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2 years ago

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Mathematics

1 answer:

MArishka [77]2 years ago

3 0

Answer:

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Step-by-step explanation:

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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:

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

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

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

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

a recipe for lasagna calls for 3 pounds of tomatoes to serve 5 people. a caterer wants to make enough lasagna to serve 110 peopl

Roman55 [17]

To do this you want to divide 110 by 5 to get 22. Now you want to multiply 3 by 22. That means the caterer need 66 pounds of tomatoes.

5 0

3 years ago

Use the identity (x^2+y^2)^2=(x^2−y^2)^2+(2xy)^2 to determine the sum of the squares of two numbers if the difference of the squ

marissa [1.9K]

Answer:

Step-by-step explanation:

(x^2+y^2)^2=(x^2)^2+2x^2y^2+(y^2)^2

Adding and substracting 2x^2y^2

We get

(x^2+y^2)^2=(x^2)^2+2x^2y^2+(y^2)^2 +2x^2y^2-2x^2y^2

And we know a^2-2ab+b^2=(a-b)^2

So we identify (x^2)^2 as a^2 ,(y^2)^2 as b^2 and -2x^2y^2 as - 2ab. So we can rewrite (x^2+y^2)^2=(x^2 - y^2)^2 + 2x^2y^2 + 2x^2y^2= (x^2 - y^2)^2+4x^2y^2= (x^2 - y^2)^2+2^2x^2y^2

Moreever we know (a·b·c)^2=a^2·b^2·c^2 than means 2^2x^2y^2=(2x·y)^2

And (x^2+y^2)^2=(x^2 - y^2)^2 + (2x·y)^2

5 0

3 years ago

What fraction of 60 is 18

nordsb [41]

10/3

hope this helped

3 0

2 years ago

Simplify.<br> (-3.9) + (6.01) - (-7.423)<br> -5.513.<br> 2.487.<br> 9.533.

lianna [129]

First, since we must follow PEMDAS, we need to do the operation that is first, which is addition.

-3.9 + 6.01 ← Adding a negative means subtracting, then giving the sign of the bigger number.

So now we solved those and we got this answer: 2.11

Now, we need to subtract and re-write the expression.

2.11 - (-7.423) = 2.11 + 7.423= 9.533

Ok....so now we have our final answer, and we have the choices above.

The only answer that matches ours is the last one.

Final answer: 9.533

Hope I helped ^_^

4 0

3 years ago

Read 2 more answers