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Looking at the equation we can tell it will be an ellipse because of the coefficients of x2 and y2 are not the same but they are the same sign (so not a hyperbola).  It's easiest to find the critical points like the center foci and vertices if it's written in the form: (x-h)2/(a2)+(y-k)2/(b2)...

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Starting with 56, the multiples of 56 (the product if 8&7) are: 56,112,168,224,280,336, and 392. Of those 7 only 168 and 336 are divisible by 6. Thus 169 and 336 are the only numbers we need to exclude from our count of multiples of 6. Now for the multiples of 6. We use the...

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For question 1, we translate english directly into math:  Cost = $31 + $0.16*miles or C = .16m + 31.  We are given the total cost C, so we can directly solve for m.   For question 2, the most direct way is to differentiate the equation with respect to x and set it...

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x=-t^2 y=2t^2-2 (answer)

For this parametric equation we have to be careful because of the squares on the t variable.  We will start with x = -t2.  Multiplying by negative 1, we get -x = t2.  We substitute this into the other equation (for the t2) and get y = 2(-x) - 2 or y = -2x-2.  Now we...

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To eliminate the parameter T, from our equations we have to substitute one into the other.  The equation y = t allows us to substitute into x=1/4t2.  We get the relation: x = 1/4y2.  If you want it in function form, you'll end up with two equations, one positive and one negative...

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This is problem similar to continuously compounded interest.  It's a simple function where t is the independent variable and B the dependent variable.  It's just a matter of plugging in two years.

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The domain of a function can be restricted pretty much anyway you want.  However, in this case, they are looking for the set of x values that can be put into the function without causing a division by zero or a point discontinuity.  In the case of f(x) = 3x+4, there are no values...

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Translating the problem directly into an equation:  y (number of quizzes) = 2*(the number of quizzes per week) x (the number of weeks) =>   y = 2x

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If the equation is written correctly above, then the solution looks like this:   5x-6x=-9 -x=-9     (Combining like terms) x=9       (mult both sides by -1) Therefore it has one real solution.