Hello please solve this with steps
Identify the number of solutions Or zeros of
F(x)=12x-32x^2+40-x^3

one real eigenvalue. find this eigenvalue, its multiplicity, and the dimension of the corresponding eigenspace.

What is eigenvalue?

In linear algebra, an eigenvector or characteristic vector of a linear transformation is a nonzero vector that, when the linear transformation is applied to it, changes at most by a scalar factor. The factor by which the eigenvector is scaled is known as the associated eigenvalue, frequently denoted by lambda.

a) -4

b) 1

c) 1

Step-by-step explanation:

a) The matrix A is given by:

[tex]A=\left[\begin{array}{ccc}-3 & 0 & 1 \\2 & -4 & 2 \\-3 & -2 & 1\end{array}\right]\\[/tex]

where lambda are the eigenvalues and I is the identity matrix. By replacing you obtain:

[tex]A-\lambda I=\left[\begin{array}{ccc}-3-\lambda & 0 & 1 \\2 & -4-\lambda & 2 \\-3 & -2 & 1-\lambda\end{array}\right][/tex]

and by taking the determinant:[tex]\begin{aligned}& {[(-3-\lambda)(-4-\lambda)(1-\lambda)+(0)(2)(-3)+(2)(-2)(1)]-[(1)(-4-\lambda)(-3)+(0)(2)(1-} \\& \lambda)+(2)(-2)(-3-\lambda)]=0 \\& -\lambda^3-6 \lambda^2-12 \lambda-16=0\end{aligned}[/tex]

and the roots of this polynomial is:

[tex]\begin{aligned}& \lambda_1=-4 \\& \lambda_2=-1+i \sqrt{3} \\& \lambda_3=-1-i \sqrt{3}\end{aligned}[/tex]

hence, the real eigenvalue of the matrix A is -4.

b) The multiplicity of the eigenvalue is 1.

c) The dimension of the eigenspace is 1 (because the multiplicity determines the dimension of the eigenspace)

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Complete Quetion

The matrix A= (−3 0 1, 2 −4 2, −3 −2 1) has one real eigenvalue. Find this eigenvalue, its multiplicity, and the dimension of the corresponding eigenspace. The eigen value = has multiplicity = and the dimension of the corresponding eigenspace is:_______.

Answer: 55.5 as a fraction is 111/2.

Answer:

55.5/100 or 111/200 in its simplest form

Step-by-step explanation:

55.5 (per)cent) - means every 100

55.5/100= 111/200

The location of the transformed point will be at the coordinate (0,4).

In mathematics, a translation moves a shape left, right, up, or down but does not turn it. The translated (or picture) shapes appear to be the same size as the original shape, showing that they are congruent. They've just moved in one or more directions.

Given that a point at (−3,−2) is transformed in two steps. It is reflected in y = x. It is translated as 3 units right and 2 units up.

The translated point will be,

(−3,−2) ⇒ (-3,2)

Translation of the point,

(-3,2) ⇒ (-3+3, 2+2) ⇒(0,4)

Therefore, the location of the transformed point will be at the coordinate (0,4).

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The adjacents angles are ∠ RTL and ∠ ETL, The obtuse vertical angles are ∠ RTL and ∠ STE, the two supplementary angles are ∠ NTE and

∠ NTR and angles supplementary to ∠ RTS is ∠ RTL

The two rays intersecting at a common point makes an angle.

Given is a figure,

Adjacent Angels =

The angles having one arm in common are called adjacent angles.

Here, adjacents angles are ∠ RTL and ∠ ETL

Vertical angles =

A pair of angles that have the same vertex and are on opposite sides of two intersecting rays makes Vertical angles

Here, vertical angles are ∠ RTL and ∠ STE

Supplementary angles =

When the sum of two angles is 180°, then they are supplementary angles.

Here, supplementary angles are ∠ NTE and ∠ NTR

We see that, the angle supplement to ∠ RTS is ∠ RTL

Hence, the correct answers are, adjacents angles = ∠ RTL and ∠ ETL, The obtuse vertical angles = ∠ RTL and ∠ STE, the two supplementary angles = ∠ NTE and ∠ NTR and angles supplementary to ∠ RTS is ∠ RTL

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The final image of triangle LMN is triangle L''M''N'' with vertices L''(-3,-5), M''(1,-4), and N''(-1,-1).

What is Translation of graph?

A graph can be horizontally translated by moving the base graph to the left or right in relation to the x-axis. Each point on a graph is moved by k units in order to translate it horizontally.

To graph triangle LMN and its image after the composition of a 90 degree rotation about the origin and a translation of (x, y) (x-3, y+2), we can first plot the vertices of triangle LMN on the coordinate plane.

pair L = (1,6);

pair M = (-2,4);

pair N = (3,2);

Next, we can apply the 90 degree rotation about the origin to the vertices of the triangle. The rotation matrix for a 90 degree rotation about the origin is given by:

[cos(90) -sin(90)][x] [y]

[sin(90) cos(90)][y] = [-x]

Substituting the coordinates of the vertices into the rotation matrix, we get:

[cos(90) -sin(90)][1] [6]

[sin(90) cos(90)][-2] = [4]

[3] [2]

Therefore, the image of triangle LMN after the rotation is triangle L'M'N' with vertices L'(-6,1), M'(4,-2), and N'(-2,3).

