OK, so you have 40 boys and 30 girls. That’s easy enough to calculate because you’re given a part:whole ratio (boys to total students) and you already know the total number of students is 70. Be careful about the second ratio, though, because it’s a part:part ratio! If the ratio of older to younger is (more…)

OK, so when you have a regular n-gon, you can figure out each angle in it using this formula: [(n-2)180]/n. In this case, 7*180/9 = 140, so we know each angle in the polygon is 140°. I couldn’t draw this quickly on the computer I’m on, so I found a good n-gon picture to mark (more…)

The midpoint formula tells you that the a segment with endpoints (a, b) and (c, d) will have a midpoint at ((a + c)/2,(b + d)/2) So we know that (x + 9)/2 = 6 and (5 + y)/2 = 3. We can solve those! (x + 9)/2 = 6 x + 9 = 12 x = 3 (5 + y)/2 = 3 5 + y = (more…)

When a system of linear equations has no solution, that means you have parallel lines, which means the lines have the same slope. So put both equations into slope-intercept form (y = mx + b) first: In order for those lines to be parallel, their slopes must be equal, which means 2/5 = -4/k. That means k must be (more…)

Just do those things and simplify: Looks like the volume of the second cylinder is half the volume of the first! 🙂 The shortcut here is to recognize that the r value gets squared but the h value doesn’t, so you can say the volume is divided by 4 then multiplied by 2. from Tumblr https://ift.tt/2De8uzO

60° is 1/6 of the circle (which has 360° of arc in total), so the length of the minor arc will be 1/6 of the circumference. 1/6 of 12π is 2π. from Tumblr https://ift.tt/2JsMj92

Huge shortcut here if you just know that for a parabola in standard ax^2 + bx + c form, the x-coordinate of the vertex will be at –b/(2a). In this case, that means it’s at –3/(2(–6)) = 3/12 = ¼. from Tumblr https://ift.tt/2CRW93a

The way to think about this (for me, anyway) begins with understanding that 2[something] + 3 = 8x – 1, and our job is to figure out what that something is. Since this question gives us answer choices, all we really need to do is try each one as the something to see what works. Since (more…)

When you have exponents with the same base and you divide them, you subtract the exponents. So from what we’re given, we know that 2x – (x – y) = 1. We can solve that for y. 2x – (x – y) = 1 2x – x + y = 1 x + y = 1 y = (more…)

Start by drawing it! Note that OC = 5 and OD = 5 because both of those are also radii. Note also that because chord CD is perpendicular to OB, it’s bisected by OB. In other words, it’s split into 2 segments each measuring 4. Things are really coming together! Because we know our Pythagorean (more…)

One of the two things being multiplied must be zero, so either x – 3 = 0 or x + 7 = 0. If x + 7 = 0, then x = –7. In that case, we can substitute into x – 3: x – 3 = –7 – 3 = –10 So x – 3 can equal 0 or –10. from Tumblr (more…)

Draw! You know point C must be on the x-axis, and that AB = BC. Since B is on the y-axis, it turns out all we need to do here is reflect point A across the y-axis. Point C must be at (8, 0), so x = 8. from Tumblr https://ift.tt/2yLFCer

The correct answer is A. Subtract c from both sides of the inequality and you’re left with 8 > 4. That’s always true! from Tumblr https://ift.tt/2Oa6SYI

In 200 ml of 30% saline, there’s (0.3)(200) = 60 ml of saline. 60 ml is 40% of what? 60 = (0.4)x 150 = x So the saline will be 40% when enough water evaporates that there’s 150 ml of solution. Therefore, 50 ml of the original 200 ml must evaporate. from Tumblr https://ift.tt/2CAqROd

Let’s work backwards, and use hours instead of distance for ease (assume the plane travels at a constant speed for our purposes). Let’s say when she woke up, she had 1 hour left in her flight. That’s half of the time she was sleeping so she must’ve slept for 2 hours. She first fell asleep (more…)