300

profit of $50: x = 10 and x = 70

NOT possible to make a profit of $2,500, because maximum profit is $500

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:

R(x) = 90x - 0.5x^2

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

P(x) = R(x) - C(x)

P(x) = 90x - 0.5x^2 - 50x - 300

P(x) = -0.5x^2 + 40x - 300

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

50 = -0.5x^2 + 40x - 300

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

x^2 - 80x + 700 = 0

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

To find if it's possible to make a profit of $2,500, we need to find the maximum profit, that is, the maximum of the function P(x).

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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