Finally, we can apply the translation of (x, y) (x-3, y+2) to the vertices of the rotated triangle to get the final image of triangle LMN. The translation matrix is given by:

       [tex][1 \ 0][x] [y][-3 \ 2][y] = [x-3][/tex]

Substituting the coordinates of the rotated vertices into the translation matrix, we get:

[1 0][-6] [1]

[-3 2][4] = [-1]

[-2] [3]

Therefore, The final image of triangle LMN is triangle L''M''N'' with vertices L''(-3,-5), M''(1,-4), and N''(-1,-1).

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Answer:

2/5^4

Step-by-step explanation:

2/5 is being multiplied four times

The correct order of sentences to bisect the angle Q is (1) draw a line from Q to where the arc crosses (2) vertex: set the compass to any convenient width (3) from where the arc crosses lag, make an arc.. (4) place the compass point on the angle Q.

We should know that an angle is the intersection of two or more straight lines.

In construction of angles, using the compass, the first thing is to locate a point say Q.  The open the leg of the compass to a convinient radius, make an arc at another point say P.  From the point P, bisect the initial arc so made then joion to the starting point Q.

Second, from the point where the arcs met on the two lines, make another two arcs above the points, then join them to the starting point Q

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An antique painting is purchased in 1980 for $995. The value increases by 3.1% every year, the increase in value of the painting in the 6th year after it was purchased is: $200.02

Increased Value is the amount obtained after deducting the Base Value from the current assessed value.

Given that,

An antique painting is purchased in 1980 for $995 = P

The value increases by 3.1% every = r

r = 3.1%

r = 3.1/100

r = 0.031

As we know,

Value of painting after t years: [tex]P (1+r)^t[/tex]

So, after 6 years:

f(6) = [tex]995 (1+0.031)^6[/tex]

or, f(6) = [tex]995 (1.031)^6[/tex]

or, f(6) = 1195.0197

or, f(6) = 1195.02

Now, at t = 0, f(0) = 995

Thus, value increased by, f(6) - f(0)

= [1195.02 - 995]

= 200.02

Thus, increase in price since it purchased = $200.02

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Answer: The slope is 5/6

Answer:

5/6

Step-by-step explanation:

The area bounded by f(x) =sin x + 1 is 2 + π on the interval [0,pi]

What is a interval?

Given that:

x-axis on the interval [0,pi]

f(x) = sin x + 1

     = integral 0 - integral π (sin x) dx + integral 0 - integral π (1) dx

     = [- cos π + cos 0] + [π - 0]

     = [-(-1) + 1 ] + π

     = 2 + π

Therefore, the area bounded by f(x) =sin x + 1 is 2 + π on the interval [0,π]

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The equation of the proportional relationship is For $10.50, you can buy 1 pound of shrimp.

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. LHS = RHS is a common mathematical formula.

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:

c = 10.50p

where total cost (c) and the number of pounds (p) of shrimp at a grocery store.

When p= 1 pounds then the cost is

c= 10.5

Hence, For $10.50, you can buy 1 pound of shrimp.

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For $10.50, you can buy 1 pound of shrimp.

have a nice day! :)

Answer:

the answer to your question is 20

Step-by-step explanation:

5 batches× 4 quarts

Answer: 4/25

Step-by-step explanation:

(2/5)^2 or can write as 2/5 times 2/5

2/5 times 2/5 = 4/25

Answer:

0.08

Step-by-step explanation:

2/5 = 0.4 x 0.4

Answer:

8

Step-by-step explanation:

The volume of a solid of cylinder with a radius of 12 and a height of 24 is

3456[tex]\pi[/tex].

Space occupied by an object in three dimensional space is called as volume of an object. In simple words space is taken by object.

Given that the cylinder with a radius of 12 and a height of 24.

Volume of a cylinder = [tex]\pi[/tex] r² h

Volume of a cylinder = [tex]\pi[/tex] (12)² × 24

Volume of a cylinder = [tex]\pi[/tex] ( 144 × 24)

Volume of a cylinder =  [tex]\pi[/tex] (3456)

Therefore, the volume of cylinder is 3456[tex]\pi[/tex].

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Answer:

c

Step-by-step explanation:

Answer:

7, - 28 , 112 , - 448 , 1792

Step-by-step explanation:

to obtain a term in the sequence multiply the previous term by r , so

a₁ = 7

a₂ = a₁ × - 4 = 7 × - 4 = - 28

a₃ = a₂ × - 4 = - 28 × - 4 = 112

a₄ = a₃ × - 4 = 112 × - 4 = - 448

a₅ = a₄ × - 4 = - 448 × - 4 = 1792

Answer: To determine whether a triangle is acute, right, or obtuse, we need to compare the lengths of its sides to the measure of its angles. The triangle is acute if all three angles measure less than 90 degrees, it is right if one angle measures exactly 90 degrees, and it is obtuse if one angle measures more than 90 degrees.

