Question

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Answer 1

@Vocaloid

Answer 2

You must be familiar with the properties of all regular and basic polygons. The diagonals for an isosceles trapezoid are always congruent. Option B.

Answer 3

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Answer 4

@Vocaloid

Answer 5

3. You must know the properties of all polygons. At least sketch a kite. Diagonals don't bisect.
4. This conditional statement is true.

Answer 6

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Answer 7

@Ferredoxin4

Answer 8

Property of parallelograms:
Parallel sides of a parallelogram are always congruent. AB is parallel to CD and BC is parallel to AD. This leads you to the conclusion that AB=CD and BC=AD.
We can now formulate the respective equations.
(1)...2x-y=7 for AB=CD
(2)...x+y=2 for BC=AD

I'd now use elimination between the two systems, find x, then plug and chug and find y.

Answer 9

can I just put 2x-y=7 equal to x+y=2 ?

Answer 10

First you can't really make two systems 'equal' to each other, you can only isolate one variable and then find the other.
Second by making them equal, you are implying that AB=AD or CD=BC, which is not necessarily true in all parallelograms.

Answer 11

I'd suggest using elimination between the two systems and eliminate the y since their coefficients are already opposite values. Then add the x terms and the constants on the other side, find x using division property of equality. Once you have x, I'd substitute that x value in the second equation (or first, whatever is your preference, but I chose second because less math) and find y using subtractive property of equality. You'll get your x and y values then.

Answer 12

Can you help me through it please, because its quite confusing

Answer 13

Do you understand the logic I used for the parallelogram?

Answer 14

Given that ABCD is a parallelogram, we can use the property that non-intersection, parallel sides must always be congruent. This is true as long as the polygon is a parallelogram.

What are the parallel sides here?

Answer 15

bc and ad?

Answer 16

correct, what's the other pair?

Answer 17

cd and ba?

Answer 18

correct. So using the property I gave you, what do you think is true of these pairs?

Answer 19

The parallel segments would be...

Answer 20

congruent

Answer 21

correct, so thereby you can imply that the values given are equivalent.

You can say that
AB=CD
and
BC=AD

do you get that?

Answer 22

Yes

Answer 23

So you can use the values given:
AB=2x-y
CD=7
and you know that AB=CD
So then you can say that
2x-y=7

correct?

Answer 24

Yes okay

Answer 25

Apply the same logic with the other pair.
BC=AD
we know that BC=x+y and AD=2
so
x+y=2

Answer 26

You now have two equations for each pair,
AB=CD is
2x-y=7
BC=AD is
x+y=2


So now you have a system of linear equations. Do you know how to do those?

Answer 27

Im not sure

Answer 28

Elimination, substitution, Cramer's rule, etc...you know these terms?

Answer 29

Okay, not Cramer's rule, but do you recall elimination and substitution from Algebra 1?

Answer 30

Yes I do

Answer 31

Do you know how to do those, specifically elimination in this case?

Answer 32

I forgot about the elimination method

Answer 33

Okay so here's what you would do:
Your equations are
\[(1)...2x-y=7\]
\[(2)...x+y=2\]
You can add these two without having to change the equations one of the like-variable's coefficients are opposite values of each other (-y and y)

2x-y=7
x+y=2
Add these 2 equations
3x=9
x=3

We have our x value as 3. Now plug and chug in one of the equations and find y.
x+y=2
(3)+y=2
y=2-3
y=-1

so x=3 and y=-1.

We can ensure these values are correct using inductive reasoning.

Answer 34

So thats the x and y ? so those are the answers?

Answer 35

yes, x=3 and y=-1

Answer 36

Got it okay that makes sense

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Answer 37

AC = 2x+9
BC = 8x-3

2x+9=8x-3

find x??

Answer 38

x=2

Answer 39

like that?

Answer 40

yes, but do you know why we did AC=BC?

Answer 41

Point C is on the perpendicular bisector of AB.

Answer 42

No, there is not enough information to conclude that point C, which lies on segment AC, is a perpendicular bisector of AB.

Answer 43

The reason why we can do AC=BD is because a property of isosceles trapezoids is that their diagonals are equivalent.

Answer 44

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Answer 45

AE = EC
1/2b + 1 = b - 15

Answer 46

Correct, now do you know why you equate AE to EC?

Answer 47

b = 32

Answer 48

they were both given

Answer 49

AE = EC the same as BE = ED

Answer 50

yes b is 32 but why?

