Suppose a system of equations has fewer equations than variables and you have found a solution to this system of equations. is it possible that your solution is the only one? explain.

Answer:

5,378,000,000

Step-by-step explanation:

5.378E9

5.378 x 10^(9)

5,378,000,000

Answer:

c

Step-by-step explanation:

In the regression model, y = β₀ + β₁ x + ε,  β₁  represents the slope of the regression line.

A regression model offers a function that explains the association between one or more independent variables and a response, dependent, or target variable. A linear regression model, for instance, may be used to explain the link between height and weight.

The standard equation of regression model is y = a + bx

The given regression model,

y = β₀ + β₁ x + ε

The coefficient of the x in the regression model shows the slope of the regression line.

Hence, β₁  represents the slope of the regression line.

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The components of the vector in rectangular form given magnitude and angle can be found by using the following formulas: [tex]x = \|\vec r\|\cdot \cos \theta[/tex], [tex]y = \|\vec r\| \cdot \sin \theta[/tex].

Let be a vector in rectangular form, that is, a vector of the form (x, y). The magnitude can be found by applying the square root of the dot product of the vector or the Pythagorean theorem and the direction is determined by applying inverse trigonometric functions:

[tex]\|\vec r\| = \sqrt{(x,y)\,\bullet\,(x,y)}[/tex]     (1)

[tex]\|\vec r \| = \sqrt{x^{2}+y^{2}}[/tex]     (2)

θ = tan⁻¹ (y/x)     (3)

And the components of the vector can be found by applying the following formulas:

[tex]x = \|\vec r\|\cdot \cos \theta[/tex]     (4)

[tex]y = \|\vec r\| \cdot \sin \theta[/tex]     (5)

The components of the vector in rectangular form given magnitude and angle can be found by using the following formulas: [tex]x = \|\vec r\|\cdot \cos \theta[/tex], [tex]y = \|\vec r\| \cdot \sin \theta[/tex].

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You can find the components of a vector given its magnitude and angle by using the cosine function to find the horizontal component, and the sine function to find the vertical component.

To find the components of a vector given its magnitude and angle, you will use basic trigonometric ratio principles. These principles typically involve the use of sine (sin) and cosine (cos) functions.

First, consider a vector V with magnitude (or length) denoted by |V| and an angle θ from the positive x-axis. The components of the vector can be resolved into horizontal (x-direction) and vertical (y-direction) components.

The x-component (Vx) of the vector can be found using the equation:
Vx = |V| cos(θ).
Similarly, the y-component (Vy) of the vector can be found using the equation:
Vy = |V| sin(θ).

These equations are derived from the definitions of the sine and cosine functions in a right triangle, which is formed by the vector V and its components.

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Time taken to complete the project if two people worked together is required.

It would taken around 3.4 hours to complete the project if both the people worked together

Time taken to complete the work by first person is 6 hours

Time taken to complete the work by second person is 8 hours

The work equation will be be

[tex]\dfrac{1}{6}+\dfrac{1}{8}=\dfrac{1}{x}\\\Rightarrow \dfrac{4+3}{24}=\dfrac{1}{x}\\\Rightarrow x=\dfrac{24}{7}\approx 3.4\ \text{hours}[/tex]

So, it would taken around 3.4 hours to complete the project if both the people worked together.

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Answer:

the answer is 28 A

Step-by-step explanation:

Answer:

32 units.

Step-by-step explanation:  

We have been given a graph of a line segment and we are asked to find the length of line segment TW.

Upon looking at our graph we can see that point U divides segment TW in two equal parts (TU and UW), which means that length of TW will be two times the length of TU or UW.    

We have been given the length of TU is 16 units. To find the length of segment TW we will multiply 16 by 2.  

[tex]\text{Length of TW}=2\times 16=32[/tex]

Therefore, the length of line segment TW will be 32 units.

Answer:

Option A is the answer.

Step-by-step explanation:

Table is given as

Year                    2010           2011            2012          2013    

Spring league      68               79              90              101  

Fall league           145             148             151              154

Now as per given table we will analyze each option given

A). Difference in spring league participation increasing every year = 79-68 = 11

Difference in Fall league increasing every year = 148-145 = 3

Therefore option A is true because [tex]\frac{11}{3}>3[/tex] Spring league is increasing more than twice as fast as fall league.

B). This option is not true because participation in the spring league is increasing nearly 4 times of Fall league.

C) False. Spring league participation is more than fall league.

D) False. Same as option C because spring league participation is more than fall league.

Answer:

5 or 10

Step-by-step explanation:

counting by 2's    - 70, 72, 74, 76, 78, 80, 82      82 is here, Incorrect

counting by 5's    -70, 75, 80, 85, 90                Never said 82, Correct

counting by 10's  - 70, 80, 90-                           Never said 82, Correct

Answer:

The correct option is 4.

Step-by-step explanation:

From the given figure it is noticed that the triangle CDG and triangle FCE have a common vertex C. So both triangle are sharing same angle at vertex C.

In triangle CDG and triangle FCE

[tex]\angle GCD\cong \angle FCE[/tex]

If the length of two adjacent sides increases, then the inclined angle remains the same.

If the side CD increased to E and side CF increased to G, then

[tex]\angle GCE\cong \angle ECG[/tex]

Therefore option 4 is correct.

The additional piece of information is needed to determine that ABDC is a parallelogram is,

⇒ AB ≅ CD

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

In quadrilateral ABDC,

⇒ AB ∥ CD.

Now,

We know that;

When opposite side of a quadrilateral are parallel and equal to each other, then the quadrilateral are called a parallelogram.

Here, In quadrilateral ABDC,

⇒ AB ∥ CD.

Hence, The additional piece of information is needed to determine that ABDC is a parallelogram is,

⇒ AB ≅ CD

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