Tuesday, March 17, 2020

The Attempted Robbery Essays

The Attempted Robbery Essays The Attempted Robbery Essay The Attempted Robbery Essay It was past midnight. Suddenly there was a knock on the door. I quickly switched on the lights. My instincts told me something was wrong. My mind quickly flew to my parents, who are currently at Grandmas to settle some urgent family matters. Could something have happened to them? Is it the police who are knocking on my door? My palm quickly started to sweat with worry. My nose suddenly picked up a smell; it was an overpowering smell of beer. My heart thumped repeatedly like horse hooves on a dirt road, giving signals to my brain to not open the door. I knew then, it was a premonition of fear and danger. But my curiosity took over any sense that I ever had. True enough, my caution was justified, for when I opened the door, two tall brooding men about 6 feet high stood in front me. They looked too drunk to stay still, as if they were wearing some slippery boots. I couldnt make out their faces because it was too dark but I didnt need to see their faces to know that they were men I should not cross. I kindly asked them to leave, but they continue to be in their drunken stupor and ignored me. They slurred swearing words towards me and my patience quickly trickled to an end and my anger rising to its peak. I felt as if I was a volcano on the verge of eruption to pour out all the lava. I screamed to them quite rudely to leave, but I regretted at once the words that I had just then uttered. As if in reply to my rude screaming, the two men started to shout obscenities at me. Then all of a sudden, something sharp glistened in the dark coming from one of the mens hand. It was a knife. I gulped in fear and judging from his strong muscles, he was indeed very strong. My brain screamed in panic and little beads of sweat formed on my forehead. I went numb with thought, and stood frozen in front of the now two menacing men. The knife-man lunged and as quick as a bolt of lightning he had the point of his knife at my throat. I was wild with increasing fear and the feeling threatened to crush me down to a collapse. My face paled to ghastly whiteness and my heart pounded like the thrumming wings of a caged bird. I continue to stand there as if I was a monument frozen for eternity. I was stunned by all the suddenness of the events and before I knew it, I was held in a vice-like grip by the other man. My heartbeat continued to thrum crazily against my ribcage and I hawked, my throat dry with fear. Reluctantly, I lead them to the drawer where my mum keeps her jewellery. I dread to think of how my mum would react after she finds out all her missing valuables that amount to thousands of dollars. The knife-man leaned over and made a grab for the trinkets. The other man momentarily forgot about me and went aside to the knife-man to also greedily swoon over all the glittery bracelets and necklaces. With sudden courage, I lifted my right hand to come down hard over the back of the knife-man. The force of the blow succeeded in taking the man right down to hit the bedside table. There was a sickening thud as the head banged against the sturdy and hard surface of the table. He was severely injured with blood covering his face and lashes of cuts from the sharp point of the table. He was dropped unconscious. The other man screamed in rage and charged towards me and with quick swiftness I grabbed the perfume on the bedside table and sprayed it into his eyes. He shrieked in fury and agony and temporarily blind, started to sightlessly grab me. I again took upon the chance to seize the chair near the work table and broke it over the mans head. He fell down, statically still. He was dead. Twenty minutes flew by and the police were already herding the then unconscious (now conscious) man into the police car. My parents were back and were alerted with the frightening experience that I had just gone through. Though still shaken, I tried my best to give my statement to the police. My parents were dumbfounded when I told them in detail what had just happened, but when I finished, they smiled and expressed relief that I was not injured. All was well.

