tan(x) = 0 or sec(x)-2 = 0 Adding 2 to each side of the second equation we get: tan(x) = 0 or sec(x) = 2 We now have two equations of the desired form. The next step is to write the general solution for each equation. The general solution expresses all the solutions to the equations. We'll start with: tan(x) = 0 We should recognize that 0 is a ...

|x-2| if x2 The rule is that if the expression within the absolute bars is positive, just remove the bars. Conversely, if negative, put a minus sign in front of the expression after removing the bars. In the given case, since x2, (x-2) is negative,therefore, |x-2|= -(x-2)=2-x

Question 988916: A taxi company charges $2.00 for the first mile (or part of a mile) and 20 cents for each succeeding tenth of a mile (or part). Express the cost C (in dollars) of a ride as a piecewise-defined function of the distance x traveled (in miles) for 0 x ≤ 2. Found 2 solutions by josmiceli, MathTherapy:

Regarding the first system of two equations, express x = -2y from the first equation and substitute to the second equation, replacing x there. You will get then (2y)^2 + y^2 = 5 4y^2 + y^2 = 5 5y^2 = 5 y^2 = 1 y = = +/- 1. Thus you obtain two solutions: a) for y = 1, x = -2y = -2.

You can put this solution on YOUR website! x² - 7x - 60 = 0 (x - 12)(x + 5) = 0 {factored into two binomials} x - 12 = 0 or x + 5 = 0 {set each factor equal to 0}

f(x)=(6-x-y)/8 first find the integral over the domain. ∫∫f(x) dx dy over 0≤x≤2 and 2≤y≤4 =(1/8)∫[10-2y]dy for 2≤y≤4 =(1/8)[40-16+4-20] =1 So f(x) is a valid JPDF. Next step is to repeat the same procedure, but limited to the given area of {0≤x≤1, 2≤y≤3} to get ∫∫f(x) dx dy over 0≤x≤1 and 2≤y≤3

Question 211094: a) For the quadratic equation kx^2 + 2x + 4 = 0, find the value of k so that the roots are equal (there is only one root). b) The roots of x^2 + (k + 8)x + 9k = 0 are equal.

Then we switch the x and y values to get the point (b,a) on the graph of the inverse function. Once you understand what you are being asked to do (I THINK!!), it is easy. Here is the first one: f(0) = -4, so (0,-4) is on the graph of the function; then the point (-4,0) is on the graph of the inverse.

find the value of k so that the system of the equation x + y + 3z = 0 4x + 3y + kz = 0 2x + y + 2z = 0 has non-trival solution This is called a homogeneous system. It has only zeros on the right side. The trivial solution for all homogeneous systems is (x,y,z) = (0,0,0). But many homogeneous systems have other, non-trivial solutions.

If (x,y) satisfies the simultaneous equations 3xy - 4x^2 - 36y + 48x = 0, x^2 - 2y^2 = 16, where x and y may be complex numbers, determine all possible values of y^2. You have to be a registered user to answer this question!