1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
patriot [66]
3 years ago
10

Given: BD bisects ABC. Auxiliary EA is drawn such that AE || BD. Auxiliary BE is an extension of BC

Mathematics
2 answers:
AnnZ [28]3 years ago
7 0
The required proof is given in the table below:

\begin{tabular}{|p{4cm}|p{6cm}|} 
 Statement & Reason \\ [1ex] 
1. $\overline{BD}$ bisects $\angle ABC$ & 1. Given \\
2. \angle DBC\cong\angle ABD & 2. De(finition of angle bisector \\ 
3. $\overline{AE}$||$\overline{BD}$ & 3. Given \\ 
4. \angle AEB\cong\angle DBC & 4. Corresponding angles \\
5. \angle AEB\cong\angle ABD & 5. Transitive property of equality \\ 
6. \angle ABD\cong\angle BAE & 6. Alternate angles
\end{tabular}
\begin{tabular}{|p{4cm}|p{6cm}|}
7. \angle AEB\cong\angle BAE & 7. Transitive property of equality \\
8. \overline{EB}\cong\overline{AB} & 8. From 7. $\Delta ABE$ is isosceles \\
9. EB = AB & 9. De(finition of congruence \\ 10. $\frac{AD}{DC}=\frac{EB}{BC}$ & 10. Triangle proportionality theorem \\
11. $\frac{AD}{DC}=\frac{AB}{BC}$ & 11. Substitution Property of equality \\[1ex] 
\end{tabular}

34kurt3 years ago
7 0

Answer:

Reasons 2 and following

2. Definition of angle bisector

3. Given

4. They are corresponding angles

5. Transitive property of equality

6. Alternate angles are congruent

7. Transitive property of equality

8. From <em>7</em> ΔABE is isosceles

9. Definition of isosceles triangle

10. Triangle proportionality theorem

11. Substituting <em>9</em> in <em>10</em>

You might be interested in
I don't know this can someone help me?
Gemiola [76]

Answer:

513.247

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
In 2011, the Institute of Medicine (IOM), a non-profit group affiliated with the Select one US National Academy of Sciences, rev
Sergio [31]

Answer:

B. Yes, there are at least 10 people with weak bones and 10 people with strong bones in each group.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, a large sample size can be approximated to a normal distribution with mean \mu and standard deviation \frac{\sigma}{\sqrt{n}}

The correct answer is:

B. Yes, there are at least 10 people with weak bones and 10 people with strong bones in each group.

7 0
3 years ago
Write an expression that represents the sum of 7 and x. Please help :)<br><br><br>Thanks!
eduard

Answer:

the sum of 7 is 7

Step-by-step explanation:

8 0
3 years ago
Some types of algae have the potential to cause damage to river ecosystems. Suppose the accompanying data on algae colony densit
Phantasy [73]

Answer:

y=-2.95836 x +234.56159

Step-by-step explanation:

We assume that th data is this one:

x: 50, 55, 50, 79, 44, 37, 70, 45, 49

y: 152, 48, 22, 35, 43, 171, 13, 185, 25

a) Compute the equation of the least-squares regression line. (Round your numerical values to five decimal places.)For this case we need to calculate the slope with the following formula:

m=\frac{S_{xy}}{S_{xx}}

Where:

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}

So we can find the sums like this:

\sum_{i=1}^n x_i =50+ 55+ 50+ 79+ 44+ 37+ 70+ 45+ 49=479

\sum_{i=1}^n y_i =152+ 48+ 22+ 35+ 43+ 171+ 13+ 185+ 25=694

\sum_{i=1}^n x^2_i =50^2 + 55^2 + 50^2 + 79^2 + 44^2 + 37^2 + 70^2 + 45^2 + 49^2=26897

\sum_{i=1}^n y^2_i =152^2 + 48^2 + 22^2 + 35^2 + 43^2 + 171^2 + 13^2 + 185^2 + 25^2=93226

\sum_{i=1}^n x_i y_i =50*152+ 55*48+ 50*22+ 79*35+ 44*43+ 37*171+ 70*13+ 45*185+ 49*25=32784

With these we can find the sums:

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=26897-\frac{479^2}{9}=1403.556

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}=32784-\frac{479*694}{9}=-4152.22

And the slope would be:

m=-\frac{-4152.222}{1403.556}=-2.95836

Nowe we can find the means for x and y like this:

\bar x= \frac{\sum x_i}{n}=\frac{479}{9}=53.222

\bar y= \frac{\sum y_i}{n}=\frac{694}{9}=77.111

And we can find the intercept using this:

b=\bar y -m \bar x=77.1111111-(-2.95836*53.22222222)=234.56159

So the line would be given by:

y=-2.95836 x +234.56159

7 0
2 years ago
HELP!!!!
Nonamiya [84]
Your answer is E. $25.

First let under 12 = u, over 12 = o, and adults = a.
We can now write the equations:

2u + 3a + 3o = 174
4u + 2a = 122
a + o = 46

Because we know that a + o = 46, and 3a + 3o is in the first equation, we can multiply 46 by 3 to get what 3a + 3o equals. This makes 138.
Now we can substitute 138 into the first equation to get 2u + 138 = 174
2u = 36
u = 18

Now that we know what u equals, we can substitute it in to the second equation to get:
4(18) + 2a = 122
72 + 2a = 122
2a = 50
a = $25

I hope this helps! Let me know if you have any questions :)
8 0
3 years ago
Other questions:
  • How can one fourthx − 3 = one halfx + 8 be set up as a system of equations?
    9·1 answer
  • Set up the equation for the following word problem and solve the equation. Let y be the unknown number.
    6·2 answers
  • Which of the following show an element of the sample space for first rolling a die and then tossing a coin? Check all that apply
    5·1 answer
  • Cards numbered 1 through 30 are placed in a bag and shuffled. One card is chosen at random. What is the probability of randomly
    14·2 answers
  • Which of the following represents an example of a population? Which of the following represents an example of a population? the
    14·1 answer
  • Help me, please asap just tell me which one it is
    5·2 answers
  • Alejandro has gone to school StartFraction 5 Over 7 EndFraction of the last 35 days. Which expression can be used to determine t
    14·1 answer
  • Graph the lines in standard form 2x+y=9
    8·2 answers
  • Got a question is the bye bye man real
    11·2 answers
  • ....................:)))))
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!