Evaluate and simplify the following complex fraction.

Answer:

a. Line

b. Plane

c. All of R^3

Step-by-step explanation:

In order to answer this question, we need to study the linear independence between the vectors :

1 - A set of three linearly independent vectors in R^3 generates R^3.

2 - A set of two linearly independent vectors in R^3 generates a plane.

3 - A set of one vector in R^3 generates a line.

The next step to answer this question is to analyze the independence between the vectors of each set. We can do this by putting the vectors into the row of a R^(3x3) matrix. Then, by working out with the matrix we will find how many linearly independent vectors the set has :

a. Let's put the vectors into the rows of a matrix :

[tex]\left[\begin{array}{ccc}-2&5&-3\\6&-15&9\\-10&25&-15\end{array}\right][/tex] ⇒ Applying matrix operations we find that the matrix is equivalent to this another matrix  ⇒

[tex]\left[\begin{array}{ccc}-2&5&-3\\0&0&0\\0&0&0\end{array}\right][/tex]

We find that the second vector is a linear combination from the first and the third one (in fact, the second vector is the first vector multiply by -3).

We also find that the third vector is a linear combination from the first and the second one (in fact, the third vector is the first vector multiply by 5).

At the end, we only have one vector in R^3 ⇒ The set of all linear combinations of the set a. is a line in R^3.

b. Again, let's put the vectors into the rows of a matrix :

[tex]\left[\begin{array}{ccc}1&2&0\\1&1&1\\4&5&3\end{array}\right][/tex] ⇒ Applying matrix operations we find that the matrix is equivalent to this another matrix ⇒

[tex]\left[\begin{array}{ccc}1&1&1\\0&1&-1\\0&0&0\end{array}\right][/tex]

We find that there are only two linearly independent vectors in the set so the set of all linear combinations of the set b. is a plane (in fact, the third vector is equivalent to the first vector plus three times the second vector).

c. Finally :

[tex]\left[\begin{array}{ccc}0&0&3\\0&1&2\\1&1&0\end{array}\right][/tex] ⇒ Applying matrix operations we find that the matrix is equivalent to this another matrix ⇒

[tex]\left[\begin{array}{ccc}1&1&0\\0&1&2\\0&0&3\end{array}\right][/tex]

The set is linearly independent so the set of all linear combination of the set c. is all of R^3.

Answer:

rational

Best of luck!

Answer:

104

Step-by-step explanation:

5/8x. - - - - - - - >. 3/8x

56+x---------------> 24+x

Then solve for x

Answer: He has 7 at the moment, technically, if he still has the bag, he still has all 36

Step-by-step explanation:

Answer:

he has noob 7

Step-by-step explanation:

Answer:

1. x= y/m - b/m

2. m= y/x - b/x

Step-by-step explanation:

hope this helps.

Answer:

The length is 12yd and the width is 6yd.

Step-by-step explanation:

Answer:

25. 8ft

26. 3m

27. 7cm

Step-by-step explanation:

Because it says each is an area of a sqare the square root will give you the side length

Answer:

39. r = 13.4

40. m = 12

Step-by-step explanation:

39. Given the equation, [tex] -0.8 + r = 12.6 [/tex], to solve for r, the following are the correct steps to take to arrive at the solution:

[tex] -0.8 + r = 12.6 [/tex] (given)

Add 0.8 to both sides of the equation (addition property of equality)

[tex] -0.8 + r + 0.8 = 12.6 + 0.8 [/tex] (this is where the error occurred.)

[tex] r = 13.4 [/tex]

40. The correct steps to take in solving the equation, [tex] -\frac{m}{3} = -4 [/tex] is as follows:

[tex] -\frac{m}{3} = -4 [/tex] (given)

Multiply both sides by 3 (multiplication property of equality)

[tex] 3*-\frac{m}{3} = 3*(-4) [/tex]

[tex] -m = -12 [/tex] (this is where the error occurred. This is what we should have at this line/step)

[tex] m = 12 [/tex] (dividing both sides by -1)

[tex] \frac{2}{3} \: cups = 2 \: serving[/tex]

[tex] \frac{ \frac{2}{3} }{2} \: cups = \frac{2}{2} \: serving[/tex]

[tex] \frac{2}{3 \times 2} \: cups = 1 \: serving[/tex]

[tex] \frac{2}{6} \: cups = 1 \: serving[/tex]

[tex] \frac{1}{3} \: cups = 1 \: serving[/tex]

So, there are ⅓ cups of flour in one serving.

