What is the constant of proportionality in the equation StartFraction x over y EndFraction = StartFraction 2 over 9 EndFraction?StartFraction 2 over 9 EndFraction
2
StartFraction 9 over 2 EndFraction
9

I NEED HELP QUICK!

Answers

Answer 1

Answer:

We have been given an equation $(x)/(y)=(2)/(9)$ . We are asked to find constant of proportionality from our given equation.

We know that two directly proportional equations are in form $y=kx$ ,where y is directly proportional to x and k is constant of proportionality.

Let us rewrite our given equation by cross multiplying as:

$2y=9x$

Now we will divide both sides of equation by 2.

$(2y)/(2)=(9x)/(2)$

$y=(9)/(2)x$

We can see that our equation is in form $y=kx$ and constant of proportionality is $(9)/(2)$ .

Answer 2

Answer:

Answer:

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A ball is dropped and bounces to a height of 5 feet. The ball rebounds to 70% of its previous height after each bounce The function that could be used to model the nth term in the sequence of heights of the ball after the initial drop is

Answers

Answer:

$T_n = 7.143(0.7^n)$

Step-by-step explanation:

If a ball bounces to a height of 5feet, the initial drop = 5feet

If the ball rebounds to 70% of its previous height after each bounce, the next height after rebouncing will be expressed as;

= 70% of 5

= 70/100 * 5

= 0.7*5

= 3.5 feet

The next height will be 0.7*3.75 = 2.45 and so on

The heights wil form a sequence as thus;

5, 3.5, 2.45...

This sequence forms a geometric progression.

To get the function that could be used to model the nth term in the sequence of heights of the ball after the initial drop, w will find the nth term of the sequence

$T_n = ar^(n-1)$

a is the first term of the sequence

n is the number of terms

r is the common ratio

From the sequence:

a = 5

$r = (3.5)/(5) = (2.75)/(3.5) = 0.7$

Substitute the given values into the formula

$T_n = 5(0.7)^(n-1)\nT_n = 5((0.7^n)/(0.7^1) )\nT_n = (5)/(0.7)* 0.7^n \nT_n = 7.143(0.7^n)$

The nth tern=m required is $T_n = 7.143(0.7^n)$

The function that models the nth term in the sequence of heights of the ball after the initial drop is an = 5 * 0.7(n-1)

The sequence of heights of the ball can be modeled using a geometric sequence, since the ball rebounds to 70% of its previous height after each bounce. The formula for a geometric sequence is:

an = a1 × r(n-1)

where an represents the nth term in the sequence, a1 is the initial term (in this case, the height of the first bounce), and r is the common ratio (in this case, 0.7). So, the function that could be used to model the nth term in the sequence of heights of the ball after the initial drop is:

an = 5 × 0.7(n-1)

Learn more about Geometric sequence here:

brainly.com/question/34246122

#SPJ3

Lana's family is planning a rectangular garden. They make a scale diagram of the garden using a scale of 1 inch to 0.5 meter. If the length of the scale diagram is 24 inches, and its width is 16 inches, what is the perimeter of the actual garden? 20 meters 40 meters 80 meters 160 meters. Please help me

Answers

Total inches: 24 x 2 + 16 x 2

= 48 + 32 = 80 inches

80 in x 0.5 = 40m

Therefore, answer is 40 metres

Answer:

the answer is 40 meters

Step-by-step explanation:

hope this helps!! <3

What is this simplified using order of operations 100-20[18-2(5+2)]

Answers

Answer: 20

Step-by-step explanation:

I need help no ilnks please and thank you also please explain how you got the answer

Answers

You want to leave a 15% tip on a meal that cost $65.00.

First, convert the 15% to an actual number that can be used in a calculation. For percents,this is always done by simply dividing the percent (in this case 15%) by 100%.So, the conversational term "15%" becomes 15% / 100% = 0.15 in terms of a real mathematical number.

Second, you need to find out what 15% of your $65.00 meal cost is.This is always done by multiplying 0.15 by $65.00, or

0.15 x $65.00=$9.75.

So, the amount of tip you are going to leave is $9.75.

This makes the total cost of your meal (to write on your charge slip or other payment)

$65.00 + $9.75 = $74.75.

A: y=50x+75
EXP: The x value 0 is at 75, making that the y-intercept. Rise/run for rise 1 -> 2 is up 50, making slope 50(x). Put it together giving you y=50x+75

Select the algebraic definition for the piecewise function graph.A. 2
B. 4
C. -3 is equal to x <-1
D. -1 is equal to x <1
E. 0
F. 1 is equal to x<3
G. -2 is equal to x<5
H. -3 is equal to x<3
I. 3

Answers

The piece-wise function is defined by:

$f(x) = 1, -3 \leq x < -1$

$f(x) = 2, -1 \leq x < 1$

$f(x) = 3, 1 \leq x < 3$

A piece-wise function is a function that has different definitions, based on the input.

In this graph:

When x is between -3(inclusive, closed circle) and -1(exclusive, open circle), the value is 1, thus, the first definition is:

$f(x) = 1, -3 \leq x < -1$

When x is between -1(inclusive) and 1(exclusive), the value is 2, thus, the second definition is:

$f(x) = 2, -1 \leq x < 1$

When x is between 1(inclusive) and 3(exclusive), the value is 3, thus, the third definition is:

$f(x) = 3, 1 \leq x < 3$

A similar problem is given at brainly.com/question/13205719

Final answer:

A piecewise function is defined by multiple sub-functions, each applying to a certain interval of the main function's domain. An example might be ' -3 is equal to x <-1', representing a portion of the function where any x-value less than -1 outputs -3.

Explanation:

Without the piecewise function graph, it's difficult to identify the correct algebraic definition. However, a piecewise function is a function which is defined by multiple sub functions. Each sub function applies to a certain interval of the main function's domain, which is why we see conditions like 'x < -1' following the function.

For instance, if we look at option C ' -3 is equal to x <-1', it suggests there is a piece of the function where any x-value less than -1 will output -3. It is important to note that these piecewise functions are visualized on a graph, often appearing as lines or curves that start or stop at certain points.