Which is the best description for the graph?

Answer:

The component of [tex]\vec u[/tex] orthogonal to [tex]\vec a[/tex] is [tex]\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)[/tex].

Step-by-step explanation:

Let [tex]\vec u[/tex] and [tex]\vec a[/tex], from Linear Algebra we get that component of [tex]\vec u[/tex] parallel to [tex]\vec a[/tex] by using this formula:

[tex]\vec u_{\parallel \,\vec a} = \frac{\vec u \bullet\vec a}{\|\vec a\|^{2}} \cdot \vec a[/tex] (Eq. 1)

Where [tex]\|\vec a\|[/tex] is the norm of [tex]\vec a[/tex], which is equal to [tex]\|\vec a\| = \sqrt{\vec a\bullet \vec a}[/tex]. (Eq. 2)

If we know that [tex]\vec u =(2,1,1,2)[/tex] and [tex]\vec a=(4,-4,2,-2)[/tex], then we get that vector component of [tex]\vec u[/tex] parallel to [tex]\vec a[/tex] is:

[tex]\vec u_{\parallel\,\vec a} = \left[\frac{(2)\cdot (4)+(1)\cdot (-4)+(1)\cdot (2)+(2)\cdot (-2)}{4^{2}+(-4)^{2}+2^{2}+(-2)^{2}} \right]\cdot (4,-4,2,-2)[/tex]

[tex]\vec u_{\parallel\,\vec a} =\frac{1}{20}\cdot (4,-4,2,-2)[/tex]

[tex]\vec u_{\parallel\,\vec a} =\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)[/tex]

Lastly, we find the vector component of [tex]\vec u[/tex] orthogonal to [tex]\vec a[/tex] by applying this vector sum identity:

[tex]\vec u_{\perp\,\vec a} = \vec u - \vec u_{\parallel\,\vec a}[/tex] (Eq. 3)

If we get that [tex]\vec u =(2,1,1,2)[/tex] and [tex]\vec u_{\parallel\,\vec a} =\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)[/tex], the vector component of [tex]\vec u[/tex] is:

[tex]\vec u_{\perp\,\vec a} = (2,1,1,2)-\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)[/tex]

[tex]\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)[/tex]

The component of [tex]\vec u[/tex] orthogonal to [tex]\vec a[/tex] is [tex]\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)[/tex].

Answer:

In the simplest of words, $1,000 at 1% interest per year would yield $1,010 at the end of the year. But that is simple interest, paid only on the principal. Money in savings accounts will earn compound interest, where the interest is calculated based on the principal and all accumulated interest.

Step-by-step explanation:

Answer:

2.25

Step-by-step explanation:

let x be cost of a hotdog

let y be cost of hamburger

so,

5x + 4y = 17.75                    eq. 1

4x + 5y = 18.25                    eq. 2

manipulate eq. 1 so solve for x:

5x = 17.75 - 4y

x = 17.75/5 - (4/5)y

x = 3.55 - (4/5)y                  eq. 3

substitute eq. 3 to eq. 2:

4(3.55 - (4/5)y) + 5y = 18.25

14.2 - (16/5)y + 5y = 18.25

14.2 + (9/5)y = 18.25

(9/5)y = 18.25 - 14.2

4.05= (9/5)y

y = 2.25

x = 3.55 - (4/5)(2.25)

x = 1.75

hotdog costs $1.75

hamburger costs $2.25

Answer:

$5750

Step-by-step explanation:

To find what 15% is in money, we do

23,000*15/100=3450 for one year

3450*5(for five years)=$17,250

Now subtract that

23,000-17,250=$5750

Answer:

6rad2

Step-by-step explanation:

Answer:

8.845 units

Step-by-step explanation:

First start by plotting the points on a graph. Doing so will give you two points that you can connect and then turn into a triangle. Find the length and height of the triangle by counting how many units long each is. The length should be 6 units, while the height should also be 6 units. You can then use the pythagorean theorum to find the length of b to c:

A^2 + B^2 = C^2

6^2  + 6^2 = C^2

36 + 36 = C^2

72 = C^2

C = 8.845 units

Answer: the answer is 7 dollars for 1 guest

Step-by-step explanation:

Answer:

3.75 tons djdhdjrjrhejejjwjwjsjs

Answer:

3.75 US tons

Step-by-step explanation:

1 ton =2000 pounds

so  7,500÷2000 =3.75

Answer:

Part A- The 1st box is 96 and the second box is 10.

PartB-

Part C-

Step-by-step explanation:

5x12=60

6x12=72

8x12=96

10x12=120

So the 1st box is 96 and the second box is 10.

5     $50

6     $60

8     $80

I know this because Harry receives $10 per hour so you have to multiply the number of hours by $10.

If Harry babysits for 5 hours, he would receive $60 but if he does yard work for 5 hours, he would receive $50. Harry would receive $10 more by babysitting than by doing yard work.

Hoped this helped.

Answer:

Divergent

Step-by-step explanation:

an = 3 sin(2/n)

Choose bn = 3 (2/n).

Using Limit Comparison Test:

lim(n→∞) an / bn

= lim(n→∞) [3 sin(2/n)] / [3 (2/n)]

= lim(n→∞) [sin(2/n)] / (2/n)

= 1

The limit is greater than 0, and bn diverges, so an also diverges.

Answer:

p = -4.33636363636

Step-by-step explanation:

subtract 2.2 from -4.001 which equals -4.001-2.2=-6.201 and divide -6.201 by 1.43p and that equals -4.33636363636 so p = -4.33636363636

Answer:

Is there a certain equation?