Sunday, March 1, 2020

How (and When) to Complete the Square 5 Simple Steps

How (and When) to Complete the Square 5 Simple Steps SAT / ACT Prep Online Guides and Tips It’s pretty much a guarantee that you’ll see quadratic equations on the SAT and ACT. But they can be tricky to tackle, especially since there are multiple methods you can use to solve them. In this article, we’re going to walk through using one specific method- completing the square- to solve a quadratic equation. In fact, we’ll give you step-by-step instructions for how to complete the square using the completing the square formula. By the end, you should have a better understanding of how and when to use this mathematical strategy! Ready to learn more? Then let’s jump in! Engineers use quadratic equations to design roller coasters! What Is a Quadratic Equation? In order to understand how to complete the square, you first have to know how to identify a quadratic equation. That’s because completing the square only applies to quadratic equations! In math, a quadratic equation is any equation that has the following formula: $ax^2 + bx + c = 0$ In this equation, $x$ represents an unknown number and $a$ cannot be 0. (If $a$ is 0, then the equation is linear, not quadratic!) Quadratic equations have all sorts of real-world applications becausethey're used to calculate parabolas, or arcs. Construction projects like bridges use the quadratic equation to calculate the arc of the structure, and even roller coasters use quadratics to design adrenaline-pumping tracks. Quadratics even fuel popular video games like Angry Birds, where the arc of each bird is calculated using the quadratic formula! So now that you know why quadratic equations are important, let’s look at one of the most common methods of solving them: completing the square. What Is Completing The Square and When Do You Use It? There are actually four ways to solve a quadratic equation: taking the square root, factoring, completing the square, and the quadratic formula. Unfortunately, taking the square root and factoring only work in certain situations. For example, let’s look at the following quadratic equation: $x^2 + 6x = -2$ Solving a quadratic equation by taking the square root involves taking the square root of each side of the equation. Because this equation contains a non-squared $\bi x$ (in $\bo6\bi x$), that technique won’t work. Factoring, on the other hand, involves breaking the quadratic equation into two linear equations that are both equal to zero. Unfortunately, trying to factor this equation doesn’t result in two linear equations! Both the quadratic formula and completing the square will let you solve any quadratic equation. (In this post, we’re specifically focusing on completing the square.) When you complete the square, you change the equation so that the left side of the equation is a perfect square trinomial. That’s just a fancy way of saying that completing the square is a technique that transforms your quadratic equation from an equation that can’t be factored into one that can. Completing the square applies to even the trickiest quadratic equations, which you’ll see as we work through the example below. Your Step-By-Step Guide for How to Complete the Square Now that we’ve determined that our formula can only be solved by completing the square, let’s look at our example formula again: $x^2 + 6x = -2$ Step 1: Figure Out What’s Missing When you look at the equation above, you can see that it doesn’t quite fit the quadratic equation format ($ax^2 + bx + c = 0$). The number that should go in the $c$ spot, which is also known as the constant, is missing. So from a logical perspective, the equation actually looks like this: $x^2 + 6x +$ __?__ $= -2$ In order to solve this equation, we first need to figure out what number goes into the blank to make the left side of the equation a perfect square. (This missing number is called the constant.) By doing that, we’ll be able to factor the equation like normal. Step 2: Use the Completing the Square Formula But at this point, we have no idea what number needs to go in that blank. In order to figure that out, we need to apply the completing the square formula, which is: $x^2 + 2ax + a^2$ In this case, the $a$ in this equation is the constant, or the number that needs to go in the blank in our quadratic formula above. Step 3: Apply the Completing the Square Formula to Find the Constant As long as the coefficient, or number, in front of the $\bi x^\bo2$ is 1, you can quickly and easily use the completing the square formula to solve for $\bi a$. To do this, you take the middle number, also known as the linear coefficient, and set it equal to $2ax$. Here’s what that would look like for our sample formula: $6x = 2ax$ This equation is basically asking what number (this is $\bi a$) multiplied by 2 will give us 6. Now that you know your equation, solving for $a$ is simple: divide each side of the equation by $2x$! So let’s see what that looks like: $$6x = 2ax$$ Divide each side by $\bo2x$: $${6x}/{2x} = {2ax}/{2x}$$ Result: $3 = a$ Look at that! We now know that $\bi a =\bo3$! But we’re not quite done with the completing the square formula yet. In order to determine what the missing constant is, we need to plug our solution for $a$ back into the completing the square formula ($x^2 + 2ax + a^2$). Whatever the result is for $\bi a^\bo2$ is the constant that we’ll plug back into our first equation ($x^2+ 6x +$ __?