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Answer: The correct option is (B).

True. The vector V₃ is a linear combination of V₁ and V₂, so at least one of the vectors in the set is a linear combination of the others and set is linearly dependent.  

Step-by-step explanation:  

Given that;

If V₁ ....... V₄ are in R⁴ and V₃ = 2V₁ + V₂ then {V₁, V₂, V₃, V₄} is linearly dependent.  

Lets {V₁, V₂, V₃, V₄}  are linearly dependent

Then there exist a scalars C₁, C₂, C₃, C₄

So that C₁V₁ + C₂V₂ + C₃V₃ + C₄V₄ = 0

where at least one of the Ci ≠ 0.  

Take C₃ ≠  0 then we have V₃ = (C₁V₁ + C₂V₂ + C₄V₄) / C₃

V₃ is a linear combination of V₁, V₂ and V₄}

that is

Given V₃ = 2V₁ + V₂

⇒ 2V₁ + V₂ - V₃ = 0

⇒ 2V₁ + V₂ + V₃ + 0V₃ = 0

Here, C₁ = 1, C₂ = 1,  C₃ = -1 and C₄ = 0

So that {V₁, V₂, V₃, V₄} is linearly dependent.

therefore option B id the right answer.

- True. The vector V₃ is a linear combination of V₁ and V₂, so at least one of the vectors in the set is a linear combination of the others and set is linearly dependent.  

B is the correct option. True, The vector V₃ is a linear combination of V₁ and V₂, so at least one of the vectors in the set is a linear combination of the others and the set is linearly dependent.  

If V₁ ....... V₄ are in R⁴ and V₃ = 2V₁ + V₂ then {V₁, V₂, V₃, V₄} is linearly dependent.  

A set of vectors is linearly dependent if some vector can be expressed as a linear combination of the others.

Let's consider {V₁, V₂, V₃, V₄}  are linearly dependent

then there exist a scalars C₁, C₂, C₃, C₄

therefore, C₁V₁ + C₂V₂ + C₃V₃ + C₄V₄ = 0

where at least one of the Ci ≠ 0.  

Lets C₃ ≠  0 then we will get

V₃ = (C₁V₁ + C₂V₂ + C₄V₄) / C₃

V₃ is a linear combination of V₁, V₂, and V₄

which means V₃ = 2V₁ + V₂

2V₁ + V₂ - V₃ = 0

2V₁ + V₂ + V₃ + 0V₃ = 0

Here, C₁ = 1, C₂ = 1,  C₃ = -1 and C₄ = 0

therefore, {V₁, V₂, V₃, V₄} is linearly dependent.

So, option B is correct here.

True. The vector V₃ is a linear combination of V₁ and V₂, so at least one of the vectors in the set is a linear combination of the others, and the set is linearly dependent.  

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The hot air balloon will descend 20.25 feet per second.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that a hot air balloon is descending at a rate of 6.75 feet per second. The height of the balloon after 3 seconds will be:-

Rate of change = Height / Time

6.75 = Height / 3

Height = 6.75 x 3 = 20.25 feet

Therefore, the hot air balloon will descend 20.25 feet per second.

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Answer: $100.00 per pound

Step-by-step explanation:

v/8=2

v=8×2

v=16

16/8=2

Answer:

v = 16

Step-by-step explanation:

v/8 =2

Lets isolate v.

Multiply 8 on both sides.

v = 16

This is a one step equation, so there isn't realy that much to it.

Answer:

A would be 54,B would be 54, C would be 65, d would be 61

Answer:

3

Step-by-step explanation:

you have to make 1/4 a reciprocal

3/4 times 4/1

=3

Answer:

3

Step-by-step explanation:

Step 1:

3/4 × 1/4         Equation

Step 2:

3/4 × 4/1      Flip Fraction

Step 3:

3/1 = 3       Multiply

Answer:

3

Hope This Helps :)

Step-by-step explanation:

Hey there!

Now, let's look into figure.

angle ACB = 65° { Base angle of triangle ABC}

angle ACB + angle BAC + angle ABC = 180°

65° + 65° + angle ABC = 180°

angle ABC = 180°-130°

Therefore, angle 50°

angle EBD = 50° ( Vertically opposite angle)

Now;

angle EBD= angle DEB = 50° ( Base angle of triangle BDE )

angle BDE + angle DEB + angle EBD = 180° ( Sum of interior angle)

angle BDE = 180° -100°

Therefore, angle BDE = 80°.

