What is the answer and how did you get the answer explain

Let $f(x)$ be a function defined for all positive real numbers satisfying the conditions $f(x) > 0$ for all $x > 0$ and $f

algol [13]

Suppose we choose $x=1$ and $y=\dfrac12$ . Then

$f(x-y)=\sqrt{f(xy)+1}\implies f\left(\dfrac12\right)=\sqrt{f\left(\dfrac12\right)+1}\implies f\left(\dfrac12\right)=\dfrac{1+\sqrt5}2$

Now suppose we choose $x,y$ such that

$\begin{cases}x-y=\dfrac12\\\\xy=2009\end{cases}$

where we pick the solution for this system such that $x>y>0$ . Then we find

$\dfrac{1+\sqrt5}2=\sqrt{f(2009)+1}\implies f(2009)=\dfrac{1+\sqrt5}2$

Note that you can always find a solution to the system above that satisfies $x>y>0$ as long as $x>\dfrac12$ . What this means is that you can always find the value of $f(x)$ as a (constant) function of $f\left(\dfrac12\right)$ .

3 0

3 years ago

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Which equation represents a line that passes through (–9, –3) and has a slope of –6?

Fiesta28 [93]

Using slope-intercept form, y = mx + b where m = slope and b = y-intercept:

We know our slope is -6. This can be interpreted as -6/1, which rise-over-run-wise, means that when y changes by 6, x changes inversely by 1.
To find that y-intercept, though, we need to find the value of y when x = 0.
Use our point (-9, -3) to find this...
We want to add 9 to x so that it becomes 0.
According to our slope, this means subtracting 54 from y.
Our y-intercept is at (0, -57), with -57 being the value of b we put in our equation.

$\boxed{y=-6x-57}$

You could also just use point-slope form:
y - y¹ = m(x - x¹)
y - (-3) = -6(x - (-9))
y + 3 = -6(x + 9)
And convert to slope-intercept if you want:
y + 3 = -6x - 54
y = -6x - 57

3 0

3 years ago

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a shop sell 200 chocolate ; vanilla and strawberry ice cream 45% of the ice cream sold are vanilla and 35% are strawberry. how m

Oksanka [162]

The number of chocolate ice creams sold is 50.

<h3>How many chocolate ice creams are sold?</h3>

There exist three kinds of flavors.

45% of the ice creams exist as vanilla

30% of the ice creams exist as strawberry

x percent of the ice creams exist chocolate

The total amount of ice cream exists 200 which equals 100%.

Therefore,

45% + 30% + x = 100%

To estimate the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to estimate the result.

Solving for x, then the value of x is,

x = 25%

Then the number of chocolate ice creams are:

25%(200) = 50.

The number of chocolate ice creams sold is 50.

To learn more about the value of x refer to:

brainly.com/question/9965443

#SPJ2

6 0

2 years ago

P1. if your school makes $0.72 profit on every 6 raffle tickets sold, how much will it make when it sells the 11th ticket

Ahat [919]

Answer:

Part 1 = $1.32

Step-by-step explanation:

.72 divided by 6 is 12. So they make 12 cents per ticket, so that means you would have to do 12 times 11 and that should get you 132 cents and that is equivalent to $1.32.

4 0

3 years ago

The area of a circle is 615.44 in2. What is the diameter of the circle? Use 3.14 for π.

Shalnov [3]

615.44 = (3.14)(radius)^2

<span>radius = square-root of (615.44/3.14) </span>

<span>diameter = radius x 2 </span>

<span>diameter = 28 inches

3.14

</span>

6 0

3 years ago

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