### Mathematic equations

16y=144 y=9 -2x-2=4 x=-3 3(2x+5)=39 x=4
6m+1=-23 m=-4 2x+15=43-5x x=4 7w-3(4w+8)=11 w=-7
-4w-4=8 w=-3 3+4x=9x+13 x=-2
0=x-2 x=2 9y+4.8=17.4 y=1.4 2x-10=44+8x x=22
x-10=-11 x=-1 9x-5=13 x=2 2(6k-1)=-38 k=-3
x+7=-15 x=-22 5x+6=2x+15 x=3 -4(8+5n)=8 n=2
x/1.8=72 x=129.6 7x-4=20+3x x=6 -2(5+6m)+16=-90 m=8

### chapter 2 alg 2

direct variation y=kx^2
inverse variation y=k/x^n
Four step Algorithm write an equation find a constant variation rewrite the variation evaluate
what does the graph look like as a y=kx^2 proabula
slope formula Y1-Y2/X1-X2
when the volume of gas varies directly and the temperatures pressure measured inversely. when the gas is 250k and temp. is 76.2 and volume is 750. what is constant variation? 750=k*250/76.2=228.6
s=16d^2 how does the value of s change if d is doubled? *2^2
s=16d^2 how does the value of s change if d is divided by 3 /3^2

### chapter 1 alg 2

consider the sequence 6,15,24,33,42 write a recursive formula c=6 Cn=Cn-1+9 15-6=9
find the first 4 terms of this sequence 13,28,53,88 5(1)^2+8 5(2)^2+8 5(3)^2+8 5(4)^2+8
find p(x)= 2x^3+5x^2-5x when x=4 2(4)^3+5(4)^2-5(4)=188
what is domain indpendant (x)
what is range dependant (y)
find the volume of the cylinder V=(pie)r^2h r= 9cm h= 12cm plug in to equcation V=(pie)(9)^2(12)=3054
rewrite the formula for H V=(pie)r^2h V/h=(pie)r^2h/h h=V/(pie)r^2

### Math vocab

angle has two sides that share a common endpoint and is measured in degrees
degrees when a circle is divided into 360 equal-sized parts, each part has an angle measure of 1 degree
vertex the common endpoint of two or more line segments that form an angle
acute angle an angle with less than 90 degrees
right angle an angle with 90 degrees
obtuse angle an angle with more that 90 degrees but less than 180 degrees
straight angle an angle with 180 degrees
complementary angles two angles whose sum equals 90 degrees
supplementary angles two angles whose sum equals 180 degrees
polygon a closed figure with three or more sides
triangle a three sided polygon whose interior angles equals 180 degrees
scalene triangle a triangle with NO equal sides and NO equal angles
isosceles triangle a triangle with TWO equal sides and TWO equal angles
equilateral triangle a triangle with THREE equal sides and THREE equal angles
acute triangle a triangle with three acute angles
right triangle a triangle with one right angle
obtuse triangle a triangle with one obutse angle
quadrilateral a closed figure with four sides and four angles
parallelograms quadrilaterals whose opposite sides are parallel and congruent
rectangle a rectangle is a parralelogram that has 4 right angles
square a parallelogram with four equal sides and four equal angles
rhombus parallelogram with 4 equal sides and its opposite angles are congruent
trapeziod a quadrilateral with one pair of parallel des
perimeter the distance around a geometric figure
area the number of square units needed to cover the surface enclosed by a geometric figure
composite figure a polygon made up of two or more geometric shapes

### Variations and Graphs

What are some examples of a constant of variation? r=5c, r=10. They are all a form of y=kx^n where k is a nonzero constant and n is a positive number.
Ex: The weight w of an adult animal of a given species is known to vary directly with the cube of its height h. a. Write an equation relating w and h. b. Identify the dependent and independent variables. Solution: An equation for the direct varation is w=kh^3 b. Because w is given in terms of h, The dependent variable is w and the independent variable is h.
What is an inverse-variation function? Its a function with a formula of the form y=k/x^n, with k not equaling 0 and n being greater than 0.
Ex: The number n of oranges you can pack in a box is approximentely inversely proportional to the cube of the average diameter d of oranges. Write an equation to express this relation. Solution: The cube of the diameter of d^3. So, n is = k/d^3
The Fundamental Theorem of Variation a. If y varies directly as x^n( That is, y=kx^n), and x is multiplied by c, then y is multiplied by c^n. b. If y varies inversely as x^n( That is, y=k/x^n), and x is multiplied by a nonzero constant c, then y is divided by c^n.
Formula for Slope of a Line =changes in vertical distance/ change in horizontal distance = change in dependent variable/ change in independent variable =rise/run
Domain and range k>0 The domain of the function with equation y=kx^2 is the set of all real numbers. When K > 0, the range is the set of nonnegative real numbers, and the parabola opens up.
Domain and range k<0 The range is thet set of nonpositive real numbers and the parabola opens down. That is, the vertex of the parabola is its maximum point.

6m+1=-23 m=-4
-4w-4=8 w=-3
9y+4.8=17.4 y=14
-2x-2=4x x=-4
x/-6=8 x=-48
2-x/5=-13 x=2/9

### math kevin

3(2x+5)=39 x=4
2(6k-1)=-38 k=-3
8(7-y)=-24 y=10
-4(8+5n)=8 n=-2
6(3x-5)-7x=25 x=5
-2x=14 x=-7
3h=12 h=4
-4f=-20 f=5
-45k=90 k=-2
2x=40 x=20
5x+10=20 x=2
5x+7=4 x=6
m/3+5=-2 m=-21
3/4x+4=-2 x=-8
-9-7x=-5 x=-2
5x+6=2x+15 x=3
7x-4=20=3x x=6
2x+15=43-5x x=4
3+4x=9x+13 x=-2
-5x+40=6x-70 x=10

### 1 step equations, 2 step equations, variables, distribution

a+4=11 7
6=g+8 -2
h-4=0 4
4x=36 9
-3=-a/13 39
3y-7=8 5
-4x+6=34 17
14+4x=38 6
7-5u=-43 10
-30=-9x-3 3
6(3x-5)-7x=25 5
18x-(8x-7)=67 6
2(9n-1)+7(n+6)=-60 -4
13(3x+15)-(10+x)=35 -9
15(t+2)+9t=6 -1
11(4-6y)+5(13y-1)=9 40
8(-2x-4)+12=-52 2
-2(5+6m)+16=-90 -8
3(2x+5)=39 4
-4(8+5n)=8 -2

### …

3(2x+5)=39 x=4
2(6k-1)=-38 x=-3
15(t+2)+9t=6 x=-1
7w-3(4w+8)=11 x=-7
-4(8+5n)=8 x=-2
2x=14 x=7
5x=10 x=2
4/x=2 x=2
21-x=-1 x=22
6x+3=8x-21 x=12
15-x=4x x=3
5x=6+2x x=2
-2(5+6m)+16=-90 x=8
x–6=–2x+3 x=3
3x+7=34 x=9
5x-9=31 x=8
2/x+7=27 x=10
4x-2=20 x=6

-2x=14 x=-7
4p=32 p=8
-6n=30 n=5
-9a=-45 9=-5
72=-3b b=24
4y+1=13 y=3
6x+2=12 x=4
-3=5k+7 k=-2
`7=-3c-2 c=-3
49=16+3y y=11
5x+6=2x+15 x=3
7x-4=20+3x x=6
2x+15=43-5x x=4
3+4x=9x+13 x=-2
x-2=1-2x x=3