Tutor profile: Jessica K.
Find the diameter of a circle whose area is 25π units squared.
To find the diameter using the area of a circle, we first need to find the radius. Since the formula area of a circle is πr^2, we can make the equation πr^2=25π and solve for r. To solve for r, we divide by π on both sides to get r^2=25, and then take the square root of both sides. We are then left with r=5. Then we may recall that the diameter of a circle is 2r, so we just multiply 5x2 to find the diameter of this circle, which is 10 units.
Simplifying algebraic expressions example: Simplify the expression 2(3x+y)-5y
Following PEMDAS rules, we start by distributing the 2 to each term in the parentheses, which makes our new expression 6x+2y-5y. After this, we combine like terms, which would be the two terms that both have y as the variable, which then makes our expression 6x-3y. Because 6x and -3y have different variables, we cannot combine them, so 6x-3y is our answer!
Solve this system of equations using elimination: 2x-3y=9 x+3y=18
Solving a system of equations means finding the point at which two lines meet, meaning their x and y coordinates will be the same. To solve for this point using elimination, we can either add or subtract the two equations depending on the variables. Based on this example, we will add the two equations. The x terms will add up to 3x, the y terms will cancel out, and the constants add up to 27. We end up with 3x=27, then divide both sides by 3 to get x=9. Then we put the value of x back into one of the equations (we will use the second one) to get 9+3y=18. Then we subtract 9 from both sides to get 3y=9. Then we divide by 3 on both sides to get y=3. So the point at which these two equations meet is (9,3)
needs and Jessica will reply soon.