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3 years ago

15 POINTS How many people swallowed spiders in their sleep? (picture below)

Mathematics

2 answers:

Ira Lisetskai [31]3 years ago

7 0

The answer is 22% of people swallow spiders in their sleep

Amanda [17]3 years ago

7 0

I think that its either 34% or 70%

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LINEAR ALGEBRA

kenny6666 [7]

Answer:

The value of the constant $k$ so that $\vec u_{3}$ is a linear combination of $\vec u_{1}$ and $\vec u_{2}$ is $\frac{7}{10}$ .

Step-by-step explanation:

Let be $\vec u_{1} = [2,3,1]$ , $\vec u_{2} = [4,1,0]$ and $\vec u_{3} = [1, 2,k]$ , $\vec u_{3}$ is a linear combination of $\vec u_{1}$ and $\vec u_{3}$ if and only if:

$\alpha_{1} \cdot \vec u_{1} + \alpha_{2} \cdot \vec u_{2} +\alpha_{3}\cdot \vec u_{3} = \vec O$ (Eq. 1)

Where:

$\alpha_{1}$ , $\alpha_{2}$ , $\alpha_{3}$ - Scalar coefficients of linear combination, dimensionless.

By dividing each term by $\alpha_{3}$ :

$\lambda_{1}\cdot \vec u_{1} + \lambda_{2}\cdot \vec u_{3} = -\vec u_{3}$

$\vec u_{3}=-\lambda_{1}\cdot \vec u_{1}-\lambda_{2}\cdot \vec u_{2}$ (Eq. 2)

$\vec O$ - Zero vector, dimensionless.

And all vectors are linearly independent, meaning that at least one coefficient must be different from zero. Now we expand (Eq. 2) by direct substitution and simplify the resulting expression:

$[1,2,k] = -\lambda_{1}\cdot [2,3,1]-\lambda_{2}\cdot [4,1,0]$

$[1,2,k] = [-2\cdot\lambda_{1},-3\cdot \lambda_{1},-\lambda_{1}]+[-4\cdot \lambda_{2},-\lambda_{2},0]$

$[0,0,0] = [-2\cdot \lambda_{1},-3\cdot \lambda_{1},-\lambda_{1}]+[-4\cdot \lambda_{2},-\lambda_{2},0]+[-1,-2,-k]$

$[-2\cdot \lambda_{1}-4\cdot \lambda_{2}-1,-3\cdot \lambda_{1}-\lambda_{2}-2,-\lambda_{1}-k] =[0,0,0]$

The following system of linear equations is obtained:

$-2\cdot \lambda_{1}-4\cdot \lambda_{2}= 1$ (Eq. 3)

$-3\cdot \lambda_{1}-\lambda_{2}= 2$ (Eq. 4)

$-\lambda_{1}-k = 0$ (Eq. 5)

The solution of this system is:

$\lambda_{1} = -\frac{7}{10}$ , $\lambda_{2} = \frac{1}{10}$ , $k = \frac{7}{10}$

The value of the constant $k$ so that $\vec u_{3}$ is a linear combination of $\vec u_{1}$ and $\vec u_{2}$ is $\frac{7}{10}$ .

4 0

4 years ago

How to factor 3n^2+3n-60

sveta [45]

$3n^2+3n-60 =\\
3(n^2+n-20)=\\
3(n^2+5n-4n-20)=\\
3(n(n+5)-4(n+5))=\\
3(n-4)(n+5)$

6 0

3 years ago

Read 2 more answers

5. Pint is a unit of which type of measurement?

MakcuM [25]

C. volume
a pint is a unit of fluid volume equal to one-eighth of a gallon

4 0

3 years ago

Read 2 more answers

Your answer is incorrect. It costs $3.68 for a pack of 16 pencils. Find the unit price in dollars per pencil. If necessary, roun

Brilliant_brown [7]

Answer:

$\frac{3.68}{16}$

$0.23$

3 0

3 years ago

nika2105 [10]

If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.

Value of X is 9 and Angle 6 is 79°

If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.

If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.

If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent.

Since, angle 1 and angle 4 are vertically opposite angles . Hence, these are equal.

∠1 = ∠4 = 11x + 2

Similarly, ∠6 and ∠7 are vertically opposite angles.

Thus, ∠6 = ∠7 = 8x + 7

If two parallel lines are cut by a transversal, then the sum of interior angles on one side is equal to 180 degree.

Therefore, ∠4 + ∠6 = 180

11x + 2 + 8x + 7 = 180

19x + 9 = 180

19x = 171

x = 9

Value of angle 6 = value of angle 7

= 8x + 7

= 8 (9) + 7

= 79 Degree

Learn more:

brainly.com/question/19670823

3 0

2 years ago