INPUT ARTICLE: Article: R=5bd6ba{\displaystyle R=5bd-6ba}. Factor out the b{\displaystyle b}: R=b(5d6a){\displaystyle R=b(5d-6a)}. Isolate the b{\displaystyle b} by dividing each side by the expression in parentheses:R5d6a=b(5d6a)5d6a{\displaystyle {
rac {R}{5d-6a}}={
rac {b(5d-6a)}{5d-6a}}}R5d6a=b{\displaystyle {
rac {R}{5d-6a}}=b} The formula is C=2r{\displaystyle C=2\pi {r}} Understand what each variable stands for. In this formula, C{\displaystyle C} is the circumference, and r{\displaystyle r} is the radius. So you need to isolate the r{\displaystyle r} to solve for the radius. Isolate the r{\displaystyle r} by dividing both sides of the equation by 2{\displaystyle 2\pi }:C2=2r2{\displaystyle {
rac {C}{2\pi }}={
rac {2\pi {r}}{2\pi }}}C2=r{\displaystyle {
rac {C}{2\pi }}=r} If desired, reverse the order of the equation for standard form: r=C2{\displaystyle r={
rac {C}{2\pi }}}. y=12x+5{\displaystyle y={
rac {1}{2}}x+5} Recall that standard form is Ax+By=C{\displaystyle Ax+By=C}. Cancel the fraction by multiplying each side of the equation by 2:2y=2(12x+5){\displaystyle 2y=2({
rac {1}{2}}x+5)}2y=x+10{\displaystyle 2y=x+10} Subtract x{\displaystyle x} from both sides of the equation:2yx=x+10x{\displaystyle 2y-x=x+10-x}2yx=10{\displaystyle 2y-x=10} Rearrange the y{\displaystyle y} and x{\displaystyle x} variables so that they are in the standard form: x+2y=10{\displaystyle -x+2y=10}. Multiply both sides by 1{\displaystyle -1}, since A{\displaystyle A} should be a positive integer for standard form:1(x+2y)=1(10){\displaystyle -1(-x+2y)=-1(10)}x2y=10{\displaystyle x-2y=-10}

SUMMARY: Solve this equation for b{\displaystyle b}. Solve the circumference of a circle formula for the radius. Rewrite this equation of a line in standard form.

INPUT ARTICLE: Article: To make caramel using the wet method, you will need two cups of white, granulated sugar, half a cup of water and a quarter teaspoon of lemon juice or cream of tartar. If you only require a small amount of caramel, you can halve the quantities provided above: one cup of sugar, a quarter cup of water and 1/8 teaspoon of lemon juice or cream of tartar. Depending on the desired thinness or thickness, your ratio of sugar to water will vary. The thinner you want the sauce, the more water you should add. Watch the mixture closely until it reaches a uniform rich, brown color. When the entire contents of the pot reach this even tone and are slightly thickened, you know the caramelizing process is done. As soon as the caramel reaches the desired color, remove it from the heat immediately. If you leave the caramel too long it will turn almost black in color and have a burnt, bitter smell. If this happens, you will need to begin again. Use your caramel to top a flan, to make caramel candies or spun sugar, or simply drizzle it over ice cream! Caramel hardens very quickly after it cools down. If you wait too long to use it on your dessert, it could be too stiff to pour or spread. If this happens, simply place the saucepan back over a low heat and wait for the caramel to liquefy again. Swirl the pan rather than stir.

SUMMARY: Gather your ingredients. Know when the caramelization is complete. Use caramelized sugar on dessert immediately.

INPUT ARTICLE: Article: Don't try to wing for someone who is significantly less appealing than you. These are harsh words, but they are true. You and your friend should be pretty similar in terms of your attractiveness, your outgoing nature, and your general appeal. Otherwise, the people you meet are likely to latch on to you, and your buddy will feel even worse. This doesn't mean that your friend can't appeal to people just because they're less attractive than you. But if they also lack charisma and flirting skills, while you're a smooth operator, then you won't have much luck. That's what the wingman is for, right? If you're winging, it's either because you owe your friend one, because you're not single, or just because you want your friend to have a good time. That means you can't switch roles and take over engaging the person that your friend has their eye on. Learn how to read cues to tell which person your friend wants. You might even want to designate hand, eye, or verbal signals beforehand. When you come up to a group, make it so they notice your friend first. Stand a bit behind and to the side of your leader literally positioning yourself like a wing. Also try to replicate the leader's attitude and body language if they're going for "super-friendly" or "super-chill," follow suit. You don't have to look like a total dud during this process, of course don't make it seem like you're hiding/lurking/cowering behind your buddy. Think of yourself as the Robin to their Batman. Let your friend make the introductions and start talking with the people, while you slowly make your way into the conversation. Otherwise, it won't be clear who's in charge. Remember that Batman always talks before Robin. If there is just one person, you can let your friend talk to them first and join in later. If there are two people, give your leader a few minutes to warm up to both of them before you join in. For the rest of the night, occupying the main target's friend(s) is your primary goal. If it's a group of two, spend your time focusing on the secondary person by distracting and keeping them busy. Try to pay as little attention as possible to the primary person, even if they seem interested in you. It's important that, once you figure out which person your friend wants, you stick to the other person from the beginning. If you try to switch off midway through, your targets will get confused.

SUMMARY:
Wing only for people who are roughly at your level. Give your leader first choice of people. Let your friend take the lead. Don't initiate the conversation yourself. Keep the target's friend busy while your leader works.