Because my answer will probably be wrong.

Step-by-step explanation:

Let’s just say that x in both cases is the same value.

Equation:

(4x + 45) = (5x - 18)

x = 63

Answer: x = 63

Step-by-step explanation:

Answer:

x = 5

Step-by-step explanation:

1. Combine like terms

2. Multiply by 1

3. Distribute

4. Subtract  3

5  from both sides of the equation

5. Simplify

6. Divide both sides of the equation by the same term

7. Simplify

Answer:

58

Step-by-step explanation:

Answer:

x = 150

Step-by-step explanation:

We know a circle is 360°, so the angles must add up to 60°.

Step 1: Set up equation

x - 120 + x - 120 = 60

Step 2: Solve for x

Step 3: Check

Plug in x to verify it is correct.

150 - 120 = 30°

150 - 120 = 30°

30° + 30° = 60°

60° + 300° = 360°

Answer:

2000 dollars

Step-by-step explanation:

Answer:

d = 1.5

Step-by-step explanation:

yes

Answer:

1.5

Step-by-step explanation:

First put like terms on one side:

-3/8d - 1/2d = -11/16 - 5/8

then make the demominators the same:

-3/8d - 4/8d = -11/16 - 10/16

add up the terms:

-7/8d = -21/16

solve for d:

d= 1.5

Answer:

x = -3

Step-by-step explanation:

The line just passes through x = -3 so, it's parallel to the Y-vector.

Answer:

9 degrees farenehit

Step-by-step explanation:

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

Explanation:

x = number of hours since 2 AM

y = temperature in degrees Fahrenheit

The starting temperature is -15 degrees, so the y intercept is b = -15.

The temperature goes up 3 degrees each hour, so the slope is m = 3

The equation is y = 3x-15

Now plug in x = 4 since 6 AM is four hours after 2 AM.

We get the following

y = 3x-15

y = 3*4-15

y = 12-15

y = -3

The temperature at 6 AM is -3 degrees Fahrenheit.

-------------------------

Check:

Start at -15 and add 3 for each hour

It might help to make a number line.

2 AM = -15 degrees

3 AM = -12 degrees

4 AM = -9 degrees

5 AM = -6 degrees

6 AM = -3 degrees

This confirms the answer.

Answer:

7.y-side by side

8.n-lines don't cross, not vertical

9.n-don't equal 90 degrees

10.n-don't equal 180 degrees

11.AOB

12.COE

13.EOD

14.DOC

15.DOC, BOA

Step-by-step explanation:

Answer:

The individual in the data set is the cars sold

There are 4 variables but 3 are numerical or quantitative

Step-by-step explanation:

See Attachment for proper format of question.

Required

The individuals in this data set are:

This data set contains:

Solving (a):

From the attachment, we have the following columns:

Cars Sold; Retail Price; Miles Per Gallon; Seats; Navigation

From the list of columns, the individual in the data set is the cars sold because it represent what is being referenced in the table

Solving (b):

In (a) above, we established the individual to be cars sold.

The other 4 elements are what the data set contains i.e. variables.

From the attachment, we have that

retail price, miles per gallon and seats are numerical data while navigation isn't.

So, we can conclude that.

There are 4 variables but 3 are numerical or quantitative

Answer:

B

D

Step-by-step explanation:

I got it right on khan. Please send thanks

Answer: graph b

Step-by-step explanation:

Answer:

A and D.  

Step-by-step explanation:

A sequence is a set of the objects or numbers in a specific order. It is a function whose domain is a set of natural numbers or non-negative integers i.e. {1, 2, 3,..}

(A)

"An arithmetic sequence is a linear function whose domain is restricted to the set of non-negative integers."  

The general form an arithmetic sequence is:

[tex]a_{n}=a_{1}+(n-1)d[/tex]

The function is linear. The sequence consists of either numbers that are increasing or decreasing based on the value of d, the common difference.

So, the statement provided is True.

(D)

"A geometric sequence is an exponential function whose domain is restricted to the set of non-negative integers."

The general form an geometric sequence is:

[tex]a_{n}=a_{1}\cdot r^{n-1}[/tex]

The function is exponential. The sequence consists of either numbers that are exponentially increasing or decreasing by the factor r, the common ratio.

So, the statement provided is True.

Answer:

the answer is 7.1 inches tall

Answer:

Diverges

Step-by-step explanation:

an = 7 / n^(1 + 1/n)

As n approaches infinity, an approaches 7 / n.

bn = 7 / n

Apply Limit Comparison Test.

lim(n→∞) an / bn

= lim(n→∞) [7 / n^(1 + 1/n)] / (7 / n)

= lim(n→∞) n / n^(1 + 1/n)

= lim(n→∞) 1 / n^(1/n)

= lim(n→∞) 1 / n⁰

= 1

The limit is greater than 0, and bn diverges, so an also diverges.

Answer:

B. "at the mall"

Step-by-step explanation:

EDU 2020

Answer:b

Step-by-step explanation:

Answer:

45.7941176471

Step-by-step explanation:

Answer:

dilation

Step-by-step explanation:

dilation will make the shape larger or smaller which will change the shape.

Answer:

2x8=16

2+26=28

he is 17 years old and in ten years he will be 27

Step-by-step explanation:

Answer:

-1200 Calories

-$287 - $175 =$112  

Sanjai was paid $112

Step-by-step explanation: