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3 years ago

Please help me with this question

Mathematics

1 answer:

BartSMP [9]3 years ago

4 0

Answer:

$3x-28=2x+25\\x=53$

Step-by-step explanation:

Parallel lines cut by a transversal are two lines which do not cross intersected by a third line. Because lines such as m and n are parallel, we have angles which are equal to each other.

Corresponding Angles - angles located in the same position in each intersection. Can be shown by translating or sliding the angle down/up.
Alternate Interior Angles - angles located inside the parallel lines across the transversal. Can be shown by reflecting and translating or rotation.
Alternate Exterior Angles - angles located outside the parallel lines across the transversal. Can be shown by reflecting and translating or rotation.

Vertical angles - angles across a vertex from one another. Can be shown by reflection.

The angles shown here are located outside the parallel lines and across the transversal from each other. Therefore we have Alternate Exteroir angles and can set them equal to each other to solve for x.

$3x-28=2x+25\\3x-2x-28=2x-2x+25\\x-28=25\\x-28+28=25+28\\x=53$

We check our work and should get equal angles:

$3(53)-28=2(53)+25\\159-28=106+25\\131=131$

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Find the dot product of the position vectors whose terminal points are (14, 9) and (3, 6).

erma4kov [3.2K]

Answer:

Step-by-step explanation:

The formula for the dot product of vectors is

u·v = |u||v|cosθ

where |u| and |v| are the magnitudes (lengths) of the vectors. The formula for that is the same as Pythagorean's Theorem.

$|u|=\sqrt{14^2+9^2}$ which is $\sqrt{277}$

$|v|=\sqrt{3^2+6^2}$ which is $\sqrt{45}$

I am assuming by looking at the above that you can determine where the numbers under the square root signs came from. It's pretty apparent.

We also need the angle, which of course has its own formula.

$cos\theta=\frac{uv}{|u||v|}$ where uv has ITS own formula:

uv = (14 * 3) + (9 * 6) which is taking the numbers in the i positions in the first set of parenthesis and adding their product to the product of the numbers in the j positions.

uv = 96.

To get the denominator, multiply the lengths of the vectors together. Then take the inverse cosine of the whole mess:

$cos^{-1}\theta=\frac{96}{111.64676}$ which returns an angle measure of 30.7. Plugging that all into the dot product formula: