All categories

3 years ago

Find the equation of the linear function represented by the table below in slope-

Mathematics

1 answer:

lisov135 [29]3 years ago

4 0

Answer:

$y = x +2$

Step-by-step explanation:

Given

The attached table

Required

Determine the equation

First, calculate the slope (m)

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Where

$(x_1,y_1) = (-3,-1)$

$(x_2,y_2) = (1,3)$

So, we have:

$m = \frac{3 - (-1)}{1 - (-3)}$

$m = \frac{3 +1}{1 +3}$

$m = \frac{4}{4}$

$m =1$

The equation in slope intercept form is calculated using

$y = m(x - x_1) + y_1$

This gives:

$y = 1(x - (-3)) -1$

$y = 1(x +3) -1$

$y = x +3 -1$

$y = x +2$

You might be interested in

What pattern do you see in the powers of 3

Roman55 [17]

$3 {?}^{2}$

5 0

4 years ago

Find f(-1) (inverse) if y=4x+2/3x-1 and x is not equal with 1/3

Setler [38]

Before we find $f^{-1}$ , let's think for a minute about what $f$ does, and what it means to find the inverse of a function. A function $f$ essentially takes a value $x$ from the domain and maps it to another value $y$ in that function's range according to a set of rules. Here, those rules are defined by the formula

$y= \frac{4x+2}{3x-1} , x \neq \frac{1}{3}$

All the inverse does is swap the domain and range of the function. Now, instead of trying to map $x$ to $y$ , we're trying to find a set of rules that'll map $y$ back to $x$ . To find those rules, all we have to do is solve the above equation for $x$ .

First, we'll multiply both sides of the equation by $3x-1$ to get it out of the denominator:

$(3x-1)y=( \frac{4x+2}{3x-1})(3x-1)$

Cancelling on the right side and distributing on the left, we get:

$3xy-y=4x+2$

Next, we collect all of our x terms on one side, and all of our non-x terms on the other:

$(3xy-y)+y=(4x+2)+y\\(3xy)-4x=(4x+2+y)-4x\\3xy-4x=2+y$

Let's rearrange the right side and factor out an x on the left:

$x(3y-4)=y+2$

And finally, we divide both sides by $3y-4$ to obtain our answer:

$[x(3y-4)]/(3y-4)=(y+2)/(3y-4)\\\\x= \frac{y+2}{3y-4}$

This equation gives us the "rules" for mapping any given y in the range back to an x in the domain. If we swap the domain and the range, we can define our function

$f^{-1}(x)= \frac{x+2}{3x-4}$

7 0

4 years ago

If Mary traveled 200 miles on foot, then traveled 200 miles on bike then traveled 200 miles by car how long did it take her to g

Serjik [45]

Step-by-step explanation:

Distance word problems are a common type of algebra word problems. They involve a scenario in which you need to figure out how fast, how far, or how long one or more objects have traveled. These are often called train problems because one of the most famous types of distance problems involves finding out when two trains heading toward each other cross paths.

In this lesson, you'll learn how to solve train problems and a few other common types of distance problems. But first, let's look at some basic principles that apply to any distance problem.

The basics of distance problems

There are three basic aspects to movement and travel: distance, rate, and time. To understand the difference among these, think about the last time you drove somewhere.

The distance is how far you traveled. The rate is how fast you traveled. The time is how long the trip took.

The relationship among these things can be described by this formula:

distance = rate x time

d = rt

In other words, the distance you drove is equal to the rate at which you drove times the amount of time you drove. For an example of how this would work in real life, just imagine your last trip was like this:

You drove 25 miles—that's the distance.

You drove an average of 50 mph—that's the rate.

The drive took you 30 minutes, or 0.5 hours—that's the time.

According to the formula, if we multiply the rate and time, the product should be our distance.

And it is! We drove 50 mph for 0.5 hours—and 50 ⋅ 0.5 equals 25, which is our distance.

What if we drove 60 mph instead of 50? How far could we drive in 30 minutes? We could use the same formula to figure this out.

60 ⋅ 0.5 is 30, so our distance would be 30 miles.

Solving distance problems

When you solve any distance problem, you'll have to do what we just did—use the formula to find distance, rate, or time. Let's try another simple problem.

7 0

3 years ago

If a semi circle has a diameter of 5 m what is the area?

klasskru [66]

Answer:

Exact answer = 10.41666666666666666666666666666pi

Estimated answer = 32.70938

Step-by-step explanation:

Semi circle formula: 1/2 * 4/3 * pi * r^3

r = 2.5

1/2 * 4/3 * pi * 2.5^3

2/3 * pi * 2.5^3

2/3 * pi * 15.625

10.416..... * pi

Exact answer = 10.417pi

We can estimate pi as 3.14

So, 10.417 * 3.14 = 32.70938

Exact answer = 10.41666666666666666666666666666pi

Estimated answer = 32.70938

8 0

3 years ago

{(-1, 4), (-1, 9), (-1, 15), (-1, 0)}

marishachu [46]

Answer:

domain is -1

range is {4, 9, 15, 0}

function: not a function

6 0

3 years ago