What is the coefficient of x² in the polynomial x³ 4x² 7x 2?

The dimensions of the marble is thus 10∛18 cm when the volume is 18000 cm³.

An object's capacity is the amount of material it can hold inside, while an object's volume is the amount of space it takes up. Here, the cubic unit is used to measure either of the two.

Cubic units are used to measure volume. The quantity of cubes needed to completely fill any given figure, such as blocks in a box, is its volume.

As there is no  definite shape is given we can assume that the shape is cube.

Volume of cube = a³

given the volume 18000cm³

dimensions of the marble,

a × a × a = 18000

a³ = 18000

a = ∛18000

a = 10∛18

a = 26.21

Hence, the dimensions of the marble is thus 10∛18 cm when the volume is 18000 cm³.

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Step-by-step explanation:

Two interior opposite angles of a triangle are equal to the exterior angel

[tex]60 + 60 = 2x - 80 \\ 120 = 2x - 80 \\ 2x = 120 + 80 \\ 2x = 200 \\ x = \frac{200}{2} \\ x = 100[/tex]

The equation x² - 4x + 3√2 = 0 has no real roots.

The roots of a quadratic equation are the values of variables satisfying the given quadratic equation.

There are three types of roots in quadratic equations, they are:

How many roots f(x) has can be seen from the discriminant's value : -

If b2 - 4ac > 0, the quadratic function has two unique real roots.

If b2 - 4ac = 0, then the quadratic function has one repeating real root.

If b2 - 4ac < 0, then the quadratic function has non-real roots.

Discriminant ; D = b² - 4ac

According to the given question, we have to find the nature of the roots of the equation, so finding the nature of the roots of all the equations separately

1.  x² - 4x + 3√2 = 0

Here, a = 1, b = -4 and c = 3√2

∵ D = b² - 4ac

∴ D = (-4)² - 4(1)(3√2)

⇒ D = 16 - 12√2

⇒ D = 16 - 12(1.414) = 16 - 16.968

∴ D = -0.968

⇒ D < 0

Consequently, there are no real roots in the equation.

2. x² + 4x - 3√2 = 0

Here, a = 1, b = 4 and c = -3√2

∵ D = b² - 4ac

∴ D = (4)² - 4(1)(-3√2)

⇒ D =  16 + 12√2 > 0

⇒ D > 0

As a result, the equation has two unique real roots.

3. x² + 5x + 3√2 = 0

Here, a = 1, b = 5 and c = 3√2

∵ D = b² - 4ac

∴ D = (5)² - 4(1)(3√2)

⇒ D = 25 - 12√2 = 8.029

⇒ D > 0

As a result, the equation has two unique real roots.

4. 3x² + 4√3x + 4 = 0

Here, a = 3, b = 4√3 and c = 4

∵ D = b² - 4ac

∴ D = (4√3)² - 4(3)(4)

⇒ D = 48 - 48 = 0

⇒ D = 0

As a result, the equation has two roots that are equal.

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The given sequence is 13, 19, 25, ...

What comprises an arithmetic series?

An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6. An arithmetic progression is another name for an arithmetic sequence.

This sequence appears to be increasing by 6 each time, so it is an arithmetic sequence. The common difference is 6. The nth term of an arithmetic sequence is given by the formula:

an = a1 + (n-1)d

where a1 is the first term, d is the common difference and n is the position of the term in the sequence.

We can use this formula to find the 48th term of the sequence:

a48 = a1 + (48-1)d

a48 = 13 + (48-1)6

a48 = 13 + 47*6

a48 = 13 + 282

a48 = 295

So, the 48th term of the sequence is 295.

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The measures of the three angles in a triangle is 84°, 30° and 66° respectively.

α + β + γ = 180° . From this, you can calculate the angles: ax, bx, and cx, as well as the unknown x. We translate these ideas into a detailed procedure for using ratios to locate missing angles in triangles in the following section.

The ratios are:

∠A = 14, ∠B = 5, ∠C = 11

Total ratio = 14 + 5 + 11= 30

The total angle in a triangle = 180°

So,

∠A= 14 / 30 × 180°= 0.46× 180°= 84°

∠B= 5/30 × 180°= 0.16 × 180°=30°

∠C= 11/30 × 180°= 0.366× 180°= 66°

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The percentage by which Ezra should multiply the dimension of the stage so that the dimensions of the image are 1/2 the size of the original blueprint is of:

50%.

