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3 years ago

How do you know if a graph is a linear function

Mathematics

1 answer:

Furkat [3]3 years ago

6 0

Answer:

You know a graph is a linear function when the equation is in the format of y=mx+b

mx is the slope

b is the y-intercept

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Find the slope of the line that goes through: (-1, -12) and (9, 68)

dimaraw [331]

Answer:

The slope of the line is 8.

Step-by-step explanation:

The points on the straight line are:

A = (-1, -12)

B = (9, 68)

Compute the slope of the line as follows:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$=\frac{68-(-12)}{9-(-1)}\\\\=\frac{68+12}{9+1}\\\\=\frac{80}{10}\\\\=8$

Thus, the slope of the line is 8.

8 0

3 years ago

Three of the angles of a quadrilateral are 120° 48° and 92° what is the size of the fourth angle

Komok [63]

360-120-48-92=100°

Each quadrilateral has 360° so simply deduct the angles to get your result.

6 0

3 years ago

Read 2 more answers

Describe a realistic situation that could cause you or someone you know to have to use money from a financial reserve

o-na [289]

Answer:

Step-by-step explanation:

Your car breaks down unexpectedly and you must have it repaired immediately. That's an example of a situation where you might use money from a financial reserve.

4 0

4 years ago

Suppose X, Y, and Z are random variables with the joint density function f(x, y, z) = Ce−(0.5x + 0.2y + 0.1z) if x ≥ 0, y ≥ 0, z

kompoz [17]

$f_{X,Y,Z}(x,y,z)=\begin{cases}Ce^{-(0.5x+0.2y+0.1z)}&\text{for }x\ge0,y\ge0,z\ge0\\0&\text{otherwise}\end{cases}$

is a proper joint density function if, over its support, $f$ is non-negative and the integral of $f$ is 1. The first condition is easily met as long as $C\ge0$ . To meet the second condition, we require

$\displaystyle\int_0^\infty\int_0^\infty\int_0^\infty f_{X,Y,Z}(x,y,z)\,\mathrm dx\,\mathrm dy\,\mathrm dz=100C=1\implies \boxed{C=0.01}$

b. Find the marginal joint density of $X$ and $Y$ by integrating the joint density with respect to $z$ :

$f_{X,Y}(x,y)=\displaystyle\int_0^\infty f_{X,Y,Z}(x,y,z)\,\mathrm dz=0.01e^{-(0.5x+0.2y)}\int_0^\infty e^{-0.1z}\,\mathrm dz$

$\implies f_{X,Y}(x,y)=\begin{cases}0.1e^{-(0.5x+0.2y)}&\text{for }x\ge0,y\ge0\\0&\text{otherwise}\end{cases}$

Then

$\displaystyle P(X\le1.375,Y\le1.5)=\int_0^{1.5}\int_0^{1.375}f_{X,Y}(x,y)\,\mathrm dx\,\mathrm dy$

$\approx\boxed{0.12886}$

c. This probability can be found by simply integrating the joint density:

$\displaystyle P(X\le1.375,Y\le1.5,Z\le1)=\int_0^1\int_0^{1.5}\int_0^{1.375}f_{X,Y,Z}(x,y,z)\,\mathrm dx\,\mathrm dy\,\mathrm dz$

$\approx\boxed{0.012262}$

7 0

3 years ago

Halfway through a bus route, 23 students have been dropped off and 48 students remain on the bus. How many students were on the

wlad13 [49]

Answer:

71 students

Step-by-step explanation:

If 48 students remain on the bus and 23 had been dropped off, all we have to do is add 48 + 23 and then you'll get the answer as of how many kids were in the beginning.

5 0

4 years ago

Read 2 more answers