Let's go over the math problems one by one. Here's a summary:

B. Circle problems:

1. Find the circumference of a circle to the nearest tenth if the radius is 12 cm. The formula for circumference is $C = 2\pi r$, where $r$ is the radius. Given $r = 12 \, \text{cm}$, you have: $C = 2\pi \times 12 \approx 75.4 \, \text{cm}$

2. Find the area of a circle in terms of pi, if the diameter is 20 cm. The formula for the area of a circle is $A = \pi r^2$. The radius $r$ is half the diameter, so: $r = \frac{20}{2} = 10 \, \text{cm}$ The area is: $A = \pi \times 10^2 = 100\pi \, \text{cm}^2$

3. Write an equation using $r$ for radius and $d$ for diameter that represents the relationship between radius and diameter. The relationship is simply: $d = 2r$ or equivalently $r = \frac{d}{2}$.

F. Cost formula: You are asked to identify the correct formula for determining the number of printers purchased. The given formula is: $T = 581s + 150p$ where $T$ is the total cost, $s$ is the number of computers, and $p$ is the number of printers.

From the options:

• A: $p = \frac{T - 581s}{150}$ (Correct choice)
• B: $p = T - 581s$
• C: $p = \frac{T - 581s}{150}$ (Correct choice)
• D: $p = T - 581s - 150$

G. Find the y-intercept: You need to find the y-intercept for the equations given.

• For $x - 5y = -20$, when $x = 0$: $0 - 5y = -20 \quad \Rightarrow \quad y = 4$

H. Solve the equations:

1. $(2x - 10) = 3(x - 10)$ Solve step by step: $2x - 10 = 3(x - 10)$ Expanding and solving: $2x - 10 = 3x - 30$ $2x - 3x = -30 + 10$ $-x = -20 \quad \Rightarrow \quad x = 20$

2. $-2(x - 10) = 3(x - 10)$ Follow a similar process to solve: $-2(x - 10) = 3(x - 10)$ $-2x + 20 = 3x - 30$ $-2x - 3x = -30 - 20$ $-5x = -50 \quad \Rightarrow \quad x = 10$

3. $\frac{x + 2}{3} - \frac{x - 15}{4} = 0$ Clear the denominators and solve: $\text{Multiply through by 12: } 12\left(\frac{x + 2}{3} - \frac{x - 15}{4}\right) = 0$ $4(x + 2) - 3(x - 15) = 0$ $4x + 8 - 3x + 45 = 0$ $x = -53$

4. $\frac{3}{3}(x - 12) = \frac{1}{6}(x + 20)$ Solve the equation: $(x - 12) = \frac{1}{2}(x + 20)$ $2(x - 12) = x + 20$ $2x - 24 = x + 20$ $x = 44$

Let me know if you'd like further explanation or if you have any specific questions!

5 related questions you might find useful:

1. How do you calculate the surface area of a sphere given its radius?
2. What is the difference between the area and circumference of a circle?
3. How can you convert between different units of measurement for the circumference?
4. How would you solve for the cost of a printer if given the total cost and number of computers?
5. How do you find the equation of a line from two given points?

Tip: When solving equations involving fractions, it's often useful to clear the denominators by multiplying the entire equation by the least common denominator (LCD).