There are 720 total different combinations, and 24 of those will have the letters DAY consecutively within all those combinations.
<u>Explanation:</u>
FRIDAY is a six letter word.
To form all combinations of letters, we would have six choices of letters to fill the first spot. Whatever letter you choose for the first spot, you then have five choices of letters to fill the second spot. Four choices of letters to fill the third spot. And so on.
So, the total number of different combinations of the six letters would be 6!
6! = 6 X 5 X 4 X 3 X 2 X 1
= 720
DAY could appear consecutively starting in 4 different spots: the 1st, 2nd, 3rd, and 4th spots of all combinations. DAY will appear consecutively 6 times in each of those 4 starting spots.
6 X 4 = 24.
So, there are 720 total different combinations, and 24 of those will have the letters DAY consecutively within all those combinations.
This can be written as:
"No greater than" does not necessarily mean less than, but it just means it cannot go over. So equal to or less than.
"The difference of a number and 2" can be represented as "n - 2"
If you were to solve this inequality, you would end up getting:
or
Hope this helps! :)
Graphing the system of equations is shown in figure attached.
Solution set is (2,-4). The lines will intersect at (2,-4)
Step-by-step explanation:
We need to graph the system of equations. 
First we will find value of x and y
Let:
Add eq(1) and eq(2)
Putting value of x in eq(1) and finding y
So, y=-4
Graphing the system of equations is shown in figure attached.
Solution set is (2,-4). The lines will intersect at (2,-4)
Keywords: System of equations
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Answer:
You need to capitalize Europe
<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:
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<em>STATEMENT REASON </em>
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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
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<em>Keywords: statement, length, reason, proof</em>
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