You want to paint a piece of pottery at an art studio. The total cost is the cost of the piece plus an hourly studio fee. There

Answer:

50

Step-by-step clarification:

The equation that represents the total cost is in the format of a linear equation y = mx + c

Here, m signifies the slope of the line

c indicates the y-intercept, showing where the line intersects the y-axis

When the equation y = 150x + 50 is plotted, it will form a linear graph where the y-intercept corresponds to 50, as observed in the standard form of a linear equation.

Response:

Step-by-step explanation:

Given data:

Annual cost for members:

Required:

Calculate the yearly expense for non-members

From the context, we infer that:

A non-member pays $0.20 per game;

Annual cost can be determined using the formula;

y = Amount * Number of Games

Where:

Amount = $0.2, Number of Games = x

Convert 0.2 to a fraction:

Divide the numerator and denominator by 2:

Therefore, the yearly expense for non-members is

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.

Answer and Detailed Explanation:

Below is the response provided