Answer:
(x+2)² + (y-3)² = 26
The graphic is showed below
Step-by-step explanation:
The circle equation is given by the expression:
(x-a)² +(y-b)² = r²
The point (a,b) represents the center, and r is the radius. So:
(x+2)² + (y-3)² = r²
If the point A (3,2) is on the circle, then we can replace it in the equation to find r:
(3+2)² + (2-3)² = r²
r² = 5² + (-1)²
r² = 25 + 1
r² = 26
So, the circle has radius r = √26, and the equation is:
(x+2)² + (y-3)² = 26
To graph it, we must put the center C(-2,3), then the radius r = √26 and form a circle, like the figure below.
Answer: 5 + 11n = 13n
Explanation:
1) Cost of n visits for a student that is a member
a) Frequent visitor program fee: $5
b) cost of n tickets at $11 each: $11n
c) total cost: $5 + $11n
2) Cost of n visits for a non-member student
a) $13n
3) Equal cost condition:
5 + 11n = 13n ← answer
That is the equation requested, which you can solve to find the number of visits for which the costs are equal:
5 = 13n - 11n
5 = 2n
5/2 = n
2.5 = n
Therefore, 3 visits in a year justifiy the cost of being a member.
We know that
if P is the centroid of triangle ABC
so
PD=(1/3)*BD
BD=3*PD-----> BD=3*3-----> BD=9 units
the answer is
BD=9 units
<h3>
Answer: 60 teachers</h3>
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Explanation:
There are 500 female students and the ratio of boys to girls is 2:5
Multiply both parts of that ratio by 100 so that the "5" turns into "500"
The ratio 2:5 turns into 200:500 showing that for every 200 male students there are 500 female students. There are 200+500 = 700 students total.
Because of this 700 figure, we'll need to multiply both parts of the ratio 3:35 by 20 so that the 35 becomes 700.
The ratio 3:35 turns into 60:700. For every 60 teachers, there are 700 students.
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Another way to solve:
The ratio of boys to girls is 2:5 which we can write as 2/5
x = number of boys
2/5 = x/500
2*500 = 5x
1000 = 5x
5x = 1000
x = 1000/5
x = 200
There are 200 boys and 500 girls, so 200+500 = 700 total.
y = number of teachers
3/35 = y/700
3*700 = 35y
2100 = 35y
35y = 2100
y = 2100/35
y = 60
There are 60 teachers