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Kevin C.'s Resources

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Let t = time after lunch, and t-1 = time before lunch.   Since she rode 96 miles for the total time, and 42 miles before lunch, she rode 96-42 or 54 miles after lunch.   remember that distance equals rate times time, and therefore, r = d/t and the rates before and after...

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OK.  Let x = number packages delivered.  She gets $57.50 each day, and $4.75 for each package.   Therefore, if y = the amount she earns per day,   y = 4.75x + 57.50.   Let y = 200.  How do you solve this problem?   200 = 4.75x...

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logx2 = 1/2.  Convert this to exponential form: x1/2 = 2, square both sides:  (x1/2)2 = 22.   This means that x = 22, or x = 4.   Check:  log42 = 1/2,  41/2 = √4 = 2.

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Another way, using algebra, is to multiply numerator and denominator by the conjugate of the numerator, thus rationalizing the numerator.   So the numerator multiplied by its conjugate:  (√(5-x) - 1)(√(5-x) + 1)  =  (5 - x) - 1 = 5 - x - 1 = 4 - x.   The...

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((1/(h+2)2- 1/4)/h.    Start by multiplying numerator and denominator by the LCD of the numerator, 4(h+2)2   This gives the following:  (4 - (h+2)2)/(h(4(h+2)2).   The numerator then is (4 - h2 - 4h - 4), when simplified, becomes -h2...

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If two lines are parallel, the slopes are equal.  The equation is written in slope y-intercept form, y = mx + b, where m = the slope and b = the y-intercept.   So the slope of the line, and therefore, its parallel, is 1/2.   So the equation of the new line is y...

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The angle, θ, between the vectors can be found using the dot product divided by the product of the magnitude of the vectors.   Cosθ = (a dot b)/(|a| times |b|).  So cos 2π/3 = - .5 and (a dot b)/12 = -.5.   That means a dot b = -6.  Can you proceed from here?...

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This notation is called the interval notation, where the square bracket, [, indicates the number following can be equal to the variable, and the parenthesis indicates that it cannot.    Therefore, in other notation, this interval is:  -4≤x<0 or 10<x<21.  In words,...

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Another approach:   x2 -1x - 72,  find 2 factors of 72 whose difference is 1.  (The reason I use the difference is because of -72.  If the last term was positive, I'd use the sum.)   The numbers are 9 and 8.   try (x - 9)(x + 8); ...

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