Answer:
Option C:
Step-by-step explanation:
Hello!
The sum of all angles in a triangle is 180°.
Add up all the angles and solve for x by setting the equation to 180°.
<h3>Solve for x</h3>
- ∠a + ∠b + ∠c = 180°
- (48 - x)° + (9x - 38)° + 90° = 180°
- 10° + 8x + 90° = 180°
- 8x = 180° - 90° - 10°
- 8x = 80°
- x = 10°
Now that we solved for x, we can plug it back into each equation to solve for each angle.
<h3>Angle A</h3>
<h3>Angle B</h3>
- 9x - 38°
- 9(10°) - 38°
- 90° - 38°
- 52°
<h3>Angle C</h3>
The answer is Option C:
The cross product of the normal vectors of two planes result in a vector parallel to the line of intersection of the two planes.
Corresponding normal vectors of the planes are
<5,-1,-6> and <1,1,1>
We calculate the cross product as a determinant of (i,j,k) and the normal products
i j k
5 -1 -6
1 1 1
=(-1*1-(-6)*1)i -(5*1-(-6)1)j+(5*1-(-1*1))k
=5i-11j+6k
=<5,-11,6>
Check orthogonality with normal vectors using scalar products
(should equal zero if orthogonal)
<5,-11,6>.<5,-1,-6>=25+11-36=0
<5,-11,6>.<1,1,1>=5-11+6=0
Therefore <5,-11,6> is a vector parallel to the line of intersection of the two given planes.
Answer:
No mode
Step-by-step explanation:
The mode is the statistical method in which the most repetitive number should be considered
Like if we take an example
1,1, 2, 2, 2, 4, 4,4,4
So here the mode is 4 as 4 is repeated 4 times
But in the given situation there is no mode as every number is written single time
