“21 less than three-fifths of a number”
1 answer:
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If 60 is a factor of n², then √60 is a factor of n. However, n is a whole number, so its factors are whole numbers.
Simplify √60:
If 2√15 is a factor of a whole number n, then √15 must be another factor to make it a whole number.
If 60 is a factor of n², then 2, 3, and 5 must be factors of n. The factors of n² are the squares of the factors of n, so 2, 2, 3, 3, 5, and 5 must be factors of n².
Now, if 2, 2, 3, 3, 5, and 5 are factors of n², then:
* 5×5=25 must also be its factor
* 2×2×3×3=36 must also be its factor
* 2×2×5×5=100 must also be its factor
Only 16 may not be a factor of n². The answer is A.
Simplify √60:
If 2√15 is a factor of a whole number n, then √15 must be another factor to make it a whole number.
If 60 is a factor of n², then 2, 3, and 5 must be factors of n. The factors of n² are the squares of the factors of n, so 2, 2, 3, 3, 5, and 5 must be factors of n².
Now, if 2, 2, 3, 3, 5, and 5 are factors of n², then:
* 5×5=25 must also be its factor
* 2×2×3×3=36 must also be its factor
* 2×2×5×5=100 must also be its factor
Only 16 may not be a factor of n². The answer is A.
<h3><u>Option A</u></h3>
is the required equation to calculate width of rectangular frame that has a total area of 140 square inches.
Given that,
Length of a rectangular frame is given as 2x + 10
Width of the rectangular frame is given as 2x + 6
Total area = 140 square inches
<em><u>The area of rectangular frame is given as:</u></em>
Plugging in values, we get
This is the required equation to calculate width of rectangular frame
Solve the above quadratic equation to get the value of "x"
<em><u>Use the quadratic equation formula:</u></em>
Here a = 4 ; b = 32 ; c = -80
x = 2 or x = -10
Now measurement cannot be negative, so taking the positve value of "x", we can calculate the width
So put "x" = 2
Width of the rectangular frame = 2x + 6 = 2(2) + 6 = 10
Thus the width of frame is 10 inches