The perimeter of the updated blueprint will be 50% of the perimeter of the original blueprint.

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

For this problem, we want for the dimensions of the updated stage to be half the dimensions of the original stage, hence the scale factor of the dilation is given as follows:

k = 1/2.

The percentage equivalent to a fraction of 1/2 is of 50%, and the perimeter of the updated stage will be 1/2 the perimeter of the original stage, as both the perimeter and the side lengths have the same unit.

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The equation and diameter CD of the parabola are x=1/10 y^2and 2√110

In this question we have four case of parabolas with vertical axes of reference, whose standard formula is:

a(x – h)2 + k

Where:(h, k) - The vertex of the parabola.

a - Least distance between the vertex and the focus of the parabola.

Please notice that p < 0 when the directrix is above the focus, otherwise p < 0. The vertex is the midpoint of line segment between the directrix and the focus.

Given;

Vertex is at origins (0,0) and latus rectum = 10 and the graph open right so a is positive and the equation is:

x=a (y-k)^2+h.

To write the equation we need to find a using the latus rectum equation.

We substitute the values.Then inverse place of a with 10

Latus rectum=|1/a|                

10=|1/a|                              

a=1/10

The equation:

x=a (y-k)^2+h                      

x=1/10(y-0)^2+0

x=1/10 y^2

-Assume the distance between C and the center is EC. If E is (11,0) and C is (11, y).

-EC=y

-The equation of the parabola is x=1/10 y^2

Now, Substitute the value of C coordinate, which

x=1/10 y^2                          

Substitute the value of C coordinate, which is (11, y).

11×10=1/(10×10) y^2    

√(y^2 )=√110                

y=EC=√110

Because the distance of EC = ED

CD=EC×2                                  

CD=√110×2

CD=2√110

Therefore, the equation of parabola and CD will be x=1/10 y^2 and 2√110

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Residual is the difference between the expected and actual y values, so r I = y I y i. A negative residual indicates that the anticipated value is excessively high, whereas a positive residual indicates that the projected value was excessively low. The goal of a regression line is to reduce the total amount of residuals.

What is Mcq, or salvage value?

When an item reaches the end of its useful life, its salvage value—or potential market value—is estimated. It can also be described as the asset's book value after depreciation has been taken into account.

What does the depreciation formula's residual value mean?

The asset's final worth is its residual value. To obtain the entire amount, it is therefore deducted from the starting value. Consequently, we are given the depreciation figure. This sum is divided by the usable years of the asset using the straight-line depreciation technique.

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The combination of two rays with the same terminal is called an angle. The vertex of the angle is the common terminal of the rays, which are referred to as the sides of the angle.

A ray is a segment of a line with one endpoint and an endlessly extending end. Two rays can be linked at their starting points to create an angle, and their other ends can stretch indefinitely.

According to the question,

the proportion of an angle's measurement to the width of its sides.

Therefore, an angle's measure is constant regardless of how far it is from its vertex.

Due to the fact that adjacent angles are two angles with a shared vertex, and side, but not interior points.

Therefore,

The combination of two rays with the same terminal is called an angle.

The vertex of the angle is the common terminal of the rays, which are referred to as the sides of the angle.

Hence the measure of an angle is the same at all distances from its vertex.

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Answer:

Step-by-step explanation:

Answer:If you make ₱ 58,000 you will be taxed ₱ 4,711. That means that your net pay will be ₱ 53,289 per year, or ₱ 4,441 per month.

Infinite series, the total of an infinite number of numbers connected in a specific method and listed in a specific order.