Now, 80° + 14x + 2 = 180° { being linear pair}

14x = 180°-82°

14x = 98°

[tex]x = \frac{98}{14} [/tex]

X = 7°

Hope it helps......

Answer:

d is ur answer maybe ok ok ok

Answer:

B. N(n+8)

Step-by-step explanation:

A rectangle's area is Length x Width

The rectange's length is not known to us. N is it's variable

It says the width is 8 units mor then the length and ask for the are of the rectangle.

Now since rectangle's area is length times width we multiply n (the length) with the width (8+n).

This would be N(n+8)

Answer:

3, 4, and 5 make a right triangle (Pythagorean triple). 3 and 4 are the legs, 5 is the hypotenuse. Another example is 9, 12, 15, with 9 & 12 as the legs and 15 as the hypotenuse on a right triangle.

Step-by-step explanation:

Pythagorean triples (measurements are whole numbers) are always in a 3:4:5 ratio; the longest side is always hypotenuse; the right angle is always opposite of the hypotenuse; the legs will be perpendicular (making right angle)

Answer:

It will take 6.66 minutes to complete one lap.

Answer:

8 cm.

Step-by-step explanation:

Area = length × width

Use the variable w instead of width.

Area = w × (w+3)

Substitute 40 for the Area

40 = w × (w + 3)

Create a table to find the greatest common factors of 40.

1 × 40, not it because 40 is 39 units greater than 1, not 3

2 ×20, not it because 20 is 18 units greater than 2, not 3

4 × 10, not it because 10 is 6 units greater than 4, not 3

5 × 8, correct because 8 is 3 units greater than 5

Now substitute 5 for w to check your answer

40 = 5 × (5 +3 )

40 = 5 × 8

40 = 40

The answer is correct.

Hope this helps!!!

A rectangle is a quadrilateral with 4 sides. In a rectangle, one side is longer than the other. The longer side is called the width and the shorter side is called the length.

The length of the rectangle is 8cm.

The formula  for the area of a rectangle is given as :

Length x Width

From the question, the length is 3 more than its width​. We can represent this mathematically as:

L = W + 3

Area of the rectangle = 40 sq. cm

Inputting this into the formula

(W + 3) x W = 40

W² + 3W = 40

W² + 3W - 40 = 0

Factorise

W² +8W - 5W - 40 = 0

W(W + 8) - 5(W + 8) = 0

(W + 8)(W - 5) = 0

To find W

W + 8 = 0

W = - 8 or

W - 5 = 0

W = 5 cm

Therefore, the width is 5cm.

To find the length, L = W + 3

L = 5 + 3

L = 8 cm

Therefore, the length is 8 cm.

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Answer:

3,0

0, -10

Step-by-step explanation:

Answer:

-23

Step-by-step explanation:

You're welcome :)

Answer:

the direction of the road

Step-by-step explanation:

To calculate the net force, we need to know the direction through which the forces are acting.

Are the forces directed towards one another or against each other?

  Net force is a vector sum of forces that acts on a body. It is that single force that can replace two or more forces acting on a body.

So, without knowing the direction, we cannot calculate the net force.

Answer:

$3.24

Step-by-step explanation:

0.87 x 7 = 6.09

9.33 - 6.09 = 3.24

Answer:

3.456 × 1011

please choose me brainliest

Answer:

a rectangle would provide the largest area for the pigs

Answer:

420m

Step-by-step explanation:

250m = 5cm

50m = 1cm

? = 8.4cm

50 x 8.4=

420m = 8.4cm

Step-by-step explanation:

firstly we need to find the scale factor

firstly we know that 250m=25000cm

25000/5=5000

so 1:5000 is scale factor.

Now let us find the distance between Sam's school and the library

if they are 8.4 cm apart on map it means that in actual distance they are

(8.4)*5000=42000 cm in reality

Answer:

D.

Step-by-step explanation:

(m^2- 4n)(m^4+4m^2n+16n^2)

Option D is our correct answer.

i.e (m² - 4n) ([tex]m^{4}[/tex] + 4nm + 16n²).

Given,

[tex]m^{6}[/tex] - 64n³

We need to find the factored form of this.

And select the correct options.

