More Problems on Conic Sections
... By2 + Cx + Dy + E = 0 (C ? 0, opens to the right or left) Examples: 3x2 – 12x + 2y + 26 = 0 (opens downward) – 2y2 + 3x + 12y – 15 = 0 (opens to the right) (3) Ellipse: both x2 and y2 appear, and their coefficients A and B have the same sign and are unequal Examples: 2x2 + 5y2 + 8x – 10y –7 = 0 (hor ...
... By2 + Cx + Dy + E = 0 (C ? 0, opens to the right or left) Examples: 3x2 – 12x + 2y + 26 = 0 (opens downward) – 2y2 + 3x + 12y – 15 = 0 (opens to the right) (3) Ellipse: both x2 and y2 appear, and their coefficients A and B have the same sign and are unequal Examples: 2x2 + 5y2 + 8x – 10y –7 = 0 (hor ...
Distributive Property Equation Inverse Operations
... Equation An algebraic or numerical sentence that shows that two quantities are equal. ...
... Equation An algebraic or numerical sentence that shows that two quantities are equal. ...
Solution
... Question 7.1. The point J = (2, 5) is in Quadrant I. Question 7.2. The point L = (4, −5) is in Quadrant IV. Question 7.3. The point B = (−4, −3) is in Quadrant III. ...
... Question 7.1. The point J = (2, 5) is in Quadrant I. Question 7.2. The point L = (4, −5) is in Quadrant IV. Question 7.3. The point B = (−4, −3) is in Quadrant III. ...
R.C. Lyndon`s theorem
... belonging to , from which all identically true equations of the same form are derivable by means of the following rules: (I) reflexivity and symmetry of equality; (II) uniform substitution for a variable in any established equation; (III) given = , substitution of for at any occurrence in an establi ...
... belonging to , from which all identically true equations of the same form are derivable by means of the following rules: (I) reflexivity and symmetry of equality; (II) uniform substitution for a variable in any established equation; (III) given = , substitution of for at any occurrence in an establi ...
8 32 ! 3 50 + 18 a) 16x2 ! 3 = 8 = 81 = 32
... to be made if the area of the desktop is 960 square inches. b) The area of a rectangle is 200 square meters. Find the length and the width of the rectangle if its length is 5 meters less than the twice the width. c) Jake launches a model rocket from the ground. The height, h, of the rocket above the ...
... to be made if the area of the desktop is 960 square inches. b) The area of a rectangle is 200 square meters. Find the length and the width of the rectangle if its length is 5 meters less than the twice the width. c) Jake launches a model rocket from the ground. The height, h, of the rocket above the ...
Equation
In mathematics, an equation is an equality containing one or more variables. Solving the equation consists of determining which values of the variables make the equality true. In this situation, variables are also known as unknowns and the values which satisfy the equality are known as solutions. An equation differs from an identity in that an equation is not necessarily true for all possible values of the variable.There are many types of equations, and they are found in all areas of mathematics; the techniques used to examine them differ according to their type.Algebra studies two main families of equations: polynomial equations and, among them, linear equations. Polynomial equations have the form P(X) = 0, where P is a polynomial. Linear equations have the form a(x) + b = 0, where a is a linear function and b is a vector. To solve them, one uses algorithmic or geometric techniques, coming from linear algebra or mathematical analysis. Changing the domain of a function can change the problem considerably. Algebra also studies Diophantine equations where the coefficients and solutions are integers. The techniques used are different and come from number theory. These equations are difficult in general; one often searches just to find the existence or absence of a solution, and, if they exist, to count the number of solutions.Geometry uses equations to describe geometric figures. The objective is now different, as equations are used to describe geometric properties. In this context, there are two large families of equations, Cartesian equations and parametric equations.Differential equations are equations involving one or more functions and their derivatives. They are solved by finding an expression for the function that does not involve derivatives. Differential equations are used to model real-life processes in areas such as physics, chemistry, biology, and economics.The ""="" symbol was invented by Robert Recorde (1510–1558), who considered that nothing could be more equal than parallel straight lines with the same length.