SAT MATH

equation of a circle

(x-h)^2 + (y-k)^2= r^2

discriminant is euqual to what when there is one disctinct zero

0

if you have 5% more than a quanitity oyu write it as

1.5(quantity)

reduced by 13% annually means

87% is left, and will be used in equation

are imaginary numbers real?

NO YOU ARE SSO STUPID FOR ASKING JK YOURE GREATQ

Sine

Opposite/ Hypotenuse

Tangent

Opposite/Adjacent

quadratic function

a(x-h)^2 +k (h.k) is vertex of parabola

area of a circular sector

a=1/2θr^2

range

difference between the highest value and the lowest value

for a polynomial p(x) the value of p(3) is -2. which of the following must be tru about p(x)?

p(x)/x-3=q(x)+r/x-3 q(x) is a poly and 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)+r=r remainder is -2

if you are given a graphed triangle and inequalities, and the area x larger 0 y larger 0 3x+y less than k. area 24

plot the points. the point on y-aaxis is (0,k) the length of the y-axis point is k. the x-axis line is k/3 the other point is (k/3,0) where it crosses x-axis. since you have base times height, just apply to are formula for traingle and solve

In the xy , y-plane, the parabola with equation 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 ​

plug in 25 for y 24=x-11)^2 so -5=x-11 5=x-11 so 16 and 6 and 16-6 =10

y=kx-1 and they say points (a,b) solve for k just

plug in a for x and b for y

Formula for length of circular arc

s=rθ

IF OYU ARE GIVEn an equation and asked to find k what do you use?

use discriminant, b^2-4ac can be used to find number of zeros and type of solutions to quadratic equation

on a box and whisker graph the line that divides the box is the

median

the point at the left end of a box and whisker graph represents the

minimum

q=1/2nv^2 dynamic presure q by moving with velocity v can be found using the formula above, where n is the constant density of the fluid. aeronautical engineer uses formula to find dynamic pressure of a fluid moving with veolucity v and the same fluid with velocity 1.5v what is the ratio of the dynamic pressure of the faster fluid to the dynamic pressure of the slower

. Let q1 be the dynamic pressure of the slower fluid moving with velocity v1, and let q2 be the dynamic pressure of the faster fluid moving with velocity v2. v2=1.5v1 substitute q2(small) = 1/2 n (v2(sub) ^2 since v2=1.5v1 just plug it in at (v2)^2 and it is rewritten and solved so 2.25)q1 2.25/1=2.25 so thats the answer yo

Midpoint Formula: Can be used for circles

/

discriminant equal to negative

0 solutions

when a percent is increasing 2% per year you would write as ___ after one you

1.02 for 2% after one year

the store owner from the question b4 says that 45 shoppers in store at any time. owner opens nnew store where there are 90 shoppers per hour. each stay 12 minutes. average number of shoppers in the new store is what percent less than average from original

1.5 shoppers per minute. stay for 12. thus, N=rt =18 shoppers in new store at any time. to find percent change 45-18/45 *100=60 yay

x^-2 becomes

1/x^2

For (14^7+7^2)^2 you

multiply the exponent by the one outside parenthesis

discriminant equal to positive

2 SOLUTIOONS

Cosine

Adjacent/Hypotenuse

The function f is defined by a polynomial. Some values of xand f(x), left parenthesis, x, right parenthesis are shown in the table above. Which of the following must be a factor of f(x), left parenthesis, x, right parenthesis?

SO YOU LOOK FOR Y=0 BC ITS AN X VALUE

To describe an interval with an absolute value inequality

Use the midpoint and the size of the interval

law of exponents written as:

X^a2/X^b2= X^a2-b2 lets say X^16^2 then X^a2-b2= this

to find the greatest possible value of x you. It is the opposite for

add the range + lowest value given. The least possible value. Then you do the highest given munis (-) range

aos from two x-intercepts

add up both and divide by 2

mean

average of all numbers add up then divide by number of numbers

when you divide to fractions you multiply the numerator by the

by the reciprocal of the denominator

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 larger circle has area of twice little cirlce. 16.5/2

