m = Δy = 6 - 3 =  3 = -1        Δx    -1 - 2   -3   Your mistake is in finding the slope. Be careful with the slope formula: if you do y2 - y1 (meaning subtract the y-coordinate of the first point from the y-coordinate of...

This requires integration by parts, which allows us to solve the integral of the product of two functions.   ∫ x2cosx dx   This integral has two functions being multiplied together, x2 and cosx. One of these we will assign to be itself, or u, and the other will be the derivative...

|3n| > 15   To solve an absolute value inequality, you write two separate equations. The first keeps the expression in the absolute value bars positive with the same inequality, while the other negates the expression in the absolute value bars with the opposite inequality. In this...

h(x) = f2(x) - g2(x) h'(x) = [f2(x) - g2(x)]' = [f2(x)]' - [g2(x)]'   We need to use the chain rule to find [f2(x)]' and [g2(x)]', that is, we need to take the derivative of (something)2, which is 2(something), and then multiply that by the derivative of that something.   [f2(x)]'...

Yes, the correct answer is 4. And you're right, you don't need the point or y-intercept since all you need is the derivative at that point (the slope) to find the normal slope.

A multiple of a number is any product of that number with another number. For 6, the first few multiples are 6 × 1, 6 × 2, 6 × 3, 6 × 4, 6 × 5 ... which are 6, 12, 18, 24, 30, and so on. 42 is a multiple of 6, since 6 × 7 = 42. So the answer is C. The other choices (2, 3,...

This is not a true statement. Use the same values for x and a to see why.   I think what you might have meant is logax = 1/logxa, (where the a on the left-hand side and the x on the right-hand side are the bases of the logarithms, not the bases of an exponent) which is true and can...

f(x) = x2/3(2 - x)   I would first distribute to make it easier to derive (otherwise we would have to use the product rule and that can get messy).   f(x) = 2x2/3 - x5/3     (remember x is really x1 or x3/3 in this case, so x2/3 times x3/3 is x5/3)   Now...

The discriminant is the expression under the radical in the quadratic formula: b2 - 4ac, where the quadratic is of the form ax2 + bx + c. In this case, a = 2, b = 9, and c = 7. b2 - 4ac = (9)2 - 4(2)(7) = 81 - 56 = 25 These are the rules for determining the nature...

When graphing a rational function, find the x-intercepts, y-intercepts, vertical asymptotes, and horizontal asymptotes. x-intercepts: x-values when y = 0 (hint: y = 0 only when the numerator = 0)      0 = x + 3     ->     x = -3, or (-3, 0) y-intercepts: y-values...

Put the equation in standard form by bringing the 4x + 1 to the left side. 7x2 - 4x - 1 = 0 We use the discriminant to determine the nature of the roots of a quadratic equation. The discriminant is the expression underneath the radical in the quadratic formula: b2 - 4ac.  b2...

First bring the 3 over to the left side of the equation to form a trinomial equal to 0. 2x2 + 5x - 3 = 0 Now we have to factor the trinomial. Since the leading coefficient, 2, is prime, we know one of the binomial factors will contain a 2x and the other will contain an x, like this:...

A linear term is a term with a degree of 1, or simply x. In this example, 2x2 is a quadratic term because the x has a degree of 2, and the 5 is just a constant. -3x is the linear term because its degree is 1 (x1 or simply x). Think of it this way too: a linear equation is in the form y = mx...

It's easiest to rewrite this using exponents. Remember that a radical becomes a fractional exponent. √(x4) + 3√(x6) + 4√(x8) = (x4)1/2 + (x6)1/3 + (x8)1/4 Now simply multiply the exponents: x4/2 + x6/3 + x8/4 = x2 + x2 + x2 = 3x2...

Since the answers are all in fractional exponents, I'm going to rewrite the expression that way: 4√(32x8y3) = (32x8y3)1/4 = (32)1/4(x8)1/4(y3)1/4 32 = 25, so (32)1/4 = (25)1/4 = 25/4 For the variables, simply multiply the exponents: (x8)1/4 = x(8 × (1/4)) = x2 (y3)1/4 =...

To find the x-coordinate of the vertex, you use the formula -b/2a. (Remember that the standard form of a quadratic is y = ax2 + bx + c.) So in this case b = 8 and a = 2. -b/2a = -8/(2·2) = -8/4 = -2 Now to find the y-coordinate, simply plug the x-value into the quadratic equation...

I'm not sure what the : is representing here... could you please clarify what this means?

It's helpful to think of radicals like variables when adding or subtracting. So just as 2x and 3x are like terms with the same variable (and therefore can be combined), 2√(6) and -3√(6) are like terms with the same radical and can be added together. 5 + 2√(6) - 3√(6) + 9 14 - 1√(6)...

To multiply radical expressions, remember to multiply the coefficients together and the radicals together. (-3√(24))(5√(20)) = (-3)(5) × √((24)(20)) = -15√(480) You might be inclined to pick choice B now, but remember that you can simplify the radical. 480 = 16 × 30    ...

To simplify a radical in the denominator, you need to rationalize by multiplying both the numerator and denominator by its conjugate. The conjugate is the same expression but with the opposite sign. In this case, the conjugate of 4 - √3 is 4 + √3.    7...