if α and β are the zero of polynomial p(x) = 3x^2 +2x + 1, find the polynomial whose zeroes are 1-α /1+α and 1-β/1+β.​

Answer: The origins of matrices can be traced back to the 18th century, with the work of mathematicians such as Gabriel Cramer, Leonhard Euler, and Joseph-Louis Lagrange. These mathematicians developed the idea of using arrays of numbers to represent systems of linear equations, which led to the development of the concept of matrices.

The term "matrix" itself was first used by James Joseph Sylvester in 1850, although it had been in use informally for some time before then. In 1858, the English mathematician Arthur Cayley first published a systematic theory of matrices, which further developed the field.

Matrix theory was primarily used in the early days to solve systems of linear equations, but it soon found applications in areas such as linear algebra, multivariate statistics, and even quantum mechanics.

In summary, the origins of matrices can be traced back to the 18th century as an idea to represent systems of linear equations, which developed over time with contributions of many mathematicians over the centuries, and now it plays an important role in many field of mathematics and science.

Step-by-step explanation:

Ordered pairs (0,4) stand in for points on the graph created by the equation 7y = -4x + 28.

A linear equation with a degree of one is referred to as a line equation. Two variables, x and y, are present in the equation of the line. The third parameter is the line's slope, which indicates the line's elevation. Y = mx + c, where m is the slope and c is the intercept cut by y, is the equation of the line in its general form.

given

7y = -4x + 28

For (3,-6)

7(-6) + 4( 3) = 28  

-42 + 12 = 28

no

For (5,0)

7(0)+4(5)= 28  

= 20

no

For (0,4)

7(4)-0=28  

Yes

For (-4,-5)

7(-5)+4( - 4)= 28

no

For (-5, 1)

7(1)+4(-5)=28

No

For (-6,3)

7(-6)+4(3)= 28

No

hence the points (0, 4) on the graph of the equation 7y = -4x + 28 are ordered pairs.

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The total area of the recreational area can be represented by the polynomial expression 26x² + 57x + 35.

The area of a rectangle is defined as the product of the length and width.

The area of a rectangle = L × W

Where W is the width of the rectangle and L is the length of the rectangle

The area of the rectangular pool is given by its length times its width, so the area of the pool is (3x - 3) meters × (2x + 7) meters = (6x² + x - 21) square meters.

The area of the patio is given by the length of the pool plus twice the extension (x) on each side, times the width of the pool plus twice the extension on each side, so the area of the patio is (3x - 3 + 2x) meters × (2x + 7 + 2x) meters = (5x + 4) × (4x + 14) = 20x² + 56x + 56 square meters.

The total area of the recreational area is the sum of the areas of the pool and the patio, so it can be represented by the polynomial expression:

20x² + 56x + 56 + 6x² + x - 21 = 26x² + 57x + 35

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Hello there!

Answer:

[tex](9, +\infty)[/tex]

Step-by-step explanation:

It has no real roots only if

[tex] \sqrt{b {}^{2} - 4ac } [/tex]

has no roots. That means that b² - 4ac is smaller than 0:

[tex]b {}^{2} - 4ac < 0 \\ 12 {}^{2} - 4 \times 4 \times k < 0 \\ 144 - 16k < 0 \\ 144 - 144 - 16k < - 144 \\ - 16k < - 144 \\ k > 9 \\ k \: \: \: in \: \: \: (9, +\infty)[/tex]

we can approach this from the standpoint of the discriminant, if the discriminant is negative then we only get complex roots or namely "imaginary" solutions or values, well, let's check before that happens, when the discriminant is 0.

[tex]\qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ y=\stackrel{\stackrel{a}{\downarrow }}{4}x^2\stackrel{\stackrel{b}{\downarrow }}{+12}x\stackrel{\stackrel{c}{\downarrow }}{+k} ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one solution}\\ positive&\textit{two solutions}\\ negative&\textit{no solution} \end{cases}[/tex]

[tex]0=(12)^2 - 4(4)(k)\implies 0=144-16k\implies 16k=144 \\\\\\ k=\cfrac{144}{16}\implies k=9\hspace{5em} \stackrel{if~k > 9\textit{, then we land on negative territory}}{{\Large \begin{array}{llll} k > 9 \end{array}}}[/tex]

Answer: y^2+8x+12

Step-by-step explanation:

The cost of  one blueberry pie and one blackberry pie is $11.30 and $11.373 respectively.

In mathematics, an expression is a group of numbers and operations. The components of a mathematical expression that perform an operation are as follows:

Operands: The numbers used in an operation are called operands. Depending on the type of operation, different terms are applied to the operands.

Given Nathan sold 13 apples pies for $147,

cost of 13 apple pies  = $147

cost of 1 apple pie = 147/13 = $11.30

Lucy sold  7 blueberry pies and 11 apple pie $204.

7 blueberry  + 11 apple pie = $204

cost of 11 apple pie  = $124.384

cost of 7 blueberry = 204 - 124.384 = $79.615

cost of 1 blue berry = 79.615/7 = $11.373

Hence the cost of 1 apple pie is $11.30 and 1 blueberry is $11.373.

