Colleen K.

Full-Time Employee in a Financial Management Program

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Pre-Calculus

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Question:

Find the midpoint between points (1 , 2) and (9 , 6).

Colleen K.

Answer:

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).

Basic Chemistry

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Question:

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.

Colleen K.

Answer:

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.

Algebra

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Question:

Find the equation of the line that passes through the points (-1 , -2) and (1 , 2).

Colleen K.

Answer:

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.

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