Tutor profile: Charnie D.
What is the area of a circle with a diameter of 16?
To find the area of a circle, the formula is: pi*(r^2) pi means 3.1415, but we generally use it to the hundredth decimal place.. so 3.14 diameter is the distance from the side of the circle to the other side while intersecting the center of the circle. r means radius, the radius is the distance from the center of the circle to the edge. Therefore radius is half of the diameter. So in our equation our diameter is 16, therefore our radius is 8. So our equation so far looks like... Area = pi*(8^2). Square the radius, so in our equation, 8^2 is 64. The solution is: Area = 64*pi but to simplify it to the purest form, you plug in pi. Area = 64*(3.14) Multiply the numbers and you should get.. Area = 200.96
Find x: -4x + 7 = -3
To find x, you must isolate the x-variable by itself on one side of the equation. By doing so, you will find the answer that would make the equation true. (True that the number you plug in for x would result in your answer being -3. Step 1: move any numbers that aren't attached to an x-variable. So you must move the -7 to the other side of the equation. To do this you must subtract both sides by 7. -4x + 7 = -3 -7 -7 ___________ Resulting in: -4x = -10 Step 2: move any numbers that are attached to the x-variable. For this case, we have to move the -4 from the x-variable. To do this you need to divide both sides by -4. (-1/4)*(-4x) = (-1/4)*(-10) x = 10/4 Simplify your answer: 10/4 is also can be broken down to (2*5)/(2*2). Remove a 2 from the top and bottom. Resulting in... 5/2. To double-check your answer, plug the solution back into the equation. -4x + 7 = -3 -4(5/2) + 7 = -3 -10 + 7 = -3 -3 = -3 CORRECT!
Find the slope of the line. 5x - 5y = 7
To find the slope of the line, you must separate the y-variable by itself: Step 1 (move anything that is not the y variable): Move the (5x) to the other side of the equation. To do this you can subtract 5x from the left side and subtract 5x on the right side. 5x - 5y = 7 -5x -5x _____________ -5y = -5x + 7 Step 2 (move anything that is attached to the y variable): Move the -5 from the y-variable. To do this you can divide both side by -5. -5y = -5x + 7 (-1/5)*(-5y) = (-1/5)*(-5x + 7) [Distribut the -1/5 to -5x + 7] y = x - 7/5 Therefore your slope is the number in front of your x. x is also known as 1x, therefore your slope of the line is 1.