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The graph's X-intercepts are ((9+55)/2,0) and ((955)/2,0), and its Y-intercept is (0,13).

When locating points or other geometrical objects precisely on a manifold, such as Euclidean space, a coordinate system is a technique that uses one or more integers or coordinates. Locating a point or item on a two-dimensional plane requires the use of coordinates, which are pairs of integers. Two numbers called the x and y coordinates are used to describe a point's location on a 2D plane. a collection of integers that represent specific locations. The figure often has two numbers. The first number denotes the front-to-back measurement, while the second number denotes the top-to-bottom measurement. For example, in (12.5), there are 12 units below and 5 above.

given

Axis of symmetry:

x=9 /2

Vertex (minimum point): (9/2,−55/2)

X-intercepts: ((9+√55)/2,0) and ((9−√55)/2,0)

Y-intercept: (0,13)

The graph's X-intercepts are ((9+55)/2,0) and ((955)/2,0), and its Y-intercept is (0,13).

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The complete table is given in the solution.

A ratio is a way to show a relationship or compare two numbers of the same kind. We use ratios to compare things of the same type.

Given that, at Disneyland there are 300 girls go on the ride and 500 boys go on the ride this represents the ratio of girls and boys that go on the ride

The ratio of girls to boys = 3:5

Therefore, The complete table is as follows:-

    Girls                                     Boys                                     Total

     3                                             5                                             8

     6                                             10                                           16

     12                                            20                                          32

     30                                           50                                          80

     300                                         500                                      800

     480                                         800                                      1280

Hence, the complete table is above

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Answer: 40 cm

Step-by-step explanation:

The wooden frame needed = perimeter of the drawing
The length of the picture: 96 :8 = 12cm
The perimeter: (12 + 8) x 2 = 40 cm

Answer: simplified to the tens digit would be 93.4 simplified overall would just be 93.

Step-by-step explanation: Hope this helps, please mark brainliest, and give thanks!

Answer: option b), option c), and option e) are correct options.

Step-by-step explanation:

Given:

The area of a rectangular room= 750 square feet

The width of the room = 5 feet less than the length of the room

The length of the room = Y

To find:

Equations that can be used to solve the value of Y i.e. the length of the rectangular room.

Solution:

The equation can be derived from using the following formula:

Area of rectangle = length * width

According to the question,

Length of the rectangular room = Y

Width of the rectangular room = 5 feet less than the length of the room

                                                       = (Y-5)

Since, Area of rectangle = length * width

Area of the rectangular field = length of the room* width of the room

                          750             = Y (Y – 5)                         ………..eqn. (1)

Or, the above equation can be solved a step further and written as

                          750             = Y2 – 5Y                          ………..eqn. (2)

                         750- Y2 + 5Y= 0                                    ………..eqn. (3)

                         750-Y (Y- 5) =0                                    ………..eqn. (4)

Apart from the above equations, if we solve eqn. (2) we get the following equation:

                          750             = Y2 – 5Y

                           Y2 – 5Y- 750= 0

                          Y2 – 30Y + 25Y- 750 = 0

                          Y (Y- 30) + 25 (Y- 30) = 0

                                                                   take Y- 30 common from L.H.S.

                           (Y -30) (Y+ 25)   = 0                            …………….eqn. (5)        

Hence, the correct options are option b), option c), and option e).

Answer:

30

Step-by-step explanation:

x + 2x + 3x = 180 (the total angle of a triangle)
6x = 180
x = 180 : 6 = 30

Answer:

x = 30°

2x = 60°

3x = 90°

Step-by-step explanation:

Internal angles of a triangle sum 180°

Then:

x + 2x +3x = 180

6x = 180

x = 180/6

x = 30°

2x = 60°

3x = 90°

The cost c in pounds of hiring a van is 235

The cost c in pounds for 1 day =45

Then cost c in pounds for  five days is c=10+45d

Which is multiple 5 days to the 45

5 x 45 = 225

Add the 10 to the answer

225 + 10 = 235

The cost  of a van hiring for number of days is 5

Then the final answer for cost c in pounds of hiring a van for five days are 235

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Answer: what

Step-by-step explanation:

Answer: To determine which store has the cheaper steak, you need to compare the price per pound of steak at each store. To do this, divide the total price by the number of pounds of steak at each store.

At Store A, the price per pound of steak is $6.38 because 25.50 / 4 = <<25.50/4=6.375>>6.375.

At Store B, the price per pound of steak is $6.71 because 40.25 / 6 = <<40.25/6=6.708>>6.708.

Therefore, Store A is cheaper because it has a lower price per pound of steak. The correct answer is Store A.

Step-by-step explanation:

The image for P(9, 1.5) after Translation is P'( 12, 1).

Each point in a figure is moved the same distance in the same direction using a type of transformation known as translation.

For example, this transformation moves the parallelogram to the right 5 units and up 3 units. It is written ( x , y ) → ( x + 5 , y + 3 ) .