Thank you.

Answer:

10.6

Step-by-step explanation:

53/5

Answer:

[tex]10\frac{3}{5}[/tex]

Step-by-step explanation:

We divide 53 by 5 which we get 10 3/5

Answer:

Step-by-step explanation:

3y = 5x - 1

y = 5/3x - 1/3

perpendicular slope is -3/5

Answer:

Step-by-step explanation:

4,3,2

Answer:

The answer is "[tex]\bold{\frac{343 \ \pi}{24} \ \text{cubic units}}[/tex]"

Step-by-step explanation:

The volume of the mass whose cross-sectional area has been perpendicular is usually sliced by the method The cross-section, which is based to parallel to y-axis;  

[tex]V = \int_{a}^{b} A (x)dx[/tex]

The semi-circular segment of the strong and seems to be perpendicular to foundation and  

Y-axis parallel.  

Its cross-section does have a diameter of: [tex](7-x)[/tex].  

It also transverse radius is: [tex]\frac{1}{2}(7-x)[/tex].  

The semi-circular segment area is,

[tex]Formula: \\\\ A(x)=\frac{1}{2} \times \pi \times r^2[/tex]

        [tex]=\frac{1}{2} \times \pi \times (\frac{(7-x)}{2})^2\\\\=\frac{1}{2} \times \pi \times (\frac{(7-x)^2}{4})\\\\=\frac{1}{8}\pi(7-x)^2\\[/tex]

when

[tex]0 \leq \ x \ \leq 7[/tex]

Calculating the volume from the solid accordingly:

[tex]V= \int_{0}^{7}\frac{1}{8} \times\pi \times (7-x)^2 dx[/tex]

   [tex]= \frac{1}{8} \pi \int_{0}^{7}(7-x)^2 dx \\\\= \frac{1}{8} \pi [\frac{(7-3)^3}{-3}]_{0}^{7}\\\\= \frac{\pi}{24} \times [7^3-0]\\\\= \frac{\pi}{24} \times 343\\\\= \frac{343 \pi}{24} \\[/tex]

Answer:

Step-by-step explanation:

Change all numbers to their decimal form.

37.5 % = 37.5 / 100 = 0.375

1/3 = 0.3333

0.3 = 0.3

40% = 40/100 = 0.4

3/5 = 0.6

Order

0.3

0.33333

0.375

0.4

0.6

there are (1/6)/(1/3) one-third in one sixth

Step-by-step explanation:

that means

no. of one-third is 1/2

Answer:

there are 2 one third in one sixth

Answer:

5

Step-by-step explanation:

You need to find how many days Stefan can feed Coco with the oats he has left. But first, you need to know how many cups of oats Stefan has left after making granola bars.

Stefan has 4

1

2

cups of oats, and he uses 3

1

4

cups to make granola bars.

Start by writing 4

1

2

with a denominator of 4. Then both fractions will have the same denominator.

4

1

2

=4

2

4

Subtract. Remember to subtract whole numbers from whole numbers and fractions from fractions.

4

2

4

–3

1

4

=1

1

4

Stefan has 1

1  

4

cups of oats left.

Answer:

  34.5%

Step-by-step explanation:

If we assume the relationship is approximately linear with time, we can use technology to draw a line of best fit through the given data. Extrapolating to the year 2030 predicts the value to be 34.5%.

In 2030, we might expect about 34.5% of male first-year college students to claim no religious affiliation.

_____

Additional comment

When it comes to religion, many factors are in play. The assumption we have made has no justification whatever, except that it provides a method for answering the question. (It also predicts the percentage to be 0 in 1963, which we believe to be unrealistic.) An exponential fit is better (r^2 = 0.97), and it predicts about 46.0%.

Answer:

[tex]\bold{(x+2))^2+(y-2)^2+(z-2)^2=17}[/tex]

Step-by-step explanation:

Given the center of sphere is: (-2, 2, 3)

Passes through the origin i.e. (0, 0, 0)

To find:

The equation of the sphere ?

