What is the number of terms in the expansion of 2x 3y 2 )( 2x 3y 2 2?

The basis for the eigenspace corresponding to lambda=5,1,4 are None,[tex]\left[\begin{array}{c}-1 \\\frac{1}{2} \\0\end{array}\right][/tex] and [tex]$\left[\begin{array}{l}2 \\ 1 \\ 1\end{array}\right]$[/tex]

[tex]$$A=\left[\begin{array}{ccc}5 & -12 & 10 \\0 & 7 & -3 \\0 & 6 & -2\end{array}\right]$$[/tex]

Eigenspace corresponding to lambda=5,1,4

The eigenspace E_lambda corresponding to the eigenvalue lambda is the null space of the matrix a [tex]\mathrm{A}-(\lambda) \mathrm{I}"[/tex]

for lambda=5

[tex]$$\mathrm{E}_5=\mathrm{N}(\mathrm{A}-5 \mathrm{I})$$[/tex]

Reducing the matrix A-5I by elementary row operations

[tex]$$\begin{aligned}A-5 I & =\left[\begin{array}{ccc}5-5 & -12 & 10 \\0 & 7-5 & -3 \\0 & 6 & -2-5\end{array}\right] \\& =\left[\begin{array}{ccc}0 & -12 & 10 \\0 & 2 & -3 \\0 & 6 & -7\end{array}\right] \\& \sim\left[\begin{array}{ccc}0 & -12 & 10 \\0 & 1 & -\frac{3}{2} \\0 & 6 & -7\end{array}\right] R_2 \rightarrow \frac{R_2}{2} \\& \sim\left[\begin{array}{ccc}1 & 0 & -8 \\0 & 1 & -\frac{3}{2} \\0 & 6 & -7\end{array}\right] R_1 \rightarrow R_1+2 R_2\end{aligned}$$[/tex]

[tex]\sim\left[\begin{array}{ccc}1 & 0 & -8 \\ 0 & 1 & -\frac{3}{2} \\ 0 & 0 & 2\end{array}\right] R_3 \rightarrow R_3-6 R_2$$\\\sim\left[\begin{array}{ccc}1 & 0 & -8 \\ 0 & 1 & -\frac{3}{2} \\ 0 & 0 & 1\end{array}\right] R_3 \rightarrow \frac{\mathrm{R}_3}{2}$$\\\sim\left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & 1 & -\frac{3}{2} \\ 0 & 0 & 1\end{array}\right] \mathrm{R}_1 \rightarrow \mathrm{R}_1+8 \mathrm{R}_3$[/tex]

[tex]$\sim\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right] R_2 \rightarrow R_2+\frac{2 R_3}{2}$[/tex]

The solutions x of A-5I=0 satisfy x_1=x_2=x_3=0 that is, the null space solves the matrix

[tex]$$\left[\begin{array}{lll}1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1\end{array}\right]\left[\begin{array}{l}x_1 \\x_2 \\x_3\end{array}\right]=\left[\begin{array}{l}0 \\0 \\0\end{array}\right]$$[/tex]

Hence The null space is [tex]\left[\begin{array}{l}0 \\ 0 \\ 0\end{array}\right] E_5[/tex] has no basis

[tex]$$\begin{aligned}& \text { case: } 2 \\& \text { for } \lambda=1 \\& \mathrm{E}_5=\mathrm{N}(\mathrm{A}-(1) \mathrm{I})\end{aligned}$$[/tex]

we reduce the matrix A-I by elementary row operations as follows.

[tex]$$\begin{aligned}A-1 & =\left[\begin{array}{ccc}5-1 & -12 & 10 \\0 & 7-1 & -3 \\0 & 6 & -2-1\end{array}\right] \\& =\left[\begin{array}{ccc}1 & -3 & \frac{5}{2} \\0 & 6 & -3 \\0 & 6 & -3\end{array}\right] R_1 \rightarrow \frac{R_1}{4} \\& \sim\left[\begin{array}{ccc}1 & -3 & \frac{5}{2} \\0 & 1 & -\frac{1}{2} \\0 & 6 & -3\end{array}\right] R_2 \rightarrow \frac{R_2}{6}\end{aligned}[/tex]