We get,

a)  [tex]$\sum_{n=0}^{\infty}$[/tex]

Infinity

b)  [tex]$\sum_{n=1}^{\infty}\left(\frac{4}{2^n}\right)$[/tex]

[tex]\sum_{n=1}^{\infty} \frac{4}{2^n}[/tex]

[tex]& =4 \cdot \sum_{n=1}^{\infty} \frac{1}{2^n} \\[/tex]

[tex]& \sum_{n=k}^{\infty}\left(a_n\right)=\sum_{n=0}^{\infty}\left(a_n\right)-a_0-a_1- \\[/tex]

[tex]& =4\left(\sum_{n=0}^{\infty} \frac{1}{2^n}-\frac{1}{2^0}\right)[/tex]

[tex]& \sum_{n=0}^{\infty} \frac{1}{2^n}=2 \\[/tex]

[tex]& =4\left(2-\frac{1}{2^0}\right)[/tex]

Then we get,

=4

c) [tex]$\sum_{n=1}^{\infty}\left(\frac{7}{10^n}\right)$[/tex]

[tex]$\sum_{n=1}^{\infty} \frac{7}{10^n}[/tex]

[tex]& =7 \cdot \sum_{n=1}^{\infty} \frac{1}{10^n} \\[/tex]

[tex]& \sum_{n=k}^{\infty}\left(a_n\right)=\sum_{n=0}^{\infty}\left(a_n\right)-a_0-a_1- \\[/tex]

[tex]& =7\left(\sum_{n=0}^{\infty} \frac{1}{10^n}-\frac{1}{10^0}\right)[/tex]

[tex]& \sum_{n=0}^{\infty} \frac{1}{10^n}=\frac{10}{9} \\[/tex]

[tex]& =7\left(\frac{10}{9}-\frac{1}{10^0}\right)[/tex]

Simplify

[tex]$7\left(\frac{10}{9}-\frac{1}{10^0}\right): \quad \frac{7}{9}$[/tex]

= 7/9

Therefore,

a) infinity, b) =4, and c) = 7/9

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It is not possible to construct a triangle with lengths of its sides 7cm, 10cm and 20cm because the sum of two sides of a triangle is greater than the third side.

Now, According to the question:

We know that:

What is triangle inequality rule?

The triangle inequality theorem states that for any given triangle, the sum of the two sides is always greater than the  third side. The Triangle is a polygon with three line segments as its boundaries.

Suppose A, B and C are three sides of a triangle, then by using triangle inequality rule, A + B > C then A, B and C make a triangle.

We have the sides:

7, 10 and 20

7 + 10 > 20

It is not possible to construct a triangle with lengths of its sides 7cm, 10cm and 20cm because the sum of two sides of a triangle is greater than the third side.

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Answer: 50 ft

Step-by-step Explanation:

First, subtract the given length from the perimeter:

*268 - (84 x 2) = 100

Then divide this by 2:

100 / 2 = 50

*We multiply the 84 by 2 since the court is assumed to have 4 sides meaning there are two sides with lengths and two sides with widths.

Method of factorization in method of substitution is a technique used to solve systems of linear equations. In this method, one of the equations is multiplied by a factor to make the coefficient of one of the variables the same. This allows the equations to be combined and solved for the remaining variables.

Method of factorization in method of substitution is a useful technique for solving systems of linear equations. It allows one to isolate a single variable and make use of substitution to solve the system. The first step is to multiply one of the equations by a factor to make the coefficient of one of the variables the same in both equations. This allows the equations to be combined and solved for the remaining variables. Once the values of the variables have been found, they can be substituted into the other equation to find the solution of the system. This technique is beneficial because it allows one to avoid tedious calculations that are often required when solving linear equations.

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Answer:

y = 0.25c + 8

Step-by-step explanation:

Let's y represent the total cost

We know

25% = 0.25

So, we will write this in the slope-intercept form y= mx +b

So, we have m = 0.25, and b = 8, so our equation is

y = 0.25c + 8

The equation is given by A = ∛ ( 375/345 ) and A = ( ∛375 ) / ( ∛ 345 )

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

A = (375/345) ^ 1/3   be equation (1)

On simplifying the equation , we get

The number raised to the power ( 1/3 ) means it is the cube root of the number ,

So , A = ∛ ( 375/345 )

Now , taking the cube root on both the numerator and denominator ,

A = ( ∛375 ) / ( ∛ 345 )

Hence , the value of A is  ( ∛375 ) / ( ∛ 345 )

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Answer:

x = -175

Step-by-step explanation:

Given:

⇒ [tex]-\frac{x}{7}-8=17[/tex]

Solution:

Work:

[tex]-\frac{x}{7}-8=17[/tex]

[tex]-\frac{x}{7}-8+8=17+8[/tex]    ⇒ Add 8 to both sides

[tex]-\frac{x}{7}=25[/tex]

[tex]7\left(-\frac{x}{7}\right)=25\cdot \:7[/tex] ⇒ Multiply both sides by 7

-x = 175

[tex]\frac{-x}{-1}=\frac{175}{-1}[/tex] ⇒ Divide both sides by -1

x = -175

Check:

Since, x = -175. We can substitute into the equation to check.

