Explain the concept of checks and balances and give examples:
Checks and balances is a system set up by the United States Constitution that allows each branch of the government (legislative, executive and judicial) to make sure the other branches aren't abusing or illegally using their power. This allows a separation of powers and a balanced and non-tyrannical government. The legislative branch (Congress) has the duty of keeping an eye on the executive and judicial branches. The executive branch (President) has the duty of keeping an eye on the legislative and judicial branches. The judicial branch (Supreme Court) has the duty of keeping an eye on the legislative and executive branches. An example of the legislative branch checking the power of the other two branches would be having the power to override the president's veto, and having the ability to remove Supreme Court judges. Checking the branches' powers allows for balanced branches. The executive branch can call on Congress for special legislative sessions at the president's request, and appointing Supreme Court judges. The judicial branch can declare legislation passed by Congress as unconstitutional, and declare any executive actions of a President as unconstitutional.
Explain the difference between a proportional tax system, a progressive tax system and a regressive tax system.
Proportional Tax System: A proportional tax system (also known as a flat tax) is a single tax bracket that taxes you all your income at the same rate no matter how much you make per year. The more you make, the more you pay in total taxes, but you always pay the same rate. An easy example would be if I was making $100,000 per year. If there was a proportional tax (or flat tax) of 10% then I would pay just 10% of my yearly income, which is $10,000. If I then made $200,000 per year, I would pay $20,000. Regardless of how much I make, I will always pay the same rate. Progressive Tax System: This system has multiple tax brackets that increase, which means that the more money you make, the higher rate you will pay in addition to paying more in total taxes. It is worth noting that this is the tax system that the United States of America uses for federal taxes. For this example, assume there are three brackets with yearly income ranges: 10%: $0 - $75,000 25%: $75,001 - $150,000 30% $150,001 - $250,000 If I currently make $50,000 yearly, I pay 10% ($5,000). If my income increases to $100,000 yearly, not only am I paying more ($25,000), but I am paying a higher rate (25%). If I then make $175,000 yearly, I will pay more and pay an even higher rate ($52,500 and 30%, respectively). Regressive Tax System: This system also have multiple tax brackets, but in a regressive system, the rates decrease as your yearly income increases. The more money you make, the more you pay in total taxes, but the rate you pay will decrease. It is worth noting that the individual states in America use the regressive tax system. For this example, assume there are three brackets with yearly income ranges: 10%: $0 - $75,000 7%: $75,001 - $150,000 5% $150,001 - $250,000 If I make $50,000 yearly, I will pay a rate of 10% ($5,000). If I then make $100,000 yearly, I will still pay more, but I will pay at a lesser rate of 7% ($7,000). If I then make $200,000 yearly, I will pay even more in total, but I will pay at an even lower rate of 5% ($10,000).
Solve the following polynomial equation and list all zeros for x: x^2+5x-14=0
This is a simple quadratic equation, as it is in the form of Ax^2+Bx+C=0 The first step you should take to finding the zeros is seeing if you can factor the terms. An easy way to do that is to try two numbers whose sum is B, and whose product is C. In this case, B=5 and C= -14. Can we find two numbers whose sum is 5 and product is -14? Yes! Those two numbers would be -2 and 7. The product of -2 and 7 is -14, and their sum is 5, matching B and C perfectly. Now that we have the two numbers, we will add each one of them to each x in separate parentheses (we have two values of x since we have x^2). The equation will be rewritten as the following: (x-2)(x+7)=0 Now that we have our equation factored, we can then find out where the zeros are by setting both (x-2) and (x+7) to 0. Like this: x-2=0 and x+7=0 Solving each for x, we will have two values of x: x=2 and x= -7 2 and -7 are our zeros. To prove that they are, try plugging each one back into the rewritten equation that we had! For 2, we would have (2-2)(x+7)=0, which is (0)(x+7)=0 and eventually 0. For 7, we would have (x-2)(-7+7)=0, which is (x-2)(0)=0 and eventually 0. All done! Our final answer is x=2, and x= -7.