(what’s a fast way to solve such a question)
1)In the xy plane, the point (3,0) is the center of a circle that has a radius of 3. Which of the following is not a point on the cirle?
A)(6,0)
B )(6,-3)
c)(3,3)
D)(3,-3)
E)(0,0)
2)if the x/y = k and k greater than zero what is x+y/x in terms of
A)k-1/k
B )k+1/k
C)1/k
D)k/k-1
E)k/k+1
( i solve it in a way which am not sure if its right or no so i need your way = ) )
jesse finds that by selecting from the different combinations of the jackets pants and shirts that he owns he can create up to 60 different outfits each consisting of one jacket and one pair of pants and one shirt. if he owns 3 jackets and 5 shirts how many pairs of pants does jesse own?
A) 4
B ) 5
C) 6
D)12
E) 15
in the figure above ABCDEF is a regular HEXAGON and AB=2 what is the area of ACDF
ACDF IS A RECTANGLE AND ABC AND DEF ARE TWO TRIANGLES ON OPPOSITE SIDES
a ) 4 square root of 3
b ) 4 square root of 2
c ) 3 square root of 3
d) 3 square root of 2
e ) 2 square root of 3
the function F is defined by f(x)=2x^2-5 what are all possible values of f(x) where -2<x<2
A) -5 less than or equal f(x) <0
B ) -5 less than or equal f(x) < 3
c) 0 less than or equal f(x) < 3
d) 0 less than or equal <8
e) 2 less than or equal f(x) <8
( i have no idea how to solve such questions )
if the radius of a circle is tripled by what percent is the area of the circle increased?
A) 200%
B ) 300%
C) 400%
D ) 500%
E) 800 %
1)B for the first one, you need to know what radius mean.
2)B x=ky, ky+y/ky=y(k+1)/ky=k+1/k
3)A 354=60
4)not clear post a pic.
5) B is the correct answer read the question correctly.
6) E is the correct answer. Plug in.
@Jr12317 4. is clear. Conventionally, vertices of a polygon are labelled in order (i.e. quadrilateral ABCD has vertices A,B,C,D in order).
CD = 2. There are multiple ways to find AC; one such way is to drop an altitude from B to AC and use 30-60-90 triangles - you should get AC = 2sqrt(3), and the area of the rectangle is 2*2sqrt(3) = 4sqrt(3), A.
@Jr12317 draw one out. In fact, A,…,F must be in order (I’ve done enough AIME/olympiad geometry to figure that out). Also, if A,…,F are labelled in order, ACDF is a rectangle.
Furthermore, there is only one rectangle with all four of its vertices on a regular hexagon of side length 2 (up to rotation), so it’s actually possible to do this problem without labelling any vertices.
@Jr12317 in number 1 do i have to draw it or there is another easy way? i know what radius mean
i still dont get question 5
and question 6 i tried to plug in and it didnt work .-.
@CrazinessISlife draw it out. Letting M be the midpoint of AC, we have that BM bisects angle ABC (since triangle ABC is isosceles), so angle ABM = 60 deg.
For 1, you can draw it out, but you don’t have to.
For 5, you want all possible values of f(x). What does f(x) look like when you graph it? (this shouldn’t be too hard). Then, restrict your domain to [-2,2]. What are the minimum and maximum values achieved?
For 6., it’s asking by what percent the area is increased. For example, if the area was 1 and the new area is 3, the area is increased by 200%, not 300%. Plug in radius = 1 and try again.
@MITer94 i got number 4thanks = )
for 1 whats the other way than drawing/?
for 6 if i try other number for the radius say 2…when its tripled its 2x3=6…so the area should be 6^2x3.14=113
and the original is 2^2x3.14=12.56 and then should i add the original area by the percent? what do i do wrong here?
@CrazinessISlife for number 1, take the given center (a,b). The easiest to find points on the circle are (a+r, b), (a-r, b), (a, b+r), and (a, b-r) where r is radius. With numbers, that is (3+3, 0), (3-3, 0), (3, 0+3) and (3, 0-3). All of those are options as answers, so use process of elimination (this is not the only way).
@CrazinessISlife for 1. just find out which point is not of distance 3 from the center (3,0). The points in choices A, C, D, and E are all 3 away from (3,0). Answer is B.
For 6, it’s easier to just write in terms of pi.
Area of a circle with radius 2: 4pi
Area of a circle with radius 6: 36pi
When the area increases from 4pi to 36pi what is the percent increase?
For 5., not really. What does the graph of y = 2x^2 - 5 look like?
You’re given a radius. Do you know the formula for the area of a circle? Just notice how it uses radius^2. There is no need to look at Pi. Here’s the best number to plug in.
Take a radius of 1 and triple it to 3. Your square become 9 from the original 1. That is 1^2 and 3^2. Well guess what, that 9 from 1 represent an 800 percent increase, which is the same as saying the area increased 9-fold.
As always, use the smallest numbers possible and look at what the suggested answers are. The 800 percent was a dead giveaway as soon as they mentioned a tripling of a number that needed to be squared as 9-1 = 8!
)
