Determine the greatest common factor of the following: 4x^2y^2, 3xy^4, 2xy^2
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10 question of spelling words and 16 questions of vocabulary are present
<em><u>Solution:</u></em>
Let "x" be the number of spelling word questions
Let "y" be the number of vocabulary word question
<em><u>There is a total of 26 questions. Therefore, we get</u></em>
number of spelling word questions + number of vocabulary word question = 26
x + y = 26 --------- eqn 1
<em><u>There are spelling word questions that worth 2 points each and vocabulary word question worth 5 points each</u></em>
The language arts test is worth 100 points
Therefore, we frame a equation as:
number of spelling word questions x 2 + number of vocabulary word question x 5 = 100
2x + 5y = 100 --------- eqn 2
<em><u>Let us solve eqn 1 and eqn 2</u></em>
From eqn 1,
x = 26 - y ------- eqn 3
<em><u>Substitute eqn 3 in eqn 2</u></em>
2(26 - y) + 5y = 100
52 - 2y + 5y = 100
3y = 100 - 52
3y = 48
<h3>y = 16</h3><em><u>Substitute y = 16 in eqn 3</u></em>
x = 26 - 16
<h3>x = 10</h3>Thus 10 question of spelling words and 16 questions of vocabulary are present
First, you plot the coordinates to visualize the problem clearly. As you can see in the picture, the longest sides could either be one of those marked in red. This could be initially determined when you use visual estimation. We measure this using the distance formula: d = √[(x2-x1)^2 + (y2-y1)^2)]
Between coordinates (0,3) and (3,6)
d = √[(3-0)^2 + (6-3)^2)]
d= 4.24 units
Between coordinates (2,1) and (5,4)
d = √[(5-2)^2 + (4-1)^2)]
d= 4.24 units
They are of equal length. Both are the longest sides which measures 4.24 units.
Between coordinates (0,3) and (3,6)
d = √[(3-0)^2 + (6-3)^2)]
d= 4.24 units
Between coordinates (2,1) and (5,4)
d = √[(5-2)^2 + (4-1)^2)]
d= 4.24 units
They are of equal length. Both are the longest sides which measures 4.24 units.