Can you please help me with this question?

Complete the proof for the following conjecture.

Ray Of Light [21]

Answer:

Statements Reasons

AC+CD=AD and AB+BD=AD Segment Addition Postulate

AC+CD=AB+BD Transitive/Substitution Property

AC=BD Given

BD+CD=AB+BD Substitution Property

CD=AB Subtraction Property

AB=CD Symmetric Property

Step-by-step explanation:

By segment addition postulate, we can say the following two equations:

AC+CD=AD and AB+BD=AD.

By either substitution/transitive property, you can say AC+CD=AB+BD.

You are given AC=BD, so we use substitution and write AC+CD=AB+AC.

After using subtraction property (subtracting both sides by AC), you obtain CD=AB.

By symmetric property, you may say AB=CD.

So let's write it into the 2 column-proof you have there:

Statements Reasons

AC+CD=AD and AB+BD=AD Segment Addition Postulate

AC+CD=AB+BD Transitive/Substitution Property

AC=BD Given

BD+CD=AB+BD Substitution Property

CD=AB Subtraction Property

AB=CD Symmetric Property

Properties/Postulates used:

Transitive property which says:

If a=b and b=c, then a=c.

Substitution property which says:

If a=b, then b can be substituted(replaced with) for a.

Subtraction property which says:

a=b implies a-c=b-c.

Segment Addition Postulate says:

If you break a segment into two smaller pieces then the measurement of that segment is equal to the sum of the smaller two segments' measurements.

3 0

3 years ago

Solve the following equation and verify the results<br>4(2x-3)+5(3x-4)=16

Licemer1 [7]

Answer:

I got x=48/23 or 2 2/23

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

Suppose we want to choose colors, without replacement, from the colors red, blue, green, and purple.

DerKrebs [107]

The number of ways when the choice is not relevant is 4

<h3>How to determine the number of ways?</h3>

The number of colors are:

Colors, n = 4

The color to choose are:

r = 3

<u>Relevant choice</u>

When the choice is relevant, we have:

$Ways = ^nP_r$

This gives

$Ways = ^4P_3$

Evaluate

Ways = 24

Hence, the number of ways when the choice is relevant is 24

<u>Not relevant choice</u>

When the choice is not relevant, we have:

$Ways = ^nC_r$

This gives

$Ways = ^4C_3$

Evaluate

Ways = 4

Hence, the number of ways when the choice is not relevant is 4

Read more about combination at:

brainly.com/question/11732255

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4 0

2 years ago

The board of an internet start up company has sixteen members. if one person is in charge of research and one is in charge of ma

Brilliant_brown [7]

The number of ways in which the position of one person in charge of research and one person in charge of marketing can be chosen from the board of 16 members is <u>240 ways</u>. Computed using permutations.

The permutation is the way of choosing a set of objects from a larger set of objects in a specific sequence.

If we are choosing r number of objects, from n number of objects in a specific sequence, then we follow permutation, and it is given as:

nPr = n!{(n - r)!}.

In the question, we are asked to find the number of ways in which the position of one person in charge of research and one person in charge of marketing can be chosen from the board of 16 members.

Since the position is to be chosen in a specific order, we will follow permutation.

The number of positions to be chosen (r) = 2.

The number of members (n) = 16.

Thus, the number of ways is given as:

nPr = n!{(n - r)!},

or, 16P2 = 16!{(16 - 2)!},

or, 16P2 = 16!/14! = 15*16 = 240.

Thus, the number of ways in which the position of one person in charge of research and one person in charge of marketing can be chosen from the board of 16 members is <u>240 ways</u>. Computed using permutations.

Learn more about permutations at

brainly.com/question/4658834

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6 0

2 years ago

The owner of a new restaurant wants to have seating for more than 75 people. There is currently a

Fudgin [204]

Answer:

$4m+3>75$