Which algebraic expression models the given word phrase 10 times the sum of a and b?

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.

Answer:

5,378,000,000

Step-by-step explanation:

5.378E9

5.378 x 10^(9)

5,378,000,000

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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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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The equation 7x-4=-2x+1+9x-5 has infinitely many solutions

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

The given equation is 7x-4=-2x+1+9x-5

We have to  take the variable terms on one side and constant on other side

In the given equation x is the variable and plus comma minus are all operators.

We need to solve for x.

7x+2x-9x=1-5+4

9x-9x=0

0=0

So the equation has infinitely many solutions

Hence, the equation 7x-4=-2x+1+9x-5 has infinitely many solutions

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The value of y in the equation is -2.5.

To determine the value of y in the equation -5y-9=-(y-1), we can start by distributing the negative sign to both terms within the parentheses. This gives us -5y-9=-y+1. Next, we can combine like terms by adding y to both sides of the equation. This simplifies the equation to -4y-9=1. To isolate y, we can subtract 9 from both sides of the equation, resulting in -4y=10. Finally, we divide both sides of the equation by -4 to find the value of y, which is -2.5.

Answer:

the answer is 28 A

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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Answer:

c

Step-by-step explanation: