Natasha is planning a school celebration and wants to have live music and food for everyone who attends. She has found a band th

Answer:

Using a scale of 2" means "will take the original and enlarge it to twice its size".

Thus, the resulting photocopy will be double the dimensions of the original.

Step-by-step explanation:

Answer:

The variable x lies within the interval of all positive real numbers less than 5 cm.

Detailed solution:

Problem statement:

Determine the volume of the open-topped box as a function of the side length x (in centimeters) of the square cutouts.

Refer to the provided diagram for clarity.

Define:

x → length in centimeters of each square cutout side

The volume of the box with open top can be written as:

Given this, we have:

By substitution:

Determine the domain of x:

Because:

Therefore:

Domain is the interval (0,5)

That means all real numbers strictly greater than zero and less than 5 cm are valid for x.

Hence, the volume V as a function of x is:

Answer:

Find below:

Step-by-step explanation:

To determine this, we will either calculate the total cost of acquiring 40 bouquets at $2.50 each or find the single bouquet’s cost at $120.

Cost of one in pack of 40 priced at $120.

120 divided by 40 equals $3

Now, we notice that $3>$2.50

This indicates Kendra has made an error by purchasing the 40 bouquet pack at $120

Hope this helps.

Answer:

A. Combining one pound of pistachios with one pound of almonds costs $20.

C. Decreasing the almond quantity by one pound leads to a total price of $40.

E. The price p (in dollars) per pound of pistachios is represented by the equation 2p + 3(p – 4) = 48.

Step-by-step explanation:

Let:

x = cost per pound of pistachios

y = cost per pound of almonds

We know that

x = y + 4 (Equation A)

2x + 3y = 48 (Equation B)

Substitute x from Equation A into Equation B:

2(y + 4) + 3y = 48

2y + 8 + 3y = 48

5y = 48 – 8

y = 8

Find x:

x = 8 + 4 = 12

Therefore, pistachios cost $12 per pound and almonds cost $8 per pound.

Verify the statements:

Case A) One pound of each equals $20.

True, since 12 + 8 = 20.

Case B) Pistachios cost twice as much as almonds.

False, because 2 × 8 = $16 ≠ $12.

Case C) Reducing almond pounds by 1 yields $40 total.

True, as 2(12) + 2(8) = 24 +16 = 40.

Case D) The almond cost modeled by 2(a – 4) + 3a = 48.

False; it should be 2(a + 4) + 3a = 48.

Case E) The pistachio cost modeled by 2p + 3(p – 4) = 48.

True, since p = a + 4 implies a = p – 4.