Determine whether the vectors u and v are parallel, orthogonal, or neither. u = <7, 2>, v = <21, 6>

Answers

Answer 1

Answer: Vectors are orthogonal if their dot product is equal to zero:
u · v = 7· 21 + 2 · 6 = 147 + 12 = 159 ≠ 0
Vectors are parallel if the angle between them is 0°, or cos ( u, v ) = 1
cos ( u, v ) = ( u · v ) / ( | u | · | v | ) =
= 159 / (√(7² + 2²) · √(21² + 6²) ) =
= 159 / ( √ (49 + 4 ) · √ ( 441 + 36 ) ) =
= 159 / (√53 · √477 ) = 159 / 159 = 1
Answer : The vectors u and v are parallel.

Answer 2

Answer:

Answer:

Parallel

Step-by-step explanation:

orthogonal: dot product of u times v= 0 degrees

utimesv= 7x21+2x6=147+12=159

Parallel: cos (u,v)=1

cos (u,v)=(u·v)/ IuI·IvI

cos (u,v)= 159/ (sqrt 7^2+2^2)·(sqrt 21^2 +6^2)

159/(sqrt 49+4) ·(sqrt 441+36)

159/(sqrt 53)·(sqrt 477)=

159/159

=1; therefore it is parallel

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How many cups of sugar is needed for 5 gallons

Answers

There are 16 cups in a gallon.

5 • 16 = 80

You need 80 cups of sugar for 5 gallons.

Find the midpoint of the segment with the following endpoints. (6, 4) and (9,9)

Answers

Answer:

15/2, 13/2.

Step-by-step explanation:

Here's a graph as well.

Answer in fraction form = (15/2, 13/2)

Answer in decimal form = (7.5, 6.5)

========================================================

Explanation:

To get the midpoint, we average the two endpoint values. We handle the x and y coordinates separately.

The x coordinates of each point are 6 and 9. They average to (6+9)/2 = 15/2 = 7.5; so you add up the x coordinates and divide by 2.

The y coordinates are handled the same way. Add them to get 4+9 = 13 and then divide by 2 to get 13/2 = 6.5

The midpoint is (15/2, 13/2) = (7.5, 6.5)

Suppose you roll a number cube. What is the theoretical probability of rolling a 2

Answers

Answer: $(1)/(6)$

Step-by-step explanation:

We know that a cube has six faces , if we roll a cube then we have chances to roll six different faces with six different number if it is not biased.

Let the number on cube be 1,2,3,4,5,6.

Thus total outcomes = 6

Then the theoretical probability of rolling a 2 is given by :-

$P(2)=\frac{\text{favorable outcome}}{\text{total outcomes}}\n\n\Rightarrow\ P(2)=(1)/(6)$

if theres six sides to the dices then the answer will be 1/6

13 over 15 divided by 7 over 10 in simplest form

Answers

If you would like to write (13/15) / (7/10) in the simplest form, you can calculate this using the following steps:

(13/15) / (7/10) = (13/15) * (10/7) = (13 * 2) / (3 * 7) = 26/21 = 1 5/21

The correct result would be 26/21.

Does a rectangle have more sides or angles

Answers

A rectangle has four right angles at 90º and four sides two of which are sets of each other.

If 3t − 7 = 5t , then 6t = how do you solve this

Answers

$3t-7=5t \ \ \ |\hbox{subtract 3t} \n -7=5t-3t \n -7=2t \ \ \ |\hbox{multiply by 3} \n \boxed{6t=-21}}$

$3t-7=5t\n5t-3t=-7\n2t=-7|\cdot3\n\boxed{6t=-21}$

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