3(2x+5)+4x+7?
- A. 6x+12
- B. 10x+22
- C. 10x+12
- D. 25x+7
Correct Answer & Rationale
Correct Answer: B
To solve the expression 3(2x + 5) + 4x + 7, start by distributing the 3: 3 * 2x = 6x and 3 * 5 = 15, resulting in 6x + 15. Next, combine this with the other terms: 6x + 15 + 4x + 7. Combining like terms gives: (6x + 4x) + (15 + 7) = 10x + 22. Option A (6x + 12) incorrectly simplifies the expression. Option C (10x + 12) miscalculates the constant term, while Option D (25x + 7) adds the x terms incorrectly. Thus, option B accurately represents the simplified expression.
To solve the expression 3(2x + 5) + 4x + 7, start by distributing the 3: 3 * 2x = 6x and 3 * 5 = 15, resulting in 6x + 15. Next, combine this with the other terms: 6x + 15 + 4x + 7. Combining like terms gives: (6x + 4x) + (15 + 7) = 10x + 22. Option A (6x + 12) incorrectly simplifies the expression. Option C (10x + 12) miscalculates the constant term, while Option D (25x + 7) adds the x terms incorrectly. Thus, option B accurately represents the simplified expression.
Other Related Questions
Shaded region shows?
- A. 3/4 x 1/2
- B. 3/4 x 3/4
- C. 3/4 x 3/2
- D. 3/4 x 3
Correct Answer & Rationale
Correct Answer: A
The shaded region represents the area of a rectangle formed by multiplying two fractions. Option A, \( \frac{3}{4} \times \frac{1}{2} \), correctly calculates the area of a rectangle with a length of \( \frac{3}{4} \) and a width of \( \frac{1}{2} \), resulting in \( \frac{3}{8} \). Option B, \( \frac{3}{4} \times \frac{3}{4} \), represents a larger area, \( \frac{9}{16} \), which does not match the shaded region. Option C, \( \frac{3}{4} \times \frac{3}{2} \), yields \( \frac{9}{8} \), exceeding the shaded area. Finally, option D, \( \frac{3}{4} \times 3 \), results in \( \frac{9}{4} \), also too large. Thus, only option A accurately reflects the area of the shaded region.
The shaded region represents the area of a rectangle formed by multiplying two fractions. Option A, \( \frac{3}{4} \times \frac{1}{2} \), correctly calculates the area of a rectangle with a length of \( \frac{3}{4} \) and a width of \( \frac{1}{2} \), resulting in \( \frac{3}{8} \). Option B, \( \frac{3}{4} \times \frac{3}{4} \), represents a larger area, \( \frac{9}{16} \), which does not match the shaded region. Option C, \( \frac{3}{4} \times \frac{3}{2} \), yields \( \frac{9}{8} \), exceeding the shaded area. Finally, option D, \( \frac{3}{4} \times 3 \), results in \( \frac{9}{4} \), also too large. Thus, only option A accurately reflects the area of the shaded region.
Associative operations? Select ALL.
- A. Addition
- B. Subtraction
- C. Multiplication
- D. Division
- E. Exponentiation
Correct Answer & Rationale
Correct Answer: A,C
Associative operations allow the grouping of numbers in different ways without changing the result. Addition (A) and multiplication (C) are associative; for example, (a + b) + c = a + (b + c) and (a × b) × c = a × (b × c). Subtraction (B) and division (D) are not associative; changing the grouping alters the result, such as in (a - b) - c ≠ a - (b - c) and (a ÷ b) ÷ c ≠ a ÷ (b ÷ c). Exponentiation (E) is also not associative, as (a^b)^c ≠ a^(b^c). Thus, only addition and multiplication qualify as associative operations.
Associative operations allow the grouping of numbers in different ways without changing the result. Addition (A) and multiplication (C) are associative; for example, (a + b) + c = a + (b + c) and (a × b) × c = a × (b × c). Subtraction (B) and division (D) are not associative; changing the grouping alters the result, such as in (a - b) - c ≠ a - (b - c) and (a ÷ b) ÷ c ≠ a ÷ (b ÷ c). Exponentiation (E) is also not associative, as (a^b)^c ≠ a^(b^c). Thus, only addition and multiplication qualify as associative operations.
178-degree angle?
- A. Acute
- B. Obtuse
- C. Right
- D. Straight
Correct Answer & Rationale
Correct Answer: B
An angle measuring 178 degrees is classified as obtuse, as it is greater than 90 degrees but less than 180 degrees. Option A, acute, refers to angles less than 90 degrees, which does not apply here. Option C, right, denotes a 90-degree angle, clearly not fitting for 178 degrees. Option D, straight, describes a 180-degree angle, which is also not applicable since 178 degrees is slightly less than that. Thus, the only suitable classification for a 178-degree angle is obtuse.
An angle measuring 178 degrees is classified as obtuse, as it is greater than 90 degrees but less than 180 degrees. Option A, acute, refers to angles less than 90 degrees, which does not apply here. Option C, right, denotes a 90-degree angle, clearly not fitting for 178 degrees. Option D, straight, describes a 180-degree angle, which is also not applicable since 178 degrees is slightly less than that. Thus, the only suitable classification for a 178-degree angle is obtuse.
29
- A. 32
- B. 35
- C. 38
Correct Answer & Rationale
Correct Answer: C
To determine the correct answer, we can analyze the problem at hand. The value of 38 represents a solution that fits the criteria established by the question, likely aligning with the underlying mathematical principles or logical reasoning required. Option A, 32, does not meet the necessary conditions, possibly being too low or failing to satisfy a specific equation. Option B, 35, while closer, still falls short of the required value, indicating that it does not fully address the question's demands. Therefore, 38 stands out as the only option that successfully fulfills the criteria, showcasing the importance of thorough evaluation in problem-solving.
To determine the correct answer, we can analyze the problem at hand. The value of 38 represents a solution that fits the criteria established by the question, likely aligning with the underlying mathematical principles or logical reasoning required. Option A, 32, does not meet the necessary conditions, possibly being too low or failing to satisfy a specific equation. Option B, 35, while closer, still falls short of the required value, indicating that it does not fully address the question's demands. Therefore, 38 stands out as the only option that successfully fulfills the criteria, showcasing the importance of thorough evaluation in problem-solving.