Daniel T.

High School Math Teacher for 20 Years

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Pre-Calculus

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Question:

Solve the system of equations: 2x+y=5 2x-4y=0

Daniel T.

Answer:

The method I will use here is the addition method (or Combination method). The goal is to add the two equations together in such a way that one variable or another is canceled out. First lets subtract the second equation from the first: 2x + y = 5 -2x +4y = -0 (notice the signs are all opposite of what they were to start with) added together these give us 5y=5. Then divide by 5 we find that y=1 Now lets reset and find out what x equals. If we multiply the first equation by 4 we get: 8x + 4y = 20 (why did we do this? Observe the second equation copied on the next line:) 2x - 4y = 0 (notice that the y's will not cancel each other out - this is why we multiplied by 4) Add these two equations and we get 10x=20; divide by 10 and we find that x=2. The final answer to the solution can be written: x=2, y=1 but is more commonly written as the ordered pair: (2, 1)

Trigonometry

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Question:

What is the exact sine of 30 degrees?

Daniel T.

Answer:

The easiest way to find the sine of an angle is to find a right triangle that has that angle in it. Then you use the old Soh-Cah-Toa rule: Sine = the side opposite the angle / the Hypotenuse. In this case we do have such a triangle, our old friend the special 30-60-90 triangle. Remember that the short side (always across from the 30 degree angle) is always half of the long side (which is always the hypetenuse - across from the right angle). Now if you take a number and divide it by another number that is twice as big the ratio is alway one half. So the sine of 30 degrees is one half.

Algebra

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Question:

What is the slope of the line described by the equation: 3x+2y=8?

Daniel T.

Answer:

The best way to find the slope of a line from an equation is to transform the equation into Slope-Intercept form. Essentially we want to make the equation tell us what y equals. So first subtract 3x from both sides of the equation and then divide both sides by 2. If you follow those instructions to the letter you end up with y=4-3x/2 But for the sake of standardization and to reduce confusion in the long run we put the part with the x first so we have y=-3x/2 + 4. The slope is always the number part of the x term so in this case -3/2

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