Question

I don’t understand this. Please help

Answer 1

5. 2nd and 4th boxes

Explanation:

These look like proportionality questions. Typically we hear about two main types of proportionalities:

1. Directly proportional, which means that two variables change in the same way (Ex. one goes up, the other goes up).
2. Inversely proportional, which means that two variables change in opposite ways (Ex. one goes up, the other goes down).

Directly proportional variables are, intuitively, on opposite sides of an equation and both in the numerator on their side. Inversely proportional variables are on opposite sides but with one in the numerator and one in the denominator.

I can't see what the top one is asking for nor the bottom of 6., but let me try and use 5. as an example. If H increases as T decreases, then the two are inversely proportional. So the form would either have to be H=1/T or T=1/H. Other variables can be thrown into the mix and not change the outcome, so the 2nd and 4th boxes are your answers for 5.

Answer 2

I'll do problem 5 to get you started.

The answer is choice B and choice D

The reason why choice B is one answer is because we have something in the form y = k/x to indicate an inverse variation. Replace x with H and y with T, and you'll get the same basic equation.

With inverse variation equations, as one variable goes down, the other variable goes up. Think of a see-saw as one way to visualize what's going on.

Or you can think of the T as T/1. So the equation T = L/H is the same as T/1 = L/H. If H were to decrease, then T would increase, and vice versa. T and H are on opposite sides of their respective fractions which may help see this opposite moving nature of each variable.

The reason why choice D is also an answer is because we can multiply both sides of T = L/H by H to get HT = L or TH = L. The equations T = L/H and TH = L are equivalent equations.