Test 5 Section 4 - #8 (page 652)

This one is based on that all-important fact: parabolas are symmetrical! When they say f(b) = f(3), that's another way of saying that you have two points, (b,y) and (3,y), and the y-values are the same. So look at the graph, and see what that y-value is!

On the graph, I'm seeing the point (3,5), so our other point must be (b,5). The only other place this graph goes through y=5 is at (-1,5), so b must equal -1.

Test 5 Section 4 - #15 (page 655)

This one is going to be a pain, because it's fractions. Blech.

Anyway, we've got 1/5 of a cup of OJ. which means we have 4/5 left to go to get to a full cup. We have to split that 4/5 up 3 ways, because the question tells us that the mix we use to fill the cup is split evenly in 3 parts.  Forget about the other parts; we only care about the OJ.

To find how much more OJ we add, first convert 4/5 to 12/15.  That's nice and divisible by 3.  What's one third of 12/15? Because that's how much more OJ we add.  We add 4/15 of a cup more OJ to our mix.

We started with 1/5 of a cup, which I'm going to convert to 3/15 now so we're adding with common denominators.  We're adding 4/15 of a cup more OJ to our mix that started with 3/15 of a cup. We end up with 7/15 of a cup of OJ.

Test 5 Section 4 - #16 (page 655)

We can kinda PLUG-IN here, even though there aren't answer choices.  It's a percent question at the heart of it, so we just need to find a way to be dealing with 100, to make our lives easier.

What we want is for 4b to be equal to 100.  That way, it's easy for us to figure out what 125% of 4b is. So let's say b = 25, which makes 4b = 100.

125% of 100 is 125, so we need to solve:

a +2b = 125 

Plug-in b = 25:

a + 2(25) = 125 

a + 50 = 125

a = 75

Then just keep on plugging in:

a/b = 75/25

a/b = 3

Our answer is 3.

Test 5 Section 4 - #13 (page 654)

The first thing we want to do any time we have weird stuff like 2 f(p) = 20 is get the f(p) out of there:

f(x) = x+1, 

so f(p)=p+1

Now let's work on solving for p:

2(p+1)=20

p+1 = 10

p=9

We're not done yet, of course.  The question asked us for f(3p), which we can now rewrite as f(27).  Just plug 27 into the function like we did with p before:

f(27) = 27 + 1

f(27) = 28

Test 5 Section 4 - #12 (page 654)

The median is just the middle number in a list. Since we're dealing with consecutive numbers, we can just list the 9 consecutive numbers that have 42 in the middle. If we want to be really careful, we can start in the middle and work outward until we have 9 numbers:

42

41, 42, 43

40, 41, 42, 43, 44

39, 40, 41, 42, 43, 44, 45

38, 39, 40, 41, 42, 43, 44, 45, 46

What's the largest number in our list?  46.