Enter the range of values for x:
1 answer:
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Answer:
<em>The coordinates of P are (-2,0)</em>
<em>The radius of the circle is 5.</em>
Step-by-step explanation:
<u>Analytic geometry</u>
The diagram shows a circle with center P, and two points A(-6,3) and B(2,-3) that form the diameter of the circle.
a)
The center of the circle lies at the midpoint of A and B. The midpoint (xm,ym) can be calculated by:
Substituting x1=-6, x2=2, y1=3, y2=-3:
Thus, the coordinates of P are (-2,0)
b) The radius of the circle is the distance from the center to any point in its circumference. We can use the distance from P to A or B indistinctly.
Given two points A(x1,y1) and P(x2,y2), the distance between them is:
Substituting x1=-6, x2=-2, y1=3, y2=0:
The radius of the circle is 5.
Greetings!
To start this problem, let's first assign a variable for the missing, consecutive odd numbers. Since they are consecutive and odd, we add two.
<u>Proof:</u> <em>3-1=2, 5-3=2</em>
The first, consecutive, odd number:
The second, consecutive, odd number:
The third, consecutive, odd number:
The fourth, consecutive, odd number:
The sum of the values are equal to 3 times the sum of the first two numbers, of which this is equal to 35 less than the fourth number. Let's create an equation to simplify this:
Complete the operations inside the parenthesis:
Distribute the parenthesis (utilizing the distributive property)
Simplify both sides:
Add -6 and -x to both sides of the equation:
Divide both sides of the equation by 5:
If is equal to -7:
The four numbers are:
I hope this helps!
-Benjamin