Rearrange that equation: x + 2y = y x = –y x/y = –1 from Tumblr https://ift.tt/2EP6ejY
Note that the SAT doesn’t test properties of even and odd like this, although the old SAT (pre-2016) used to. The product of two numbers will be even if and only if one or both of the numbers being multiplied is even. Therefore, you know any card showing an odd number must have an even (more…)
A semicircle is exactly half a circle, so take the formula for circumference (C = 2πr) and divide by 2. Since r = 2, you end up with (2π(2))/2 = 2π. That covers the curved part. You know the straight part has a length of 4 because the radius of the semicircle is 2. 4 + 2π is (more…)
d = 30 + 2(40 – s) The machine begins the day with $30 inside, so that’s the “30 +” part. Easy enough. The variable s is defined as how many sodas the machine has in it, but what we really care about is how many sodas are sold. We know the machine begins the day with (more…)
Trigonometry does the trick here. Below is that line making a 42° angle with the positive x-axis. I’ve also drawn a dotted segment to make myself a neat little right triangle. Remember that slope is rise over run—how high the line climbs divided by how far it travels right. In this case, the dotted segment (more…)
You can make two equations here. First, you know the total number of marbles is 103, so: The second equation is more complicated, so let’s do it in parts. First, he gives away 15 red marbles, so he should have r – 15 left. He gives away 2/5 of his blue marbles, so he should have (more…)
This question comes from my own book, so my tips on how to deal with these can be found in the same chapter. The main key to getting it right is making sure you translate the words into math correctly. Note that although the question tells you that Tariq makes brownies and Penelope makes cookies, (more…)
Draw this out. Start with the two points you’re given. Now remember that the shape is a rectangle, and that you’re told that point B is on the x-axis. The only way that happens is if B is at (5, 0). Point D, by the same logic, must be at (–3, 2). Now draw the rectangle (more…)
Start with the second equation, which tells you that t = 4. If t = 4, then you can rewrite the first equation as follows (and solve): 4u – u = 18 3u = 18 u = 6 from Tumblr https://ift.tt/2oP7c55
Think of it this way: the g function is doing SOME AS-YET-UNKNOWN THINGS to (–x + 7) to turn it into (2x + 1). Of the simple mathematical operations probably at play here (addition, subtraction, multiplication, division) what could be going on? First, the only way you go from –x to 2x is you multiply by –2. So (more…)
One way to make sure you get questions like these right is to plug in some values to see which equation makes sense. For example, you might choose to plug in 0 for h here because you know that at zero feet above sea level the boiling point should be 212° F. Choices C and D (more…)
If it’s falling at a constant rate during the period, then we can conclude that it fell (3.4 mb/hr)(5 hr) = 17 mb. Now we just need to convert mb to mm Hg, using the given scale. Solve that for x and you get roughly 12.8. from Tumblr https://ift.tt/2w1cbUe
I’ll draw this as best I can: Look OK? Now let me draw a few more segments in blue… See what’s going on there? All of the small triangles in the figure are the same! (You can prove this with triangle similarity/congruence rules easily enough—I won’t spend the time doing so here, though.) We (more…)
The thing to remember about functions is that they do the same thing to whatever is inside the parentheses. So don’t worry about the r vs. the h. They could use x, or a little star symbol, or whatever else they want. What matters is that the function f, as defined here, will equal zero (more…)
Whenever you have to square both sides to solve, you have to check for extraneous solutions. That tells you m could be 2 or –10, but because part of the solution was squaring both sides, you need to run both possible solutions through the original equation.Try 2 first: That works, now how about –10? Nope. Remember (more…)