Math+9

Math Math 9

Use this space to discuss what we did today including any assignments. Also, summarize your learning here. Use text, examples, any diagrams or pictures to help you with your explanation.  The work sheets we did before we got the book!!! Whole #'s -it means 2 cubed -2*2*2 - it means to multiply 2 by itself 3 times
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Types of # systems
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Sientific notation .0000610 = 6x10 to the power of -6 10 to the power of -1 = 1/10
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__Chapter 1 - Integers 1.1 - Order of Operations with Positive Integers__ BEDMAS - Brackets - Always begin by simplifying within the brackets. - Exponents - Do exponents right after you do the brackets and before you do any other operation. - Division/Multiply - After you do the exponents, work from left to right, dividing/multiplying as you see them. - Addition/ Subtracting - After you do the dividing/multiplying, work from left to right, adding/ subtracting as you go. i.e.7{2+5[3+2(6+4)]}=

__1.2 - Evaluating Variable Expressions Using Positive Integers__ Variable - any letter or symbol that can be used to represent numbers. Variable expression(algebraic expression) - any combination of variables and numbers using mathematical operations.

//**Geometry- Angles 1. Acute Angle - any angle < 90 2. obtuse angle - any angle > 90 but < 180 3. Right angle - any angle = 90 4. straight angle - any angle =180 5. Reflex Angle- Any angle >180 but < 360. 6. Congruent Angles - two angles that have the same measure 7. Adjacent angles - two angles that share a common vertex and a common arm 8. Complementary angles - two angles that add up 90. 9. Supplementary angles -two angles that add up to 180. 10. Linear pair - two adjacent angles that add up to 180. 11. Opposite angles - Congruent angles formed when two lines intersect. 12. Transversal- a line that intersects two other lines 13. Corresponding angles - corresponding angles are~= if: e angle 1,1 14. Parallel lines -two lines are parallel lines if they are equidisant apart at all times 15. Perpendicular - two lines are = if they meet at 90 16. Interior alnernate angles - interior alternate angles are = if e, 11e2 17 Exterior alternate angles**//

We learned about: Squares, Trapezoids, Isosceles Trapezoids, Parallelogram, Rhombus, rectangles
 * __Chapter 9__**
 * __9.1__**
 * Geometric Figures and Perimeter**

Polygons:
 * **Number of sides** ||
 * **Name** ||
 * || 3 ||
 * Triangle ||
 * || 4 ||
 * quadrilateral ||
 * || 5 ||
 * pentagon ||
 * || 6 ||
 * hexagon ||
 * || 8 ||
 * actagon ||

Circles: Diameter-is the length from one side of the circle to the other, threw the middle Radius-is the length to the middle of the circle from the outer line, and half the diameter Sector: Is the a portion of the circle Sector angle-the angle between the radii Congruent: Things are said the be congruent when they have the same shape and size

When you get your answer u always put a u behind it, the u stands for units. To find the perimeter of a sector you use C= pie d
 * Perimeter-** is the distance around something

Every different shape has a different formula to get area. Rectangles-A=lw Square-a=s2 Parallelogram-A=bh Triangle-A=bh over 2 Trapezoid-A=(a+b)h over 2 Circle-A=pie r2
 * __9.2__**
 * Area-** is the amount of surface area

Different shapes have different formulas. The right prism-V=lwh The right cylinder-V=pie r2h The pyramid-V=(a base)h The right cone-V=pie r2h over 3 the sphere-V=4pie r3 over 3
 * __9.3__**
 * Volume-**the area inside the shape

This week we have been working on metric conversions. Km Hm Dam M Dm Cm Mm

If you go up from mm to cm you divide ex: 600mm to cm is so you divide it by 10 then the answer is 60cm.

7.8 power of polynomials

example 1- (x+5)^5

soultion (x+5)^2 means (x+5)(x+5) after this step distrubiute x to the x in the other bracket and then to the 5. After this distrubiut the 5 to the x and the 5 to the five. after this just simplify.

S- square the first number M- multiply the terms inside the brackets D- Double S- Square the last number

to remember this processe just remember "small mcdonalds shake"

F- First O- Outside I- Inside L- Last to remember this processe just remember tin FOIL

Once you know how to multiply two monomials it is easy to multiply a ploynomial by a monomial by simply using the distributive property of multiplication

1- r(5r-8) 2- 6(4y+9) 3- 4(8d-3)

1- (x+8)(x+6) 2- (m+9)(m-8) 3- (m-n)(m+9)

1- (X+3)^2 2- (5X-1)^2 3- (r-6s)^2

example-

5x-4y=28

If you go down then you multiple by 10 ex: 600cm to mm is 6000mm.

To find the area: Km Hm Dam M Dm Cm Mm

To find the area you have km2 so you have to double your answer. Ex: 23 m2 and to change it to cm2 to the jump thing there are to jumps so 23 is 2300 but then you have to double it because it is squared so the answer is 230000.

To find the volume: Km Hm Dam M Dm Cm Mm

To find the volume you do the same thing you do with area the only difference is that it is cubed not square. So 6cm3 to change it to mm3 it will be 6000 because on the thing you do your jumps and there is one jump so then you make it cubed so you add three zeros instead of one.

Effects on the volume of changing a dimension if you have on a object and add another on it is doubled if you have three it triples. The volume of a rectangle prism is 24u3. Determine the dimensions of five possible prisms using __only whole numbers.__ __Ex:__ Length width height volume surface area 6u 2u 2u 24u3 56u3 Kite - looks like a diamond and has two congruent sides polygon- figure having 3 unusually sides congruent- angle that are equal in measure adjacent-angle that are next to each other

**Dividing monomials** Ex. __24x__ 3xy 1. first you divide the constants 24 divide by 3 = 8 2. next you do the variables You subtract the top for the bottom or the bottom from the top. X-x = o 3. you do the next variables Y, because there is no other viable to go with y it is just left alone. The finished product __8__  Y  Example 2 __27a²b3c__ -18a3b3c4 The answer is __3 __ -2 ac3

Tally chart- to organize data Fequency table-since the tally chart shows the shows the frequencies the chart class intervals- the equal intervals; like the numbers that u divid things into
 * __Organizing Data[[image:tally_chart.jpg]]__**

__Measures of central tendency__ Developing the ideas
 * //The Mean//** of a set of numbers is the average of the numbers:that is, the sum of all the numbers divided by the number of the numbers
 * //The Median//** of a set of numbers is the middle number when the numbers are arranged in order. If there is an even number when the numbers, the median is the mean of the two middle numbers.
 * //The Mode//** of a set of numbers is the most frequently occuring number. There may be more than one mode, or there may be no mode.