Question

sessions for the long-time client package, will she be able to create this package for her clients? A) No, because the closest package that she can offer consists of three hot yoga and three zero gravity yoga sessions. B) No, because the closest package that she can offer consists of four hot yoga and four zero gravity yoga sessions. C) Yes, because she can offer five hot yoga and five zero gravity yoga sessions. D) Yes, because she can offer six hot yoga and six zero gravity yoga sessions. 13\. Cuthbert is conducting a chemistry experiment that calls for a number of chemicals to be mixed in various quantities. The one amount of which he is unsure is grams of potassium, \(p\). If Cuthbert is certain that \(\left(3 p^2+\right.\) \(14 p+24)-2\left(p^2+7 p+20\right)=0\), what is one possible value of \(3 p+6\), the exact number of grams of potassium that Cuthbert would like to use for this experiment? A) 20 B) 18 C) 12 D) 10

Short answer

B) 18

Step-by-step solution

Simplify the given equation

We are given the equation: \((3p^2 + 14p + 24) - 2(p^2 + 7p + 20) = 0\) First, distribute the -2 into the second term inside the parentheses: \(3p^2 + 14p + 24 - 2p^2 - 14p - 40 = 0\) Now, combine like terms: \(3p^2 - 2p^2 + 14p - 14p + 24 - 40 = 0\) \(p^2 - 16 = 0\)

Solve the quadratic equation

We have the simplified equation: \(p^2 - 16 = 0\) Now we can see it's a difference of squares, so we can factor it as: \((p + 4)(p - 4) = 0\) So, by the zero-product property, p = -4 or p = 4

Calculate 3p + 6 for each value of p

1) For p = -4: 3p + 6 = 3(-4) + 6 = -12 + 6 = -6. 2) For p = 4: 3p + 6 = 3(4) + 6 = 12 + 6 = 18 As we found two possible values of 3p+6, we need to check the answer choices. Looking at the options, we can see that -6 is not present, but 18 is. The correct answer is: B) 18