[tex]-\frac{-175}{7}-8=17[/tex]

[tex]-\frac{-175}{7}=25[/tex]

[tex]25-8=17[/tex] ⇒ Statement = True (25 minus 8 is 17.

Hence, x = -175

Lenvy~

The value of x when y = 1000 is 8.59.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

y = 1.7952 x [tex]2.0657^x[/tex]

Substitute y = 1000

1000 = 1.7952 x [tex]2.0657^x[/tex]

10³ = 1.7952 x [tex]2.0657^x[/tex]

Taking logs on both sides.

log 10³ = log (1.7952 x [tex]2.0657^x[/tex])

3 log 10 = log 1.7952 + x log 2.0657

3 x 1 = 0.25 + 0.32x

3 = 0.25 + 0.32x

0.32x = 3 - 0.25

x = 2.75/0.32

x = 8.59

Thus,

The value of x is 8.59.

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The solution of the given equation 3x²+ 5x +2= 0 is given by :

option c. x = -2 / 3 or x = -1.

As given in the question,

Given equation is equal to :

3x²+ 5x +2= 0

Solve the given equation by splitting the middle term of the quadratic equation we have,

3x²+ 5x +2= 0

⇒ 3x²+ 3x + 2x + 2 = 0

⇒ 3x ( x + 1 ) + 2 ( x + 1 ) = 0

⇒ ( 3x + 2 ) ( x + 1 ) = 0

⇒ ( 3x + 2 ) = 0 or ( x + 1 ) = 0

⇒ x = -2 / 3 or x = -1

From the given options :

option c. x = -2 / 3 or x = -1 is the solution.

Therefore, the solution of the given equation 3x²+ 5x +2= 0 is equal to :

option c. x = -2 / 3 or x = -1 .

The above question is incomplete, the complete question is:

Which of the following is a solution of the equation 3x²+ 5x +2= 0?

a. x = 2/3 or x = 1

b. x = -2/3 or x = 1

c. x = -2/3 or x = -1

d. x = 2/3 or x = -1

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Answer:

Step-by-step explanation:

Answer: 256

Step-by-step explanation:

Remove any grouping symbol such as brackets and parentheses by multiplying factors.Use the exponent rule to remove grouping if the terms are containing exponents.Combine the like terms by addition or subtraction.Combine the constants.

The interval over which f(x) = x² - x - 1 has an average rate of change of zero is (1/2, 1/2) as it is the only point at which the average rate of change is zero.

An average rate of change of zero means that the function is not increasing or decreasing over the interval in question. To find the interval over which f(x) has an average rate of change of zero, we need to find the critical points of the function. A critical point is a point at which the function's derivative is equal to zero or is undefined.

The derivative of f(x) = x² - x - 1 is:

f'(x) = 2x - 1

Setting f'(x) = 0, we get:

2x - 1 = 0

Solving for x, we get:

x = 1/2

Since this is the only critical point of the function, it is the point where the function has an average rate of change of zero. To determine the interval, we need to check the sign of the function's derivative on either side of the critical point.

f''(x) = 2 > 0

So x = 1/2 is the minima of the function

f'(x) = 2(1/2) - 1 = 0, at x = 1/2

so f'(x) > 0 for x < 1/2 and f'(x) < 0 for x > 1/2

Therefore the interval over which f(x) has an average rate of change of zero is (1/2, 1/2) or {1/2}.

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Answer:

For the first one, the answer would be:

2/3 * 3/8 = 6/24 because,  all you have to do is multiply straight across.

2 * 3 = 6 and 3 * 8 = 24

6/24 can be simplified to 1/4 because 6 with go into the denominator 4 times, so the simplified fraction will be 1/4.

