Present a state-space equation that describes a system with the following differential equation y (3) (t) +12y (2) (t) + 3y(¹) (t) + y(t) = x(t)

Answer:

8

I wish you luck in your assignments.

To write the expression in its simplest form, we need to simplify each term and then combine like terms.

The first term of the expression is 2x²y. This term is already in its simplest form and doesn't require any further simplification.

The second term of the expression is xy. This term is also in its simplest form and doesn't require any further simplification.

The third term of the expression is -3x. This term is also in its simplest form and doesn't require any further simplification.

The fourth term of the expression is 12x.xy. To simplify this term, we need to distribute the 12 over the x and y. So, we get 12x.y.

Now that all terms are simplified, we can combine like terms. Since the terms xy and 12x.y are the same, we can add them together to get (12+1)xy = 13xy.

So, the expression in its simplest form is 2x²y + 13xy - 3x.

We can further simplify the above expression by combining x²y and xy together as (x²+1)xy = x³y

So, the final expression in its simplest form is x³y + 13xy - 3x.

There would be exactly 42 tiles in the 10th pattern.

As Tiles are exceeding by the multiple of 4, So, there will be exactly 42 tiles in the 10th pattern.

A recurring arrangement of numbers, forms, colors, and other elements constitutes a pattern in mathematics. The Pattern can be connected to any kind of occasion or thing. When a group of numbers are arranged in a particular way, the arrangement is referred to as a pattern.

A pattern in mathematics is a series of recurring figures, shapes, or numbers. Any kind of event or thing can be connected to a pattern. A pattern has a rule that identifies the items that are part of the pattern and those that are not.

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Answer:

The length of the third side is 7.

Step-by-step explanation:

We can use the Pythagorean theorem to evaluate the length of the third side.

[tex]a^2+b^2=c^2[/tex]

Let the third side be [tex]a[/tex].

Lets solve for [tex]a.[/tex]

Subtract [tex]b^2[/tex] from both sides.

[tex]a^2=c^2-b^2[/tex]

Take the square root of both sides.

[tex]a=\sqrt{c^2-b^2}[/tex]

We are given

[tex]c=\sqrt{58} \\b=3[/tex]

Lets evaluate [tex]a[/tex].

[tex]a=\sqrt{(\sqrt{58} )^2-3^2}[/tex]

Simplify.

[tex]a=\sqrt{58-9}\\a=\sqrt{49} \\a=7[/tex]

Answer:

Not sure if this is what you are looking for because there isn’t much information given but the equation for this problem would be

25x+18.25

Step-by-step explanation:

Hope this helps

Answer:

(5x - 3)(x - 3)

Step-by-step explanation:

Yes, the expression "5x^2 - 8x + 9" can be factored.

One way to factor it is to find the two numbers that multiply to give 9 (the constant term) and add to give -8 (the coefficient of x). These two numbers are 3 and -3.

We can use these two numbers to factor out the common factor (x - 3) from the expression:

5x^2 - 8x + 9 = (5x^2 - 8x) + 9

= (5x^2 - 8x + 9) - 9 + 9

= (5x^2 - 8x + 9) - (3x - 3x)

= (5x - 3)(x - 3)

So the fully factored form of the expression is (5x - 3)(x - 3)

So, (5x - 3) and (x - 3) are the factors of the expression "5x^2 - 8x + 9"

Note that the question is about numbers in multiples of 6 or which can be divided equally by 6. Thus the likely number of people who must show up to practice so that the coach can make these teams are 6, 12, 18, 24, 30, 36, 48, and so on. The bottom line is that the number must be a common multiple of 6.

One way to show that each of the numbers above will equal an exact team of 6 without anyone left off is by dividing each by 6. If we get an integer, then we are correct. Thus:

Hence, the above Common Multiples are correct.

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Answer:

1.5 on edg

Step-by-step explanation:

When two triangles are similar, the reduced ratio of any two corresponding sides is called the scale factor of the similar triangles. In Figure 1, Δ ABC∼ Δ DEF. Figure 1 Similar triangles whose scale factor is 2 : 1. The ratios of corresponding sides are 6/3, 8/4, 10/5.

Answer:

The answer is D!

