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jok3333 [9.3K]
3 years ago
11

Complete the proof for the following conjecture.

Mathematics
1 answer:
Ray Of Light [21]3 years ago
3 0

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.

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miv72 [106K]

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Answer:

  x = -3/2

Step-by-step explanation:

The zeros of the function are the values of x that make the factors zero:

  x = -4, x = 1

The axis of symmetry is the vertical line halfway between these zeros.

  x = (-4 +1)/2 = -3/2

The equation of the axis of symmetry is x = -3/2.

8 0
3 years ago
luis spent 8.75 on snacks at a basketball game. candy costs 1.25$ per package and chips cost .50$. Luis bought 10 snacks how man
ale4655 [162]

Answer:

Luis bought 5 packages of candy and 5 bags of chips

Step-by-step explanation:

1.25 for candy

0.50 for chips

1.25c + 0.50c = 8.75

First I tried to see how many times I could multiply 1.25, the answer that made the most sense was 5 because not only is 5 + 5 = 10, but when it equals the amount of money. So I changed my equation:

1.25(5) + 0.5(5)

6.25 + 2.5 = 8.75

5 0
3 years ago
Find the sum of the odd integers between 24 and 50
morpeh [17]

Answer:

  481

Step-by-step explanation:

There are several ways you can get there.

1. There are only 13 numbers, so you can write them down and add them up.

  25 + 27 + 29 + ... + 47 + 49 = 481

__

2. You can use the formula for the sum of an arithmetic sequence. This one has a starting value of 25, an ending value of 49, and 13 terms.

  Sum = ((start) + (end))/2 × (number of terms) = (25 +49)/2×13 = 481

__

3. You can use a formula for the terms of the series and evaluate the sum.

  an = 25 +2(n -1) = 2n +23

\sum\limits_{n=1}^{13}{(2n+23)}=2\sum\limits_{n=1}^{13}(n)+\sum\limits_{n=1}^{13}{(23)}=2\dfrac{13\cdot 14}{2}+13\cdot 23=481

4 0
2 years ago
Please help me out with this math problem
Novosadov [1.4K]
Answer: 74.8%

This answer is approximate.
The value is rounded to the nearest tenth of a percent.

==========================================

Explanation:

Let,
X = area of the larger circle
Y = area of the smaller circle
Z = area of the shaded region = X - Y

The goal is to compute the ratio Z/X to get the answer we want

Let's find area of the larger circle
Area of circle = pi*(radius)^2
A = pi*r^2
X = pi*8.01^2
X = 64.1601pi
This is the exact area in terms of pi

Now repeat for the smaller circle
A = pi*r^2
Y = pi*4.02^2
Y = 16.1604pi

Subtract those results to find the value of Z
Z = X-Y
Z = 64.1601pi-16.1604pi
Z = 47.9997pi
This is the exact area of the red donut region

Divide Z over X to get the probability of landing in the red region
Z/X = (47.9997pi)/(64.1601pi)
Z/X = (47.9997)/(64.1601) <--- note how the pi terms cancel
Z/X = 0.74812 which is approximate

Convert to a percent
Move the decimal point 2 spots to the right
0.74812 ---> 74.812%

Then round this to one decimal place
74.812% ---> 74.8%

5 0
3 years ago
If (7^2)x=1 what is x
Stella [2.4K]
1/49 ..................
6 0
2 years ago
Read 2 more answers
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