# Solving Quadratics by Factoring week 6

This week I learned how to solve quadratic equations using the quadratic formula. The first step will have to be make sure your equation is equal to zero. In the example I have provided it is also equal to zero so all I need to do is substitute the values. Make sure to simplify the equation to get an answer. Some quadratic equations can have 2 solutions. In this case there are 2 solutions and some can have one solution. That is what I learned in math last week.

# Factoring week 5

This week I learned how to multiply and divide radicals using simple steps. When you divide radicals if the denominator has a square root then you have to rationalize the denominator which means that I multiply the bottom with the top and then I use the distributive property or foil to get like terms and then I collect them and get my answer. For some other dividing problems you have to use a conjugate which means that I multiply the radical at the bottom by the same one except I need to have different signs, if the expression is positive then you have to multiply it by the same numbers but instead of the plus it has to be a minus. Because then it will create one zero pair and you get the expression that you need to have at the bottom. After you get that expression you just multiply it by the top and then you get your denominator that has no radical and its simplified. In my example I used the conjugate one so their is a visual to show how you solve those expressions. And if the bottom square root can be simplified to a simpler radical then you should change it so then you can work with easy radicals. I worked smarter than harder and that ugly radical becomes an easy one.

What I learned this week is how to write an entire radical from a mixed radical. The first thing you do is look at the square root number or cube root. Than the number that is in front you multiply it by your perfect square and after it is done you have to multiply the number that is inside of the square root by your first number squared. I found it easier to calculate it when its in a fraction cause you just square the number on the top and what is done at the top must be done as well at the bottom. Then you multiply that fraction by the one in the square root. That is how you write an entire radical from a mixed radical. Here is the example that I did from the workbook and since you can’t have negatives inside a square root you leave it on the outside, and that is what I shown in my answer. Also don’t forget to simplify the fraction if it is possible.

# Geometric Sequences

In class last week we learned how to calculate geometric sequences using a specific formula and you know that it is a geometric sequence if it has a common ratio and since the equation gave me my common ratio it made it easier to calculate. But some equations the r is unknown and to solve it you have to isolate the variable and then use the ratio number you get and substitute into your formula.

Ms Burton I am sorry but my blog post didn’t properly post on Friday because shaw turned off my wifi and I had no idea until today in the morning when I decided to check.

# Arithmetic sequences

5,10,15,20,25

common d= 5

$t_{50}= 5+{(50-1)}{(5)}$

$t_{50}= 5+{(49)}{(5)}$
$t_{50}=5+245$
$t_{50}=249$

$tn= 5+(n-1) 5$ $t_{n}= 5+{(49n)}{-5}$ $t_{n}= -245n-5$

$S_{50}=\frac{50}{2}{(5+250)}$
$S_{50}={25}{(255)}$
$S_{50}={6375}$