Order from least to greatest -3, 1/6, -1/6, 0.5
2 answers:
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Answer:
=
Step-by-step explanation:
In order to add fractions, the denominators must all be the same value (the lowest common denominator). The <em>lowest common denominator</em> is the smallest value that all of the given denominators (in this case, the denominators are 4, 14, and 7) can divide into.
Here, the smallest number that all three of the given denominators can perfectly divide into is 28:
28 ÷ 4 = 7
28 ÷ 14 = 2
28 ÷ 7 = 4
<em>Therefore, our lowest common denominator is 28.</em>
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The next step is to change our numerators to match our lowest common denominator. To do this, we have to multiply the numerator by the same value that we would need to multiple the denominator by in order to get our lowest common denominator.
For our first term of 1/4, we need to multiply our denominator (4) by 7 in order to get our lowest common denominator of 28. So, we need to also multiply our numerator by 7:
×
=
<em>Therefore, our first term becomes </em><em>.</em>
For our second term of 5/14, we need to multiply our denominator (14) by 2. So, we need to also multiply our numerator by 2:
×
=
<em>Therefore, our second term becomes </em><em>.</em>
For our third term of 6/7, we need to multiply our denominator (7) by 4. So, we need to also multiply our numerator by 4:
×
=
<em>Therefore, our third term becomes </em><em>.</em>
Now that they all have the same denominator, we simply have to add all three together:
+
<em> </em>+<em> </em>
<em> </em>=
When we simplify this into a mixed number, we get:
=
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A 2 x 2 matrix has 2 rows and 2 columns
A specific 2 x 2 matrix a with no zero entries at all is
From the question, we understand that the matrix is a 2 x 2 matrix.
A 2 x 2 matrix is represented as:
Also from the question we understand that the elements of the matrix are non-zero.
This means that:
An example of such matrix is:
Note that there are several matrices that fit the given construction requirement
Read more about matrix at:
For the circular cover we have:
A) The area is 379.94 ft²
B) The length of the rope must be 68.2 ft
<h3>How to get the area of the cover?</h3>Remember that the area of a circle of radius R is given by the formula:
Where pi = 3.14
In this case, the diameter of the pool is 20ft, then the radius is:
R = 20ft/2 = 10ft
And it must extend 12 inches beyond, then the radius of the cover must be:
R = 10ft + 12in
Now, we know that 1ft = 12 in, then we can rewrite the radius as:
R = 10ft +1ft = 11ft
Then the area of the cover is:
B) now we want to get the length of the rope, we know that the rope runs along the cover, then the length of the rope must be equal to the circumference of the cover.
Remember that the circumference of a circle of radius R is:
Then the length of the rope will be:
If you want to learn more about circles:
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