Question

i need some answers checked

Answer 1

@Vocaloid

Answer 2

good

Answer 3

see how point P is ~outside~ the triangle

Answer 4

yeah

Answer 5

good

Answer 6

(i'm just gonna switch over to my other account, Mercury, so I can balance out the smartscores a bit)

Answer 7

hm, not quite, the circumcenter ~is~ equidistant from the vertices (part of the definition)

Answer 8

any other ideas?

Answer 9

A?

Answer 10

there's only one circumcenter (the balancing point)

looking at B, that's true (definition of circumcenter)

however there's nothing stating the circumcenter is equidistant from the midpoints so D must be the solution

Answer 11

oh, alright...

Answer 12

wait..

Answer 13

are you using another account or something?

Answer 14

yes (I'm trying to distribute the smartscore points a bit more evenly since my main account has a lot more points than everybody elses)

Answer 15

ah, alright.

Answer 16

good

Answer 17

good

Answer 18

going to get some dinner be back in a bit

Answer 19

okay

Answer 20

good

Answer 21

huh

this diagram is kind of confusing me but they're probably looking for the incenter which is a bit closer to point C i think

Answer 22

good

Answer 23

good

Answer 24

hm not quite, CPCTC would mean we are comparing corresponding parts of different triangles

notice how they are using the fact that the triangles are ~isosceles~ to state that angles ABC and ACB are equal

so ~isosceles triangle theorem~

Answer 25

good

Answer 26

hm not quite

we know that all the dashed lines are equal (definition of circumcenter)

we also know that each side of the triangle gets split in half (again, definition of circumcenter)

but which choice would we ~not~ be able to know based on this info?

Answer 27

MI?

Answer 28

that's a good guess but since we know JI we know that MI is just half of that

notice how LN is the distance from the center to the side of the triangle, we don't know anything about that from the circumcenter definition

so LN = your sol'n

Answer 29

SU is only the bisector if TU and UV are equal

so you just need to set 3x + 18 = 4x + 8 and solve for x

Answer 30

10

Answer 31

48

Answer 32

it asks for the value of x, so 10 not 48

Answer 33

good

Answer 34

good

Answer 35

hm, not quite

incenter means that all the dashed lines are equal

Answer 36

good

Answer 37

good

Answer 38

good

Answer 39

the incenter is the intersection of the angle bisectors, right? so we have to at least measure all the angles to bisect them

Answer 40

so the top right one

Answer 41

good

Answer 42

two thirds rule for centroids

UR is 2/3 of TR or in other words

5x = (2/3)(6x+12) solve for x

Answer 43

uh...

Answer 44

start by distributing the 2/3

remember the distributive property

A(B+C) = A*B + A*C

Answer 45

okay..

Answer 46

i need a bit of help trying to figure this one out..

Answer 47

(2/3)(6x+12)

using the logic that A(B+C) = A*B + A*C

(2/3)(6x+12) = (2/3)*6x + (2/3)*12 = ?

Answer 48

(2/3)(18x)=no wait..

Answer 49

12?

Answer 50

order of operations

start by multiplying (2/3)*6x

then multiply (2/3)*12

then add the results together

Answer 51

12, 4, and 8

Answer 52

24

Answer 53

where are you getting 12

(2/3)*6x = 4x (can't forget about the x)
(2/3)*12 = 8

Answer 54

therefore

(2/3)(6x+12) = 4x + 8

Answer 55

now going back to the original equation

5x = 4x + 8

solve for x

Answer 56

8

Answer 57

good so 8 = your sol'n

Answer 58

good

Answer 59

each of the midsegments is half the length of the side it's parallel to

Answer 60

in other words, since FD is parallel to AC, FD is one half the length of AC

therefore AC = ?

Answer 61

if FD is half of AC

that means AC is twice FD = ?

Answer 62

9.16

Answer 63

good, so that's your sol'n

Answer 64

hm, this one is actually false

they're describing the orthocenter which doesn't have the 2/3 rule (that's the centroid)

Answer 65

good

Answer 66

good

Answer 67

good

Answer 68

hm not quite

the original point is (2,-3) which means x = 2 and y = -3

so (-y,x) = ?

Answer 69

3,-2?

Answer 70

almost, notice how the sign on x doesn't change

so (3,2) = your sol'n

Answer 71

good

Answer 72

A is too close to the edge of the table

if you try mirroring ball C over the dashed line

it ends up being on ball B not A