What is the area of a circle with a diameter of 10?
The first thing we must do is to identify the formula for finding the area of a circle. The formula is A = πr^2. Don't be discouraged by the weird symbols. π is simply a constant in math found by dividing the circumference of a circle with its diameter (many times in math, we can leave it as π or write is as 3.14). The ^ symbol simply means that it is an exponent (in this case we will multiply r times r). Notice in the problem, we are not given the radius. However, we are given the diameter and we know that the diameter is double the radius. We can find the radius by dividing the diameter by 2. When we do this we get 10/2 which is 5. So, we know that the radius is 5 and we are now ready to plug in to our formula. A = π5^2 or A = π(5)(5). We can get 2 different answers. The exact answer would be A = 25π. For the approximate answer, we would go ahead and use the π button on our calculator or possibly 3.14 depending on the instructions. In this case, the approximate answer would be A = 78.5. Also remember that for area, our unit will be units^2.
Solve the given equation for x: 2x + 3 = 7
In order to solve an equation, we want to get the "x" by itself. We do this by canceling out everything on the same side of the equals sign as x (the 2 that is multiplied with x and the 3 that is added to the 2x). We start by getting rid of the 3 because it is further from the x (we use PEMDAS to simplify expressions on 1 side of an equals sign, but we reverse the order when solving equations). In order to cancel out a positive 3, we must subtract 3. However, whatever you do to the left side of the equals sign, you must do to the right side. After subtracting 3, we are left with 2x on the left side of the = and 4 on the right side (7-3). Lastly, we must get rid of the 2 that is currently being multiplied by "x". The opposite of multiplication is division so we must now divide by 2 to "get rid" of it. Again, what you do to one side must also be done to the other side of the =. After dividing both sides by 2, we are left with x = 2 (4/2). The good thing about solving equations is you can check your answer by plugging it back in to the original equation. When doing this, we get 2(2) + 3 = 7 which is a true statement so we know that we have the correct answer.
How do you find the slope of a line given 2 points?
First, you must identify the x (1st) and y (2nd) components of the given points. The point that is displayed first, we can call (x1,y1) and the point that appears second we can call (x2,y2). Next we will need to subtract y2-y1 (be careful if y1 is negative because a negative minus a negative will change the sign to a positive). We then will follow the same process for the x: x2-x1 (again be careful if your x1 is negative). We then place the answer from subtracting the "y" values over the answer we got from subtracting the "x" values in the form of a fraction. Lastly we check to see if we can reduce the fraction (again, be cautious of your signs). This will give you the slope of a line.