[tex]$$$\sim\left[\begin{array}{ccc}1 & 0 & 1 \\ 0 & 1 & -\frac{1}{2} \\ 0 & 6 & -3\end{array}\right] R_1 \rightarrow R_1+3 R_2$\\$\sim\left[\begin{array}{ccc}1 & 0 & 1 \\ 0 & 1 & -\frac{1}{2} \\ 0 & 0 & 0\end{array}\right] R_3 \rightarrow R_3-6 R_2$[/tex]

Thus, the solutions x of (A-I) X=0 satisfy

[tex]$\left[\begin{array}{ccc}1 & 0 & 1 \\ 0 & 1 & -\frac{1}{2} \\ 0 & 0 & 0\end{array}\right]\left[\begin{array}{l}x_1 \\ x_2 \\ x_3\end{array}\right]=\left[\begin{array}{l}0 \\ 0 \\ 0\end{array}\right]$[/tex]

x_3=t

[tex]$\Rightarrow \mathrm{x}_1=-\mathrm{t}, \mathrm{x}_2=\frac{\mathrm{t}}{2}$[/tex]

[tex]$\vec{x}=\left[\begin{array}{c}-t \\ \frac{t}{2} \\ t\end{array}\right]=\left[\begin{array}{c}-1 \\ \frac{1}{2} \\ 1\end{array}\right] t$[/tex]

The Basis for the nullspace A-I will be: [tex]$\left.\left(\begin{array}{c}-1 \\ \frac{1}{2} \\ 1\end{array}\right]\right)$[/tex]

case:3

lambda=4

[tex]$$\mathrm{E}_5=\mathrm{N}(\mathrm{A}-(4) \mathrm{I})$$[/tex]

we reduce the matrix A-4I by elementary row operations as follows.

[tex]$\begin{aligned} A-4 \mid & =\left[\begin{array}{ccc}5-4 & -12 & 10 \\ 0 & 7-4 & -3 \\ 0 & 6 & -2-4\end{array}\right] \\ & =\left[\begin{array}{ccc}1 & -12 & 10 \\ 0 & 3 & -3 \\ 0 & 6 & -6\end{array}\right] \\ & \sim\left[\begin{array}{ccc}1 & -12 & 10 \\ 0 & 1 & -1 \\ 0 & 6 & -6\end{array}\right] R_2 \rightarrow \frac{R_2}{3}\end{aligned}$[/tex]

[tex]$\begin{aligned} & \sim\left[\begin{array}{ccc}1 & 0 & -2 \\ 0 & 1 & -1 \\ 0 & 6 & -6\end{array}\right] \mathrm{R}_1 \rightarrow \mathrm{R}_1+12 \mathrm{R}_2 \\ & \sim\left[\begin{array}{ccc}1 & 0 & -2 \\ 0 & 1 & -1 \\ 0 & 0 & 0\end{array}\right] \mathrm{R}_3 \rightarrow \mathrm{R}_3-6 \mathrm{R}_2\end{aligned}$[/tex]

Thus, the solutions x of (A-4IX)=0 satisfy

[tex]$$\left[\begin{array}{ccc}1 & 0 & -2 \\0 & 1 & -1 \\0 & 0 & 0\end{array}\right]\left[\begin{array}{l}x_1 \\x_2 \\x_3\end{array}\right]=\left[\begin{array}{l}0 \\0 \\0\end{array}\right]$$[/tex]

x_3=t

[tex]$\Rightarrow \mathrm{x}_1=2 \mathrm{t}, \mathrm{x}_2=\mathrm{t}$[/tex]

[tex]$$\vec{x}=\left[\begin{array}{c}2 t \\t \\t\end{array}\right]=\left[\begin{array}{l}2 \\1 \\1\end{array}\right] t$$[/tex]

The Basis for the nullspace A-4 I will be [tex]\left(\left[\begin{array}{l}2 \\ 1 \\ 1\end{array}\right]\right)[/tex]

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27 2/10

   or

27 1/5

----------------------------------

Answer:

n = - 1 , n = 3

Step-by-step explanation:

n² - 2n - 3 = 0 ( add 3 to both sides )

n² - 2n = 3

to complete the square

add ( half the coefficient of the x- term)² to bpth sides

n² + 2(- 1)n + 1 = 3 + 1

(n - 1)² = 4 ( take square root of both sides )

n - 1 = ± [tex]\sqrt{4}[/tex] = ± 2 ( add 1 to both sides )

n = 1 ± 2

Then

n = 1 - 2 = - 1

n = 1 + 2 = 3

Answer:

7. .44

8. .009

Step-by-step explanation:

7. 44 ÷ 100 = .44

8. 9 ÷ 1000 = .009

The estimated perimeter of an ellipse if the major axis has a length of 15 ft and the minor axis has a length of 7.5 ft id found to be 37.3 feet .