The value of the equation is P ( 4 , 4 ) , where P is the point of intersection of the equations

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 first equation be represented as A

Now , the value of A is

4x - 2y = 8  

Adding 2y on both sides of the equation , we get

2y + 8 = 4x

Subtracting 8 on both sides of the equation , we get

2y = 4x - 8   be equation (1)

Now , let the second equation be represented as B

Now , the value of B is

y = ( 3/2 )x - 2

On simplifying the equation , we get

2y = 3x - 4   be equation (2)

Now , subtracting equation (2) from equation (1) , we get

4x - 8 - ( 3x - 4 ) = 0

4x - 8 - 3x + 4 = 0

x - 4 = 0

Adding 4 on both sides of the equation , we get

x = 4

Substitute the value of x = 4 in equation ( 1 ) , we get

2y = 8

y = 4

So , the value of x = 4 and y = 4

The equations are plotted on the graph and the point of intersection is the solution to the equation , P ( 4 , 4 )

Hence , the equations are solved

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The new coordinates of the polygon are J'(-5/2, 3/2), K'(1, 3/2), L'(1, -3/2), M'(-5/2, -3/2).

Transformation is the movement of a point in the coordinate plane. Types of transformation are reflection, rotation, translation and dilation.

Dilation is the enlargement or reduction in the size of a figure by a scale factor.

Given the coordinates of polygon J(-5, 3), K(2, 3), L(2, -3), M(-5, -3). For a dilation with a scale factor of 1/2, the new coordinates are:

J'(-5/2, 3/2), K'(1, 3/2), L'(1, -3/2), M'(-5/2, -3/2).

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A fraction whose value is less than 1 is called a proper fraction. The numerator is less than the denominator.

A fraction represents the part of a set of objects. It has two parts separated by a dividing line, generally written a/b, where a is numerator and b is denominator.

There are 3 types of fraction. They are

1. Proper fraction

A proper fraction is a fraction whose numerator is less than the denominator. It makes the value is less than 1.

Example: 1/4, 3/5.

2. Improper fraction

An improper fraction is a fraction whose numerator is more than the denominator. The value is more than one.

Example: 6/5, 7/4.

3. Mixed fraction

A mixed fraction is a combination of a whole number and a proper fraction. It is the quotient and the remainder of improper fraction.

Example:

From the explanation, we get a fraction that the value is less than one is a proper fraction.

Your question is incomplete, but most probably your full question was

A fraction whose value is less than 1 is called ...

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Answer:

1) y=0.56x

2)y=5x

3)y= 0.25x

Step-by-step explanation:

1) 2.24/4 = $0.56 (Cost per carton)

2) 15/3=5 ( miles ran per hour)

3) 3/12 = 0.25 (cost per ounce)

Makena deposited $0.70 per day.

In mathematics, the middle value—which is determined by dividing the sum of all the values by the total number of values—is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.

Given:

The savings account last month: $6.74, $5.21, $5.53, and $3.52.

Makena deposited $6.74,$5.21,$5.53 and $3.52 in her saving account.

To find the average amount she saves per day.

We add all the deposited savings

= ( 6.74 + 5.21 + 5.53 + 3.52)

= $21.031

Now, Makena Saved per day for the month = $21.031/30

                                                                        =$0.70

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The lateral surface area of the cone is:

A = 84.3 in²

We know that for a cone of height H and a radius R, the lateral surface area is given by the formula:

A = pi*R*( √(H² + R²))

Where pi = 3.14

Here the height is 12 inches, and the diameter is 4.4 inches, then the radius is:

R = 4.4i/2 = 2.2 in

Then the lateral surface area is:

A = 3.14*2.2in*( √((12in)² + (2.2in)²))

A = 84.3 in²

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The slope is 1/2 throughout the entire line.

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Answer:

Step-by-step explanation:

Lorenzo is running the 100-meter dash and after 67 meters his right shoe falls off. So the remaining distance that Lorenzo has to run with 1 shoe is:

100-meter dash - 67 meters = 33 meters

So, Lorenzo has to run 33 meters with 1 shoe.

Answer:

Step-by-step explanation:

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Answer: 45 degrees

Step-by-step explanation:

By the inscribed angle theorem, the measure of an inscribed angle is half the measure of the intercepted arc. The measure of the central angle ∠POR of the intercepted arc ⌢PR is 90°. Therefore, m∠PQR=12m∠POR =12(90°) =45°.

We can restricted domain of the quadratic(y=x^2 +4) is {-∞,0} or {0,∞}.

What is Quadratic Equation?

Having the form ax^2 + bx + c = 0, quadratic equations are second-degree algebraic expressions. From the term "quad," which meaning square, comes the word "quadratic." A quadratic equation is a "equation of degree 2," to put it another way. A quadratic equation is employed in numerous situations.  In addition, there are many uses for quadratic equations in physics, engineering, astronomy, etc.

There are a maximum of two solutions for x in the second-degree quadratic equations. These two solutions for x are denoted as (, ) and are also known as the roots of the quadratic equations.

What is Domain?

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

It cannot have an inverse function because the largest exponent is even (2), unless the domain is constrained.

