Rectangle A measures 12 cm by 3 cm. Rectangle B is a scaled copy of Rectangle A. Select all of the measurement pairs that could

Complete question;

A booster club financed pizzas for an end-of-season celebration. The cost was $13 for each pepperoni pizza and $11 for each plain pizza. They purchased a

total of 18 pizzas for the event, totaling $212.

Organize the numbers into an equation that represents this scenario with x being the number of pepperoni pizzas and y being the number of plain pizzas purchased.

Answer:

13x + 11y = 212

Step-by-step explanation:

Two varieties of pizza were purchased: pepperoni and plain. The pepperoni variety cost $13 each while the plain one cost $11 each. In total, they bought 18 pizzas.

The overall expenditure on the pizzas was $212.

total number of pizzas = 18

total amount spent on pizzas = $212

x represents the number of pepperoni pizzas

y represents the number of plain pizzas

The cost of the pepperoni pizzas is derived by multiplying the number of pizzas by their individual price. The same calculation applies for the plain pizzas.

Therefore, by summing the costs of both pizza types, we arrive at the total price for the pizzas.

13x + 11y = 212

Answer:

It could either be 455 or 680, based on assumptions.

Step-by-step explanation:

Assuming the three choices are distinct, we can calculate...

  15C3 = 15·14·13/(3·2·1) = 35·13 = 455

ways to create the pizza.

___

In the case where two or more of the toppings may be identical, this would lead to...

  2(15C2) + 15C1 = 2·105 + 15 = 225

additional combinations, resulting in a grand total of...

  455 + 225 = 680

unique pizza varieties.

__

There is a multiplication factor of 2 for the two-topping selections, since it allows for variations like double anchovies and tomatoes or double tomatoes and anchovies when the topping choices are anchovies and tomatoes.

_____

nCk = n!/(k!(n-k)!)

Answer:

Refer to the explanation below.

Step-by-step explanation:

We start with a small aircraft that flies 760,320 yards within a duration of 2 hours.

A)

The formula for distance is:

To isolate the rate r, we divide both sides by time:

B)

To calculate the rate in yards per hour, divide the total yards by the hours taken. Therefore:

Perform division:

Thus, the aircraft speeds at 380,160 yards every hour.

C)

There are 1,760 yards in a mile.

To compute the speed in miles per hour, we apply dimensional analysis.

We recognize the rate is 380,160 yards per hour:

To cancel "yards" from the numerator, we multiply by 1 mi/1,760 yards. Therefore:

This eliminates yards:

Now, multiply the values across:

Then divide:

The final rate for the plane is 216 miles per hour.

D)

Miles are a more appropriate measurement in this context because the distance is substantial, making it impractical to express using yards. A rate of 380,160 yards per hour is excessive, whereas 216 miles per hour provides a clearer understanding.

Here, 'a' relates to 0.

There are two scenarios for 'r' and 't'.

Scenario 1.

Both are positioned on the same side to the right of 'a'.

In this case, 'r' would equal 5, and 't' would equal 7.

The midpoint between 'r' and 't' is .

Scenario 2.

If both are found to the left of 'a'.

Then 'r' would equal -5, while 't' would equal -7.

The midpoint is .

Scenario 3.

If 'r' is right of 'a' and 't' is left of 'a'.

Thus 'r' equals 5 and 't' equals -7.

The midpoint is .

Scenario 4.

If 'r' is left of 'a' while 't' is right of 'a'.

In this case, 'r' corresponds to -5 and 't' corresponds to 7.

The midpoint is .

The potential midpoint coordinates for 'rt' are 6, -6, 1, and -1.