Nokea
Solve the equation 3(2x+5)=11x+5 for x. Which of the following is correct?
- A. 1
- B. 2
- C. -1
- D. -2
Correct Answer: B
Rationale: To solve the equation, distribute 3 to both terms inside the parentheses: 6x + 15 = 11x + 5. Then, move 11x to the left side by subtracting it from both sides: 6x - 11x = 5 - 15. Simplify to get -5x = -10. Divide by -5 to isolate x: x = 2. Therefore, the correct answer is x = 2. Choices A, C, and D are incorrect because they do not match the correct solution obtained by solving the equation step by step.
You may also like to solve these questions
Which of the following relationships represents no correlation between two variables?
- A. As a student's class attendance decreases, the student's overall grade remains the same
- B. As the number of hours a person exercises decreases, the weight of that person increases
- C. As the number of miles driven increases, the amount of gasoline in the tank decreases
- D. As the amount of water a plant receives increases, the growth rate of the plant increases
Correct Answer: A
Rationale: Choice A represents no correlation between two variables as it states that as a student's class attendance decreases, the student's overall grade remains the same. This scenario shows no relationship between class attendance and grade. In contrast, choices B, C, and D show clear correlations between the variables mentioned. Choice B indicates a negative correlation between exercise hours and weight gain, choice C indicates a negative correlation between miles driven and gasoline in the tank, and choice D indicates a positive correlation between water intake and plant growth rate, making them all examples of correlated relationships.
What is the mathematical expression for 'Twelve less than thrice a number'?
- A. 3x-12
- B. 12-3x
- C. 3-12x
- D. 12x-3
Correct Answer: A
Rationale: The phrase 'thrice a number' translates to 3x, and 'twelve less than' means subtracting 12 from it. Therefore, the correct expression is 3x-12. Choice B, '12-3x', represents '12 less than a number thrice,' which is the opposite of the given phrase. Choice C, '3-12x', does not correctly interpret the phrase provided. Choice D, '12x-3', represents 'a number thrice less than twelve,' which is not the same as the original phrase.
What is any number raised to the power of zero?
- A. One
- B. Itself
- C. Zero
- D. Two
Correct Answer: A
Rationale: The correct answer is A: One. Any number raised to the power of zero is always equal to 1. This is a fundamental property of exponentiation. Choice B, 'Itself,' is vague and does not specify a numerical value. Choice C, 'Zero,' is incorrect as any nonzero number raised to the power of zero is 1, not 0. Choice D, 'Two,' is incorrect as any number raised to the power of zero is 1, not 2.
How do you find the least common multiple?
- A. List all multiples of the numbers, then find the smallest common one
- B. List all factors of the numbers, then find the largest common one
- C. Divide the largest number by the smallest
- D. Multiply the two numbers together
Correct Answer: A
Rationale: The correct way to find the least common multiple is to list all the multiples of each number and then identify the smallest common multiple. Choice A is correct because it describes the correct process. Listing factors, as suggested in choice B, helps in finding the greatest common factor, not the least common multiple. Dividing the largest number by the smallest, as mentioned in choice C, does not help find the least common multiple. Multiplying the two numbers together, as stated in choice D, results in their least common multiple when the numbers have no common factors.
If (D) is the distance traveled and (R) is the rate of travel, which of the following represents the relationship between D and R for the equation D=2R?
- A. D is twice as much as R
- B. R is twice as much as D
- C. R is two times D
- D. D is two more than R
Correct Answer: A
Rationale: The equation D=2R means that D equals 2 times R, which translates to D being twice the value of R. Therefore, choice A, 'D is twice as much as R,' is the correct representation of the relationship between D and R. Choice B, 'R is twice as much as D,' incorrectly reverses the roles of D and R. Choice C, 'R is two times D,' incorrectly states the relationship between R and D. Choice D, 'D is two more than R,' does not accurately reflect the relationship presented in the equation.