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2 years ago

What is the slope of the line shown?

Mathematics

1 answer:

Sever21 [200]2 years ago

5 0

Answer:

Slope = -3

Step-by-step explanation:

Slope formula:

$\frac{y2}{x2} - \frac{y1}{x1} = m$

m = slope.

Substitute the point values given into the formula:

$\frac{2}{2} - \frac{8}{0} = ?$

Solve:

$\frac{2}{2} - \frac{8}{0} = \frac{ - 6}{2} = - 3$

The slope of your line is -3.

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Noah has a summer tree-trimming business. Based on experience, Noah knows that his profit, P, in dollars, can be modelled by = −

crimeas [40]

Solving quadratic equations, it is found that he needs to charge:

1. He needs to charge $40 to break even.

2. He needs to charge $30 for a profit of $600.

<h3>What is a quadratic function?</h3>

A quadratic function is given according to the following rule:

$y = ax^2 + bx + c$

The solutions are:

$x_1 = \frac{-b + \sqrt{\Delta}}{2a}$

$x_2 = \frac{-b - \sqrt{\Delta}}{2a}$

In which:

$\Delta = b^2 - 4ac$

The profit equation in this problem is:

P(x) = -3x² + 150x - 1200.

He breaks even when P(x) = 0, hence:

-3x² + 150x - 1200 = 0.

The coefficients are a = -3, b = 150, c = -1200, hence:

$\Delta = 150^2 - 4(-3)(-1200) = 8100$

$x_1 = \frac{-150 + \sqrt{8100}}{-6}$

$x_2 = \frac{-150 - \sqrt{8100}}{-6} = 40$

He needs to charge $40 to break even.

For a profit of $600, we have that P(x) = 600, hence:

-3x² + 150x - 1200 = 600.

-3x² + 150x - 1800 = 0.

The coefficients are a = -3, b = 150, c = -1800, hence:

$\Delta = 150^2 - 4(-3)(-1800) = 900$

$x_1 = \frac{-150 + \sqrt{900}}{-6}$

$x_2 = \frac{-150 - \sqrt{900}}{-6} = 30$

He needs to charge $30 for a profit of $600.

More can be learned about quadratic equations at brainly.com/question/24737967

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1 year ago

The ratio of fiction to nonfiction books in the library is 4:5. If there are 900 books in a collection, how many are fiction?

jekas [21]

There will be excactly 400 fiction books. The ratio of fiction to all is 4 to 9, or 4 to 900.

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2 years ago

A ramp was constructed to load a truck. If the ramp is 10 feet long and the horizontal distance from the bottom of the ramp to t

NeX [460]

Pythagoras theorem is a basic relationship in geometry between the three sides of a right triangle. The height from the ground to the top of the ramp 6. 0 ft. Option D is correct.

<h3>What is the Pythagoras theorem?</h3>

Pythagoras theorem is a basic relationship in geometry between the three sides of a right triangle.

It indicates that the area of the hypotenuse square is equal to the sum of the areas of the squares on the other two sides.

The given data in the problem will be;

L is the length of ramp= 10 feet

x is the horizontal distance from the bottom of the ramp = 8 feet

h is the height from the ground to the top of the ramp=?

According to Pythagoras theorem,

$\rm H^2=P^2+B^2 \\\\ \rm l^2=h^2+X^2 \\\\ \rm 10^2=h^2+8^2 \\\\ \rm h=\sqrt{100-64 } \\\\ \rm h=36 \\\\ \rm h=6 ft$

Hence the height from the ground to the top of the ramp 6. 0 ft. Option D is correct.

To learn more about the Pythagoras theorem refer to the link;

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1 year ago

Help me match these pleasee and explain!

DiKsa [7]

3x=9 is C
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2 years ago

4000 + 12 343 x 2 =(A)

Vikentia [17]

Answer:

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Step-by-step explanation:

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2 years ago