Factor ab + bc+ b² + ac.

A. (a + b)(b + c)

B. (a + c)(b + c)

C. b(a + b)(b + c)​

Answer: The fundamental theorem of algebra states that the equation 2x^2+8x+14=0 has at least one complex root, which means that there are numbers that can be plugged into x that make the equation equal to zero. ✅

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Step-by-step explanation:

The fundamental theorem of algebra states that for any non-constant polynomial equation with real or complex coefficients, there is at least one complex root (or solution).

In the case of the equation 2x^2+8x+14=0, the theorem guarantees that this equation has at least one complex root, which means that there are numbers that can be plugged into x that will make the equation equal to zero.

So, the fundamental theorem of algebra guarantees that for the equation 2x^2+8x+14=0, there exists at least one complex solution that makes the equation true. In this case, the solutions are x = -1+i and x = -1-i ✅

Answer:

the awsner is 20 I believe so don't trust me or trust me i don't care

Step-by-step explanation:

I don't know

Answer:

9/64

Step-by-step explanation:

1 3/4 x (15/4-3 1/2) divided by 1 1/3

2   3/4x1/4 divided by 4/3

3    3/16 divided by 4/3

4     3/16x3/4=9/64

The graph solution is in the attached images, for all the systems of inequalities.

What is the graph of a function?

The graph of a function is a visual representation of the relationship between the input values (x-coordinates) and the output values (y-coordinates) of the function. In other words, it is a visual representation of the function's rule.

The graph of a function can take many different forms, depending on the function's rule. Linear functions, for example, will produce a straight line on the graph.

we have the following inequalities:

i)

y > 3x - 17,

y ≤ -4x +11.

ii)

4x - 4y > -40,

-5x + 5y < 10.

iii)

x + 3y ≥ 31,

4x - 2y ≥ -2,.

iv)

5x + y < 3,

5x + y > 37

Hence, the graph solution is in the attached images, for all the systems of inequalities.

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So, on solving the provided question, we can say that coefficient of the variable in the expression 2 − 5x − 4 8 is 5

A coefficient in mathematics is a polynomial, a series, or the multiplicative coefficient of a particular term in an expression. Typically numeric, however any expression is permitted. The term "parameter" can also refer to the coefficients themselves if they are variables. A number times a variable equals a coefficient. Coefficient examples include:  The coefficient is 14 in phrase 14c 14c 14c. The coefficient is 1 for word g. multiplies the variable by this amount. example  Given that "z" is a variable and that 6z is the definition of the term, the coefficient is 6. One is the coefficient of the square of x.

here,

coefficient of the variable in the expression 2 − 5x − 4 8 is 5

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Answer:

y = 7

Step-by-step explanation:

The equation of a horizontal line is worth memorizing. It is:

y = anumber

(and just in case for future reference the equation of a vertical line is

x= anumber)

Well, you are given one point (3,7).That is in the form (x,y). So x is 3 and y is 7.

y is 7

y = 7

(if it helps...horizontal lines have 0 slope. So m = 0. The equation in point-intercept form is

y = mx + b

y = 0x + b

y = b this is the y= anumber) originally mentioned here)

On solving the provided question we can say that the value of trigonometry value is - [tex](sin^2x - cos^2x )( 1- sin^2xcos^x)\\[/tex]

The area of mathematics known as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, around the third century BC. from the use of geometry in astronomical study. The area of mathematics known as exact methods deals with specific trigonometric functions and how they might be used in calculations. There are six popular trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics of triangles, particularly right triangles, is called trigonometry. The study of geometry, however, is the characteristics of all geometric figures.

[tex]sin^6 x - cos^6x\\(sin^3x)^2 - (cos^3x)^2\\(sin x - cosx)(sinx + cosx)(1 + sinx cosx)(1 - sinx cosx)\\(sin^2x - cos^2x )( 1- sin^2xcos^x)\\[/tex]

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The student's error is that 16 has to be prime factorized as (2)⁴ or 2 × 2 × 2 × 2.

Prime factorization is defined as the method of writing a number as the product of two or more prime numbers.

Prime numbers are numbers which has only two factors, 1 and the number itself.

Given number is 16.

We have to factorize 16 as a product of prime factors.

Student wrote it as,

16 = 2 × 8

The error here is that 8 is not a prime number. We have to again factorize 8 to get the required factored form.

8 = 2 × 4

4 = 2 × 2

So combining all these,

16 = 2 × 2 × 2 × 2

So 16 can be prime factorized as 16 = 2 × 2 × 2 × 2.

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The midpoint formula is a mathematical formula used to find the midpoint of a line segment, given the coordinates of the two endpoints of the segment. In class 11, it is defined as:

Midpoint = ( (x1 + x2)/2 , (y1 + y2)/2 )

Where (x1, y1) and (x2, y2) are the coordinates of the two endpoints of the line segment, and (x, y) are the coordinates of the midpoint of the segment.

