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
1.085/12 value?
- A. 90
- B. 90 * 5/1.085
- C. 90 * 5/12
- D. 90.5
Correct Answer & Rationale
Correct Answer: C
To find the value of 1.085/12, we need to simplify the expression. Option C, 90 * 5/12, correctly represents a simplified fraction of 90 divided by 12, multiplied by 5. This yields a value consistent with the original division. Option A (90) is incorrect as it does not involve the division by 12. Option B (90 * 5/1.085) incorrectly uses 1.085 as a divisor instead of 12, leading to an inaccurate calculation. Option D (90.5) is also incorrect as it does not relate to the division of 1.085 by 12, resulting in a value that does not reflect the operation required.
To find the value of 1.085/12, we need to simplify the expression. Option C, 90 * 5/12, correctly represents a simplified fraction of 90 divided by 12, multiplied by 5. This yields a value consistent with the original division. Option A (90) is incorrect as it does not involve the division by 12. Option B (90 * 5/1.085) incorrectly uses 1.085 as a divisor instead of 12, leading to an inaccurate calculation. Option D (90.5) is also incorrect as it does not relate to the division of 1.085 by 12, resulting in a value that does not reflect the operation required.
15 + 3(7 + 1) - 12?
- A. 21
- B. 25
- C. 27
- D. 172
Correct Answer & Rationale
Correct Answer: C
To solve the expression 15 + 3(7 + 1) - 12, follow the order of operations (PEMDAS/BODMAS). First, calculate the expression inside the parentheses: 7 + 1 equals 8. Next, multiply by 3: 3 * 8 equals 24. Now, add 15: 15 + 24 equals 39. Finally, subtract 12: 39 - 12 equals 27. Option A (21) is incorrect as it does not account for the multiplication. Option B (25) mistakenly adds instead of correctly subtracting the final value. Option D (172) is far too high, likely due to miscalculating the operations. Thus, the final result is 27, confirming option C as the correct choice.
To solve the expression 15 + 3(7 + 1) - 12, follow the order of operations (PEMDAS/BODMAS). First, calculate the expression inside the parentheses: 7 + 1 equals 8. Next, multiply by 3: 3 * 8 equals 24. Now, add 15: 15 + 24 equals 39. Finally, subtract 12: 39 - 12 equals 27. Option A (21) is incorrect as it does not account for the multiplication. Option B (25) mistakenly adds instead of correctly subtracting the final value. Option D (172) is far too high, likely due to miscalculating the operations. Thus, the final result is 27, confirming option C as the correct choice.
Graph for data over time?
- A. Bar
- B. Line
- C. Stem-and-leaf
- D. Box-and-whisker
Correct Answer & Rationale
Correct Answer: B
A line graph is ideal for displaying data over time as it effectively shows trends and changes by connecting data points with a continuous line, making it easy to visualize patterns. Option A, a bar graph, is better suited for comparing discrete categories rather than illustrating changes over time. Option C, a stem-and-leaf plot, is primarily used for displaying the distribution of numerical data and is not designed for time-series analysis. Option D, a box-and-whisker plot, summarizes data distribution and highlights outliers but does not convey trends over time effectively.
A line graph is ideal for displaying data over time as it effectively shows trends and changes by connecting data points with a continuous line, making it easy to visualize patterns. Option A, a bar graph, is better suited for comparing discrete categories rather than illustrating changes over time. Option C, a stem-and-leaf plot, is primarily used for displaying the distribution of numerical data and is not designed for time-series analysis. Option D, a box-and-whisker plot, summarizes data distribution and highlights outliers but does not convey trends over time effectively.
Digit 1 in ten thousands 9 in ones? Select ALL.
- A. 12,679
- B. 12,769
- C. 12,796
- D. 21,679
- E. 21,769
Correct Answer & Rationale
Correct Answer: A,B: 1 ten thousands, 9 ones. C: 6 ones. D,E,F: 2 ten thousands. Place values must match both conditions.
To identify numbers with 1 in the ten thousands place and 9 in the ones place, we analyze each option. - **A (12,679)**: The digit 1 is in the ten thousands place, and 9 is in the ones place, meeting both criteria. - **B (12,769)**: Here, 1 is again in the ten thousands place, and 9 is in the ones place, satisfying the conditions. - **C (12,796)**: The digit in the ones place is 6, not 9, which disqualifies it. - **D (21,679)**: The digit in the ten thousands place is 2, failing to meet the first condition. - **E (21,769)**: Similarly, 2 is in the ten thousands place, not 1. - **F (21,796)**: Again, 2 is in the ten thousands place, disqualifying this option. Only options A and B fulfill both requirements, confirming their validity.
To identify numbers with 1 in the ten thousands place and 9 in the ones place, we analyze each option. - **A (12,679)**: The digit 1 is in the ten thousands place, and 9 is in the ones place, meeting both criteria. - **B (12,769)**: Here, 1 is again in the ten thousands place, and 9 is in the ones place, satisfying the conditions. - **C (12,796)**: The digit in the ones place is 6, not 9, which disqualifies it. - **D (21,679)**: The digit in the ten thousands place is 2, failing to meet the first condition. - **E (21,769)**: Similarly, 2 is in the ten thousands place, not 1. - **F (21,796)**: Again, 2 is in the ten thousands place, disqualifying this option. Only options A and B fulfill both requirements, confirming their validity.