Interior Angles

An angle is the figure formed by two rays sharing a common endpoint, called the vertex of the angle. The magnitude of the angle is the "amount of rotation" that separates the two rays, and can be measured by considering the length of circular arc swept out when one ray is rotated about the vertex to coincide with the other.

Two angles are sometimes called congruent if there exists an isometry that transforms one of the angles into the other angle. We can specify an angle by using a point on each ray and the vertex.

An Interior Angle is an angle inside a shape.The interior angles of a triangle add upto 180°The measures of the interior angles in a polygon are consecutive integers.

Acute angles are angles whose measure is less than 90°

These are some types of angles in geometry.

Arithmetic Sequence and and Arithmetic Numbers

Let us learn about Arithmetic Sequence and and Arithmetic Numbers.

Before we know about Arithmetic sequence, we shall first know what is meant by a sequence; a sequence is a set of numbers that follow a pattern. We call each number in the sequence a term.

An arithmetic sequence is a sequence where each term is found by adding or subtracting the same value from one term to the next. We call this value "common sum" or "common difference"

An arithmetic sequence is a linear function. Instead of y=mx+b, we write a_n=dn+c where d is the common difference and c is a constant.

Using the above definition let us solve the Arithmetic Sequence Problems listed below.

If the first term of an arithmetic sequence is -3 and the eighth term is 11, find d and write the first 10 terms of the sequence.

In this problem,

A = -3 n = 8 A8 = 11

If these values are substituted in the formula for An, we have

11 = -3 + (8 - 1) d

11 = -3 + 7d

14 = 7d

d = 2

The first ten terms are -3, -1, 1, 3, 5, 7, 9, 11, 13, 15

COORDINATE GEOMETRY

The coordinate plane is a basic concept for coordinate geometry. It describes a two-dimensional plane in terms of two perpendicular axes: x and y. The x-axis indicates the horizontal direction while the y-axis indicates the vertical direction of the plane. In the coordinate plane, points are indicated by their positions along the x and y-axes. On the coordinate plane, the slant of a line is called the slope. Slope is the ratio of the change in the y-value over the change in the x-value.

In coordinate geometry, the equation of a line can be written in the form, y = mx + b, where m is the slope and b is the y-intercept.

In coordinate geometry, two lines are parallel if their slopes (m) are equal.

In the coordinate plane, two lines are perpendicular if the product of their slopes (m) is –1.

We get coordinate Geometry help through online tutoring.

DEFINE STANDARD DEVIATION

If we have to define standard deviation then it will be:-

Standard deviation is a measure of how far apart the data are from the average of the data. If all the observations are close to their average then the standard deviation will be small.

Standard deviation is a widely used measure of the variability or dispersion, being algebraically more tractable though practically less robust than the expected deviation or average absolute deviation. The standard deviation of a Normal probability distribution is the same as that of a random variable having that distribution. Computation of the standard deviation is a bit tedious.

Let us now see how to find Standard Deviation.

Below are the steps to involved in computing Standard Deviation

Compute the mean for the data set.

Compute the deviation by subtracting the mean from each value.

Square each individual deviation.

Add up the squared deviations.

Divide by one less than the sample size.

Take the square root.

Quadratic Equation

Quadratic equation is a polynomial equation of the second degree. The general form is

Ax² + bx +c = 0

where a ≠ 0. (For a = 0, the equation becomes a linear equation)

Any equation of type ax² + bx + c = 0 where a, b, and c are constants and a <> 0, is the equation in quadratic standard form.

Quadratic formula

A quadratic equation form with real or complex coefficients has two (not necessarily distinct) solutions, called roots, which may or may not be real, given by the quadratic Equation formula.

If a, b, and c are real numbers and the domain of f is the set of real numbers, then the zeros of f are exactly the x-coordinates of the points where the graph touches the x-axis.

If the discriminant is positive, the graph touches the x-axis at two points, if zero, the graph touches at one point, and if negative, the graph does not touch the x-axis.