I have a history test one week from today. How should I study?
In order to reduce stress, you should start studying as earlier as possible. Did your teacher give you a study guide? You should definitely fill it out, because teachers often pull questions for the test right from the study guide. Did you take notes in class? First, organize them by topic. Then, you should read over those, and if there is anything you don't remember or don't understand, try finding it in the index of your textbook and reading the section on that concept, or even watching a video on youtube. Next, make flashcards from your study guide and/or class notes, including key concepts, people, and places. If there is some concept that your teacher mentioned multiple times, it's important and you should know it. Then study those flashcards for an hour or two a day, every day. You can quiz yourself, or have a friend, parent, or sibling quiz you. Studying for an hour or more a day may sound tiring, but it is much better than trying to cram the night before the test. Don't forget to take breaks every once in a while, to have a snack and let your brain rest. The night before your test, eat a healthy dinner and try to go to bed early. A good night's sleep is essential for doing well.
You are shopping for a new shirt, and your favorite store is having a sale. Originally, the shirt cost 20 dollars, but a sign says that every shirt is 25% off. How much does the shirt cost now?
We need to find out how much 25% of 20 dollars is, and then subtract that amount from the original 20 dollars. Two this, we need to write 25% as a decimal. This is 0.25 because we move the decimal place 2 to the left when dealing with percents to fractions. Then we need to multiply 0.25 times 20. An easier way to do this will be to convert 0.25 into a fraction, which is 1/4 because 0.25 fits into 1 four times. Then (1/4) x 20 = 20/4 = 5. So 25% of 20 is 5. Then 20-5 = 15 so the final price of the shirt after the sale is 15 dollars. Alternatively, if the sale is 25% off, that means that 100-25 = 75% of the price is left over. Then we can do 0.75 x 20 = (3/4) x 20 = 60/4 = 15 dollars.
Simplify the following expression: [(k^2 + 3k - 70)/(5k + 50)] x [(5k + 50)/(7k^2 - 49k)].
First, notice that the left expression has (5k+50) in the denominator and the right expression has (5k+50) in the numerator. Since anything divided by itself is 1, we can cancel both of those expressions and we are left with (k^2 + 3k - 70)/(7k^2 - 49k). Now let's simplify the numerator: k^2 + 3k - 70. We need to factor by finding 2 numbers that multiply to -70 and add to 3, such as -7 and 10. Therefore, the numerator will be (k-7)(k+10). Now let's look at the denominator: (7k^2 - 49k). Since both 7k^2 and -49k are divisible by 7k we can pull that out as a common factor to get: 7k(k -7). Now overall, we have [(k-7)(k+10)]/(7k(k-7)). Since both the numerator and denominator have (k-7), we can cancel that from both the top and bottom. Then we have our final answer: (k+10)/7k.