Answer:
x = 9
Step-by-step explanation:
set a proportion: 8/12 = 6/x => 8x = 72 => x = 9
Separate the vectors into their <em>x</em>- and <em>y</em>-components. Let <em>u</em> be the vector on the right and <em>v</em> the vector on the left, so that
<em>u</em> = 4 cos(45°) <em>x</em> + 4 sin(45°) <em>y</em>
<em>v</em> = 2 cos(135°) <em>x</em> + 2 sin(135°) <em>y</em>
where <em>x</em> and <em>y</em> denote the unit vectors in the <em>x</em> and <em>y</em> directions.
Then the sum is
<em>u</em> + <em>v</em> = (4 cos(45°) + 2 cos(135°)) <em>x</em> + (4 sin(45°) + 2 sin(135°)) <em>y</em>
and its magnitude is
||<em>u</em> + <em>v</em>|| = √((4 cos(45°) + 2 cos(135°))² + (4 sin(45°) + 2 sin(135°))²)
… = √(16 cos²(45°) + 16 cos(45°) cos(135°) + 4 cos²(135°) + 16 sin²(45°) + 16 sin(45°) sin(135°) + 4 sin²(135°))
… = √(16 (cos²(45°) + sin²(45°)) + 16 (cos(45°) cos(135°) + sin(45°) sin(135°)) + 4 (cos²(135°) + sin²(135°)))
… = √(16 + 16 cos(135° - 45°) + 4)
… = √(20 + 16 cos(90°))
… = √20 = 2√5
Plug in your coefficients
Answer:

Step-by-step explanation:
<h3>45° - 45° - 90° triangle:</h3>
The ratio of sides of 45 - 45 - 90 triangle is a : a : a√2.
a is the side opposite to 45°.
From the figure, a = 5√11
The side opposite to 90° is a√2.
y = a√2

Option D) (0, 0)
<h2>
Explanation:</h2>
The complete question is:
_______________________________________
On the coordinate plane, Kyle graphs a line that represents a proportional relationship between x and y. Which point MUST be on the line?
A) (0, 1)
B) (1, 0)
C) (1, 1)
D) (0, 0)
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A proportional relationship between x and y can be written in a mathematical language as follows:

For any non-constan k-value. As you can see, this k-value represents the slope of a line. Remember that the Slope-intercept form of a line is given by:

In the case of
the y-intercept is zero, so the line passes through.
In conclusion, <em>Kyle's graph is a line that represents a proportional relationship between x and passes through point (0, 0)</em>
<h2>Learn more:</h2>
Direct variation: brainly.com/question/13881905
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