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3 years ago

Over the course of a year, a company goes from 115 employees to 124 employees. Build an equation.

Mathematics

2 answers:

k0ka [10]3 years ago

5 0

115+x=124
subtract 115 from both sdies
x=9
9 employees gained

oksano4ka [1.4K]3 years ago

4 0

Answer

Bulid the equation for the statement given in the question.

To prove

As given in the question.

Over the course of a year

A company goes from 115 employees to 124 employees this represented the change in the employees in company.

Let us assume that the change in the employees in the company be x.

Than the equation becomes

x + 115 = 124

x = 124 - 115

x = 9

Therefore this represented the increase in number of employees by 9 .

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Write the equation of a line with slope 3 and passing through the point (1,-1)

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2 years ago

Let L be a tangent line to the hyperbola x y = 2 at x = 9 . Find the area of the triangle bounded by L and the coordinate axes.

mafiozo [28]

Answer:

$A = 4$

Step-by-step explanation:

The equation of the slope of the tangent line L is obtained by deriving the equation of the hyperbola:

$y = \frac{2}{x}$

$y'=-2\cdot x^{-2}$

The numerical value of the slope is:

$y' = -2 \cdot (9)^{-2}\\y' = -\frac{2}{81}$

The component of the y-axis is:

$y = \frac{2}{9}$

Now, the tangent line has the following mathematical model:

$y = m \cdot x + b$

The value of the intercept is found by isolating it within the equation and replacing all known variables:

$b = y - m \cdot x$

$b = \frac{2}{9}-(-\frac{2}{81} )\cdot (9)\\b = \frac{4}{9}$

Thus, the tangent line is:

$y = -\frac{2}{81}\cdot x + \frac{4}{9}$

The vertical distance between a point of the tangent line and the origin is given by the intercept.

$d_{y} = \frac{4}{9}$

In order to find horizontal distance between a point of the tangent line and the origin, let equalize y to zero and clear x:

$-\frac{2}{81}\cdot x + \frac{4}{9}=0$

$-\frac{2}{9}\cdot x + 4 = 0$

$x = 18$

$d_{x} = 18$

The area of the triangle is computed by this formula:

$A = \frac{1}{2}\cdot d_{x}\cdot d_{y}$

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$A = 4$

4 0

3 years ago

HURRY QUICK!!

antiseptic1488 [7]

After plotting all the three points, we get the parabolic equation in the form is 2(x - 1)²-34.

<h3>What is parabola?</h3>

Any point on a parabola, which has the shape of a U, is situated at an equal distance from the focus, a fixed point, and the directrix, a fixed line.

General equation of the quadratic equation,

Y = ax² + bx +c

Given points,

(-2, 0),

(-1, -10),

(4, 0).

Putting the points in the general equation,

Putting (-2, 0), we get

0 = 4a - 2b + c

Putting (-1, -10), we get

-10 = a - b +c

Putting (4, 0), we get

0 = 16a + 4b +c

Solving all equations we get,

a = 2 , b = -4 , c = -16

After putting the values,

Y = 2x²- 4x- 16

2(x² - 2x - 8)

2(x²- 2x + 1 - 1 - 16)

=2(x - 1)²-34

Hence we get the required equation in the parabolic form.

To know more about parabola, visit :

brainly.com/question/21685473

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