Answer: the answer is D
Step-by-step explanation: I got it right
Answer:
k = - 2
Step-by-step explanation:
( 2x - y )²
Formula : -
( a - b )² = a² + b² - 2ab
Here,
a = 2x
b = y
( 2x - y )²
= ( 2x )² + y² - 2 ( 2x ) ( y )
= 4x² + y² - 4xy
So,
( 2x - y )² = 4x² + y² - 4xy
( 2x + y )²
Formula : -
( a + b )² = a² + b² + 2ab
Here,
a = 2x
b = y
( 2x + y )²
= ( 2x )² + y² + 2 ( 2x ) ( y )
= 4x² + y² + 4xy
So,
( 2x + y )² = 4x² + y² + 4xy
( 2x - y )² - ( 2x + y )²
= 4x² + y² - 4xy - ( 4x² + y² + 4xy )
= 4x² + y² - 4xy - 4x² - y² - 4xy
= 4x² - 4x² + y² - y² - 4xy - 4xy
= 0 + 0 - 8xy
= - 8xy
( 2x - y )² - ( 2x + y )² = 4xyk
- 8xy = 4xyk
Divide 4xy on both sides,
- 8xy / 4xy = 4xyk / 4xy
- 2 = k
k = - 2
Therefore, the value of k is - 2.
<em>Answer:</em>
Complete proof is written below.
Facts and explanation about the segments shown in question :
- As BC = EF is a given statement in the question
- AB + BC = AC because the definition of betweenness gives us a clear idea that if a point B is between points A and C, then the length of AB and the length of BC is equal to the length of AC. Also according to Segment addition postulate, AB + BC = AC. For example, if AB = 5 and BC= 7 then AC = AB + BC → AC = 12
- AC > BC because the Parts Theorem (Segments) mentions that if B is a point on AC between A and C, then AC > BC and AC>AB. So, if we observe the question figure, we can realize that point B lies on the segment AC between points A and C.
- AC > EF because BC is equal to EF and if AC>BC, then it must be true that the length of AC must greater than the length segment EF.
Below is the complete proof of the observation given in the question:
<em />
<em>STATEMENT REASON </em>
___________________________________________________
1. BC = EF 1. Given
2. AB + BC = AC 2. Betweenness
3. AC > BC 3. Def. of segment inequality
4. AC > EF 4. Def. of congruent segments
<em />
<em>Keywords: statement, length, reason, proof</em>
<em>
Learn more about proof from brainly.com/question/13005321</em>
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Answer:
1246 teams
Step-by-step explanation:
We are told there are 7women & 6men.
If 5 people are selected and there must be more women than men in the team.
This means there must be a minimum of 3 women.
Thus;
For 3 women;
7C3 × 6C2 = 525
For 4 women;
7C4 × 6C3 = 700
For 5 women;
7C5 × 6C0 = 21
Thus;
Total = 525 + 700 + 21 = 1246 teams
(5, 12) e (-10, -3)
x.......y...1
5.....12..1
-10..-3..1
12x -10y -15 + 120 -5y + 3x = 0
12x + 3x - 10y - 5y - 15 + 120 = 0
15x - 15y + 105 = 0 :(5)
3x - 5y + 21 = 0
m = -a/b
m = -3/-5
m(5) = 3/5
y-yo = m(x-xo)
y-14 = 3/5*(x-7)
y-14 = 3x/5 - 7/5
3x/5 - y + 14 - 7/5 = 0
3x/5 - 5y/5 + 70/5 - 7/5 = 0
3x - 5y + 70 - 7 =0
3x - 5y + 63 = 0
m(s) = -3/-5 = 3/5
m(r) = m(s) --> são paralelas
