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Damm [24]
2 years ago
12

U and v are position vectors with terminal points at (6, 14) and (3, 7), respectively. Find the terminal point of 2u - v.

Mathematics
1 answer:
e-lub [12.9K]2 years ago
6 0

Answer:

The terminal point of 2u - v is (9 , 21) ⇒ 3rd answer

Step-by-step explanation:

The position vector is the vector whose starting point is the origin (0 , 0)

You can find it from its terminal point on it (a, b), the vector is <a - 0 , b - 0> = <a , b>

∵ u is a position vector with terminal point (6 , 14)

∴ u = <6 - 0 , 14 - 0>

∴ u = <6 , 14>

∵ v is a position vector with terminal point (3 , 7)

∴ v = <3 - 0 , 7 - 0>

∴ v = <3 , 7>

∵ 2u - v = 2<6 , 14> - <3 , 7>

- Multiply 6 and 14 by 2

∴ 2u - v = <12 , 28> - <3 , 7>

- Add subtract 3 from 12 and 7 from 28

∴ 2u - v = <9 , 21>

∴ The terminal point of 2u - v = (9 , 21)

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Which representation of a transformation on a coordinate grid does not preserve congruence?
Alex17521 [72]

Answer:

B

Step-by-step explanation:

Consider all options:

A. Transformation with the rule

(x,y)\rightarrow (x,-y)

is a reflection across the x-axis.

Reflection across the x-axis preserves the congruence.

B. Transformation with the rule

(x,y)\rightarrow \left(\dfrac{7}{8}x,\dfrac{7}{8}y\right)

is a dilation with a scale factor of \frac{7}{8} over the origin.

Dilation does not preserve the congruence as you get smaller figure.

C. Transformation with the rule

(x,y)\rightarrow (x+6,y-4)

is a translation 6 units to the right and 4 units down.

Translation 6 units to the right and 4 units down preserves the congruence.

D. Transformation with the rule

(x,y)\rightarrow (y,-x)

is a clockwise rotation by 90^{\circ} angle over the origin.

Clockwise rotation by 90^{\circ} angle over the origin preserves the congruence.

3 0
3 years ago
Bryant collects a set of 20 data representing the lengths of worms he found in the garden. The variance of the set of measuremen
Varvara68 [4.7K]

Answer:

6 millimeters

Explanation:

The standard deviation is the square root of the variance.

Since the variance is 36, the standard deviation would be

√36 = 6

4 0
3 years ago
Read 2 more answers
I need help please thank you
aliya0001 [1]
\frac{ x^{2}-25 }{ x^{2}-3x-10 }
\frac{(x+5)(x-5)}{(x-5)(x+2)}
\frac{x-5}{x+2}

5 0
3 years ago
Melissa buys 2 1/2 pounds of salmon and 1 1/4 pounds of swordfish. She pays a total of $31.25, and the swordfish cost $.20 per p
julsineya [31]

Answer:

The combined cost of 1 pound of salmon and 1 pound of swordfish is $16.66

Step-by-step explanation:

Let us assume the cost of 1 pound salmon = $ m

So the cost of 1 pound of 1 pound swordfish cat = $ ( m - 0.20)

Now, the Amount of salmon purchased  = 2 1/2 pounds

2\frac{1}{2}  = 2 + \frac{1}{2} = 2 + 0.5 = 2.5

So, the amount of salmon purchased = 2.5 pounds

Cost of buying 2.5 pounds = 2.5 x ( 1 pound cost)

= 2.5 ( m) = $ 2.5 m  ...... (1)

Also, the Amount of swordfish purchased  = 1 1/4 pounds

1\frac{1}{4}  = 1 + \frac{1}{4} = 1 + 0.25 = 1.25

So, the amount of swordfish purchased = 1.25 pounds

Cost of buying 1.25 pounds = 1.25 x ( 1 pound cost of swordfish)

= 1.25 ( m - 0.20) = $ 1.25 m - 0.25       .... (2)

Now, the combined cost paid  = $ 31.25

⇒Cost of buying (2.5 pounds salmon  +  1.25 pounds swordfish) = $ 31.25

or, 2.5 m +   1.25 m - 0.25  = 31.35       (from (1) and (2))

or, 3.75 m = 31.60

or, m = 31.60/3.75 =  8.43

⇒ m = $8.43

So, the cost of 1 pound salmon = m = $8.43

and the cost of 1 pound swordfish = m - 0.20 = $8.43 - 0.20 = $ 8.23

Hence, the combined cost  1 pound of salmon and 1 pound of swordfish = $8.43 + $ 8.23 =  $ 16.66

6 0
3 years ago
What is .674 as a percentage?
stiks02 [169]
.674 as a percentage would be 67.4%

To find the percentage of a decimal, move the decimal two places to the right!

I hope this helps! Please thank my answer and mark my answer as the brainliest if it was the most helpful <3

4 0
3 years ago
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