Read Fred's conclusion. If the sum of the digits of a number is a multiple of 3. then the number is a multiple of 6. Which state
1 answer:
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Answer:
<h3>Answer:</h3>
(5, -2, -3)
<h3>Explanation:</h3>We assume your equations are ...
- x +3y -z = 2
- 4x +2y +5z = 1
- 3x +0y +z = 12
These have solution (x, y, z) = (5, -2, -3).
_____
<em>How we know</em>
Trying the choices in the last equation eliminates the first and last. Trying the second choice in the first equation eliminates it, leaving the 3rd choice as the answer you're looking for.
We also know because we can ask a graphing calculator to solve the matrix equation (or row-reduce the augmented matrix).
<em>Comment on this problem</em>
The hardest part of this problem is figuring your intent. The equations are not well-separated, so we have a hard time telling what is a constant and what is a coefficient. It took a couple of guesses to sort it out. A little editing before posting would be helpful.
Answer
A = 46.3°
B = 75.7°
c = 3.5
Explanation
We will be using both Cosine and Sine rule to solve this.
For Cosine rule,
If a triangle ABC has angles A, B and C at the points of the named vertices of the tringles with the sides facing each of these angles tagged a, b and c respectively, the Cosine rule is given as
c² = a² + b² - 2ab Cos C
a = 3.0
b = 4.0
C = 58°
c² = 3² + 4² - 2(3)(4)(Cos 58°)
c² = 9 + 16 - (24)(0.5299)
c² = 25 - 12.72 = 12.28
c = √12.28 = 3.50
To find the other angles, we will now use Sine Rule
If a triangle ABC has angles A, B and C at the points of the named vertices of the tringles with the sides facing each of these angles tagged a, b and c respectively, the sine rule is given as
So, we can use the latter parts to solve this
B = ?
b = 4.0
C = 58°
c = 3.5
We can then solve for Angle A
The sum of angles in a triangle is 180°
A + B + C = 180°
A + 75.7° + 58° = 180°
A = 180° - 133.7° = 46.3°
Hope this Helps!!!