Which of the following groups are subsrts of rational numbers

Irina-Kira [14]

5miles/8km = xmiles/80km

8x=400

x=50

4 0

3 years ago

Tara is using matrix multiplication to find image points of a translation. She is translating the image 2 units left and 4 units

Ahat [919]

Assuming that this is just on a 2-D coordinate plane, we must convert the expressions on to a 3-D plane since translation cannot be done on a 2-D plane. This is done by adding a dummy coordinate that does not change. Let us use "1" for this case.

Matrix:
| 0 0 -2 |(x) = (x - 2)
| 0 0 4 |(y) = (y + 4)
| 0 0 1 |(1) = 1

7 0

3 years ago

A clothing business finds there is a linear relationship between the number of shirts, Q ,it can sell and the price, P , it can

Vlad [161]

Answer:

P = -0.004Q + 149

Step-by-step explanation:

The general form of the linear equation is:

$P=aQ+b$

The slope of the equation (a) can be found by using the two given points (4,000; $133) and (27,000; $41)

$a = \frac{\$41-\$133}{27,000-4,000}\\a=-0.004$

Applying the point (4,000; $133) to the equation below yields in the linear equation for Price as a function of the number of shirts:

$P-P_0=a(Q-Q_0)\\P-133=-0.004(Q-4,000)\\P = -0.004Q+149$

The linear equation is:

P = -0.004Q + 149

8 0

2 years ago

a gift shop sells 160 wind chimes per month at $150 each. the owners estimate that for each $15 increase in price, they will sel

adell [148]

Answer:

The price per wind chime that will maximize revenue = $ 315

Step-by-step explanation:

Given - A gift shop sells 160 wind chimes per month at $150 each. the owners estimate that for each $15 increase in price, they will sell 5 fewer wind chimes per month.

To find - Find the price per wind chime that will maximize revenue.

Proof -

Given that,

Total Wind chimes selling = 160

Price of each Wind chime = $150

Now,

Given that, for each $15 increase in price, they will sell 5 fewer wind chimes per month.

So,

Let the price = 150 + 15x

So,

Number of wind Chimes sold per month = 160 - 5x

So,

Total Revenue, R = (150 + 15x)(160 - 5x)

= 24000 - 750x + 2400x - 75x²

= 24000 + 1650x - 75x²

⇒R(x) = 24000 + 1650x - 75x²

Differentiate R with respect to x , we get

R'(x) = 1650 - 150x

Now,

For Maximize Revenue, Put R'(x) = 0

⇒1650 - 150x = 0

⇒150x = 1650

⇒x = 1650/150

⇒x = 11

∴ we get

Price per Wind chime = $ 150 + 15(11)

= $ 150 + 165

= $ 315

So,

The price per wind chime that will maximize revenue = $ 315

3 0

3 years ago

What is the constant of proportionality in the equation? y=5x 0 1 4 or 5

Ann [662]

Answer:

hope it helps...

Step-by-step explanation:

The value of the constant of proportionality is k=5k=5

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y/x=ky/x=k or y=kxy=kx

The value of the constant k is equal to the value of the slope

In this problem we have

y=5xy=5x ------> is a linear direct variation

The slope is m=5m=5

therefore

The value of the constant of proportionality is k=5k=5

4 0

3 years ago