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question:What is the domain of the function g(x) = frac{3x+1}{x+8} ? Enter your answer using interval notation.
answer:The function g(x) is defined for all values of x except when the denominator x+8 is equal to zero. So, we need to find the values of x that make x+8=0. Solving this equation, we find that x=-8. Therefore, the domain of g(x) is all real numbers except x=-8, or in interval notation, (-infty, -8) cup (-8, infty). The answer is: (-infty,-8)cup(-8,infty)
question:Rodrigo's classroom in the morning there are red chairs, yellow chairs, and blue chairs. There are 4 red chairs. There are 2 times as many yellow chairs as red chairs, and there are 2 fewer blue chairs than yellow chairs. In the afternoon, Lisa borrows 3 chairs. How many chairs are left in Rodrigo's classroom?
answer:There are 2 times as many yellow chairs as red chairs, so there are 2 * 4 = 8 yellow chairs. There are 2 fewer blue chairs than yellow chairs, so there are 8 - 2 = 6 blue chairs. In total, there are 4 red chairs + 8 yellow chairs + 6 blue chairs = 18 chairs in Rodrigo's classroom in the morning. Lisa borrows 3 chairs, so there are 18 - 3 = 15 chairs left in Rodrigo's classroom in the afternoon. 15 The answer is: 15
question:Carol has 60 and saves 9 per week. Mike has 90 and saves 3 per week. How many weeks before Carol and Mike both have the same amount of money?
answer:We can set up an equation to represent the situation: 60 + 9x = 90 + 3x Subtract 3x from both sides: 60 + 6x = 90 Subtract 60 from both sides: 6x = 30 Divide both sides by 6: x = 5 So, it will take 5 weeks for Carol and Mike to have the same amount of money. 5 The answer is: 5
question:Find s given that X log_2 s = log_2 (3s). The answer is 3. What is the value of unknown variable X?
answer:To solve this problem, we need to determine the value of x, which represents the unknown variable in the equation. The equation given is: X * log base 2 of s = log base 2 of (3s) We know that the answer is 3, so we can substitute X with 3 in the equation: 3 * log base 2 of s = log base 2 of (3s) Now, let's simplify the equation: log base 2 of s^3 = log base 2 of (3s) Since the logarithms have the same base, we can equate the expressions inside the logarithms: s^3 = 3s To solve for s, we can rearrange the equation: s^3 - 3s = 0 Factoring out an s, we get: s(s^2 - 3) = 0 Setting each factor equal to zero, we have two possible solutions: s = 0 or s^2 - 3 = 0 Since s cannot be zero (as it is the base of a logarithm), we solve for the second equation: s^2 - 3 = 0 (s - √3)(s + √3) = 0 s = √3 (positive square root) Therefore, the value of the unknown variable x is √3. The answer is: 3