# Math 10 – week 18 – elimination

This week in math 10 we learned how to solve equations with using elimination. Elimination in incredibly similar to using insertion.

The first step to solving something using elimination is to add or subtract. in this case I will use subtract.

7x+y=15

3x+y=3

I’m going to make all of the number in the second equation negative

7x+y=15

-3x-y=-3

Now to subtract. Note: when using elimination, make zero pares with x or y

4x=12

Now to divide by 4

X=3

We can then insert x back into the equation to find out y

7(3)+y=15

21+y=15

X=-6

my core competencies reflection:

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# Math 10 – week 15 – graphing

This week in math 10, we learned how to tell what a graph will look like by looking at a linear equation. The equation is: y=mx+b

m = slope

b = y intercept

lets take a look at this picture and find the equation.

Remember the equation for slope is y/x or rise/run. So, after finding to nice points, the slope is 7/1, witch can be simplified to just 7. The y-intercept for this line -8, so the equation for this line is: Y=7x – 8.

Know, lets to the opposite, take an equation and make a graph from it: Y=1/3x + 4.

My recommendation would be to start form the y-intercept and then add the slope

Y=1/4x + 2

# Math 10 – week 17 – substation

This week in math 10 I learned how to solve equations with using substitution. The steps for substitute are as fallows:

1. Pick an equation to rearrange
2. Substitute equation
3. Solve equation
4. Substitute the number just found, back into the rearranged equation
5. Verify solution on both equations

The equations being solved for this example will be y-x=1 and 2x+3y=18.

The first step is to pick an equation to rearrange and rearrange it. The best option is always the equation with a coefficient of 1. So, the best option for rearranging is y-x=1.

y-x=1

y-x+x=1+x

y=1+x

The second step is to insert the rearranged equation and substitute into the second equation. We are going to put y=1+x into 2x+3y=18. We are going to want to put 1+x into the equation where the y is in the second equation because y is equal to 1+x.

y=1+x and 2x+3y=18 becomes 2x+3(1+x)=18

If you notice, the equation has become a simple 9th grade equation.

The next step is to solve the equation

2x+3(1+x)=18

2x+3+3x=18

5x+3=18

5x+3-3=18-3

5x=15

5x/5=15/5

x=3

Now to take the number we found (3) and insert it back into the rearranged equation (y=1+x).

y=1+4

y=4

Now to verify the numbers in both equation

y-x=1

4-3=1

2x+3y=18

2(3)+3(4)=18

6+12=18

# Math 10 – Week 16 – converting equations

This week in math 10, we learned about the different form of equations and how to change between them.

Here are the different equations:

Slope intercept form

y=mx+b

Slope Point form

y-y2=m(x-x2)

General form

0=mx+y+b

Slope intercept form to Slope Point form (y=mx+b to y-y2=m(x-x2))

We want to take the equation y=4x+8 and convert it to slope point form. This is one of the most simple conversion.

The first step is to fin a point to convert: (0,8) being put into the slope changes to (1,12)

Next, you would just inster the number into the equation: y-12=4(x-1)

Slope intercept form to General form (y=mx+b to 0=mx+y+b)

This conversion is also very simple. All you need to do to subtract y:

y=4x+8

-y

0=4x-y+8

Slope Point form to General form (y-y2=m(x-x2) to 0=mx+y+b)

This conversion is a little more complicated. The first step is to convert form slope point form to slope intercept form:

We need to find the y-intercept, you can do that by applying the slope to the point in the equation: y-12=4(x-1) turn into y=4x+8.

You then can apply the conversion for Slope intercept form to General form.

# Math 10 – week 13 – analysis

This week in math team we learned how to dissect graphs and connect it to a story. Here the graphs that we will be dissecting.

George and his family watched a movie together and the graph show the relationship between the amount of popcorn and time.

We can dissect George’s graph first. It starts on the y axis so we can assume he has a full bole of popcorn at the start of the movie. The line on the graph goes down really fast and ends up the x axis really early so we can deduce that he ate all of his pop corn really fast.

Know lets dissect George’s sister’s graph. Her graph starts at the same place as before, so she had a full bole of popcorn at that start of the movie. her graph is really curvy, so we can assume that she was eating the popcorn slowly at times and fast too.

Geroge’s dad’s graph is next. There is a strate line in the graph so he did not eat any popcorn for a while.

Gorege’s mom did not get her pop corn right at the star of the movie, I know this because it dose not start at the y-axis. There is a long strate line and we can

# Math 10 – week 12 – function notation

This week in math we learned how to write function notation. There are 3 different types, equation, mapping, and function notation.

