This week in math 10 we learned how to add and subtract polynomials and monomials this could be done by grouping up the like terms from both polynomials a like term is a term whose variables and exponents are the same and then simplifying the answer by combining the like terms or subtracting them based on the question. After that arrange the remaining terms in order of decreasing degree. An example of this would be in the equation (2×2 + 6x +5) + ( 3×2 – 2x – 1) we would start by grouping them which equals 2×2+3×2+6x-2x+5-1 we then add the like terms together this can be done by adding the amount of each like term variable together or just plain adding the constant terms together. This equals 5×2+4x+4 and this is the answer to the question. Another example of subtracting polynomials is (5×2+3x-2)-(x2+2x-4) we first start off doing the same as adding polynomials and group up the like terms this equals 5x+x2+3x+2x-2-4 then we subtract them instead of adding to get the answer in order of decreasing degree this equals (4x-x+2)

I learned how to find the other sides of a right triangle using the Pythagoras theory with only one side and angle this can be done by first finding the trigonometric ratio that the side we have and the other one we don’t are both in. Then cross multiply the ratio and the angle with the side we don’t have as a variable and the side in their ratio form. An example of this being done was if we had the adjacent of angle 30 and the angle is 40 to find the hypotenuse we know that they are both in cosine ratio with the adjacent divided by the hypotenuse we write it as 30/A then we can cross multiple by the angle 40 cosine this equation equals (Cos 40 = 30/h) then the hypotenuse is 39.2(nearest tenth). Another example of this being done is if we had the hypotenuse is 20 and the angle we have is 16 then we want to find the adjacent side we can notice that they are both in cosine ratio which we write as x/20 then we cross multiply that by cos 16 which equals 19.2 so 19.2 is the adjacent side.

This week at school we learned how to find the trigonometric ratios of a right-angle triangle which can be found by first determining where the angle is which is the acute angle given this is the variable θ then we find out what type of side they are from this. The longest side in the triangle is the hypotenuse the side next to the angle is the adjacent side and the opposite side is opposite to the angle. we use those sides in the formulas  sin(θ) = Opposite / Hypotenuse, cos(θ) = Adjacent / Hypotenuse and  tan(θ) = Opposite / Adjacent. An example of this is if a right triangle has a hypotenuse side of 6 in length and an opposite side of 3 based on the given angle the sine ratio is 3/6= 2. Another example is if a triangle’s adjacent side length to the given acute angle is 4 and the longest length side of the hypotenuse is 5 then the cosine ratio of this right triangle is 4/5. to find the ratio angle we use the second function of a scientific calculator and press the ratio we have these functions are cos-1, sin-1, and tan-1.

This week I learned to do scientific notation which is a form of writing big numbers in smaller this can be done by moving the decimal point in your number until there is only one non-zero number this number is the base. the coefficient is always 10 to the power of the number of times you moved to the right or left this is the exponent. if you moved to the right the power is positive and to the left it’s negative. To show the scientific form we show the base we found is multiplied by ten with the exponent found. An example of this is 370000= 3.700 then since we moved to the left 4 times it’s positive and then the scientific form is 3.7 x 10^4 the expanded form is 3.7 x 10 x 10 x 10 x 10 which is the scientific form without exponents and 370000 is the standard form. Another example of scientific notation we can show is from this number  0.000087 so first we moved the decimal point to the right 5 times so the base is 8.7 which we multiple by 10 to the power of 5 where we write 8.7 x 10^-5 the other form of this number is expanded with is 8.7 x 0.00001 the standard form is 0.o00087

this week in math I learned how to find the prime factorization and 3 ways to show results. you can find the prime factorization by repeatedly dividing the number by the lowest prime factor and dividing that quotient until it can’t anymore and moving on to the next lowest factor it can divide into until there is any left. then those prime factors that we divided by including how many times I divided each of them which can be shown using exponents are the prime factors of this number. I can show this by showing the number then beside with an equal sign the prime factors and the factors with multiple times can be shown like this “ ” and how many times they were divided by. Another way would be to show the number and draw two lines connected to the prime factor and the result and do that over and over like a brain idea web but with numbers. the 3rd way is basically the 2nd but in a 2-column graph where the prime factors are in the first column and the quotients are on the 2nd column

1. I can use math when I am shopping to add subtract and multiply by the amount of money needed to buy something so that I can get the best price for an item for example if I was buying apples and there was a different pack of the different amount I would have to weigh them and see which has the best value. I can also use math to calculate the discount or tax on an item to see exactly how much I am paying for it
2. I can use math when I am cooking or baking and I need a specific quantity of an ingredient or I need to wait for an amount to cook and have to change it. for example, if I need a 1/2 a 1/4, or a 1/8 of an item I need math for that.
3. I can use math when I am looking at my bank account to calculate the interest percentage over time, or to see how much I am going to have after adding or subtracting money from it.