Question

Use the conditional statement to answer the question.

If a whole number is even, then the number is divisible by 4.

Are the statement and its converse true?

A. Both the statement and its converse are false.

B. Both the statement and its converse are true.

C. The statement is true, but the converse is false.

D. The statement is false, but the converse is true.

Answer 1

@Vocaloid

Answer 2

any ideas? are all even whole numbers divisible by 4?

Answer 3

the answer is C

Answer 4

not quite

the original statement is not true (there are whole numbers like 6 that are not divisible by 4)

Answer 5

B

Answer 6

like I just said, the statement is ~not~ true.

Answer 7

what about its converse? if a number is divisible by 4, is it always even?

Answer 8

let's start listing all the numbers divisible by 4

4, 8, 12, 16, 20...

are these all even?

Answer 9

no

Answer 10

so between 4, 8, 12, 16, and 20, which one is odd?

Answer 11

remember: an even number is divisible by 2

so I asked "are all of these numbers even" and you said "no" which means you saw an odd number - which one is it? or are they all even?

Answer 12

well, 4,8,12,16,20 are all even numbers

so the converse of the statement is true

so: statement is false, converse is true
which points us to choice D

Answer 13

yea they're are all even numbers

Answer 14

Use the conditional statement to answer the question.

If today is Monday, then yesterday was Sunday.



Can the statement be written as a biconditional statement and why?


A. Yes, because the statement and its converse are both true

B. No, because the statement is true, but its converse is false

C. No, because the statement and its converse are both false

D. No, because the statement is false, but its converse is true

Answer 15

any ideas?

the statement: If today is Monday, then yesterday was Sunday.

the converse: if yesterday was Sunday, then today is Monday

are the statement and converse true or false?

Answer 16

Yes, because the statement and its converse are both true

Answer 17

good that's your sol'n

Answer 18

Is each biconditional statement true or false?



Select True or False for each statement.

True False

A number is a multiple of 3 if and only if the number is odd.

A number is even if and only if the number is divisible by 2.

A number is prime if and only if the number is not a multiple of 4.

Answer 19

well let's go one by one

A number is a multiple of 3 if and only if the number is odd.

is this always true? or are there even numbers that are multiples of 3?

Answer 20

False. A number is divisible by 3 if the sum of its digits is divisible by 3

Answer 21

good, there are #'s like 6 that are even multiplies of 3

what about statement 2?

A number is even if and only if the number is divisible by 2.

is this always true or are there exceptions?

Answer 22

TRUE

Answer 23

good, true

what about statement 3?

A number is prime if and only if the number is not a multiple of 4.

is this always true or are there prime numbers that are multiples of 4?

Answer 24

False. A number is prime if its only factors are 1 and itself.

Answer 25

hm. wait a sec :S

Answer 26

apparently they want false for the last one (I don't personally agree but then your solution should be false true false then)

Answer 27

Which answers are examples of deductive reasoning?

Select each correct answer.


A. Jonathan leaves for school at 7:30 a.m. and is on time. Jonathan will always be on time if he leaves at 7:30 a.m.

B. All three angles in an equilateral triangle measure 60°. TriangleABC is an equilateral triangle. Therefore, all three angles in triangleABC measure 60°.

C. Mary and Sue are friends. Mary enjoys fishing, running, and rock climbing. Sue likes fishing and rock climbing. Sue must also like running.

D. The local grocery store charges $3 for a gallon of milk. Joe is going to the local grocery store to buy milk. Therefore, Joe expects to spend $3 for a gallon of milk.

Answer 28

any ideas? deductive reasoning starts with a generalization and then uses that to make a statement about something specific

Answer 29

D and B

Answer 30

good

Answer 31

Use the law of syllogism to form a conclusion from the given premises.

Premise 1: If a polygon was reflected across a line, then a rigid transformation was performed.

Premise 2: If a rigid transformation was performed, then the image and pre-image are congruent.

Select from the drop-down menus to correctly complete the conclusion.

Conclusion: If _______________, then ________________

for the first line

A. the image and pre-image are congruent

B. a polygon was reflected across a line

C. a rigid transformation was performed

D. a figure is a polygon


for the second line

A. a figure was reflected across a line

B. a rigid transformation was performed

C. the figure was transformed

D. the image and pre-image are congruent

Answer 32

law of syllogism:

statement 1: if p then q
statement 2: if q then r

final statement: if p then r

try to apply this logic to see what p and r are and choose the right options

Answer 33

If a polygon was reflected across a line, then the image and pre-image are congruent.

Answer 34

good

Answer 35

Conclusion: If ( 1 a polygon was reflected across a line ) then( 2 the image and pre-image are congruent )

Answer 36

yes.

Answer 37

wait a min

Answer 38

that's right

Answer 39

yes.

Answer 40

Which statement about this argument is true?



Argument:

If Sindy leaves on time, she catches the bus.

Sindy left on time.

She caught the bus.




A. The argument is valid by the Law of Syllogism.


B. The argument is valid by the Law of Detachment.

C. The argument is valid, but does not follow the Law of Syllogism or the Law of Detachment.

D. The argument is invalid.

Answer 41

any ideas? do you think it might be syllogism or detachment or neither?

Answer 42

the law of syllogism is based on deduction of reasoning so my most educated guess would be A. the argument is valid by the law of Syllogism

Answer 43

hm not quite

Answer 44

notice how it gives the "if" statement first, then gives p, then states that q is true

so this is law of detachment

Answer 45

B then

Answer 46

good

Answer 47

Which answers are examples of the Law of Syllogism?

