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1 year ago

PLS HELP ASAP! 30 POINTS! functionf(x) is graphed on the coordinate plane.

Mathematics

1 answer:

lorasvet [3.4K]1 year ago

7 0

The function will be given f(x) = -4 ( x -0.5)

<h3 /><h3>What is the equation of a line passing through two points?</h3>

Graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

Suppose the given points are (x₁, y₁) and (x₂, y₂), then the equation of the straight line joining both two points is given by

$\rm (y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)$

We can see that the line is passing through the points ( 0.5,0) and ( 0,-2). so we will find the function by using the equation of the line passing through two points.

Write an equation for the trend line.

(x₁, y₁) → (0.5,0)

(x₂, y₂) → (0, -2)

Then we have

y - 0 = ( -2 - 0)/( 0 - 0.5)(x - 0.5)

y - 0 = ( -2/-0.5) ( x - 0.5)

y = -4 ( x -0.5)

Learn more about straight-line equations here:

brainly.com/question/380976

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2 years ago

The ratio of the circumference of two circles is 3:2.What is the ratio of their area

Nezavi [6.7K]

The ratio of their area is 9/4

<h2>Explanation:</h2>

We use ratios to compares values. In this exercise, we are comparing the circumference of two circles, which is:

$3:2$

and we want to know what is the ratio of their area. Recall that the circumference of a circle is given by:

$C=2\pi r \\ \\ \\ Where: \\ \\ C:Circumference \\ \\ r:Radius \ of \ the \ circle$

If we define:

$C_{1}: \ Circumference \ of \ circle \ 1 \\ \\ C_{2}: \ Circumference \ of \ circle \ 2 \\ \\ r_{1}: \ Radius \ of \ circle \ 1 \\ \\ r_{2}: \ Radius \ of \ circle \ 2$

Then, the ratio of the circumference of two circles is 3:2 is:

$\frac{C_{1}}{C_{2}}=\frac{2\pi r_{1}}{2\pi r_{2}}=\frac{3}{2} \\ \\ \therefore \frac{r_{1}}{r_{2}}=\frac{3}{2}$

The area of a circle is given by:

$A=\pi r^2 \\ \\ A:Area \\ \\ r:Radius$

So the ratio of their area can be found as:

$\frac{A_{1}}{A_{2}}=\frac{\pi r_{1}^2}{\pi r_{2}^2} \\ \\ \\ A_{1}:Area \ of \ circle \ 1 \\ \\ A_{2}:Area \ of \ circle \ 2$

So:

$\frac{A_{1}}{A_{2}}=\frac{r_{1}^2}{r_{2}^2}=\left( \frac{r_{1}}{r_{2}} \right)^2 \\ \\ \frac{A_{1}}{A_{2}}=\left(\frac{3}{2}\right)^2 \\ \\ \boxed{\frac{A_{1}}{A_{2}}=\frac{9}{4}}$