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ivanzaharov [21]
3 years ago
6

Find an equation of the line passing through the point (2, -3) and has slope -4. Then rewrite your linear equation in the slope-

intercept function form f(x) = mx+b
Mathematics
1 answer:
Tresset [83]3 years ago
8 0

Answer:

y=-4x+5

Step-by-step explanation:

y+3=-4(x-2)

y+3=-4x+8

-3. -3

y=-4x+5

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First you have to order the numbers form smallest to greatest
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12 stars / 30 balloons = x / 120 balloons
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Answer: 48 stard

Step-by-step explanation:

12 stars = 30 balloons

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A circle has a diameter of 29 feet. What is the area? *
11111nata11111 [884]

Answer:

The answer is

<h2>660.5 square feet</h2>

Step-by-step explanation:

Area of a circle = πr²

where r is the radius

From the question

diameter = 29 feet

To find the radius given the diameter we use the formula

radius =  \frac{diameter}{2}  \\ radius  =  \frac{29}{2}  \\  = 14.5 \:  \: feet

So the area of the circle is

A =  {14.5}^{2} \pi \\  = 210.25\pi \\  = 660.519...

We have the final answer as

<h3>660.5 square feet</h3>

Hope this helps you

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3 years ago
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5 0
3 years ago
Show that every triangle formed by the coordinate axes and a tangent line to y = 1/x ( for x &gt; 0)
vfiekz [6]

Answer:

Step-by-step explanation:

given a point (x_0,y_0) the equation of a line with slope m that passes through the  given point is

y-y_0 = m(x-x_0) or equivalently

y = mx+(y_0-mx_0).

Recall that a line of the form y=mx+b, the y intercept is b and the x intercept is \frac{-b}{m}.

So, in our case, the y intercept is (y_0-mx_0) and the x  intercept is \frac{mx_0-y_0}{m}.

In our case, we know that the line is tangent to the graph of 1/x. So consider a point over the graph (x_0,\frac{1}{x_0}). Which means that y_0=\frac{1}{x_0}

The slope of the tangent line is given by the derivative of the function evaluated at x_0. Using the properties of derivatives, we get

y' = \frac{-1}{x^2}. So evaluated at x_0 we get m = \frac{-1}{x_0^2}

Replacing the values in our previous findings we get that the y intercept is

(y_0-mx_0) = (\frac{1}{x_0}-(\frac{-1}{x_0^2}x_0)) = \frac{2}{x_0}

The x intercept is

\frac{mx_0-y_0}{m} = \frac{\frac{-1}{x_0^2}x_0-\frac{1}{x_0}}{\frac{-1}{x_0^2}} = 2x_0

The triangle in consideration has height \frac{2}{x_0} and base 2x_0. So the area is

\frac{1}{2}\frac{2}{x_0}\cdot 2x_0=2

So regardless of the point we take on the graph, the area of the triangle is always 2.

6 0
3 years ago
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