1) A line goes through the points (3,5) and (-1,17) A- Find an equation of the line in point slope form B- Find an equation of the line in slope intercept form C- Write an equation for a line that is parallel to this line and passes through the point (5,-4) 2) Solve -4≤2x-10 and express the answer on a number line 3) Solve -3<3x-6≤12 and express the answer in interval notation 4)The price of tickets at the beginning of each school year for a home football game for the University of Corning is given in the table below: Year Price (dollars) 1973 6.10 1975 7.30 1977 9.50 1979 11.20 1981 12.90 1983 14.60 1985 16.30 1987 18 This data can be modeled by the equation p= 0.865t+3.34 where p is the price of tickets and t is the number of years since 1970. Use this equation to predict the ticket price in 2020, rounded to the nearest cent.
Family of Curves
A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.
XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.
Lines and Angles
In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.
1) A line goes through the points (3,5) and (-1,17)
A- Find an equation of the line in point slope form
B- Find an equation of the line in slope intercept form
C- Write an equation for a line that is parallel to this line and passes through the point (5,-4)
2) Solve -4≤2x-10 and express the answer on a number line
3) Solve -3<3x-6≤12 and express the answer in interval notation
4)The price of tickets at the beginning of each school year for a home football game for the University of Corning is given in the table below:
| Year |
Price (dollars) |
| 1973 | 6.10 |
| 1975 | 7.30 |
| 1977 | 9.50 |
| 1979 | 11.20 |
| 1981 | 12.90 |
| 1983 | 14.60 |
| 1985 | 16.30 |
| 1987 | 18 |
This data can be modeled by the equation p= 0.865t+3.34 where p is the price of tickets and t is the number of years since 1970. Use this equation to predict the ticket price in 2020, rounded to the nearest cent.
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