0 = (2x +4)(3x - 9) Let x= a and x=b be the solutions to the equation above. What is the value of (a)(b)?
Answer: -6 For 0 = (2x +4)(3x - 9), we can find the solutions by setting (2x +4) and (3x - 9) equal to 0. 2x +4 = 0 2x = -4 x = -2 This is one solution 3x - 9 = 0 3x = 9 x = 3 This is another solution We are told to let a and b be the solutions, meaning a and b are -2 and 3. The order does not matter, because we are multiplying. The questions asks to multiply a and b together. -2 x 3 = -6 This is our final answer
There are only two candidates in tomorrow's elections, and one of them must be elected. If the first candidate is elected, then taxes will be raised in order to build the bridge that he has promised to construct. If the the second candidate is elected, then she will not be able to increase the school's budget without increasing taxes. Furthermore, if she is elected, she will increase the school's budget. Therefore, after tomorrow's elections__________________. Which one of the following most logically completes the argument?
Correct Answer: taxes will be raised. This is the correct answer, because it is the only thing that will be true, regardless of who wins the election. There are only two scenarios available. Either the first candidate wins, or the second one does. In the first scenario, the taxes end up being raised. The reason is irrelevant. In the second scenario, we are told that the person elected "will not be able to increase the school's budget without increasing taxes." This means that increasing taxes is a NECESSARY CONDITION for increasing the school's budget. In other words, IF the school budget is increased, THEN the taxes were raised. Furthermore, we are told that IF this candidate wins, THEN the school budget will in fact be raised. If we follow this chain of conditional statements, then the second scenario will result in taxes being raised as well. Therefore, of the two possible scenarios, BOTH lead to increased taxes. Hence, the taxes must be raised.
The product (3x^-5)(4x^-5) is equal to which of the following? A. 12 B. 12x C. 12/x^10 D. 1/12x^10
Correct Answer: C In order to multiply these terms together, start off by multiplying the coefficients (3 x 4 = 12) (3x^-5)(4x^-5) = 12(x^-5)(x^-5) When multiplying exponents with the same bases, we add the exponents and keep the base. (-5 + -5 = -10) 12(x^-5)(x^-5) = 12x^-10 We don't like having negative exponents, so we must rewrite this. (Remember: x^-1 = 1/x^1) The 12 stays on top, because we are only moving the number with the exponent. 12x^-10= 12/x^10 <----Final Answer