Perimeter is calculated as

= 2*pi*r*r

=  2 *3.14 * sqrt (15/2² +7.5/2²)/2

= 6.28 x sqrt (56.25+14.0625/2 6.28) *sqrt (35.15625) 6.28 * 5.929270613

= 37.235 feat

An ellipse is the locus of all the points on a plane whose distances from two fixed points in the plane are always same. The fixed points, which are encompassed by the curve, are known as foci , singular of focus.

The constant ratio is the eccentricity of the ellipse and the fixed line is directrix. Eccentricity is an element of  ellipse which denotes elongation and is symbolized by the letter 'e'.

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The factor of expression 3x² 12xy is 3x². To find the factor, we need to divide 12xy by 3x². We start by dividing the coefficients, 12 divided by 3 is 4. Then we divide the x terms, x divided by x is 1. Finally, we divide the y terms, y divided by y is 1. Therefore, the factor of 3x² 12xy is 3x².

The factor of  expression 3x² 12xy is 3x². To find the factor, we need to divide 12xy by 3x². We start by dividing the coefficients, 12 divided by 3 is 4. Then we divide the x terms, x divided by x is 1. This means that the x part of the factor is 3x. Next, we divide the y terms, y divided by y is 1. This means that the y part of the factor is y. When we combine the two parts, 3x and y, we get the factor of 3x². Therefore, the factor of 3x² 12xy is 3x². This means that 3x² is a factor of 12xy, which can be seen by multiplying 3x² by 4y, which results in 12xy. This shows that 3x² is a factor of 12xy.

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The length AC will be 5.83 and the angle ACD will be 34.45°.

The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle are termed trigonometry.

The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.

The length AC will be calculated as,

AC² = 5² + 3²

AC = √ ( 25 + 9 )

AC = √34

AC = 5.83

The angle ACD will be,

tanθ = P / B

θ = tan⁻¹ = ( 4 / 5.83)

θ = 34.45°

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Answer:

The total cost of the science class trip to the zoo is $1200

Step-by-step explanation:

The cost of the science class trip to the zoo is $1200, and the cost of Mr. Sexton's class trip to the state park is $1000.

Step 3 is Define the problem Goals.

there are 8 steps, which are as follows,

1- Define the Problem

2- Clarification of the Problem

3- Define the problem Goals

4- Identify main Cause of the Problem

5- Develop a Action Plan

6- Execute that  Action Plan

7- Analyze the Results

8- Continuous Improvements

Problem solving

Problem solving is the method of determining the problem and then clarify the doubts and prepare a action plan and then execute the action plan and find out the desired results and if the results are not appropriate then improve the action plan and your way of doing until you get the desired results.

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Answer: slope=2

Step-by-step explanation:

using y=mx+b, we know the equation of the line is y=2x. The slope is the m term so we know that the slope is 2.

y < 4/5x - 1/5 ,y > -4/5x + 1/5, y < 2x + 6, y > 2x + 6 are all in slope-intercept form

The slope intercept form in math is one of the forms used to calculate the equation of a straight line, given the slope of the line and intercept it forms with the y-axis. The slope intercept form is given as, y = mx + b, where 'm' is the slope of the straight line and 'b' is the y-intercept.

so the given equation are also in the form of slope intercept form

y < 4/5x - 1/5

y > -4/5x + 1/5

y < 2x + 6

y > 2x + 6

are all in slope-intercept form (y = mx + b) where m is the slope and b is the y-intercept.

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The irrational numbers to children can be explained as the numbers  that can be written as a nonrepeating or nonterminating decimal .

What are Irrational Numbers ?

The real numbers that can be represented as a nonrepeating or a nonterminating decimal but not as a fraction, and the decimal that goes on forever without repeating.

For Example : [tex]\sqrt{2} , \sqrt{5} , \sqrt{7}[/tex] are few example of irrational numbers .

