Solve the equation. 3(x−9)=30

The volume V of a gas varies inversely as the pressure P and directly as the temperature A certain gas has a volume of 10 liters

Ad libitum [116K]

Answer:

Joint variation states that:

If z is directly proportional to x and inversely proportional to y,

i.e, $z \propto x$ , $z \propto \frac{1}{y}$

then the equation is in the form: $z = k\frac{x}{y}$ where k is the constant of variation.

From the given information: The volume V of a gas varies inversely as the pressure P and directly as the temperature

i.,e $V \propto T$ , $V \propto \frac{1}{P}$

by definition of joint variation:

$V = k\frac{T}{P}$ .....[1] where k is the constant of variation.

It is also given that a certain gas has a volume of 10 liters(L) , a temperature of 300 kelvins(K), and a pressure of 1.5 atmosphere(atm).

Substitute these given values in [1] to solve for k;

$10 = k\frac{300}{1.5}$

Simplify:

$10 = 200k$

Divide by 200 both sides we have;

$k = \frac{10}{200} =\frac{1}{20}$

Now, if a gas has a temperature of 400 kelvins and a pressure of 5 atm.

To find the volume (V);

Now substitute the given data and value of k in [1] we have;

$V = \frac{1}{20} \cdot \frac{400}{5} = \frac{20}{5} = 4$

Therefore, the Volume of a gas is, 4 liters

5 0

2 years ago

Simplify the radical expression √(5) + 6√(5)

Evgesh-ka [11]

Answer is C) 7√(5)
cause

√(5) + 6√(5)
=√5 (1+6)
= 7√5

8 0

3 years ago

Jenny bought a 5 notebooks and 2 pencils, and the total was 9 dollars.

weeeeeb [17]

You would solve this with simultaneous equations, so if we write it as:
5n + 2p = 9
3n + 2p = 6
(subtract)
2n = 3
÷ 2
notebooks = 1.5

Now you would substitute it in:
(3 × 1.5) + 2p = 6
4.5 + 2p = 6
- 4.5
2p = 1.5
÷ 2
pens = 0.75

So your final answer is notebooks are $1.50 and pens are $0.75, I hope this helps!

6 0

3 years ago

Which statement explains how the lines 2x + y = 4 and y = one halfx + 4 are related?

KatRina [158]

Answer:

They are perpendicular

Step-by-step explanation:

To solve this problem .

we will convert the equations in slope intercept form.

Slope intercept form of equation is y = mx+c

where m is slope of line and c is y intercept.

________________________________

equation 1 is

2x+y = 4

=> y =4 - 2x or y = -2x + 4

comparing it with y = mx + c

m = -2 , c = 4

_________________________________________

equation 2 is y = one halfx + 4 ( one half is same as 1/2)

so equation is

y = x/2 +4

comparing it with y = mx + c

m = 1/2 , c = 4

_________________________________________

Now lets evaluate options

They are parallel. wrong option

For lines to be parallel slope should be same.

But here slope are different -2 and 1/2 .

Thus lines are not parallel.

__________________________________________

They are perpendicular. correct option

For lines to be perpendicular, product of slope should be equal to -1.

-2*1/2 = -1

we can see that product of slope should be equal to -1 .

Thus lines are perpendicular

______________________________________

They are the same line. wrong option

For lines to be same both slope and y intercept should be same.

Y intercept is same but the slopes are different -2 and 1/2 .

Thus lines are not the same line.

__________________________________________

They are not related. wrong option

As we have found that the lines are perpendicular .

So this option is intuitively wrong

4 0

3 years ago

You are looking for a new cell phone plan. The first company, Cellular-Tastic (f), charges a monthly fee of $35 and $0.11 per mi

Bingel [31]

Answer:

A. 200 minutes

Step-by-step explanation:

4 0

2 years ago