If a circle has an area of 49π what is the circumference of the circle ?
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<h3>3 Answers: Choice D, Choice E, Choice F</h3>
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Explanation:
The inequality 6x - 10y ≥ 9 solves to y ≤ (3/5)x - 9/10 when you isolate y.
Graph the line y = (3/5)x - 9/10 and make this a solid line. The boundary line is solid due to the "or equal to" as part of the inequality sign. We shade below the boundary line because of the "less than" after we isolated for y.
Now graph all of the points given as I've done so in the diagram below. The points in the blue shaded region, or on the boundary line, are part of the solution set. Those points are D, E and F.
We can verify this algebraically. For instance, if we weren't sure point E was a solution or not, we would plug the coordinates into the inequality to get...
6x - 10y ≥ 9
6(5) - 10(2) ≥ 9 .... plug in (x,y) = (5,2)
30 - 20 ≥ 9
10 ≥ 9 ... this is a true statement
Since we end up with a true statement, this verifies point E is one of the solutions. I'll let you check points D and F.
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I'll show an example of something that doesn't work. Let's pick on point A.
We'll plug in (x,y) = (-1,1)
6x - 10y ≥ 9
6(-1) - 10(1) ≥ 9
-6 - 10 ≥ 9
-16 ≥ 9
The last inequality is false because -16 is smaller than 9. So this shows point A is not a solution. Choices B and C are non-solutions for similar reasons.
The perimeter of a square with side a = 7.2 cm is 28.8 cm. Yes there exists a direct proportional relationship between Side length and Perimeter of square
<h3><u>Solution:</u></h3>Given that side of square "a" = 7.2 cm
We have to find the perimeter of square
<em><u>The perimeter of square is given as:</u></em>
Perimeter of square = 4a
Where "a" represents the length of side of square
Substituting the given value a = 7.2 cm in above formula, we get perimeter of square
Perimeter of square = 4(7.2) = 28.8 cm
<em><u>Are the perimeter of the square and the length of its side directly proportional quantities?</u></em>
The Perimeter is equal to a constant times the Side length, or the Perimeter divided by the Side length is equal to four. So this is definitely a proportional relationship between Side length and Perimeter.
Two values are said to be in direct proportion when an increase in one results in an increase in the other.
So when length of sides increases, perimeter also increases
Hence perimeter and length of side of square are directly propotional quantities