For example, if the two endpoints of a line segment are (5,6) and (9,11)

Midpoint = ( (5 + 9)/2 , (6 + 11)/2 )

Midpoint = (7,8.5)

The midpoint of the line segment with endpoints (5,6) and (9,11) is (7,8.5)

It's worth noting that this formula can be adapted for three-dimensional points, where the midpoint formula would be

((x1 + x2)/2, (y1 + y2)/2, (z1 + z2)/2)

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Enlarging or contracting a figure's size is known as dilatation. In other words, a scale factor is used to either enlarge or diminish the image while maintaining similarity between the preimage and the image.

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Answer: 2 and 3

Step-by-step explanation:

Answer:

7.5

Step-by-step explanation:

10 + ( 7 × 1.5) = 20.5

6 + ( 7 × 13 ) = 13

20.5 - 13 = 7.5

Answer: x=1,y=3

Step-by-step explanation:

Given,

y - 1 =2x

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

Again,

We have,

y = 2x + 1

Now replacing the value of y from (i)

2x + 1= -x +

or, 2x + x= 3

or,3x= 3

So x=1

Now,

y=2x +1

or, y=2×1+1

so y=

Answer:

x=1, y=3. (1, 3).

Step-by-step explanation:

2y-2=4x

y=-x+4

----------

2y-2=4x implies 2(y-1)=2(2x), so y-1=2x.

(-x+4)-1=2x

-x+4-1=2x

-x+3=2x

3=2x-(-x)

3=2x+x

3=3x

x=3/3

x=1

y=-1+4=3

 Answer:

If two expressions are equal to each other, and you add the same value to both sides of the equation, the equation will remain equal. When you solve an equation, you find the value of the variable that makes the equation true. In order to solve the equation, you isolate the variable.

Step-by-step explanation:

The trend line equation to estimate the hiker's elevation after 150 minutes is 2033 feet.

Given that,

A trend line's equation for the hiker's elevation is y = 9.16x + 659.

We must determine,

The trend line equation is used to calculate the hiker's elevation after 150 minutes.

In response to the question,

A trend line's equation for the hiker's elevation is y = 9.16x + 659.

Where x is the number of minutes and y is the elevation of the hiker in feet.

Substitute the value of x = 150minute in the given equation to find the trend line to estimate the hiker's elevation after 150minutes.

Therefore,

y = 9.16x + 659

x = 150

y = 9.16(150) + 659

y = 1374 + 659

y = 2033

As a result, the trend line equation for estimating the hiker's elevation after 150 minutes is 2033 feet.

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Answer:

[tex]27)x {}^{3} + 3x {}^{2} - 10x - 24 \\ 28)x {}^{3} - 9 {}^{2} + 8x + 60[/tex]

Step-by-step explanation:

Greetings!!

[tex]27)(x - 3)(x + 2)(x + 4)[/tex]

Expand; (x-3)(x+2): x^2-x-6

Apply FOIL method: (a+b) (c+d) = ac+ad+bc+bd

[tex](x - 3)(x + 2) = x.x + x.2 - 3.x - 3.2[/tex]

simplify

[tex]x {}^{2} - x - 6[/tex]

[tex]x {}^{2} - x - 6.(x + 4)[/tex]

distribute parentheses

[tex] = x {}^{2} .x + x {}^{2} .4 - x.x - x.4 - 6.x - 6.4 \\ = x {}^{3} + 4x {}^{2} - x {}^{2} - 6x - 24[/tex]

simplify/ Add similar elements

[tex]x {}^{3} + 3x {}^{2} - 10x - 24[/tex]

Thus, use the same format for question number 28 and you will get the value

[tex]x {}^{3} - 9x {}^{2} + 8x + 60[/tex]

If you have any questions or there is sth unclear tag me on comment box

Hope it helps!!

The formula for a triangle is the area of a triangle = ½ × base × height. The formula for a square is the area of a square = side2.

This formula is used to calculate the area of any triangle when the base and height are known. For example, if the base of a triangle is 10 cm and the height is 5 cm, the area of the triangle is 25 cm2.

The formula for a square is the area of a square = side2. This formula is used to calculate the area of any square when the side length is known. For example, if the side of a square is 10 cm, the area of the square is 100 cm2. To calculate this, we can use the formula by squaring 10 (102 = 100).

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Answer:

Step-by-step explanation:

104 units

By replacing the values of the point in the quadratic equation, we can see that it is not a solution.

Here we have the quadratic equation:

y = 3x^2 + 5

And we want to see if the point 3x^2 + 5 is a solution of the quadratic equation.

To check that, we need to replace the values of the point in the equation and see if the equation is true.

