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ololo11 [35]
3 years ago
14

AB ≅ BC and AD ≅ CD What additional information would make it immediately possible to prove that triangles AXB and CXB are congr

uent using the HL theorem? What additional information would make it immediately possible to prove that triangles AXD and CXD are congruent using the SSS congruence theorem?
Mathematics
2 answers:
MrRissso [65]3 years ago
8 0

Answer:

1: C/AC and BD are perpendicular.

2: B/AX and CX are congruent.

Step-by-step explanation:

kobusy [5.1K]3 years ago
5 0

It is given that, B ≅ BC and AD ≅ CD  

We need BD perpendicular to AC, then only we can say  triangles AXB and CXB are congruent using the HL theorem.

If BD perpendicular to AC, means that AB and CB are the hypotenuse of triangles AXB and CXB respectively.

from the given information ABCD is a square

If BD and AC bisect each other then AX = CX

Then only we can  immediately possible to prove that triangles AXD and CXD are congruent by SSS congruence theorem

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Use the Euclidean Algorithm to demonstrate that 621 and 82 are relatively prime to each other. Explain.
8090 [49]

Answer:

621 and 82 are relatively prime.

Step-by-step explanation:

Two integers are relatively prime (or coprime) if there is no integer greater than one that divides them both (that is, their greatest common divisor is one).

The greatest common divisor of two integers <em>a</em> and <em>b</em> is the largest integer that divides them both.

The Euclidean algorithm is an efficient method for computing the greatest common divisor of two integers, without explicitly factoring the two integers.

The Euclidean algorithm solves the problem:

<em>Given integers a, b find </em>d=gcd(a,b)<em />

The Euclidean algorithm provides a fast way to determine <em>d</em> without knowing the prime factors of <em>a</em> or <em>b</em>. Here is an outline of the steps:

  1. Let a=x, b=y
  2. Given <em>x</em>, <em>y</em>, use the division algorithm to write x=yq+r, \quad 0\leq r\leq |y|.
  3. If r = 0, stop and output <em>y</em>; this is the gcd of a, b.
  4. If r \neq 0, replace (<em>x, y</em>) by (<em>y, r</em>). Go to step 2.

The division algorithm is an algorithm in which given 2 integers N and D, it computes their quotient Q and remainder R.

Let's say we have to divide N (dividend) by D (divisor). We will take the following steps:

Step 1: Subtract D from N repeatedly until we get a result that lies between 0 (inclusive) and D (exclusive) and is the smallest non-negative number obtained by repeated subtraction.

Step 2: The resulting number is known as the remainder R, and the number of times that D is subtracted is called the quotient Q.

Applying the above steps,

621-82=539\\539-82=457\\457-82=375\\375-82=293\\293-82=211\\211-82=129\\129-82=47\\\\621=82\cdot7+47

621 = 82\cdot 7 + 47\\ 82 = 47\cdot 1 + 35\\ 47 = 35\cdot1 + 12\\ 35 = 12\cdot2 + 11\\ 12 = 11\cdot1 + 1\\ 11 = 1\cdot11 + 0

The gcd(621, 82) is 1. Therefore, 621 and 82 are relatively prime.

5 0
2 years ago
PLEASE ANSWER FAST!! Find the 29th term of this sequence:-121,-108,-95,-82...
Julli [10]

Answer:

The 29th term is

<h2>243</h2>

Step-by-step explanation:

The above sequence is an arithmetic sequence

For an nth term in an arithmetic sequence

U(n) = a + ( n - 1)d

where n is the number of terms

a is the first term

d is the common difference

From the question

a = - 121

d = -108 -- 121 = - 108 + 121 = 13

Since we are finding the 29th term

n = 29

The 29th term of the sequence is

U(29) = - 121 + ( 29 - 1) 13

= -121 + 28(13)

= -121 + 364

The final answer is

<h2>243</h2>

Hope this helps you

4 0
3 years ago
1. find the degree of the monomial 6p^3q^2
natali 33 [55]

Theses are the answers for connections.

1.C

2.B

3.A

4.D

5.D

6.A

7.D

Hope this helps! Have a great day!

3 0
2 years ago
Read 2 more answers
Tomas buys a bag of 5 peaches for $3.55. Write and solve an equation to find how much money, m, Tomas paid for each peach
Orlov [11]

Answer:

Step-by-step explanation:

$3.55 ÷ 5 = .71 each peach

7 0
3 years ago
The heights of a certain type of tree are approximately normally distributed with a mean height p = 5 ft and a standard
arsen [322]

Answer:

A tree with a height of 6.2 ft is 3 standard deviations above the mean

Step-by-step explanation:

⇒ 1^s^t statement: A tree with a height of 5.4 ft is 1 standard deviation below the mean(FALSE)

an X value is found Z standard deviations from the mean mu if:

\frac{X-\mu}{\sigma} = Z

In this case we have:  \mu=5\ ft\sigma=0.4\ ft

We have four different values of X and we must calculate the Z-score for each

For X =5.4\ ft

Z=\frac{X-\mu}{\sigma}\\Z=\frac{5.4-5}{0.4}=1

Therefore, A tree with a height of 5.4 ft is 1 standard deviation above the mean.

⇒2^n^d statement:A tree with a height of 4.6 ft is 1 standard deviation above the mean. (FALSE)

For X =4.6 ft  

Z=\frac{X-\mu}{\sigma}\\Z=\frac{4.6-5}{0.4}=-1

Therefore, a tree with a height of 4.6 ft is 1 standard deviation below the mean .

⇒3^r^d statement:A tree with a height of 5.8 ft is 2.5 standard deviations above the mean (FALSE)

For X =5.8 ft

Z=\frac{X-\mu}{\sigma}\\Z=\frac{5.8-5}{0.4}=2

Therefore, a tree with a height of 5.8 ft is 2 standard deviation above the mean.

⇒4^t^h statement:A tree with a height of 6.2 ft is 3 standard deviations above the mean. (TRUE)

For X =6.2\ ft

Z=\frac{X-\mu}{\sigma}\\Z=\frac{6.2-5}{0.4}=3

Therefore, a tree with a height of 6.2 ft is 3 standard deviations above the mean.

6 0
3 years ago
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