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adoni [48]
3 years ago
7

If u, v, and w are nonzero vectors in r 2 , is w a linear combination of u and v?

Mathematics
1 answer:
Tju [1.3M]3 years ago
8 0
Not necessarily. \mathbf u and \mathbf v may be linearly dependent, so that their span forms a subspace of \mathbb R^2 that does not contain every vector in \mathbb R^2.

For example, we could have \mathbf u=(0,1) and \mathbf v=(0,-1). Any vector \mathbf w of the form (r,0), where r\neq0, is impossible to obtain as a linear combination of these \mathbf u and \mathbf v, since

c_1\mathbf u+c_2\mathbf v=(0,c_1)+(0,-c_2)=(0,c_1-c_2)\neq(r,0)

unless r=0 and c_1=c_2.
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3 years ago
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16. Find the values of x and y. (2y + 5) (5x - 17) (3x – 11)º
serg [7]

Answer:

x = 26

y = 9

Step-by-step explanation:

(5x - 17)° + (3x - 11)° = 180° (angles in a straight line)

Solve for x

5x - 17 + 3x - 11 = 180

Collect like terms

5x + 3x - 17 - 11 = 180

8x - 28 = 180

Add 28 to both sides

8x = 180 + 28

8x = 208

Divide both sides by 8

x = 208/8

x = 26

Also:

(2y + 5)° + 90° + (3x - 11)° = 180° (angles on a straight line)

Plug in the value of x and solve for y

2y + 5 + 90 + 3(26) - 11 = 180

2y + 5 + 90 + 78 - 11 = 180

Collect like terms

2y + 162 = 180

Subtract 162 from both sides

2y = 180 - 162

2y = 18

y = 9 (dividing both sides by 2)

6 0
3 years ago
When factoring the equation 9x2+9x+2 what two numbers will the "9x" term be broken into?
Andrew [12]

Answer:

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2 years ago
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What is the interquartile range of the data set? Enter the answer in the box. Key: 1|5 means 15
Aneli [31]
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Since the number of values is odd, the median will be the middle value i.e. 4th value which is 43. Median divides the data in two halves:

1st Half = 28, 40, 43
2nd Half = 45, 50, 50

Q1 or the First Quartile is the middle value of the lower or 1st half which is 40.
Q3 or the Third Quartile is the middle value of the upper or second half, which is 50.

IQR or the Inter Quartile Range is the difference of Q3 and Q1.

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Given that y is directly proportional to x. If y = 30 and x= 5, write an equation that connects y with x.
Licemer1 [7]

Given:

y is directly proportional to x.

y=30 when x=5

To find:

The equation that connects y with x.

Solution:

It is given that, y is directly proportional to x. So,

y\propto x

y=kx                     ...(i)

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Therefore, the required equation is y=6x.

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