In simpler words : the irrational number is a number that is not rational. which means It is a number which cannot be written as a ratio of two integers or cannot be written as fraction.

and If a fraction has a 0 in the denominator , it is an irrational number .

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The inequalities that represent the situation are 15x + 10y ≥ 400 and x + y ≤ 35 and the viable solutions are (10, 25), (20, 12), (35, 0) and (20, 20)

From the question, we have the following parameters that can be used in our computation:

These parameters above mean that

15x + 10y = Total earnings

x + y = Number of hours

So, we have

15x + 10y ≥ 400

x + y ≤ 35

The above represent the inequalities of the situation

In (a), we have

15x + 10y ≥ 400

x + y ≤ 35

Next, we test the options

(10, 25)

15 * 10 + 10 * 25 ≥ 400 ⇒ 400 ≥ 400

10 + 25 ≤ 35 ⇒ 35 ≤ 35

True

(10, 20)

15 * 10 + 10 * 20 ≥ 400 ⇒ 350 ≥ 400

10 + 20 ≤ 35 ⇒ 30 ≤ 35

False

(20, 12)

15 * 20 + 10 * 12 ≥ 400 ⇒ 420 ≥ 400

20 + 12 ≤ 35 ⇒ 32 ≤ 35

True

(35, 0)

15 * 35 + 10 * 0 ≥ 400 ⇒ 525 ≥ 400

35 + 0 ≤ 35 ⇒ 35 ≤ 35

True

(20, 20)

15 * 20 + 10 * 20 ≥ 400 ⇒ 500 ≥ 400

20 + 20 ≤ 35 ⇒ 40 ≤ 35

False

Hence, the viable solutions are (10, 25), (20, 12), (35, 0) and (20, 20)

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By drawing a number line and then marking it as 0 and 1, and by dividing the distance in 3 equal parts we can graph 1/3 on the number line, where each part will be equal to the 1/3.

A number line is a diagram of a graded straight line used to represent real numbers in introductory mathematics. It is assumed that every point on a number line corresponds to a real number, and that every real number corresponds to a point.

A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present.

For drawing 1/3 on a number line, we will follow the following steps:

We will first draw a line and mark 0 and 1 on it.

In between 0 and 1, we will divide the total distance into 3 equal parts, where one part will represent (1/3)th portion.

Hence. by marking there we can locate 1/3 on the number line.

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The correct question may be like:

How do you plot 1/3 on a graph.

Answer: 1/2

Step-by-step explanation:

The question is asking you to find how many centimeters in the scale drawing equal 1 foot on the actual building. The answer will be 1/2 because 1 centimeter is equal to 2 feet in reality. But since we want to know the answer of how many centimeters is in 1 foot, we will divide that in half, to get an answer of 1/2 centimeter, or A.

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The amount made in commission is $67.5.

The amount made in sales by the store is $682.5.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Amount sold last week = $750.

Commission = 9%

The amount of commission.

= 9/100 x 750

= $67.5

The sales made last week by the store.

= 750 - 67.5

= $682.5

Thus,

$67.5 was made in commission.

$682.5 was made from sales.

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Answer: The Gradient of line A and B are

2 and -1

Step-by-step explanation:

For the given two points A(x1, y1) and B(x2, y2)

The gradient of the line AB is y2-y1/x2-x1

So the gradient of line A is

5-1/2-0

2

the gradient of line B is

5-0/0-5

-1

Angle ADC = 120 degrees.

A certain portion of a circle that is created based on two radius of the same circle and one arc. Area of sector for a circle with radius r is given by π r²Ф/ 360°

Given, two circles of radius 1 unit and 2 unit which have same center D.

We know area of a circle = π r²

Area of larger circle = π 2² = 4π

it is said that the total area of the shaded region that means area of a particular sector is 1/12 of the area of the larger circle.

area of sector, ACD = 1/12 ×4π

as per the question, the ACD sector is located in the smaller circle that has radius 1 unit.

formula for area of sector ACD = π r² ×Ф/360°

where,Фis the central angle of ACD sector

and Ф = ADC

from the above statement, 4π/12 = π r² ADC/360

                        ADC = 1/3×360°

ADC = 120 degrees

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On solving the provided question, we can say that the required probability is = 13/204.

