Category: Math 10

Using the formula y2 – y1/x2 – x1 to find slope

Ex. (5,-7)(7,5)

y2 – y1 is the y value of the second pair minus the y value of the first pair. In this case: 5 – (-7) which is equal to 5+7 = 12

x2 -x1 is the x value of the second pair minus the x value of the first pair. In this case: 7-5 = 2

This becomes 12/2 which is equal to 6

Finding the slope from two point on a graph

The formula for slope of a line is rise/run

Ex. (-1,6)(2,8)

To get from (-1,6) to (2,8) on a graph you have to go up the Y axis 2 and across the X axis 3

Which makes your Rise/Run: 2/3

The slope of this line is 2/3

The X value is also the independent variable and input

The Y value is also the dependent variable and output

When you’re looking at a set of all X values its called the Domain

When you’re looking at a set of all Y values its called the Range

A Function is a relation where each input (x value) is only related to one output (y value)

However it doesn’t matter if the outputs are related to more than one input

Finding the GCF in polynomials

(4x^2y)(8x^3y)

expand (4x^2y) into (2)(2)(x)(x)(y)

expand (8x^3y) into (2)(2)(2)(x)(x)(x)(y)

The numbers that the expanded version have in common are:

(2)(2)(x)(x)(y)

when you multiply these together you end up with 4x^2y which is your greatest common factor

Greatest Common Factor in polynomials

If the expression has numbers that have common factors you can pull them out.

4x – 8 + 6

The greatest common factor here would be 2 which means the polynomial would become:

2(2x – 4 + 3)

Using SOH CAH TOA to find the side of a right angle triangle

Say you have a triangle where you know an acute angle and the hypotenuse and you’re trying to find the opposite side. You would use Sin. (SOH Sin Opposite Hypotenuse)

Ex. Sin 39 = x/9

(9)Sin39 = x/9(9)

x = 5.7

(39 = angle, x = opposite side, 9 Hypotenuse)

The formula for the surface area of a sphere is 4Pi(r)^2

The formula for the volume of a sphere is V=4/3πr^3

This week we learned about Exponent Laws.

When you’re multiplying two numbers with exponents, you add the exponents together. When you’re dividing two numbers with exponents, you subtract the exponents. If there is two exponents to one number {ex. (3^2)^4 } you multiply the exponents together.

The formula for surface area of a cone is (Pi)(radius^2) + (Pi)(Radius)(Slant)

To find the slant height you can use the radius, height and unknown slant height to make a right triangle. Then use the Pythagorean theorem to find the missing side.