We know that the vertex is at x = 0 since our equation is already in vertex form;

a(x - h)^2 + k, or 1(x - 0) + 4

In order to limit the domain to only one side of x = 0

either  {-∞,0} or {0,∞}

Therefore, We can restricted domain of the quadratic(y=x^2 +4) is {-∞,0} or {0,∞}.

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Answer: 2x = 1/2

You just have to simplify the expression

Hope this helps !

So on solving the provided question, we can say that - in the circle angle DGF = 59 .

Every point in the plane that is a certain distance away from a certain point forms a circle (center). It is, thus, a curve formed by points moving in the plane at a fixed distance from a point. At every angle, it is also rotationally symmetric about the center. A circle is a closed two-dimensional object where every pair of points in the plane are equally spaced out from the "center." A line that goes through the circle creates a specular symmetry line. At every angle, it is also rotationally symmetric about the center.

here,

in the circle

angle AGC = angle DGF

so angle DGF = 59

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Answer:

Step-by-step explanation:

7 left 3 up

(x-7)(y+3)

Answer:

r

Step-by-step explanation:

e

Answer:

25%

Step-by-step explanation:

percent change = (new value - old value)/(old value) × 100%

percent change = (20 - 16)/(16) × 100%

percent change = 25%

Answer: 2 and 5.

Step-by-step explanation: We can use algebra to solve for the original numbers. Let's call the smaller number "a" and the larger number "b". From the information given, we know that:

x = b + a^2

y = b - a

The volunteer tells the magician that x = 9 and y = 3. So we can use these values to create a system of equations:

b + a^2 = 9

b - a = 3

To solve for the original numbers, we can first add the two equations together to eliminate b:

a^2 + 2a + 2 = 12

a^2 + 2a = 10

a^2 + 2a - 10 = 0

(a + 5)(a - 2) = 0

This tells us that the two solutions for a are -5 and 2. But since a is a positive integer, we know that it must be 2.

We can now substitute this value of "a" back into the original equations to find "b":

b + a^2 = 9

b + 2^2 = 9

b + 4 = 9

b = 5

So the original numbers are 2 and 5.

The equation of the line that passes through the point (1,7) with slope

3|5 is 5y=3x+32

Finding the slope between two points on a line and solving for the y-intercept in the slope-intercept equation y=mx+b allows us to formulate an equation for that line.

To find an equation of a line given the slope and a point.

Identify the slope.

Identify the point.

Substitute the values into the point-slope form, y − y 1 = m ( x − x 1 ) . y − y 1 = m ( x − x 1 ) .

Write the equation in slope-intercept form.

According to the given equation

y=mx+c

where m=3/5

To find c we substitute the values of x as 1 and y as 7

y=3/5x+c

7=3/5+c

c=32/5

Hence substituting c in the equation we get

5y=3x+32

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The equation that she can use as statement 5 is c) (3x + 24): 51 = 3x: 85.

To prove that x = 12, Dora must first prove that the segments ST and RQ are parallel. This can be done by showing that the angles formed by their intersection are congruent.

Since the angles, QRT and STP are congruent (statement 2) and the angles SPT and QPR are congruent (statement 3), the Triangle-Angle Angle Similarity Postulate can be applied to show that triangle SPT is congruent to triangle QPR (statement 4).

Now, the corresponding sides of the two triangles must be in proportion in order to prove that x = 12. For this, Dora can use the equation (3x + 24) : 51 = 3x : 85 (statement 5). This equation states that the ratio of the lengths of the corresponding sides of the two triangles is equal to the ratio of 3x to 51 and 3x to 85, respectively.

Since the ratio of the sides of the two triangles must be equal, then 3x + 24 must be equal to 85 and 3x must be equal to 51. Solving for x, we get x = 12, proving that if segment ST is parallel to segment RQ, then x = 12.

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The complete question

Look at the figure shown below. Dora is writing statements as shown to prove that if segment ST is parallel to segment RQ, then x = 12.

1.Segment ST is parallel to segment QR

Given

2.Angle QRT is congruent to angle STP

Corresponding angles formed by parallel lines and their transversal are congruent.

3.Angle SPT is congruent to angle QPR

Reflexive property of angles.

4.Triangle SPT is congruent to triangle QPR

Angle-Angle Similarity Postulate

5.?Corresponding sides of similar triangles are in proportion.

Which equation can she use as statement 5?

(3x + 24) : 3x = 85 : 51

(3x + 24) : 81 = 3x : 51

(3x + 24) : 51 = 3x : 85

34 : 24 = 3x : 51

Answer:

"x-9" can also be written as "x minus nine" or "nine subtracted from x"