A. (m2 + 4n)(m4 − 4m2n + 16n2)

B. (m − 4n2)(m2 + 4mn2 + 16n4)

C. (m + 4n2)(m2 − 4mn2 + 16n4)

D. (m2 − 4n)(m4 + 4m2n + 16n2)

It is given as:

( a - b ) ( a² + ab + b² )

Find the factored form [tex]m^{6}[/tex] - 64n³

We can write this as,

[tex](m^{2})^3[/tex] - 4³n³

(m²)³ - (4n)³

This is in the form of (a³ - b³).

Applying this formula.

Now,

(m² - 4n) ((m²)² + 4nm + (4n)²)

(m² - 4n) ([tex]m^{4}[/tex] + 4nm + 16n²)

Thus Option D is our correct answer.

i.e (m² - 4n) ([tex]m^{4}[/tex] + 4nm + 16n²).

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Answer:

b

Step-by-step explanation:

Answer:

Step-by-step explanation:

7x + 9 + 5x + 3 = 180

7x + 5x = 180 - 3 - 9

12x = 168

x = 168 / 12

x = 14

Answer:

14

Step-by-step explanation:

By applying the vertical angle theorem to 5x + 3, using same-side exterior angle theorem, we can find that:

(7x + 9) + (5x + 3) = 180

Now to find x, we can just solve for x in the equation we found.

(7x + 9) + (5x + 3) = 180

Combine like terms.

12x + 12 = 180

Subtract 12 from both sides.

12x = 168

Divide both sides by 12.

x = 14

So the value of x would be 14.

I hope you find my answer and explanation to be helpful. Happy studying.

Answer:

x= 20.05 degree

180= 43.25+36.50+5x

180= 79.75+5x

5x=180-79.75

5x=100.25

x=20.25

ANGLE B= 100.25

Answer:

y + 4x

Step-by-step explanation:

For this problem, we will simply combine like terms using the distributive property and the commutative property.

First, let's use the commutative property:

2y + x + 3x - y

= 2y - y + x + 3x

Second, let's use the distributive property:

2y - y + x + 3x

= y ( 2 - 1 ) + x ( 1 + 3 )

= y ( 1 ) + x ( 4 )

= y + 4x

Hence, the simplification of 2y + x + 3x - y is y + 4x.

Cheers.

Answer:

78°

Step-by-step explanation:

Since, angles A and B are complementary.

[tex]\therefore m\angle A + m\angle B = 90\degree \\

\therefore (3x+9)\degree + (x - 11)\degree = 90\degree \\

\therefore (3x +x +9-11)\degree = 90\degree \\

\therefore (4x - 2)\degree = 90\degree \\

\therefore 4x - 2 = 90\\

4x = 90+2\\

4x = 92\\ \\ x = \frac{92}{4} \\ \\ x = 23 \\ \\ \because m\angle A = (3x+9)\degree \\ \therefore \: m\angle A = (3 \times 23+9)\degree \\ \therefore \: m\angle A = (69+9)\degree \\ \huge \red{ \boxed{ \therefore \: m\angle A = 78\degree }}[/tex]

Answer:I may not be right but i think it D Im sorry if im wrong

Answer:

3.75

Step-by-step explanation:

Answer:

$3.75

Step-by-step explanation:

All you are going to do is multiply .05 or 5% by 75.

.05 * 75 = 3.75

(So now you are going to add 3.75 to $75 because the tax is 3.75)

75 + 3.75 = $78.75

(So you would pay $3.75 in tax)

Hope this helped!!

The answer is 200 because when you divide 110 from 55% you get 200.

Of the students in the marching band, 55% plan to go to the school dance, so there are 200 students in the marching band.

A certain portion or amount in every hundred is referred to as a percentage. The fraction is denoted by the sign "%," and its denominator is 100.

The Latin word "per centum," which means "by the hundred," is where the word "percentage" originally came from. With 100 as the denominator, percentages are fractions. To put it another way, it's the relationship between a component and a whole in which the value of the whole is always assumed to be 100.

From the given values in the question,

Assume that total number of students in marching band is x.

55% of x = 110 or,

(55/100) × x = 110

x = (110 × 100) / 55

x = 200.

Hence, it concludes that there are total 200 students are in the marching band.

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Answer:

20(9-n)

Step-by-step explanation:

Answer:

20(9-n)

Step-by-step explanation: I did I’d on a piece of paper and got that for my answer hope this helped