Select each correct answer.


A. Sally goes to the mall every Saturday. Today is Saturday. Therefore, Sally will go to the mall today.

B. If a quadrilateral is a rectangle with 4 equal sides, then it is a square. QuadrilateralABCD is a rectangle with 4 equal sides. Therefore, quadriateral ABCD is a square.


C. If a square is a rectangle and if a rectangle is a parallelogram, then a square is a parallelogram.

D. If there is a children’s movie playing at the cinema, Maria’s mother will take her to see it. When Maria’s mother takes her to the movie, she buys Maria popcorn. Therefore, if there is a children’s movie playing at the cinema, Maria’s mother will buy popcorn for Maria.

Answer 48

any ideas? remember the

if p then q , if q then r, therefore p then r
format

Answer 49

C and A

Answer 50

C yes
A no, A is law of detachment

any thoughts on D or B? remember the format

Answer 51

D

Answer 52

good so C+D

Answer 53

Which answers are examples of the Law of Detachment?

Select each correct answer.


A. If two angles are vertical angles, then they have the same measure. Angle A and angle B are vertical angles. So, the measure of angle A is equal to the measure of angle B.

B. If it snows tomorrow, then my dentist appointment will be canceled. If my dentist appointment is canceled, then I will clean under my bed. Therefore, if it snows tomorrow, then I will clean under my bed.

C. If an object is a square, then it is a rhombus. If it is a rhombus, then it is a quadrilateral. Therefore, if an object is a square, then it is a quadrilateral.

D. Jonathan’s cars are all white. Sarah is driving one of Jonathan’s cars. Therefore, Sarah is driving a white car.

Answer 54

any ideas? remember the format of detachment

Answer 55

Jonathan’s cars are all white. Sarah is driving one of Jonathan’s cars. Therefore, Sarah is driving a white car.


If two angles are vertical angles, then they have the same measure. Angle A and angle B are vertical angles. So, the measure of angle A is equal to the measure of angle B.

Answer 56

good so A&D.

Answer 57

https://learning.k12.com/d2l/common/viewFile.d2lfile/Database/MTAyODA4OTg/G-CO.A.3%20Q1.JPG?ou=437405

Jennifer draws the rectangle ABCD shown. This figure has ______________
(number of) lines of symmetry. The figure has rotational symmetry of ____________ degrees.

Answer 58

any ideas? how many ways can you cut a rectangle so that both sides are mirror images of each other?

Answer 59

4

Answer 60

hm, not quite, that's a common mistake though

only the pink lines produce mirror images

the green line produces two equal sides but they're not in the same orientation so it's not symmetric

so there are only 2 lines of symmetry

Answer 61

any ideas about the rotational symmetry angle?

Answer 62

The angle of rotational symmetry is the smallest angle for which the figure can be rotated to coincide with itself.

Answer 63

ok, that's the definition, but what is the number?

Answer 64

notice how the 180 degree rotation is the smallest that produces the same image

so the angle of rotation is 180.

Answer 65

sorry i was having difficulties

Answer 66

it is 180 degrees

Answer 67

good.

Answer 68

the figure has what again

Answer 69

and the figure has rotational symmetry of ______________

Answer 70

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Vocaloid
notice how the 180 degree rotation is the smallest that produces the same image

so the angle of rotation is 180.
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 71

both 180 ?

Answer 72

the first blank is asking about the lines of symmetry which we said was 2

the second blank is asking about the angle of rotation which is 180.

Answer 73

K GOTCHA

Answer 74

https://learning.k12.com/d2l/common/viewFile.d2lfile/Database/MTAyODE2NTk/G-CO.A.3%20Q2.JPG?ou=437405

Which transformation carries the trapezoid onto itself?

A. reflect over the line x = –3


B. reflect over the line x = 3


C. reflect over the line y = 3


D. reflect over the line y = –3

Answer 75

any ideas? try drawing where the line of symmetry would be.

Answer 76

the answer is A

Answer 77

not quite

a horizontal line at -3 has what equation?

Answer 78

(4, -3)

Answer 79

that is a coordinate point. that is not an equation.

a horizontal line at ___ has the equation y = ____

so a horizontal line at -3 has the equation y = -3 = your solution.

Answer 80

https://learning.k12.com/d2l/common/viewFile.d2lfile/Database/MTAyODE4MTU/G-CO.A.3%20Q3.JPG?ou=437405

Which of the following symmetries apply to the parallelogram? (Select all that apply.)

A. Reflective symmetry over the line y = 3/5x


B. Rotational symmetry of 180 degrees about the origin.


C. Reflective symmetry over the line y = 5/3x

Answer 81

any ideas? as a hint two of the three choices are right

Answer 82

way ahead of you, B and C

Answer 83

not quite, the purple line y = 5/3x will not work because it's not a line of symmetry (the two halves are not mirror images of each other)

so A+B is the better solution.

Answer 84

Which of the following would have the greatest lines of symmetry?

A. Equilateral Triangle


B. Irregular Hexagon


C. A Square


D. Regular Hexagon

Answer 85

any ideas? which shape is regular + has the most sides?

Answer 86

REGULAR POLYGON

Answer 87

D. Regular Hexagon

is regular and has 6 sides which is more than the triangle and square so D is the best solution.

Answer 88

Vocaloid thank you for all your help today but how come you were free all of a sudden all today ?

Answer 89

and one question in your opinion do you think pagers are better than the iphones today ?

Answer 90

I'd rather stay on topic, if that's all the math help you need i'm going to close this

Answer 91

k