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

probability of 1st card =  1/4

since the card is not replaced

total number remaining cards = 51

second card 13/51

the required probability is = 13/204

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Answer:

2

Step-by-step explanation:

0.2(x+50)-6=0.4(3x+20) multiply both sides by 10 to clear the decimals

2(x + 50) = 4(3x + 20) distribute across the terms in the parentheses

2x + 100 = 12x + 80 subtract 80, 2x from both sides

20 = 10x divide both sides by 10

x=2

Answer:

6 1/4 pounds

Step-by-step explanation:

There are 7 1/2 pounds of potatoes, which is equivalent to 7 1/2 = 7.516=120

120 ounces of potatoes.

If 1/6 of the potatoes are rotten, then 1/6*120 = 20

20 ounces of potatoes are rotten.

Thus, the weight of the good potatoes is 120-20 = 100

100 ounces.

Converting this back to pounds, we get

100/16 = 6 1/4

6 1/4 pounds.

The  set of equations correctly representing x are as follows:

(x + 1/2) and (x = 7/2).

A set or group of equations that you solve all at once is referred to as a "system" of equations. The simplest linear system is one that has two equations as well as two variables. Linear equations (those that graph as straight lines) are easier to understand than non-linear ones.

Systems of equations in mathematics are a collection of relationships between different unknown variables that can be stated in terms of algebraic expressions. They are also known as simultaneous equations. Graphing, substitution, as well as elimination by addition, are methods that can be used to find the solutions to a basic system of equations.

Sum means addition (+).

Given that sum of a number, x and 1/2 is 4.

This means the adding  two numbers

x+1/2=4

Now make x the subject of formula,

x=4-1/2

Finding the L.C.M  = 8-1/2

                        x=7/2

                     ∴ x=3 1/2

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Answer:

[tex]\sqrt[3]{x^{9} x}[/tex]

Step-by-step explanation:

When you are multiplying powers that have the same bases (in this case x) you add the exponents. If you do not see an exponent, the exponent is 1.

9 + 1 = 10

According to the following graph, the reflection point of (-3,4) across the line y = 2 is (-3,0).

The term reflection point in math is defined as

Here we need to find the reflection point of (-3, 4) across the line y = 2.

Here first we have t plot the point on the graph, and then we have to plot the line equation y = 2 on the graph,

Here in order to find the reflection of a point along the x-axis, then we have to keep the abscissa constant and see the reflection of ordinate along the x-axis.

Based on these rule, the resulting graph is obtained as follows.

Through the graph we have identified that the resulting reflection point is (-3,0).

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Answer:

so i will be honest I've done this before and it may be 64 or 120

Step-by-step explanation:

It may be one of these answers I'm doing as much as I can to help

The only difference is a -2 in x in 1 transformation in 2 transformation. The function is shifted up by b units with f (x) + b.

Transformations can be divided into four categories: translation, reflection, rotation, and dilation. Rotate, reflect, or translate the geometric figures on a coordinate plane. The label given to a function, f, that maps to itself is the transformation, or f: X X. The pre-image X is transformed into the picture X after the transformation. It is possible to utilize any operation, or a combination of operations, in this transformation, including translation, rotation, reflection, and dilation.

given

J(2, 2), (3, 4), H(4,3), G(3,0) to J'(-1,2), I'(0, 4), H'(1, 3), G'(0, 0)

in 2 transformation as the only change is that -2 in x in 1 transformation

The function is shifted up by b units with f (x) + b.

The function is shifted downward by b units when f (x) b.

The function is moved left by b units when f (x + b) is used.

The function is moved right b units by the expression f (x b).

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The proportion and percentage is as follows;

[tex]$\begin{array}{cccc}\text { Score Interval } & f & \text { Proportion } & \text { Percentage } \\ 9-10 & 29 & 0.19 & 19 \% \\ 7-8 & 53 & 0.34 & 34 \% \\ 5-6 & 50 & 0.32 & 32 \% \\ 3-4 & 22 & 0.14 & 14 \% \\ 1-2 & 1 & 0.01 & 1 \%\end{array}$[/tex]

A percentage represents a ratio or fraction with a denominator that is always 100 as opposed to a proportion, which asserts the equivalent of two ratios or fractions.

