add the numbers together: 9+3+11 = 23
you want the ratio of total number of grapes to total number of fruits
this should be consistent no matter how many fruits you have, so:
9/23 = x/161
cross-multiply and solve for x (number of grapes in a total of 161 fruits)
23x =...

okay, that's an upside-down U and the maximum value is at the top
if you put the function in vertex form you can easily find the vertex:
group the first two terms and factor out the negative (essentially factoring out -1):
p = - (x²-14x) + 54
complete the square by taking...

bring all terms to one side and set equal to 0
4n²+12n+6=0
factor out 2
2(2n²+6n+3)=0 ===> 2n²+6n+3=0
complete the square
2(n²+3n+9/4) + 3 = 0 + 9/2 ===> 2(n+3/2)² = 3/2 ===> (n+3/2)² = 3/4
take square root of...

10 e's
--------- = 10/2 = 5/1 = 5
2 g's

separate the first two terms on the left and factor out 5
5(m² + (12/5)m ) + 6 = 0
take half the middle coefficient (12/5), square it, and add it to the terms in parentheses
5(m² + (12/5)m + 36/25) + 6 = 0 + 36/5 (this has the effect of adding 36/5 to both sides)
simplify...

assuming those are 3 terms and not 2 you should start by noting all restrictions for x. In this case, x cannot be 0 because we can't divide by 0.
multiply both sides by the lcm (2x)
9 + 2x = 8 ===>
2x = -1 ===>
x = -1/2

you need to simplify the expression by collecting like terms:
(-9 + 4)x² + (6 + -1)x + (2 + -1) = -5x² + 5x + 1

range value is the y value
domain value is the x value
(a) find y when x = 0
y = 2x-1 = 2(0)-1 = -1
y = -1
(b) find x when y = 5
5 = 2x-1
6 = 2x
x = 3

if the roots are r1 and r2, then the simplest equation is the quadratic:
(x-r1)(x-r2) = 0
since yours are -3 and 5, the simplest (quadratic) equation is:
(x - -3)(x - 5) = 0
(x+3)(x-5) = 0
which expands to x²-2x-15 = 0

simple interest equations:
A = P(1+rt) = P + Prt
I = Prt
A = accumulated...

Cost = $31/$1000 * $24000 = $744
Quarterly payment = $744 / 4 = $186

4x - y = 7
-2x + y = -5 (rearranging the first equation)
---------------------------------------------
2x = 2 ...

check the number of digits in the number
you have 3 possibilities:
1-digit numbers
2-digit numbers
3-digit numbers
the only 3-digit candidate you have is 100 and that results in a 1, so this is an easy case
for a 1-digit number the only way for the digits to add to 1 is for that number to be =...

suiye is right, and that way is probably even quicker, but another way to arrive at the answer is to set up an equation
four consecutive integers: x, (x+1), (x+2), and (x+3)
sum them up and get 86
x + x+1 + x+2 + x+3 = 86
now solve for x, the smallest...

they ask for parametric equations and they give you the speed
this is really projectile motion (the ball is moving both in the x and y dir. due to downward acceleration)
but to answer the question you only need the quantities for the x-dimension:
v(t) = 140
x(t)...

(a)
from a = v²/r we get 0.86 = v²/3.6
which leads to v = 1.76 m/s
period is the time it takes to complete a full cirle (your distance)
from v = d/t we get 1.76 = 2π(3.6) / T
which leads to T = 12.9s
(b)
again from...

multiply both sides by 2
1/2 x + y = -16
rearrange, leaving y alone on one side
y = -1/2 x - 16

(1) y = -2(x²-6x ) - 22 (rewrite)
(2) y = -2(x²-6x+9) - 22 (take half the coeff of -6 (-3), square it, and add it to the expression
(3) y = -2(x²-6x+9) -22 + 18 (u essentially subtracted...

12z - 3 -2(10) = 3(3)
12z - 3 - 20 = 9
12z - 23 = 9
12z = 32
z = 32/12 = 8/3

depends on the type of question. if it's a yes/no question (in other words it requires only a yes or no for an answer), then you use the word -ma (this is toneless) at the end.
there are other type of questions, (like when, who, what, how)....these questions have their chinese counterparts
what -...