Which formula shows a joint variation?

Answers

Answer 1

Answer:

The answer is the first option: I, II and III.

The explanation is shown below:

1. By definition, there is a joint variation when a variable depends on two or more different variables. Therefore, you can express it as following:

$y=kxz$

Where $x,y$ and $z$ are the variables and $k$ is the constant of proportionality.

As you can see, $y$ is directly proportional to $x$ and $z$ .

2. Keeping the information above, you have:

I) $V=lwh$ ( $V$ varies jointly with $l$ , $w$ and $h$ .

II) $V=(1)/(3)r^(2)h\pi$ (If $(\pi)/(3)$ is the constant of proportionality, $V$ varies jointly with $r^(2)$ and $h$ ).

III) $V=Bh$ ( $V$ varies jointly with $B$ and $h$ .

Answer 2

Answer:

Answer : I, II and III

To find volume formula that shows joint variation we analyze each option

Joint variation always depends on atleast two dependent variables

for example y = kxy

The variable y depends on x and y and k is constant of proportionality

V= lwh

It means volume depends on length , width and height. 1 is the constant of proportionality .

$v=(1)/(3) \pi r^2h$

V depends on radius r and height h. Here 1/3 pi is the constant of proportionality

V= BH

V depend on base b and height h . 1 is the constant of proportionality .

So answer is I, II , III

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A couch sells for $820. Instead of paying the total amount at the time of purchase, the same couch can be bought by paying $400 down and $60 per month for 12 months. How much is saved by paying the total amount at the time of purchase?

Answers

Answer:

$300

Step-by-step explanation:

The couch is sold in two ways; outright payment or installment payment.

Outright payment would cost = $820

Installment payment = down payment + monthly charges

Down payment = $400

Monthly charges for a period of one year (12 months) = 12 × $60

= $720

Installment payment would cost = $400 + $720

= $1120

Amount saved by paying total amount at the time of purchase = $1120 - $820

= $300

Thus, the outright buying the couch would save $300.

An element with a mass of 570 grams decays by 26.7% per minute. To the nearest minute, how long will it be until there are 40 grams of the element remaining?

Answers

Answer: x ≈ 9

Step-by-step explanation:

Near the end of the picture 8.553364=x

x ≈ 9

What is the approximate circumference of a circle with a radius of 3 centimeters?

Answers

1.5 I think would be the correct answer not sure

Which statement is true regarding the graphed functions?f(0) = 2 and g(–2) = 0
f(0) = 4 and g(–2) = 4
f(2) = 0 and g(–2) = 0
f(–2) = 0 and g(–2) = 0

Answers

let's analyze each case to determine the solution

case 1) f(0) = 2 and g(–2) = 0

For x=0-----> find the value of f(0) in the graph-----> f(0)=4

For x=-2-----> find the value of g(-2) in the graph-----> g(-2)=0

therefore

the statement of the case 1) is false

case 2) f(0) = 4 and g(–2) = 4

For x=0-----> find the value of f(0) in the graph-----> f(0)=4

For x=-2-----> find the value of g(-2) in the graph-----> g(-2)=0

therefore

the statement of the case 2) is false

case 3) f(2) = 0 and g(–2) = 0

For x=2-----> find the value of f(2) in the graph-----> f(2)=0

For x=-2-----> find the value of g(-2) in the graph-----> g(-2)=0

therefore

the statement of the case 3) is true

case 4) f(–2) = 0 and g(–2) = 0

For x=-2-----> find the value of f(-2) in the graph-----> f(-2) is greater than 12

For x=-2-----> find the value of g(-2) in the graph-----> g(-2)=0

therefore

the statement of the case 4) is false

therefore

the answer is

f(2) = 0 and g(–2) = 0-------> this statement is true

The correct option is $\boxed{\left(c\right)f\left(2\right)=0{\text{ and }}g\left({-2}\right)=0}$ .

Further explanation:

Consider a function $f\left(x\right)$ as $y$ .

$\boxed{f\left(x\right)=y}$ ...... (1)

Consider the function $g\left(x\right)$ as $z$ .

$\boxed{g\left(x\right)=z}$ ...... (2)

Substitute 0 for $x$ in equation (1) to obtain the value of $f\left(0\right)$ and also the value of $f\left(0\right)$ can be obtained from the graph by finding the value of $y$ at $x=0$ .

$\boxed{f\left(0\right)=4}$

Substitute 2 for $x$ in equation (1) to obtain the value of $f\left(2\right)$ and also the value of $f(2)$ can be obtained from the graph by finding the value of $y$ at $x=2$ .

$\boxed{f\left(2\right)=0}$

Substitute $-2$ for $x$ in equation (2) to obtain the value of $g(-2)$ and also, the value of $g(-2)$ can be obtained from the graph by finding the value of $z$ at $x=-2$ .

$\boxed{g\left({-2}\right)=0}$

Now check the option that is satisfied by the obtained value.

In the option (a) the value of $f(0)$ is 2 which is not equal to the obtained value so this option is not correct.

In the option (b) the value of $f(0)$ is 4 which is not equal to the obtained value so this option is not correct.

In the option (c) the value of $f(2)$ is 0 which is equal to the obtained value and the value of $g(-2)$ is 0 which is also equal to the obtained value so this option is correct.

In the option (d), the value of $f(-2)$ is 0 but from the graph it can be observed that the value of $f(-2)$ is greater than 12, so this option is not correct.

Learn more:

1. Problem on Function brainly.com/question/1691598

2. How to solve Function brainly.com/question/1632445

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Function

Keywords:

Graphed function, f(0), f(2),g(0), f(x), g(x), intercept, intersection, axis, vertical, horizontal, lines, parabola function.

About 4 out of every 5 people are right-handed. If there are 30 students in a class, how many would you expect to be right-handed? How many to be left-handed?

Answers

Answer:

You would expect 24 right handed and 6 left handed

Step-by-step explanation:]

5 x 6 =30

9s − 5 s = 8 knnnkjbkbbhjhghuj

Answers

9*8=72

72-5=67

The final answer is 67.

Please mark Brainliest

Thank you

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