We need to replace:

x = 5

y = 0

We will get:

0 = 3*5^2 + 5

0 = 3*25 + 5

0 = 75 + 5

0 = 80

This is a false equation, then (5,0) is not a solution.

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On solving the provided question, we can say that Volume of cuboid = 2x(3x+4)(3x-4)

Volume = [tex]18x^3 + 48x^2 + 32x[/tex]

A cuboid is a solid or three-dimensional form in geometry. A cuboid is a convex polyhedron having 8 vertices, 12 sides, and 6 rectangular faces. Another name for a cuboid is a cuboid. A cube is a cuboid with six square faces. Boxes include things like books and bricks. The following are the key variations between cubic and cubic: In contrast to a cube, which has rectangular faces, a cube has six equally sized square faces. Even though the cube and cuboid structures have a similar appearance, they differ in some ways in terms of side length, diagonal, and area.

here,

we have a cuboid

Volume of cuboid = 2x(3x+4)(3x-4)

Volume = [tex]18x^3 + 48x^2 + 32x[/tex]

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The solution of (15 feet, 51.5 feet) represents the perimeter of a shape with a longest side of 15 feet.

Equation is a mathematical statement that express the equality of two expression use in equal sign.

The equation for this perimeter can be written as y = 2.5x + 14, where y is the perimeter of the shape and x is the longest side of the shape.

Thus, when x is 15 feet, the perimeter of the shape is 51.5 feet, as represented by the solution (15 feet, 51.5 feet).

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positive number to the power negative 1 is a number that is always less than 1.

Explanation: a-m = 1/am. when calculate have the result when a positive number is raised to the power of -1, we always get a number that is less than one; for example, 2-1 = 1/2 < 1.

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The ratio of people who prefer streaming to the people surveyed is 25:50, or 1:2.

Ratio is a comparison of two or more numbers or quantities that indicates the relative size of the quantities. Ratios are expressed in the form of a fraction or decimal, and they are used in mathematics, statistics, and other sciences. Ratios can be used to compare the sizes of different objects or values, or to compare the relationships between different numbers. Ratios are often used to measure the efficiency of a process or the relationship between different variables.

This ratio indicates that half of the people surveyed prefer to stream movies, while the other half prefer to rent DVDs.

Of the 50 people surveyed, 5 had no preference, meaning that 45 out of the 50 people had a preference for either streaming or renting DVDs.

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Triangle ABC is dilated by a scale factor of 1/2, the line A”B” equals Line AB divided by two

An equation is an expression composed of variables and numbers linked together by mathematical operations.

Translation is the movement of a point up, down, left or right in the coordinate plane.

Dilation is the increase or decrease in the size of a figure.

Triangle A”B”C” is formed using the translation (x+2, y+0) and the dilation by a scale factor of 1/2 from the origin.

Since there is a dilation by a scale factor of 1/2, hence:

A"B" = AB * 1/2

A"B" = AB/2

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For the expression (x - 8)(x + 8), using the arithmetic operation the value for x is x = 8.

What is arithmetic operation?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

The given expression is - (x - 8)(x + 8)

Use the arithmetic operation of multiplication -

(x - 8)(x + 8)

x(x + 8) - 8(x + 8)

x² + 8x - 8x -64

Now, use the arithmetic operation of addition and subtraction -

x² + 8x - 8x -64

x² - 64

Now, collect the like terms on each side -

x² = 64

x = √64

Now, solve the radical form to get the value of x -

x = √64

x = 8

Therefore, the value of x is obtained as x = 8.

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Answer:

c.

Step-by-step explanation:

The number of shares that Ade and Ola possess will be 1500 and 2500, respectively.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Ade and Ola share a sum of 4000.00 in a ratio of 3:5.

Let 'x' and 'y' be the number of shares that Ade and Ola have, respectively. Then the equations are given as,

x / y = 3 / 5            ...1

x + y = 4000        ...2

From equations 1 and 2, then we have

(3/5)y + y = 4000

(8/5) y = 4000

y = 2500

Then the value of the variable 'x' is calculated as,

x + 2500 = 4000

x = 1500

The number of shares that Ade and Ola possess will be 1500 and 2500, respectively.

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AAA(Angle angle angle) Theorem can be used to prove given triangles as similar.

As we know we have to show all three angles equally.

so we have to show the similarities between T(DNM) and T(DFE) ....

(T Means Triangle.)

(A Means Angle)

As  D is a common vertex in both the triangles

by equations 1, 2, and 3 we can conclude that all three angles of T(DFE) =  T(DNM)

SO By the AAA rule, we can say that the two Triangles are similar.

Now we can say all the sides of T(DFE) will be in all propositions of T(DNM).

Like DN/DF=DM/DE=NM/FE

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