Lesson 1 McGraw Book: In order to answer a question like : (3x+2)/ 2x is equivalent to a, b, c, d, you cna

distribute division just like multiplication, so 3x/2x + 2/2x

if you have to use quadratic equation by you have 3x^2-6x+12 you can

factor out 3

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

first, you do 2^3x which can be rewritten 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

Lesson 1 McGraw Book: BE CAREFUL NOT TO OVER DISTRIBUTE. IF there are two numbers in a parenthesis, remember they

go together

If the increase/decrease is linear it should grow by a

grow by a constant amount, the common difference FIXED AMOUNT=LINEAR

if the increase/ decrease is exponential it should

increase proportionally to the preivous amount by a factor of a common ratio

distinct zeros

list each zero once

​S(P) ​ ​D(P) ​​ ​= ​2 ​ ​1 ​​ p+40 ​=220−p ​​ The quantity of a product supplied and the quantity of the product demanded in an economic market are functions of the price of the product. The functions above are the estimated supply and demand functions for a certain product. The function S(P)S(P)S, left parenthesis, P, right parenthesis gives the quantity of the product supplied to the market when the price is PPP dollars, and the function D(P)D(P)D, left parenthesis, P, right parenthesis gives the quantity of the product demanded by the market when the price is PPP dollars.

slope 1/2 for increase in 1 increase in 10 in p will yield 5

if you have a box and have to find equation look for

slope just calculateq

The angles shown to the left are acute and sina= cos b so a=4k-22 and b=6k-13 what is value of k

so 4k-22+6k-13= 90 bc its right right so k=12.5

x arithmetic mean of m and 9, y is average of 2m and 15, and z is average of 3m and 18, what is average of x,y, and z in terms of m?

so average arithmetic mean os sum of numbers divided by 2. so x= m+9 2 , y= 2m+15 2 , z= 3m+18 [ m+9 2 + 2m+15 2 + 3m+18 2 ] 3 so simplifies to m++7

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=a(x+3)(x-1) the graph of thee euqation in the xy-plane is a parabola with vertex (m,n) which of the following is equal to n.

so first, you find the axis of symmetry. x=k. that is 1/2 the distance from both xs. so (-3+1)/2=-1 then plug that in for x. thats it .

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

The line y=kx +4y, equals, k, x, plus, 4, where k is a constant, is graphed in the xy, y-plane. If the line contains the point (c,d)(c,d)left parenthesis, c, comma, d, right parenthesis, where c \neq 0c≠0c, does not equal, 0 and d \neq 0d≠0d, does not equal, 0, what is the slope of the line in terms of ccc and ddd?

so remember d=kc+4 then just solve for k

ok so bitch what if the question is like bla/ax-2 = 3x-3 + bla/ax-2 and find a

so what you do is multiply by ax-2 so then you end up with bla= 8ax^2-3ax-bla so since youll have something x^2 on one side and ax^2 on the other, the coefficients have to be equal so you then just solve by putting the numbers equal like -8a=24 or somethin

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)

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

shoppers enter at N=rT store owner decides 84 per hour. 5 min in checkout line also btw N=number of shoppers per store r= average rate and t =average stay in minutes

so you convert to minutes. 1.4 per minuet. then muliply by 5 so 7

so then you have trinagle ABC measure of angle b = 90 and AC=20 BC=16 then what is sin of similar DEF if it is 1/3 length of corresponding angles of ABC

so you find out that the missing side is 12. and SOH so sinF= 12/20 or 3/5

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 handed what in the world do you do to find the probability rh student selected is female?

so you just make system of equations Let x be the number of left-handed female students and let y be the number of left-handed male students. 5x+9y=122 X+y+18 then just solve so you get x=10 and y=8. 50 of the 122 right-handed students are female. so 50/122=.41 done adn done

kx−3y=4 ​ ​4x−5y=7 ​​ ​​ In the system of equations above, kis a constant and x and y are variables. For what value of k will the system of equations have no solution?

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/3

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

median + FOR DOT GRAPHS

the middle of the numbers even number the cross out method 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 something like that

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 ask a temp incerase of 5/9 is equivalent to one degree up in c.

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 increase of 9 5 degrees Fahrenheit. yes its equivalent to 1.8 bc 5/9=1.8 no bc it has to be 9/5