Given:

P(9, 1.5) with Translating Vector (3, -0.5).

So, Applying the Translation we get

P(9 + 3, 1.5 + (-0.5))

= P(12 , 1.5- 0.5)

= P(12, 1)

hence, the image is P'( 12, 1).

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Answer:

[tex] \sf \: b) \: 45[/tex]

Step-by-step explanation:

The values given are,

→ u = 7

→ d = 10

→ e = 3.2

Now the expression is,

→ 15(d - u)

Evaluating the expression,

→ 15(d - u)

→ 15(10 - 7)

→ 15 × 3

→ 45

Hence, option (b) is correct.

Answer:45

Step-by-step explanation:

15(10-7)

15(3)

multiply and get 45

Answer: 5/6

Step-by-step explanation:

The reciprocal of a number is 1 divided by that number. The reciprocal of 6/5 is 5/6.

Answer:

5/6

Step-by-step explanation:

Well to find a fraction's reciprocal all you need is to flop it like this

6/5 => 5/6

so 5 takes the place of 6 and 6 takes the place of 5

that's how 6/5 turns into 5/6

Answer:

Step-by-step explanation:

you should give the function, if i haven't it, how can i help you.

i can give u some tips, put 1.5, 2.5, 2 in function respectively. then calculate them, u will get the answer.

Answer:

The expression 56 with a variable of -1 is not well defined. The term 56 is a constant number, and the variable of -1 is also a constant. Therefore there is nothing to evaluate.

Step-by-step explanation:

If you want to evaluate the expression 56*(-1) it would give -56 as output because -1 is a scalar and multiplying with a scalar will change the sign of the constant 56 but it won't change its value.

In other words, to evaluate an expression, it needs to have a mathematical operation or function, operands, and/or variables that can be replaced with values or expressions. Without any operation, there's nothing to evaluate.

On soloing the provided question we can say that - Area of the Circle - Area of the Triangle - Area of the Square is the area of the darkened area. A = 210-123 = 87 sq unit

Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is a graphical representation of a triangle having vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.

the sum of the areas of the circle, the triangle, and the square.

Area of the Circle - Area of the Triangle - Area of the Square is the area of the darkened area.

A = 210-123 = 87 sq unit

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The line passes through the point (-10,1) and has a slope of 3/20 has the equation as: y - 1 = 3/2 (x + 10)

The general form of a linear equation is y - y₁ = m (x - x₁).

It draws attention to the line's slope and one of the line's points (that is not the y-intercept)

The point slope formula is given by y - y₁ = m (x - x₁), where:

y = output value

y₁= the given y coordinate point

m = slope

x = input value

x₁ = the given x coordinate

substituting the point (-10,1) and slope 3/2

y - y₁ = m (x - x₁)

y - 1 = 3/2 (x + 10)

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Answer:

Below

Step-by-step explanation:

1+2+3+4+5 =15       5 lengths will require   4 cuts

Answer:

Step-by-step explanation:

Step: Solve−3x−4y=15for x:

−3x−4y=15

−3x−4y+4y=15+4y(Add 4y to both sides)

−3x=4y+15

−3x

−3

=

4y+15

−3

(Divide both sides by -3)

x=

−4

3

y−5

Therefore , as a result Two of a triangle's sides and the included  SAS angle are said to be congruent if they match the corresponding sides and angles of another triangle.

The Side-Angle-Side rule is applied to check the congruence of a set of triangles. The SAS rule states that a triangle is congruent if its two sides and included angles match those of another triangle.

Here,

if the first triangle's two sides and one of its included angles are equal to the second triangle's sides and one of its included angles.

Consequently, the SAS declares two triangles to be congruent. Two triangles are said to be congruent if their matching two sides and their included angles are found in a single triangle, according to the SAS theorem of congruence.

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Answer:

x = 14

Step-by-step explanation:

2(x + 4) = 3( -2 + x)  distribute the 2 and the 3.

2(x) + 2(4) = 3(-2) + 3(x)

2x + 8 = -6 + 3x  Subtract 2x from both sides

2x - 2x + 8 = -6 +3x -2x

8 = -6 +x  Add 6 to both sides

8 + 6 = 6 - 6 + x

14 = x

Answer: 1/104976

Step-by-step explanation:

You can get rid of negative exponents by flipping the number. So in this case,  the expression would change to: 1/(36)^2 x (9)^2.

From there, simplify the expression. 36 squared is 1296. 9 squared is 81. Multiply those together to get 104,976.

1/104976 is your answer!

Answer:

7/8

Step-by-step explanation:

Step 1: Count the total number of letters in the word FOOTBALL

There are 8 letters in the word FOOTBALL.

Step 2: Count the number of letters that are not L

There are 7 letters that are not L.

Step 3: Calculate the probability

The probability that the letter chosen is not an L is 7/8.

Answer:

109.18

Step-by-step explanation:

Subtract 13.4-7.2 then solve the triangle (base x height) getting 32.86. Next solve the rectangle getting 76.32. Then add all of it concluding in 109.18.