__ $= -2$). So let’s take a look: $x^2+ 2ax + a^2$ where $a = 3$ Add $\bi a$ into the equation: $x^2 + 2(3)x + 3^2$ Put in simplest terms: $x^2 + 6x + 9$ So now we know that our constant is 9. Now it's time to plug in some numbers! Step 4: Plug the Constant Into the Original Formula Now that you know the constant, it’s time to put it into the blank in our original formula. Once you do that, the equation will look like this: Original formula: $x^2 + 6x +$ __?__ $= -2$ Formula with constant:$x^2 + 6x + 9 = -2 + 9$ Put in simplest terms: $x^2+ 6x + 9 = 7$ You might be wondering why we’re adding 9 to the right side of the equation. Well, remember: in math, you can never do something to one side of an equation without doing it to the other side, too. So because we’re adding 9 to our equation to make it a perfect square, we also have to add 9 to the right side of the equation to keep things balanced. If you forget to add the new constant to the right side of the equation, you won’t get the right answer! Step 5: Factor the Equation We’ve already done a lot of work, and there’s still a little more to go. Now it’s time for us to solve the quadratic equation by figuring out what x could be. But now that we’ve turned the left side of our equation into a perfect square, all we have to do is factor like normal. Completed quadratic formula: $x^2 + 6x + 9 = 7$ Factor left side of the equation: $(x + 3)^2 = 7$ Take the square root: $√{(x + 3)^2}= √7$ Subtract 3: $x =  ±Ã¢Ë†Å¡7 - 3$ Final solutions: $x =√{7} - 3$ and $x =√{-7} - 3$ What If There’s a Coefficient in Front of $x^2$? The step-by-step guide we gave you above only works if there’s no coefficient, or number, in front of $x^2$. If there is a coefficient, you have to eliminate it. Once you do that, you can solve the quadratic equation through the method we outlined above. So how do you remove the coefficient? Actually, it’s not as hard as it sounds. To show you how, let’s look at a new quadratic equation: $2x^2- 12x = -8$ How to Factor Out the 2 n order to remove the 2, you’ll need to divide both sides of the equation by 2. It’s really that simple! So let’s take a look at how that works: Original formula: $2x^2- 12x = -8$Divide everything by 2: $x^2- 6x = -4$ By doing this, you’ve made the coefficient in front of the $x^2$ into 1, so now you can solve the equation by completing the square like we did above. Additional Completing the Square Resources We know that completing the square can be tricky, which is why we’ve compiled a list of resources to help you if you’re still having trouble with how to complete the square. More Sample Problems As you already know, practice makes perfect. That’s why it’s important to work as many quadratic equations as you need to in order to feel comfortable solving these types of problems. Luckily for you, completing the square can be used to solve any quadratic equation, so as long as the practice questions are quadratics, you can use them! One great resource for this is Lamar University’s quadratic equation page, which has a variety of sample problems as well as answers. Another good resource for quadratic equation practice is Math Is Fun’s webpage. If you scroll to the bottom, they have quadratic equation practice questions broken up into categories by difficulty. Completing the Square Tutorial Videos If you’re a visual learner, you might find it easier to watch someone solve quadratic equations instead. Khan Academy has an excellent video series on solving quadratic equations, including one video dedicated to showing you how to complete the square. YouTube also has some great resources, including this video on completing the square and this video that shows you how to tackle more advanced quadratic equations. Completing the Square Calculator If you want to check your work, there are some completing the square calculators available online. It can be a good way to make sure you’re working problems correctly if you don’t have an answer guide. But be forewarned: relying on a tool like this won’t help you retain the information! Make sure you’re putting in the hard work to learn how to complete the square so you aren’t blindsided by these types of questions on test day. Now What? Working with quadratic equations is just one element of algebra you’ll need to master before taking the SAT and ACT. A good place to start is mastering systems of equations, which will help you brush up on your fundamental algebra skills, too. One of the most helpful math study tools is a chart of useful mathematical equations. Luckily for you, we have a master list of the 31 formulas you must know to conquer the ACT. If you think you need a more comprehensive study tool, test prep books are one way to go. Here’s a list of our favorite SAT Math prep books that will help set you on the path to success.