Okay so i'm confused about this question. Write an inequality for the phrase ''two more than three times a number is at most 53.
1 answer:
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Answers:
Equation is
Center is (-1, -2)
Radius = 5
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Work Shown:
center = (h,k) = (-1,-2)
radius = 5
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Explanation:
I grouped up the x and y terms separately. Then I added 1 to both sides to complete the square for the x terms. I cut the 2 from 2x in half, then squared it to get 1. In the next step, I cut the 4 from 4y in half to get 2, which squares to 4. So that's why I added 4 to both sides to complete the square for the y terms.
Each piece is factored using the perfect squares factoring rule which is a^2+2ab+b^2 = (a+b)^2
The last equation is in the form (x-h)^2 + (y-k)^2 = r^2
We can think of x+1 as x - (-1) to show that h = -1
Similarly, y+2 = y-(-2) = y-k to show that k = -2
The center is (h,k) = (-1,-2)
The radius is r = 5 because r^2 = 5^2 = 25 is on the right hand side in the last equation above.
Given:
The system of inequalities:
To find:
Whether the points (–3,–2) and (3,2) are in the solution set of the given system of inequalities.
Solution:
A point is in the solution set of the given system of inequalities if it satisfies both inequalities.
Check for the point (-3,-2).
This statement is true.
This statement is also true.
Since the point (-3,-2) satisfies both inequalities, therefore (-3,-2) is in the solution set of the given system of inequalities.
Now, check for the point (3,2).
This statement is false because .
Since the point (3,2) does not satisfy the second inequality, therefore (3,2) is not in the solution set of the given system of inequalities.