Given

[tex]$\begin{array}{cccc}\text { Score Interval } & f & \text { Proportion } & \text { Percentage } \\ 9-10 & 29 & 0.19 & 19 \% \\ 7-8 & 53 & & \\ 5-6 & 50 & & \\ 3-4 & 22 & 0.14 & 14 \% \\ 1-2 & 1 & 0.01 & 1 \%\end{array}$[/tex]

To estimate the total frequency:

Total = sum f

Total = 29 + 53 + 50 + 22 + 1

Total = 155

The proportion (p) exists calculated by:

[tex]$p = \frac{f}{\text { Total }}[/tex]

The percentage (P) exists calculated by:

P = p × 100 %

For interval 7 - 8, we have:

p = 53 / 155 = 0.34

P = 0.34 × 100 % = 34 %

For interval 5 - 6, we have:

p = 50 / 155 = 0.32

P = 0.32 × 100 % = 32 %

So, the complete table is:

[tex]$\begin{array}{cccc}\text { Score Interval } & f & \text { Proportion } & \text { Percentage } \\ 9-10 & 29 & 0.19 & 19 \% \\ 7-8 & 53 & 0.34 & 34 \% \\ 5-6 & 50 & 0.32 & 32 \% \\ 3-4 & 22 & 0.14 & 14 \% \\ 1-2 & 1 & 0.01 & 1 \%\end{array}$[/tex]

The complete question is:

A statistics content developer at Aplia wanted to know whether study skills are related to memory quality. She invited student volunteers to perform an online memory task. The students saw a list of 60 words and were then asked to recognize a list of five brand new words that are related to words that were on the original list. Students were also asked to provide their GPAs.

Consider the following data set, which was collected from student volunteers in 2009. The table gives the frequency for the number of incorrectly identified related words. Use the dropdown menus to complete the table by filling in the missing values for the proportions and percentages.

Score Interval f Proportion Percentage

9â10 29 0.19 19%

7â8 53

5â6 50

3â4 22 0.14 14%

1â2 1 0.01 1%

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a. The ratio of rows of corn to beans is 13 : 12 or 13/12 or 13 to 12.

b. The ratio of rows of lettuce to the total number of rows in the garden is 5 : 52 or 5 to 52 or 5/52.

a. The ratio using the word 'to' is corn to beans.

In its most basic form, a ratio is a comparison between two comparable quantities.

There are two types of proportions One is the direct proportion, whereby increasing one number by a constant k also increases the other quantity by the same constant k, and vice versa.

If one quantity is increased by a constant k, the other will decrease by the same constant k in the case of inverse proportion, and vice versa.

We know a ratio between a and b can be written as a : b, a/b or a to b.

From the given information the ratio of rows of corn to beans is,

corn/beans = 13/12 Or 13 : 12 Or 13 to 12.

The ratio of rows of lettuce to the total number of rows in the garden is,

lettuce/total number of rows in the garden = 5/52 Or 5 : 52 Or 5 to 52.

The ratio using the word 'to' is corn to beans.

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The solution to the polynomial is x = -1, x = 1/2 and x = -1

From the question, we have the following parameters that can be used in our computation:

2x³ - x² - 2x + 1

Expand

2x³ - x² - 2x + 1 = 2x³ - x² - 2x + 1

Factorize the expression

This gives

2x³ - x² - 2x + 1 = x²(2x - 1) - 1(2x - 1)

Factor out 2x - 1

2x³ - x² - 2x + 1 = (x² - 1)(2x - 1)

Express x² - 1 as difference of two squares

2x³ - x² - 2x + 1 = (x - 1)(x + 1)(2x - 1)

So, we have

(x - 1)(x + 1)(2x - 1) = 0

Solve for x

x = 1, x = -1 and x = 1/2

Reorder the solutions

x = -1, x = 1/2 and x = -1

Hence, the solution is x = -1, x = 1/2 and x = -1

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We would need to multiply the first equation by -4 to eliminate the y variable when solving the system of equations by elimination.

The first equation is: 3x + 4y = 5

To eliminate the y variable when solving the system of equations by elimination, we need to multiply the first equation by -4. This is because when two equations are multiplied by the same number, any terms that have the same variable will be eliminated when the equations are added together.

Formula:

3x + 4y = 5

-4(3x + 4y = 5)

3x + 4y = 5

-12x - 16y = -20

Thus, we would need to multiply the first equation by -4 to eliminate the y variable when solving the system of equations by elimination.

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