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.
which is 
which is 
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.
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:
which returns an angle measure of 30.7. Plugging that all into the dot product formula:
gives you a dot product of 96
<u>Answer:</u>
- The simplified expression is "7p/4 + 2 1/2" or "1.75p + 2.5".
<u>Step-by-step explanation:</u>
- 2p + 3/4p + 6 - p - 3 1/2
- => (2p - p + 3/4p) + (6 - 3.5)
- => 1.75p + 2.5
Hence, the simplified expression is "<u>7p/4 + 2 1/2</u>" or "<u>1.75p + 2.5</u>". Any of these would work.
Hoped this helped.
Answer:
5y + 3x + 9
Step-by-step explanation:
Whenever something is multiplied by the same variable, you can combine the coefficients. In this case, first you'd move the values with the same variable next to each other, for simplicity:
7y-2y+3x+3+6
Then, combine like terms.
5y+3x+3+6
5y+3x+9
Answer:
2 4 6
Step-by-step explanation:
Among the students who did not make the honor roll. Then the relative frequency of having no curfew will be 7.
<h3>How to find the relative frequency?</h3>
Relative frequency is the ratio of the considered sub-group count to the total count. (so its frequency of the considered sub-group relative to the total frequency).
Curfew No Curfew No
Honor Roll: 18 10
No Honor Roll: 2 7
Among the students who did not make the honor roll.
Then the relative frequency of having no curfew will be 7.
Learn more about relative frequency here:
brainly.com/question/8358304
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