5•x=12 help me help me!

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

5/6-1/8 Solve by finding a common denominator A)30/48 B)34/48 C)38/48 D)42/48

GrogVix [38]

Answer:

B) 34/48

Step-by-step explanation:

The easiest common denominator to find is the product of the denominators you have.

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The difference is ...

$\dfrac{5}{6}-\dfrac{1}{8}=\dfrac{5}{6}\cdot\dfrac{8}{8}-\dfrac{1}{8}\cdot\dfrac{6}{6}\\\\=\dfrac{40-6}{48}=\boxed{\dfrac{34}{48}}$

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Additional comment

The difference numerator and denominator have a common factor of 2, so can be reduced to 17/24. The denominator 24 could have been used as the common denominator from the start.

5/6 -1/8 = 20/24 -3/24 = 17/24 . . . . reduced result

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Using the least common denominator does not always result in a reduced sum or difference. If some other denominator is used (as here), then you can be assured that the result will need to be reduced to get to lowest terms.

8 0

2 years ago

Identify the terms of the expression 9a+4b-18

madreJ [45]

Hey there!

We may ask. What exactly is a term anyways.

Well, a term is a single number, a variable, or a number and a variable that would have to be multiply together. This is what a term would be.

Therefore, as we look above, we see the following equation.

9a+4b-18

18 is a term

4b is a term

9a is a term

This whole thing, would be called an expression, as this is expression something. Perhaps the amount of students who ate ice-cream at a football game, or something similar.

I hope you found this helpful! :)

6 0

3 years ago

Which of the binomials below is a factor of this trinomial? x² - 4x-12

noname [10]

Answer:

(x +2) (x-6)

Step-by-step explanation:

x^2 -6x + 2x + 12 =

x^2 -4x + 12

5 0

3 years ago

Last year the dept of the river was 4.2 feet deep. THIS YEAR UT DROPPED 11% find the depth of the f the river this year

Romashka [77]

Answer:

new depth =

4.2/100 X 89 = 3.738 feet

4 0

3 years ago