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4 years ago

5

busby County is rectangular. a map of the county on a coordinate plane shows the vertices of the county at (-5,8),(8,8),8,-10),a

nd (-5,-10).each unit on the map represents 1 mile. what is the county's perimeter?

1 answer:

Korvikt [17]4 years ago

7 0

The perimeter is 62 miles

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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

What are the next three terms in the sequence 2, -4, -16, 32

Nikitich [7]

Answer:

128, -256, -1024

Step-by-step explanation:

multiply 32 by 4, multiply 128 by -2, multiply -256 by 4

5 0

2 years ago

What is the value of -12- (-35)?

maksim [4K]

Answer:

-12-(-35)

=-12+35

=23

5 0

3 years ago

Read 2 more answers

Question 1 (Essay Worth 1 points) Which of the following expressions are equivalent to –3.5(2 – 3n) – 2.5n? A: –7 – 8n B: –7 + 8

zzz [600]

B is the anwser that I got

5 0

3 years ago

Graph and label each figure and it’s image under the given translation. Give the coordinates of the image.

lutik1710 [3]

Answer:

See below ~

Step-by-step explanation:

<u>Question 3 : (x, y - 5)</u>

K' = (-3, 2 - 5) = <u>(-3, -3)</u>
L' = (1, 4 - 5) = <u>(1, -1)</u>
M' = (-1, 0 - 5) = <u>(-1, -5)</u>
N' = (-5, -2 - 5) = <u>(-5, -7)</u>

<u></u>

<u>Question 4 : (x + 4, y + 1)</u>

D' = (-4 + 4, 3 + 1) = <u>(0, 4)</u>
E' = (0 + 4, 2 + 1) = <u>(4, 3)</u>
F' = (-2 + 4, -6 + 1) = <u>(2, -5)</u>
G' = (-6 + 4, -5 + 1) = <u>(-2, -4)</u>

5 0

2 years ago