Answer:
Step-by-step explanation:
The general equation of a circle is , x² + y² + 2gx + 2fy + c = 0
Substituting the three points we get the following equations,
2g +14f +c=-50
14g - 2f + c =-50
16g +12f + c = -100
Solving these equations we get,
g =-4, f = -3, c = 0
Hence general equation of circle is,
x² + y² - 8x - 6y = 0
Answer:
√446 ≈ 21.12 cm
Step-by-step explanation:
The longest dimension of a rectangular prism is the length of the space diagonal from one corner to the opposite corner through the center of the prism. The Pythagorean theorm tells you the square of its length is the sum of the squares of the dimensions of the prism:
d² = (15 cm)² +(11 cm)² +(10 cm)² = (225 +121 +100) cm² = 446 cm²
d = √446 cm ≈ 21.12 cm
The longest line segment that can be drawn in a right rectangular prism is about 21.12 cm.
_____
<em>Additional comment</em>
The square of the face diagonal is the sum of the squares of the dimensions of that face. The square of the space diagonal will be the sum of that square and the square of the remaining prism dimenaion, hence the sum of squares of all three prism dimensions.
<span>D. One hundred random students from the sixth grade is the best choice given!
</span><span>
Reasons why the other answers and not good choices.
A. The first 100 students from an alphabetical list of the entire school, is incorrect because his only concern is the 6th graders, by including everyone he would negatively skew the data.
B. The first 100 students from an alphabetical list of sixth graders, is incorrect because its unfair to those with names starting later in the alphabet.
C. One hundred random students from the entire school </span>is is better but still incorrect because his only concern is the 6th graders, <span>by including everyone he would again negatively skew the data.</span>
Answer:
Its -12 if a is meant to be multiplied
