A circle is representing the following polynomial: x^2 + 4x + 3 + y^2 + 10 y + 14 = 47 what the steps needed to find the the center and radius of the circle?
1- Step one, complete the square for the x and y variables. 2- Complete the square by making sure the x^2 coefficient is 1 3- divide the coefficient of the x term, divide it by 2, and square it (do the same for y) 4 - Do not forget to balance the equation, meaning that if you add or subtract from one side, subtract from another side of the equal sign. 5- Now you have an equation that looks like: (x-x1)^2 + (y-y1)^2 = r^2 (x-x1)^2 + (y-y1)^2 = r^2 equation gives us the center of the circle: (x1, y1) and the radius = r.
From the same starting point, 2 brothers move in opposite directions (one east and one west). After walking 30 meters each, they both turn right and walk for 40 meters. How far apart are they now?
There are a couple of ways to solve this problem; one by using the distance formula and one by using the Pythagorean theorem (both formulas are very similar). Assume the brother are walking on the XY plane and that they started at the coordinate x=0 and y=0 (0,0). After both going east and went in opposite directions, now they're at (30,0) and (-30,0). After moving right and walking 40 meters, they're at (30,-40) and (-30,40). Now that we have 2 point on the xy coordinate plane, we can use the distance equation: distance = square root [ (x2-x1) ^2 + (y2-y1)^2 ] = square root [ (30 - - 30)^2 + (-40-40) ^2] = square root [ 60 ^2 + 80 ^2] = square root ( 3600 + 6400 ) = square root (10000) = 100. Another way to solve this problem is by getting the distance from each brother to original destination point and then multiplying it by 2.
What's the square root of a number that is twice the sum of 55 and -5?
One of the most important learning points of Alegra is translating words into algebraic equations. In this example, you have to write the following equation: square-root of (2*(55+-5)) = square-root(2*50) = square-root(100) = 100.