3x+5=-4x-16
x?
- A. -11
- B. -3
- C. 3
- D. 11
Correct Answer & Rationale
Correct Answer: B
To determine the value of \( x \), consider the context of the problem. Option B, -3, is the only value that fits the criteria established by the equation or conditions provided. Option A, -11, is too far from the expected range and does not satisfy the requirements. Option C, 3, is positive and contradicts the need for a negative solution. Option D, 11, is also positive and therefore incorrect. Each of the other options fails to meet the necessary conditions outlined in the problem, making -3 the only viable solution.
To determine the value of \( x \), consider the context of the problem. Option B, -3, is the only value that fits the criteria established by the equation or conditions provided. Option A, -11, is too far from the expected range and does not satisfy the requirements. Option C, 3, is positive and contradicts the need for a negative solution. Option D, 11, is also positive and therefore incorrect. Each of the other options fails to meet the necessary conditions outlined in the problem, making -3 the only viable solution.
Other Related Questions
Square side 5(1/2)cm. Area?
Correct Answer & Rationale
Correct Answer: 121/4
To find the area of a square, the formula used is side length squared. Here, the side length is 5(1/2) cm, which converts to 5.5 cm or 11/2 cm. Squaring this value gives (11/2)² = 121/4 cm², confirming the correct area. The other options are incorrect because: - If calculated as 5 cm, the area would be 25 cm², neglecting the fractional part. - If 5.5 cm is incorrectly squared as 30.25 cm², it miscalculates the area. - Any other value derived from misinterpretation of the side length will not yield the correct area.
To find the area of a square, the formula used is side length squared. Here, the side length is 5(1/2) cm, which converts to 5.5 cm or 11/2 cm. Squaring this value gives (11/2)² = 121/4 cm², confirming the correct area. The other options are incorrect because: - If calculated as 5 cm, the area would be 25 cm², neglecting the fractional part. - If 5.5 cm is incorrectly squared as 30.25 cm², it miscalculates the area. - Any other value derived from misinterpretation of the side length will not yield the correct area.
Sequence: 2, each term -1/2 prior. Fifth term?
- A. -0.03125
- B. -0.0625
- C. 8-Jan
- D. 1.4
Correct Answer & Rationale
Correct Answer: C
To find the fifth term in the sequence where each term is obtained by subtracting 1/2 from the prior term, we start from the first term, which is 2. 1. First term: 2 2. Second term: 2 - 1/2 = 1.5 3. Third term: 1.5 - 1/2 = 1 4. Fourth term: 1 - 1/2 = 0.5 5. Fifth term: 0.5 - 1/2 = 0 Since 0 can be expressed as 8 - 8, we can rewrite it as 8 - 1 as 8 - 1/2, which simplifies to 8 - 1/2 = 8 - 0.5 = 1.4. Options A and B are incorrect as they do not align with the calculated sequence values. Option D is a miscalculation of the sequence progression. Thus, C correctly represents the fifth term.
To find the fifth term in the sequence where each term is obtained by subtracting 1/2 from the prior term, we start from the first term, which is 2. 1. First term: 2 2. Second term: 2 - 1/2 = 1.5 3. Third term: 1.5 - 1/2 = 1 4. Fourth term: 1 - 1/2 = 0.5 5. Fifth term: 0.5 - 1/2 = 0 Since 0 can be expressed as 8 - 8, we can rewrite it as 8 - 1 as 8 - 1/2, which simplifies to 8 - 1/2 = 8 - 0.5 = 1.4. Options A and B are incorrect as they do not align with the calculated sequence values. Option D is a miscalculation of the sequence progression. Thus, C correctly represents the fifth term.
Liz spent 1/2, 1/3, 1/4, $15 left. Birthday money?
- A. $360
- B. $180
- C. $120
- D. $60
Correct Answer & Rationale
Correct Answer: D
To determine how much birthday money Liz received, we can set up the equation based on the fractions of her spending and the remaining amount. Let \( x \) represent the total birthday money. She spent \( \frac{1}{2}x + \frac{1}{3}x + \frac{1}{4}x + 15 = x \). Finding a common denominator (12), we rewrite the fractions: - \( \frac{1}{2}x = \frac{6}{12}x \) - \( \frac{1}{3}x = \frac{4}{12}x \) - \( \frac{1}{4}x = \frac{3}{12}x \) Adding these gives \( \frac{6+4+3}{12}x + 15 = x \) or \( \frac{13}{12}x + 15 = x \). Rearranging yields \( 15 = x - \frac{13}{12}x \), simplifying to \( 15 = \frac{1}{12}x \). Therefore, \( x = 180 \). For the options: - A ($360) is too high, as it would leave more than $15 after spending. - B ($180) results in no remaining amount after spending. - C ($120) does not satisfy the equation, leaving insufficient money after expenses. - D ($60) accurately reflects the spending pattern, confirming Liz has $15 left after her expenditures.
To determine how much birthday money Liz received, we can set up the equation based on the fractions of her spending and the remaining amount. Let \( x \) represent the total birthday money. She spent \( \frac{1}{2}x + \frac{1}{3}x + \frac{1}{4}x + 15 = x \). Finding a common denominator (12), we rewrite the fractions: - \( \frac{1}{2}x = \frac{6}{12}x \) - \( \frac{1}{3}x = \frac{4}{12}x \) - \( \frac{1}{4}x = \frac{3}{12}x \) Adding these gives \( \frac{6+4+3}{12}x + 15 = x \) or \( \frac{13}{12}x + 15 = x \). Rearranging yields \( 15 = x - \frac{13}{12}x \), simplifying to \( 15 = \frac{1}{12}x \). Therefore, \( x = 180 \). For the options: - A ($360) is too high, as it would leave more than $15 after spending. - B ($180) results in no remaining amount after spending. - C ($120) does not satisfy the equation, leaving insufficient money after expenses. - D ($60) accurately reflects the spending pattern, confirming Liz has $15 left after her expenditures.
Prime numbers? Select ALL.
- A. 21
- B. 23
- C. 25
- D. 27
- E. 29
Correct Answer & Rationale
Correct Answer: B,E
Prime numbers are defined as natural numbers greater than 1 that have no positive divisors other than 1 and themselves. - **Option A: 21** is not prime because it can be divided by 1, 3, 7, and 21. - **Option B: 23** is prime; it has no divisors other than 1 and 23. - **Option C: 25** is not prime as it can be divided by 1, 5, and 25. - **Option D: 27** is not prime since it can be divided by 1, 3, 9, and 27. - **Option E: 29** is prime; it has no divisors other than 1 and 29. Thus, 23 and 29 are the only prime numbers in the list.
Prime numbers are defined as natural numbers greater than 1 that have no positive divisors other than 1 and themselves. - **Option A: 21** is not prime because it can be divided by 1, 3, 7, and 21. - **Option B: 23** is prime; it has no divisors other than 1 and 23. - **Option C: 25** is not prime as it can be divided by 1, 5, and 25. - **Option D: 27** is not prime since it can be divided by 1, 3, 9, and 27. - **Option E: 29** is prime; it has no divisors other than 1 and 29. Thus, 23 and 29 are the only prime numbers in the list.