Unfolding the lateral surface shows why it forms a rectangle. The side faces around the base of a prism are all rectangles, each with height equal to the prism’s height and width equal to a base edge. When you lay these faces flat in a row, their heights align, and their widths add up to the base’s perimeter. That entire flattened strip is a single rectangle, with height the prism’s height and width equal to the base perimeter. A circle or triangle wouldn’t fit because the lateral surface is made of straight faces, and a square wouldn’t accommodate the continuous strip of side faces. So the unfolded lateral surface is a rectangle.

Mode is the value that appears most often in a data set. In this set, 4 shows up twice while the others—2, 7, and 9—each appear once. Because 4 has the highest frequency, it is the mode. The other numbers don’t fit because they occur less frequently. (There would be more than one mode only if another value also appeared twice.)

Solving linear inequalities by isolating x and keeping the inequality direction when you divide by a positive number. Start with 5x - 7 ≤ 3x + 5. Subtract 3x from both sides to collect the x terms: 2x - 7 ≤ 5. Then add 7 to both sides: 2x ≤ 12. Divide by 2 (a positive number), which keeps the inequality direction the same: x ≤ 6. This means all numbers x that are 6 or smaller satisfy the inequality. For example, x = 6 gives 23 ≤ 23, which is true, while x = 7 gives 28 ≤ 26, which is false. So the best answer is x ≤ 6.

Like terms are terms that share the same variable part—exactly the same variable raised to the same power. The coefficients in front of that shared variable part can be different, and that difference is what you use when you combine like terms. So, terms like 3x and -5x are like terms because they both have the same variable part, x, with the same exponent. Their coefficients can differ, and you would add or subtract those coefficients when simplifying, giving -2x in this case. Terms that have different variable parts, like 3x and 4x^2, are not like terms, because the variable part isn’t the same. Constants are terms with no variable at all; two constants are like terms with each other, since they have the same (empty) variable part. The description that best captures this is that like terms have the same variable part, and their coefficients may differ.