## week 10 in math 10

this week in math 10 I learned that if we have a binomial that says $x^2-81$ for example, this is considered a perfect square because $x^2$ = (x)(x) , 81= (9)(9). there is no middle term because when factored it would look like (x-9)(x+9), then if you were to expand this back out, the -9 and the +9 would cancel out and become 0, leaving the answer to be a binomial instead of a trinomial. (x)(x)= $x^2$ + (x)(9)= +9x (-9)(x) = -9x (-9)(9) = -81

$x^2$ + 9x – 9x -81 .    the +9x and the -9x cancel out to be zero

for this to be a “perfect square” we need to make sure that each term is a perfect square and that the sign is subtraction, not addition

## week 9 in math 10

this week we started our unit on polynomials, this was mainly review but i learned how to model binomials multiplied by binomials or binomials multiplied by trinomials or trinomials by trinomials etc, by using an area model. i also learned that you can use this type of model to model more than one digit number multiplication. for modeling polynomials, its all done in a box. if i had ( $2x^2+3x$ )(x-5) you would draw a square and divide it into 4 even squares, one for each piece of the expression and along the top you would write $2x^2+3x$ then along the side you would write x-5 and you would fill in the box as if it were a multiplication chart so it would look like this….

then you add all of the squares together and combine like terms to get a simplified expression

## week 8 in math 10

this week in math 10 I learned how to check that my answers are correct when solving a triangle, so I know that 90⁰ is greater that 45⁰ which is greater than 1⁰, also to remember that the angles in a triangle add up to 180, if my triangle looks like this after ive attempted to solve it:

i need to make sure that angle B is greater than A which is bigger than C, because angleB represents 90 degrees which has to be the largest, angle A represents 60 degrees which would be the second largest, it is between 89 and 45. and angle C would be the smallest because its 30 degrees, between 45 and 1. then the side lengths across from those angles also have to be greatest to smallest in that order.

## week 7 in math 10

this week in math 10 we started our unit on trigonometry. I learned how to use my calculator to calculate the side lengths of triangles using sine, cosine and tangent. I also learned that you can also calculate the angles ex if sinB= 12/30, where B is the angle, to find the angle you put $sin^{-1}12/30$ and get 23.57812….rounded to the nearest whole number = 24 degrees. I also learned how that works, so we have sinB=o.4 and we have to isolate B so we divide each side by sin $sinB/sin=0.4/sin^1$ which equals $b=0.4/sin^1$ . now we have to move $sin^1$ to the top of the fraction so it becomes $B=sin^{-1}0.4$ because the exponent of 1 now becomes negative.  then you punch $sin^{-1}0.4$ into a calculator to find B

would look something like this:

## song analysis and Building an understanding- english10

1. In this song he is saying that this girl is pretty much perfect and has no need to change.
2. Bruno mars is speaking to this girl saying that shes perfect, doesn’t need to change etc etc
3. words use of denotation. Abstract thinking ex. “when you smile the whole world stops and stares for a while”  when she smiles he thinks more of it, not just as some girl smiling out of happiness, the smile means something to him.
4. I don’t think the tone changes because the whole idea of this song is him saying how perfect this girl is and that doesn’t change throughout the lyrics
5. each stanza ranges from 3-8 lines. the song repeats ex “her eyes her eyes make the stars seem like theyre not shining” and this pattern continues with other compliments he gives such as ” her hair her hair falls perfectly without her trying” the first stanza is AABCCB
6. the title is good “just the way you are” considering the song is about a girl being perfect just the way she is. I think theres some symbolism in this song, when he describes “when you smile the whole world stops and stares for a while” her smile is a symbol of something that is bright enough or noticeable to turn heads
7. the lyrics definitely affect the reader of the poem because this guy is saying all of these nice things about a girl, it just makes you think of how shes feeling by this and how sweet he is to do so

just they way you are BAU

## week 6 in math 10

this past week in math 10 I learned that you can calculate the volume of a prism by taking the volume of a pyramid with the same height and bottom, and multiplying it by 3. this also works to find the volume of a pyramid by taking the volume of a prism with the same height and bottom, and dividing it by 3. from this I learned that formula for the volume of a pyramid is the area of the base, multiplied by the height, all divided by 3 or multiplied by $1/3$

## week 5 in math 10

this week in math 10 we started our unit on measurement. we went over conversions in the metric system and imperial. At first I did not understand how to do this at all but with some practice and a little help I am starting to understand it way more. we also did some work on surface area and volume, Ms Burton showed us how to write out everything you are thinking step by step, I found this helpful because it kept me from losing track of numbers and getting lost in the question.

## week 4 in math 10

this week in math 10 I learned about scientific notation, it is basically how you can turn a large number ex. 34500000000.00 into a simple expression that is easy to work with. we have $a*10^n$ “a” needs to be greater than 1 and less than 10. “n” just represents the unknown exponent. so to find “a” we need to move the decimal from 34500000000.00 so the number follows the rules of “a”. it becomes 3.45 because 3.45 is greater than 1 and less than 10. now the decimal “n” becomes the number of times we moved the decimal over so n=10 and the expression becomes $3.45*10^{10}$ now if the number were to be 0.000000345 same rules apply only the exponent will be negative because you are moving the decimal to the right this time the expression would be $3.45*10^7$

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