1: equation

5x+4

You can input any number in this equation and there will be no overlapping outputs. This is the t-chart for the equation that can then be charted on a plane

 x y -3 -11 -2 -6 -1 -1 0 4 1 9 2 14 3 19

2: mapping

This is the same equation but in map notation: f:(x)→5x+4

The f at the start is the name of the function (eg: g,h,k). the arrow means happed onto. So if I where to use function f to solve if x=3, it would look like this:

f:(3)→5(3)+4

f:(3)→15+4

f:(3)→19

3: function

This is what the same equation would look like in function notation: f(x)=5x+4

The function still has a name(f) and the equal sign(=) is mapped onto.

This is what it looks like to solve if x=3:

f(3)=5(3)+4

f(3)=15+4

f(3)=19

# Math 10 – week 11 – domain and Range

Domain and Range

This week in math 10, I learned how to identify a coordinate plain’s Domain and Range.

The horizontal line, also known as the x-axis, is used to find the domain, and the vertical line, also known as the y-axis, is used to find the range.

To understand how to find Domain and Range, I will simplify it to only one line. Know to explain the next few examples.

Example #1

To describe this line, you list out the places where the dots are: {2,3,4,5}. You can not answer the question like this: {2-5} because that would imply decimals.

Example #2

The that arrow means that all numbers smaller than -6 are possible solutions for the equation and the unshaded circle means that -6 is not a possible solution. The answer would be written like this: {-6˃x}

Example #3

The fact that there are 2 circles means that all the possible solutions have to bee in between those 2 numbers. The shaded circle means that that the number circled is a possible answer. The answer would be written like this: {-1≤x˂7}

Know to introduce Range in.

Example #4

Starting with the Domain. The answer would be any real number because there is no base point and the arrows go both ways. For the range, the answer would be 8 because the height dose not vary.

D {xR}

R {8}

# Math 10 – Week 10 – Factoring Ugly trinomials

This week in math 10, we learned how to factor ugly trinomials. What makes a trinomial ugly? The coefficients are big numbers. For this blog post, I will solve this polynomial: 2x2+17x+35

First I must multiply and leading coefficient (2) and the constant together (35), to get the total (2*35=70).

Next, I will list out all of the factors of 70 and see with set can add to 17:

70

1*70

2*35

5*14

7*10

7+10=17 so I can now put all of these number into the box to do the reverse box method.

 2x2 7x 10x 35

Note: It dose not matter where you but the xs.

Now I can fill not the box. To find the outside find what is similar between the number in the row or column. 2x2 and 7x have x common. 10x and 35 have 5 in common. 2x2 and 10x have 2x in common. 7x and 35 have 7 in common

 2x 7 x 2x2 7x 5 10x 35

Now I can take the out side number and put them into an equation.

(x+5)(2x+7)

# Week 7 – Math 10 – Factoring Polynomials

This week in math 10 we learned how to Factoring Polynomials. There are several ways to factor polynomials.

Common factors: To make an equation easier to understand, you can find a common factor in the numbers. The example I will be using is: $2x^2$ + 12x + 10

all number in this equation have a common factor of 2, so we have to divide all the hole equation. and this is the result: 2($x^4$ + 6x + 5)

Trinomials: $x^2$ -11 + 28

In order to factor the example above, we need to find 2 numbers that add or subtract to -11 and multiply to 28. To Start,  I will create a list of factors for 28: 1,2,4,7,14,28

7+4=11 so -7-4=-11 and that means our simplified equation is:

(x-7)(x-4)

Binomials: $x^2$ – 25

(x-5)(x+5)

# Week 6 – Math 10 – Multiplying polynomials

This week we learned how to multiply polynomials in several different ways. In order to multiply polynomials, you need to understand the distributive property and the multiplication exponent law, but I will explain them when they come up. I this I will explain how to multiply a trinomial (3 terms) by a binomial (2 terms) in 2 ways. The example I will be solving is (5x2-3x+6)(4x+5)

Way 1: algebraically

First I can start with expanding. Each term in the first bracket will multiply into terms in the second, because of the distributive property. This is what the equation would look expanded:

5x2(4x)+5x2(5)-3x(4x)-3x(5)+5(4x)+5(5)

Know I can do the individual multiplication:

20x3+25x2-12x2-15x+20x+20

The reason 5x2(4x)=20x3 is according to the multiplication exponent law. There in an invisible exponent of 1 on the 4x.

Before I combine like terms I like to organize my equation to make things easier for myself. I organize the equation by like terms then I combine. This equation is already organized so I can skip that step.

Like terms combined: 20x3+13x2+5x+20

Way 2: visually

(5x2-3x+6)(4x+5)

You start with making a box with lines separating it to the number of terms

Then you fill in the polynomials to their respective sides. put each term on a line like this

 4x 5 5x2 -3x 6

Then I would do the multiplication in the individual squares

 4x 5 5x2 20x3 25x2 -3x -13x2 -15x 6 24x 30

Know I can right out the hole equation and combine like terms.

Written out: 20×3+25×2-12×2-15x+20x+20

Like terms combined: 20×3+13×2+5x+20