Find the midpoint between points (1 , 2) and (9 , 6).
The midpoint between two points can be found by: M = ( (x1 + x2) / 2, (y1 + y2) / 2). With this, we can plug in our values: M = ( (1 + 9) / 2 , (2 + 6) / 2) = (5 , 4).
A cube with a side of 3.2 inches has a mass of 86 grams. What is the density in g/cm^3? Round to the nearest hundredth.
The density of an object is its mass over its volume. First we need to find the volume of the cube where we know its side, s, equals 3.2 inches. V = s^3 = (3.2 cm)^3 = 32.768 cm^3. Now we can solve for density: D = (86 g) / (32.768 cm^3) = 2.6245 g/cm^3. Rounding to the nearest hundredth we get 2.62 g/cm^3.
Find the equation of the line that passes through the points (-1 , -2) and (1 , 2).
The equation of a line is y = mx + b. The first step in solving this problem would be to use the two points to solve for the slope, m, of the line. m = (y2 - y1) / (x2 - x1) = (2 - -2) / (1 - -1) = 4 / 2 = 2. Now we need to solve for the y-intercept, b. To do this, we can use either of the two points given to us in our problem statement for our x and y values. Because we just solved for m, we can now use these values in our equation of a line, y = mx + b, to solve for b. Using point (1 , 2) we get: 2 = 2*1 + b, so b = 2 - 2 = 0. To prove this value is correct, we can check by using our other point (-1 , -2): -2 = 2*-1 + b, where b = -2 + 2 = 0. Now that we know b = 0, our final equation for this line is y = 2x.