Answer 17/18 , 19,20
Step-by-step explanation:
Answer:
#1: 5
#2: 
Step-by-step explanation:
Inverse of Pythagorean Theorem: c²-b²=a²
c² b² a²
13²- 12² = 25
= 5
Pythagorean Theorem: a²+b²=c²
a² b² c²
2² + 6² = 40
c = 
Answer:
97.98
Step-by-step explanation:
The area of the parallelogram PQR is the magnitude of the cross product of any two adjacent sides. Using PQ and PS as the adjacent sides;
Area of the parallelogram = |PQ×PS|
PQ = Q-P and PS = S-P
Given P(0,0,0), Q(4,-5,3), R(4,-7,1), S(8,-12,4)
PQ = (4,-5,3) - (0,0,0)
PQ = (4,-5,3)
Also, PS = S-P
PS = (8,-12,4)-(0,0,0)
PS = (8,-12,4)
Taking the cross product of both vectors i.e PQ×PS
(4,5,-3)×(8,-12,4)
PQ×PS = (20-36)i - (16-(-24))j + (-48-40)k
PQ×PS = -16i - 40j -88k
|PQ×PS| = √(-16)²+(-40)²+(-88)²
|PQ×PS| = √256+1600+7744
|PQ×PS| = √9600
|PQ×PS| ≈ 97.98
Hence the area of the parallelogram is 97.98
Answer:
-11xy-14y+4x
Step-by-step explanation:
Answer:
Option B) (x + 3)^2 + (y – 1)^2 = 8 is the correct answer.
Step-by-step explanation:
The equation of a circle with center (h,k) and radius r is given by:

Given
Center = (h,k) = (-3,1)
=> h = -3
=> k = 1
The distance between the center of circle and the point through which the circle passes will be the radius.
The distance formula is given by:

Given

Putting the values in the formula

Putting the values of h,k and r in general form of equation

Hence,
Option B) (x + 3)^2 + (y – 1)^2 = 8 is the correct answer.