The standard form is
(x-xo)² + (y-yo)² = r²
Where xo,yo is the center of the circumference
and r is the radius.
We find the distance between the points to determine the <span>diameter
d=sqrt ((9-2)</span>² + (4-4)²<span>) = sqrt (49) = 7
The radius of the circumference is d/2 = 7/2 = 3.5
And we can see that those points are at the same coordinate y = 4
The center is given then by , x = (9+2)/2 = 5.5
y = (4+4)/2 = 4
The equation results
(x-5.5)</span>² + (y-4)² = (3.5)²<span>
</span>
Answer:
Natalie's age is 14
Sasha's age is 17
Step-by-step explanation:
Let
Sasha's age be "s", and
Natalie's age be "n"
<u>Sum of Sasha and Natalie is 31:</u>
s + n = 31
<u>Twice Natalie is 11 more than Sasha:</u>
2n = s + 11
We ca solve this equation for s first:
s = 2n - 11
We put this into first equation and solve for n first:
s + n = 31
2n - 11 + n = 31
3n = 31 + 11
3n = 42
n = 42/3 = 14
Natalie's age is 14
Also, s = 2n - 11
s = 2(14) - 11
s = 28 - 11
s = 17
Sasha's age is 17
Answer:
(x+3)(x+4)(x-4)
x+2 and x-3 are not factors but x-4 is
Step-by-step explanation:
let's factor it :)
x^3 + 3x^2 - 16x -48
first we will factor this:
x^3 + 3x^2
x^2(x + 3)
then factor the second part :
- 16x - 48
-16(x + 3)
so now,
x^2(x + 3) - 16(x + 3)
factor out x+3
(x+3)(x^2 - 16)
factor x^2 - 16
(x+3)(x+4)(x-4)
Answer:
66
Step-by-step explanation:
If there are <em>n</em> students, then the number of pairs is 
.
With 12 students, 
pairs can be formed.
The reason the formula works is this: Each of the 12 students can be paired with 11 other students (no student is paired with him/her self). But counting 12 x 11 = 132 counts each pair <u>twice</u>. Example: student A can be paired with student B,..., student B can be paired with student A. The pair was counted two times.
See the attached image that shows pairings of 5 students. There are
5(5 - 1)/2 = 5(4)/2 = 10 pairs.
B. The product of two irrational numbers if rational
Example: The square root of 2 times the square root of 3, is the square root of 6, which is still irrational.