Solution:

First of all, let us have a look at the equation of a sphere:

[tex](x-a)^2+(y-b)^2+(z-c)^2=r^2[/tex]

Where ([tex]x,y,z[/tex]) are the points on sphere.

[tex](a, b, c)[/tex] is the center of the sphere and

[tex]r[/tex] is the radius of the sphere.

Radius of the sphere is nothing but the distance between any point on the sphere and the center.

We are given both the points, so we can use distance formula to find the radius of the given sphere:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}[/tex]

Here,

[tex]x_1 =0 \\y_1 =0 \\z_1 =0 \\x_2 =-2 \\y_2 =2 \\z_2 =3[/tex]

So, Radius is:

[tex]r = \sqrt{(-2-0)^2+(2-0)^2+(3-0)^2}\\\Rightarrow r = \sqrt{4+4+9} = \sqrt{17}[/tex]

Therefore the equation of the sphere is:

[tex](x-(-2))^2+(y-2)^2+(z-2)^2=(\sqrt{17})^2\\\bold{(x+2))^2+(y-2)^2+(z-2)^2=17}[/tex]

Answer:

x = -3n/4

Step-by-step explanation:

Answer:  t > 6/5

In decimal form, this would be t > 1.2

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

Work Shown:

6t > t+6

6t-t > t+6-t ...... subtracting t from both sides

5t > 6

5t/5 > 6/5 .... dividing both sides by 5

t > 6/5

t > 1.2

Answer:

The answer is -11

Step-by-step explanation:

3+(-14) is basically writing out 3-14 which is -11

Answer:

-11

Step-by-step explanation:

3+(−14)

Subtract 3 from 14 to get −11.

−11

Answer:

Which of the following graphs show a proportional relationship?

Choose all answers that apply:

The answer is A.

Using the proportional relationship concept, the graph of a straight line through the origin is seen in option (A).

So, option (A) is the correct option.

"If the relationship between two quantities is a proportional relationship, this relationship can be represented by the graph of a straight line through the origin with a slope equal to the unit rate."

In a proportional relationship, two quantities vary directly with each other.

We can represent relationships in several ways:

1. An equation in the form of y = kx , where k is the constant of proportionality or unit rate.

2. A graph of a straight line that passes through the origin.

3. A set or table of ordered pairs that show equivalent ratios.

4. A verbal description that describes a describe proportional relationship between two quantities.

Explanation for correct option:

According to the given options

The graph of a straight line through the origin is seen in option (A).

So, option (A) is the correct option.

Explanation for other options:

In option(B),

The graph of a straight line does not passes through the origin.

So, option (B) is not correct

In option(C),

Graph is not given

So, it is also not correct

Hence, the graph of a straight line through the origin is seen in option (A).

So, option (A) is the correct option.

Learn more about proportional relationship here

https://brainly.com/question/8879344

#SPJ2

Answer:

5

Step-by-step explanation:

Since, A, B, C, D are collinear.

[tex] \implies A - B - C - D \\

\therefore \: AD = (AB + BC) + CD \\ \therefore \: 18 = AC + CD.. (\because AB + BC =AC) \\ \therefore \: 18 = 8 + CD \\ \therefore \: 18 - 8 = CD \\ \therefore \: 10 = CD \\ \\ \because \: BC + CD = BD \\ BC = BD - CD \\ BC = 15 - 10 \\ BC = 5 \\ [/tex]

Answer:

x > 10/7

Step-by-step explanation:

Take LCM and do cross Multiplication. You will get,

24x + 4x + 8 > 48

or, 28x > 40

or, x > (40/28)

This gives, x > 10/7

Answer:

2.38

Step-by-step explanation:

subtract 4.9 on both sides

x = 2.38

x + 4.9 = 7.28

x = 7.28 - 4.9

x = 2.38

Answer:

No Solution

Step-by-step explanation:

Step 1:

17 + 28 = - 5 ( 4x - 9 )

Step 2:

45 = - 20x + 45

Step 3:

- 20x = 0

Answer:

No Solution

Hope This Helps :)

Answer:

358 u literally just waited your time u could have used a calculator

Step-by-step explanation:

Answer:

Quotient = 358

Remainder = 3

Answer:

800,000

Step-by-step explanation:

The numbers are above 5 making it round up not down

Its the Right Answer on the Test. Hopes This Helps.

Thank You