(Im not so sure what to do about the second one, so I would need to see what the options look like)

For the third:

The answer would be 3/3, because:

2 * 3 = 6

5 * 3 = 15

And the result fraction is 6/15, which matches what the image shows!

Step-by-step explanation:

Hope it helps! =D

Answer: 343

Step-by-step explanation:

7 to the 3rd power

⇒7³

⇒7 × 7 × 7

⇒343 ... answer

hope that helps...

Answer:

A 30-60-90 triangle is a special type of right triangle where the angles are 30 degrees, 60 degrees, and 90 degrees. The side opposite the 30 degree angle is called the "short leg", the side opposite the 60 degree angle is called the "medium leg", and the side opposite the 90 degree angle is called the "long leg".

The ratios of the sides in a 30-60-90 triangle are always in the proportion of 1 : √3 : 2 . To find the legs of a 30-60-90 triangle when given the long leg, you can use these ratios.

If the long leg is "x", then the short leg is x/2 and the medium leg is x*√3/2.

For example, if the long leg is 8 cm, you can use these ratios to find the short leg and medium leg:

The short leg is 8 cm / 2 = 4 cm

The medium leg is 8 cm * √3 / 2 = 4 * √3 cm = 4 * 1.732 cm = 6.928 cm (approx)

So, in this example, the short leg is 4cm and the medium leg is 6.928cm (approx).

It's always a good idea to draw a diagram and label the sides to help you visualize the problem and check your answer.

Step-by-step explanation:

Answer: B, $16.26 per 6 yards

Step-by-step explanation:

$11.04/ 4 yd is $2.76 a yd

$16.26/ 6 yd is $2.71 a yd

$19.11/ 7 yd is $2.73 a yd

$13.85/ 5 yd is $2.77 a yd

Answer:

x = 1, x = 5

Step-by-step explanation:

|x−7|=|2x−8|  ==> there are 2 ways to simplify this equation:

1. x - 7 = 2x - 8

2. -(x - 7) = 2x - 8

Let's first solve equation 1:

x - 7 = 2x - 8

-7 = x - 8  ==> subtract x on both sides

x - 8 + 8 = -7 + 8  ==> add 8 on both sides

x = 1  ==> simplify

Now let's solve equation 2:

-(x - 7) = 2x - 8

-x - (-7) = 2x - 8  ==> distribute the negative sign to x and -7

-x + 7 = 2x - 8  ==> subtracting a negative number is equivalent to adding a

                               positive number

7 = 3x - 8  ==> add x on both sides

15 = 3x ==> add 8 on both sides

x = 5 ==> divide 3 on both sides

Hence, the answers are x = 1 and x = 5.

Answer: -2, -7

Step-by-step explanation:

Mike's car will be worth £4116 at the start of 2017 as the car decreases in value by 30% every year

At the start of 2014, Mike's car is worth £12000,

we shall calculate the decreased worth of the same car to the start of 2017 as follows:

At the end of 2014, 30% of £12000 is calculated as;

£12000 × 30/100 = £3600

At the start of 2015, the car will be worth

£12000 - £3600 = £8400

At the end of 2015, 30% of £8400 is calculated as;

£8400 × 30/100 = £25200

At the start of 2016, the car will be worth

£8400 - £2520 = £5880

At the end of 2016, 30% of £5880 is calculated as;

£5880 × 30/100 = £1764

At the start of 2017, the car will be worth

£5880 - £1764 = £4116

Therefore, Mike's car will decrease in value to worth £4116 at the start of 2017.

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Steps To Convert From Base 10 to Base 2

The number system is a way of representing the quantity of a physical item.

For example, the number system that is widely used by humans is the decimal number system, which is a number system that uses 10 kinds of symbols. In everyday life, the number system that is widely used by humans is the decimal number system, which is a number system that uses 10 kinds of symbols. if it is associated with Computer Logic it is represented by two-state elements, namely off and on which is the concept used in the binary number system which only uses 2 kinds of values to represent value quantities.

In addition, the Number System uses a certain number of bases or bases (base / radix). There are 4 types of number systems that have to do with computers, which include:

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