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- area of a circular sector a=1/2θr^
- Formula for length of circular arc s=rθ
- Sine Opposite/ Hypotenuse
- Cosine Adjacent/Hypotenuse
- Tangent Opposite/Adjacent
- Midpoint Formula: Can be used for circles/
- equation of a circle (x-h)^2 + (y-k)^2= r^
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- To describe an interval with an absolute value inequality
- If the increase/decrease is linear it should grow by a
- if the increase/ decrease is exponential it should
- Shape of distribution: right tailed
- Shape of distribution: left tailed Use the midpoint and the size of the interval grow by a constant amount, the com- mon ditterence FIXED AMOUNT=LIN- EAR increase proportionally to the preivous amount by a factor of a common ratio
- For (14^7+7^2)^2 you multiply the exponent by the one out- side parenthesis
- when you divide to fractions you multiply the numerator by the by the reciprocal of the denominator
- range ditterence between the highest value and the lowest value
- median + FOR DOT GRAPHS the middle of the numbers even number the cross out
4 / 19 odd number the middle add both then divide by two For graphs you have to count the ones even if they are both for 50 or some- thing like that
- mean average of all numbers add up then divide by number of num- bers
- to find the greatest possible value of x you. It is the opposite for
- box and whisker graph
- the point at the left end of a box and whisker graph represents the
- on a box and whisker graph the line that di- vides the box is the add the range + lowest value given. The least possible value. Then you do the highest given munis (-) range minimum median
- distinct zeros list each zero once
- distance formula
- equation for a circle
- quadratic function a(x-h)^2 +k (h.k) is vertex of parabola
- when a percent is increasing 2% per year you would write as after one you 1.02 for 2% after one year
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- Lesson 1 McGraw Book: BE CAREFUL NOT TO OVER DISTRIBUTE. IF there are two numbers in a parenthesis, remember they
- Lesson 1 McGraw Book: In order to answer a question like : (3x+2)/ 2x is equivalent to a, b, c, d, you cna go together distribute division just like multiplica- tion, so 3x/2x + 2/2x
- law of exponents written as: X^a2/X^b2= X^a2-b lets say X^16^2 then X^a2-b2= this
- reduced by 13% annually means 87% is left, and will be used in equation
- 8+i/3-2i what do you do to find A of a+bi solve all the way, and the simplified 2+i a=2 so thats the answer
- C=5/9(F+31) what do you do if oyu have three things like I. they ask II. III.then they ask a temp increase is equivalent to 1.8? then they y=mx+b so m=5/9 so one degree raise is equivalent to saying that an increase of 1 degree Celsius is equal to an in- ask a temp incerase of 5/9 is equivalent to one crease of degree up in c.
degrees Fahrenheit. yes its equivalent to 1.8 bc
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- so what if, and listen close now, what if you have a problem like 3x-y=12 what is the value of 8^x/2^y
- so then you have trinagle ABC measure of an- something x^2 on one side and ax^2 on the other, the coeflcients have to be equal so you then just solve by putting the numbers equal like -8a=24 or somethin first, you do 2^3x which can be rewrit- ten as (2^3)x/2y so then you have a common base between numerator and denominator and you can rewrite as 2^3x-y and they says they says 3x- y=12 so 2^12 done ya so you find out that the missing side is gle b = 90 and AC=20 BC=16 then what is sin of 12. and SOH so sinF= 12/20 or 3/ similar DEF if it is 1/3 length of corresponding angles of ABC
- so this fu looks hard but hes actually super easy all oyu gotta do is just believe you can be who...just kidding,. so heres the question. so theyre like this box and it has left and right handed students. they say that 5X rh females as left, and 9X rh males as left. then they give total of 18 left handed students and 122 right so you just make system of equations Let x be the number of left-handed fe- male students and let y be the number of left-handed male students. 5x+9y= X+y+ then just solve so you get x= and handed what in the world do you do to find the y=8. probability rh student selected is female?
