4.56 natural numbers or a whole numbers integers rational numbers Irrational numbers or real numbers ​

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:

RT = 20

Step-by-step explanation:

Given that,

Point S lies on the line segment RT.

We have, ST = 3x-8, RT = 4x and RS = 4x-7

It is clear that, RT = RS+ST

Putting the values, we get :

4x = 4x-7 + 3x-8

Taking like terms together,

4x-4x-3x = -7-8

-3x = -15

x = 5

Put the value of x in RT = 4x.

So,

RT = 4(5)

RT = 20

Hence, length of RT = 20.

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:

The demand d as a function of price is [tex]d=\frac{800}{3} -\frac{40p}{3}[/tex]

The demand if the price is $ 8 per gallon is 160 millions of gallons.

Step-by-step explanation:

You know that the price-demand equation for gasoline is 0.3d + 4p = 80

To write demand d as a function of price p, you must solve for or isolate demand d, remembering that:

So:

0.3d + 4p = 80

0.3d = 80 - 4p

[tex]d=\frac{80 - 4p}{0.3}[/tex]

[tex]d=\frac{80}{0.3} -\frac{4p}{0.3}[/tex]

[tex]d=\frac{800}{3} -\frac{40p}{3}[/tex]

The demand d as a function of price is [tex]d=\frac{800}{3} -\frac{40p}{3}[/tex]

To determine how much is the quantity demanded if the price is $ 8 per gallon, you simply plug that value into the previously determined expression and perform the corresponding calculations:

[tex]d=\frac{800}{3} -\frac{40*8}{3}[/tex]

[tex]d=\frac{800}{3} -\frac{320}{3}[/tex]

d= 160

The demand if the price is $ 8 per gallon is 160 millions of gallons.

Answer:

104

Step-by-step explanation:

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

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

Then solve for x

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:

12cm^2

Step-by-step explanation:

Area of a rectangle = Length × Width

Length = 5.6cm

Width= 2.1cm

Area of the rectangle = Length × Width

= 5.6cm × 2.1cm

= 11.76 centimeter square

Area of the rectangle = 11.76 centimeter square

Answer to two significant figures

There are two figures before the decimal and two figures after the decimal

Since, the question asked us to 2 significant figures, then we will focus on the two figures before the decimal point.

11.76

Using .76 round 11 to the nearest whole number

We have,

12 centimeter square

12cm^2

Answer:

1. x= y/m - b/m

2. m= y/x - b/x

Step-by-step explanation:

hope this helps.

Answer:

80

Step-by-step explanation:

Answer:

(-8, 2)

Step-by-step explanation:

Count 4 units to the right.

Answer:

173.79

Step-by-step explanation:

173.89 - 0.1 you move to the decimals place then remove that number once

The number 173.79 is 0.1 less than 173.89

Two or more expressions with an Equal sign is called as Equation.

We need to find how less is 0.1 than 173.89

In words zero point one is less than One hundred seventy three point eight nine.

To find this we have to use subtraction operator or difference.

Subtraction is an operation that represents removal of objects from a collection

Subtract 0.1 from 173.89

173.89-0.1

We get 173.79

Hence, the number 173.79 is 0.1 less than 173.89

To learn more on Equation:

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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

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Answer:

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

Step-by-step explanation:

Answer:

Quotient = 358

Remainder = 3

Answer: Bill Has 19$

Step-by-step explanation:

Answer:

Step-by-step explanation:

4,3,2

Answer:

Step-by-step explanation:

3y = 5x - 1

y = 5/3x - 1/3

perpendicular slope is -3/5

Answer:

area of square = l²= 4489m²

l=√4489 = 67m

Step-by-step explanation:

2.02 into 10 raised to 7 is the answer

Answer:

C

Step-by-step explanation:

Because the dolphin increases his elevation, the amount he increases is added to the original elevation to get the second elevation.

Therefore:

-16 3/4 + 5x = -5 1/4

This option is not in the options but if we rearrange the left side from

- 16 3/4 + 5x

to:

5x - 16 3/4

We get the last option C.

Hope this helped!

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

Step-by-step explanation:

4+(-3)=1

because when you open brackets + and - will be -, so 4-3=1

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]

[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:

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:

   x=[tex]\frac{y2 }{9}[/tex]

Step-by-step explanation:

2nd step: [tex]3\sqrt{x}=y[/tex]

third step: [tex]\frac{3\sqrt{x} }{3} = \frac{y}{3}[/tex]

fourth step: [tex]\sqrt{x} =\frac{y}{3}[/tex]

answer:    x=[tex]\frac{y2 }{9}[/tex]

Answer:

Here you go buddy.

Answer:

1.Toast your hot dog bun if you like.

2.Grab pan with little bit of water

4.Place hotdog and cook until chang color on both sides

5. Place a cooked hot dog inside the bun.

6.Add sauces.

6.Put on chunky condiments next.

7.Top it with cheese if you like.

8.Finish the dog with your favorite spices.

9. Put the assembled hot dog on a plate.

10.Serve your favorite snacks on the side.

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:

56

Step-by-step explanation:

Answer:

6000

Step-by-step explanation:

we dont know how many people are in each plane but based on the average it should be this