Ask question

Ask question

All categories

3 years ago

12

Graph y<2/3x+1 Click or tap the graph to plot a point.

1 answer:

vivado [14]3 years ago

5 0

Answer:

See below

Step-by-step explanation:

a) Create a table containing a few values of x and y

<u> x </u> <u> y </u>

-2 -⅓

-1 ⅓

0 1

1 1⅔

2 2⅓

(b) Draw the graph

Plot the points and draw a straight line through them. Make it a <em>dashed line,</em> because the line does not include the points.

Your graph should look like Fig. 1.

<em>(d) Check a point to see if it satisfies the inequality. </em>

An easy one to check is the origin, (0, 0).

0 < ⅔(0) + 1

0 < 1

The area <em>below </em>the graph satisfies the inequality.

<em>(e) Shade in the area below the graph </em>

This shows that all points in that area satisfy the inequality. The final graph should look like Figure 2.

You might be interested in

Function f is an exponential function. It predicts the value of a famous painting, in thousands of dollars, as a function of the

nalin [4]

Answer:

$y=8 \cdot (\frac{5}{4})^x$

$f(x)=8 \cdot (\frac{5}{4})^x$

or

$f(x)=8 \cdot (1.25)^x$

Step-by-step explanation:

We are going to see if the exponential curve is of the form:

$y=a \cdot b^x$ , ( $b\neq 0$ ).

If you are given the $y-$ intercept, then $a$ is easy to find.

It is just the $y-$ coordinate of the $y-$ intercept is your value for $a$ .

(Why? The $y-$ intercept happens when $x=0$ . Replacing $x$ with 0 gives $y=a \cdot b^0=a \cdot 1=a$ . This says when $x=0 \text{ that} y=a$ .)

So $a=8$ .

So our function so far looks like this:

$y=8 \cdot b^x$

Now to find $b$ we need another point. We have two more points. So we will find $b$ using one of them and verify for our resulting equation works for the other.

Let's do this.

We are given $(1,10)$ is a point on our curve.

So when $x=1$ , $y=10$ .

$10=8 \cdot b^1$

$10=8 \cdot b$

Divide both sides by 8:

$\frac{10}{8}=b$

Reduce the fraction:

$\frac{5}{4}=b$

So the equation if it works out for the other point given is:

$y=8 \cdot (\frac{5}{4})^x$

Let's try it. So the last point given that we need to satisfy is $(2,12.5)$ .

This says when $x=2$ , $y=12.5$ .

Let's replace $x$ with 2 and see what we get for $y$ :

$y=8 \cdot (\frac{5}{4})^2$

$y=8 \cdot \frac{25}{16}$

$y=\frac{8}{16} \cdot 25$

$y=\frac{1}{2} \cdot 25}$

$y=\frac{25}{2}$

$y=12.5$

So we are good. We have found an equation satisfying all 3 points given.

The equation is $y=8 \cdot (\frac{5}{4})^x$ .

4 0

3 years ago

The diagram shows two campsites on opposite ends of a lake and two triangles formed by intersecting segments from the campsites.

Aleks [24]

Answer:

x=42.3m

Step-by-step explanation:

x/47=82.8/92

92x=3891.6= 42.3m is the distance

6 0

3 years ago

I really need help on this one...ASAP!

Leokris [45]

4(a+12)=32
4a+48=32
4a=-16
a=-4

6 0

3 years ago

Read 2 more answers

Convert: 76.8°f = ________ °c<br> a. 21.5<br> b. 25<br> c. 170.24<br> d. 24.89

lesya [120]

The answer to convert 76.8 fahrenheit to Celsius is D

3 0

3 years ago

Read 2 more answers

Fill in the blanks to complete the table.

fomenos

Answer:

you plug in the numbers into the function

Step-by-step explanation

function 1 is blank 1 is 17

2) is 16 3) is 15 4) is 12 5) is 7 6) is 0 and so on

for function 2 blank 1 is 1

2) is 0 3) is -1 4) is -2 5) is -3 6) is -4 and so on

does that help?

4 0

3 years ago