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- shoppers enter at N=rT store owner decides 84 per hour. 5 min in checkout line also btw 50 of the 122 right-handed students are female. so 50/122=.41 done adn done so you convert to minutes. 1.4 per min- uet. then muliply by 5 so 7
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- 3m+ 2 ] 3 so simplifies to m++
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- the function f(x) = x^3-X^2-x- 11/4 is graphed in xy plane above. if k is a constant such that the equation f(x)=k has three real solutoions, which of the following could be the value of k? 2,0,-2, or -3 (graph not give sorry)
- q=1/2nv^ dynamic presure q by moving with velocity v can be found using the formula above, where so y=k and remember you check all the solutions so y=-3 is the only one that worked for this wit hthree real solutions . Let q1 be the dynamic pressure of the slower fluid moving with velocity v1, and let q2 be the dynamic pressure of n is the constant density of the fluid. aeronau- the faster fluid moving with velocity v2. tical engineer uses formula to find dynamic v2=1.5v pressure of a fluid moving with veolucity v and substitute q2(small) = 1/ n (v2(sub) the same fluid with velocity 1.5v what is the ^2 since v2=1.5v1 just plug it in at ratio of the dynamic pressure of the faster fluid (v2)^2 and it is rewritten and solved so to the dynamic pressure of the slower
- for a polynomial p(x) the value of p(3) is - 2. 2.25)q 2.25/1=2.25 so thats the answer yo p(x)/x-3=q(x)+r/x-3 q(x) is a poly and which of the following must be tru about p(x)? 4 is remainder so since is is a degree 1 polymnomial ,remainder is real so p(x)=(x−3)q(x)+r, where r is real. then since p(3) is -2, −2=p(3)=(3−3)q(3)+r=(0)q(3)+
13 / 19 The line y=kx +4y, equals, k, x, plus, 4, where k so remember d=kc+4 then just solve is a constant, is graphed in the xy, y- plane. If the line contains the point (c,d) (c,d)left paren- thesis, c, comma, d, right parenthesis, where c \neq 0 c0 c, does not equal, 0 and d \ neq 0 d 0 d, does not equal, 0, what is the slope of the line in terms of ccc and ddd?
- kx−3y= 4x−5y= for k so you solve for for y for both. then the slopes have to be equal bc they are parallel so you do 4/5=k/ In the system of equations above, kis a con- stant and x and y are variables. For what value of k will the system of equations have no solu- tion?
- In the xy , y-plane, the parabola with equation plug in 25 for y 24=x- 11)^2 so -5=x- 11 y=(x−11)^2 interscets the line with equation y = 25, equals, 25 at two points, A and B. What is the length of AB 5=x-11 so 16 and 6 and 16-6 =
- if you have to use quadratic equation by you have 3x^2-6x+12 you can
- if you have a box and have to find equation look for
14 / 19 factor out 3 slope just calculateq
- S(P) slope 1/2 for increase in 1 increase in 10 in p will yield 5
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- are imaginary numbers real? NO YOU ARE SSO STUPID FOR ASKING JK YOURE GREATQ
17 / 19 IF OYU ARE GIVEn an equation and asked to find k what do you use?
- discriminant is euqual to what when there is one disctinct zero use discriminant, b^2-4ac can be used to find number of zeros and type of solutions to quadratic equation
- discriminant equal to positive 2 SOLUTIOONS
- discriminant equal to negative 0 solutions
- x^-2 becomes 1/x^
- if you have a problem like x^a/x^b=16 and x^-2=1/16 what is the value of b-a so first conver x-2 to 1/x^2 then set that equal to 1/16. cross multiply and you get 4. then conver x^b/x^a=16 to x^b-a. plug in 4 for x, and solve for 2
- y=kx-1 and they say points (a,b) solve for k just plug in a for x and b for y
- if you have h and k are functions such that h(x)=x+3 and h(g(2))=9, which of the following describe g(x). so first, you plug in g(x) to the h(x) thing, so g(2)+3=9. g(2)=.6 with the x value 2, the equation must equal 6
- y=a(x+3)(x-1) the graph of thee euqation in the so first, you find the axis of symmetry. xy-plane is a parabola with vertex (m,n) which of the following is equal to n. x=k. that is 1/2 the distance from both xs. so (-3+1)/2=-1 then plug that in for thats it.
19 / 19 is (k/3,0) where it crosses x-axis. since you have base times height, just apply to are formula for traingle and solve
- given a circle inscribed in a square in a circle creates 45,45,90. then its just r r and rsquareroot2 the bigger circle is pi(rsquareroot2)^2= 2pir^2. the larg- er circle has area of twice little cirlce. 16.5/