In the case of a triangle with sides 3, radical7, and 4, we can use the Pythagorean theorem to find the measure of its angles. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Since we know that one side of the triangle has length 4, and another side has length radical7, we can use the theorem to find the length of the third side, which is the hypotenuse. We can write this as an equation: 4^2 + radical7^2 = x^2, where x is the length of the hypotenuse. Solving for x, we get x = 5.

Since the length of the hypotenuse is 5, and one of the other sides has length 4, we can conclude that this triangle is a right triangle. Therefore, the triangle is a right triangle and not acute or obtuse.

The strategy that does not work to solve the system is the one in option D

"Multiply the first equation by 3 and the second equation by 2"

Here we have the following system of equations:

4x - 3y = 8

2x + 9y = -3

To solve it, we can take a linear combination of the two equations, for example if we do what the first option says and we multiply the first equation by 3 we get:

3*4x - 3*3y = 3*8

12x - 9y = 24

Now we can add this to the other equation to get:

(12x - 9y) + (2x + 9y) = 24 - 3

14x = 21

And the system can be solved.

Now, the option that does not help us to solve the system is the third option:

"Multiply the first equation by 3 and the second equation by 2"

If we do that we will get the equations:

12x - 9y = 24

4x + 18y = -6

If we add these two equations no variable is canceled.

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In mathematics is an expression which is made up of variables and constants, along with algebraic operations

x = 1

3(5x+1) = 13x + 5

3(5x) + 3(1)

15x + 3 = 13x + 5        

-13x         -13x

2x + 3 = 5

 __-3__-3____

2x = 2

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When the coloured water evaporates and condenses on the inside of the top cup, there is no colour in the water on the inside surface of the cup.

As water molecules in the air cool, they slow down and combine into tiny droplets of liquid water. This process is called condensation. This happens when water molecules in the air touch the outside of a cold mug exposed to air.

Water vapour in the air is extracted by several techniques, such as cooling the air below the dew point, exposing the air to a desiccant, using membranes that allow only water vapour to pass, collecting the mist, or pressurizing the air. I can do it.

Common examples are water forming on the outside of a cold mug, or moisture forming on a car window on a cool night.

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The angle made between the two pieces of plywood found using the law of sines is approximately 85°

The law of sines states that the ratio of the sine of an angle to the length of the opposite side is the same for the three angles and sides of the triangle.

[tex]\dfrac{sin(A)}{a} = \dfrac{sin(B)}{b} = \dfrac{sin(C)}{c}[/tex]

The length of one plywood = 7 feet

The angle made by the 7 feet plywood with the ground = 31°

Length of the other sheet of plywood = 4 feet

Using the law of sines, we get;

sin(31)/4 = sin(B)/7

sin(B) = 7 × (sin(31)/4)

∠B = arcsine(7 × (sin(31)/4)) ≈ 64.33°

The angle between the two pieces of wood is therefore;

Angle = 180° - 31° - 64.33° = 85°

The measure of the  angle formed between the two plywood is about 85°

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Answer:

A=3, b=2, t=0 to t=5, covering 6 days. $3, $6, $12, $24, $48, $96.

Step-by-step explanation:

A is the starting amount at t=0. b is the base, two because the amount doubles each day. b would be 3 if it tripled every day. t is the final day number, counting from zero.

Answer:

x = 14.56 units

Step-by-step explanation:

each scarf's 0.4166 yards of blue scarf

This problem can be solved using a straightforward algebraic equation. For each scarf, Ayana requires many yards of blue cloth.

When solving a straightforward equation, visualize the equals symbol (=) as the fulcrum or center of a balance.

The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.

In order to answer this question, let's say that each scarf needs x square inches of purple fabric and y square inches of blue fabric.

A total of six scarves are reportedly required. It is assumed that a total of 10 yards of fabric—the combined amount of the purple and the blue fabrics—will be utilized.

So that we may solve this equation.

We use x and y as 6x and 6y as 6 scarves are needed.

10 yards of cloth were used in total (6x + 6y).

Next up It goes without saying that 1 yard of purple cloth is required for each and every scarf.

Therefore, a total of 6 * 1(1/4) yards is required for 6 scarves.

As a result, 6x becomes 6 * 1/4 yards.

This equates to 6 yards of purple material

We now solve for the required amount of blue cloth.

6y = 10 -30/4  = 40-30/4 = 10/4

However, the yards are for six scarves, therefore we need to divide it by six to obtain the amount of material for one scarf.

Each scarf needs 0.4166 yards of blue fabric, or y = (10/4)/6 =10/4 *1/6 =10/24 = 5/12 yards.

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Answer: 4x^3+1

Step-by-step explanation:

Answer:

Assuming you want to convert this to slope-intercept form.

Step-by-step explanation:

y=1/3x+3

Subtract 2x from both sides, then divide both sides by negative 6

if you want to graph it, this is what your graph should look like

** See attached photo**

Answer:

m=-3

Step-by-step explanation:

use slope formula to solve

m=rise/over=y2-y1/x2-x1