Answer 51

No, it's because another property of parallelograms:
Diagonals intersect at their midpoints.

Answer 52

yes thats another reason

Answer 53

then to find AE we have to substitute the b

Answer 54

AE = 1/2(32) + 1

Answer 55

AE = 16+1

Answer 56

which is 17

Answer 57

so AE is 17.

Answer 58

Correct?

Answer 59

@Ferredoxin4

Answer 60

I was away, I'm back. Let me see.

Answer 61

correct.

Answer 62

Okay

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Answer 63

34=2x-10



x=22

?

Answer 64

yes correct

Answer 65

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Answer 66

Measure of L is the same as M.



Since M equals 66, then L also is 66.

Answer 67

correct

Answer 68

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Answer 69

y=-x+4, SV=VS, 1=4x-y

Answer 70

y=-x+4 into 1=4x-y

1=4x-(-x+4)

=> 1=4x+x-4

=> 1=5x-4

=> 1+4=5x-4+4

=> 5=5x

=> 5/5=5x/5

=> x=1

Answer 71

Correct, due to CPCTC. Now use systems of linear equations (I would use substitution)

Answer 72

x=1 into y=-x+4

y=-x+4=-1+4=3

Answer 73

x=1, y=3 ?

Answer 74

Correct x=1 and y=3

Answer 75

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Answer 76

We can draw several implications here and eventually conclude that 2x+3=40, then solve for x.

Answer 77

x=37/2

Answer 78

yes

Answer 79

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Answer 80

Using CPCTC we can conclude that BC=EF.
This means that 3x-5=x
find x

Answer 81

x=5/2

Answer 82

correct

Answer 83

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47=3x-1

?

Answer 84

Incorrect. Don't make implications off of the graphic, as it may trick you. It says that ABC=DFE. Using CPCTC, we can say that angle F is equal to angle B, or that 3x-1=100. Now solve for x.

Answer 85

okay

101/3

Answer 86

yes

Answer 87

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Answer 88

I'd say mark up the diagram so it's easier to understand, or draw it on paper.

Answer 89

wouldnt it just be 4 and 6

Answer 90

AB of the shorter triangle and AC of the larger triangle are similar segments. Similar segments are a proportion.
This means we can say that

\[\frac{ AB }{ AC } = \frac{ BE }{ CD }\]

Plug in their values

AB=4
AC=6
BE=x
CD=3

Answer 91

\[\frac{ 4 }{ 6 }=\frac{ x }{ 3 }\]
x would be 2.

Answer 92

Ohh okay that makes sense

Answer 93

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Answer 94

16/8 = x/20

Answer 95

x=40

Answer 96

Correct.

Answer 97

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Answer 98

Use proportions
We can say that TV~WS and WR~TR
Then make the proportion:

\[\frac{ 18 }{ 10 } = \frac{ x+6 }{ x+2 }\]

Use cross multiplication and find x

Answer 99

x=3

Answer 100

yes

Answer 101

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Answer 102

same concept as before, form a proportion on the similar segments

Answer 103

12/8=x+14/x+8 ?

Answer 104

yes correct

Answer 105

x=4

Answer 106

yes

Answer 107

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Answer 108

5x-6=2x+12?

Answer 109

correct, do you know why?

Answer 110

because thats the measure of the two triangles

Answer 111

no, it doesn't have to do with triangles. Since both angles x and y share the same arc, which is arc WZ, we can conclude that angles x and y are congruent.

Answer 112

oh okay

Answer 113

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Answer 114

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Answer 115

@Ferredoxin4

Answer 116

Use the distance formula:

Answer 117

This one doesn't need it though, just imagine the points on the cartesian plane or draw a sketch. It would be 1 unit away.

Answer 118

Got it

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Answer 119

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thats the graph we can draw on

Answer 120

So first you can graph the function using a few test points. Do you know how to calculate focus and directrix?

Answer 121

No im not sure

Answer 122

okay here's how you would do it:

1. First change the equation so it matches this:
4py=x^2, where 4p=a
2. Find p.
3. if a>0, then the focus is k+p and the directrix is y=k-p, where k is from (h,k)
Graph them

Answer 123

Correction to #1, you would convert it to
(x-h)^2 = 4p(y-k) if it's a vertical axis
I just wrote that because in this case there is no bx or c value.

Answer 124

4p=a
remains the same.