Rewrite (5)/(6)x+2=(7)/(8) so that is doesn't have any fractions. Don't use decimals in the answer.

Answer : The answer is B= -12

a. Φ(t)= P.D.[tex]P^{-1}[/tex] is the fundamental matrix of the homogeneous system.

b. [tex]P^{-1}[/tex]= 1/√5 || 1 2 || || -2 1 || is the inverse

c. x(t)= Φ(t)∫ Φ(t)-1.b(t) dt + Φ(t).[tex]x_0[/tex]

d. The solution to the system is x(t)= || e-t/√5 (1-e2t)/2√5 - (2e2t -3)/2√5 || || 1/√5 e-t/√5 +2/√5 (e2t-1)/2√5 ||

In this problem, we will solve the nonhomogeneous system.

Firstly, we will write a fundamental matrix for the associated homogeneous system 1 1 2 0.

a) Fundamental matrix for the homogeneous system

The homogeneous system of equations can be written as:

X'=AX

Here, X is the vector of unknowns, and A is a matrix of constants.

For the given homogeneous system of equations, we have:

1 1 2 0X1' X2'= 1 2 X1X2

X'= AX

Thus, the matrix A can be written as:

A= 1 2 1 0

Now, let us solve the eigenvalue problem for matrix A as follows:

| A - λI |= 0

⇒| 1 - λ 2 || 1 || λ - 0 || 1 || 2 || 0 - λ || 0 |

⇒ (1-λ)(0-λ)-2⋅1=0

⇒ λ2 - λ - 2 = 0

On solving, we get:

λ1 = -1 and λ2 = 2

Thus, the eigenvectors corresponding to these eigenvalues are:

For λ1 = -1, A - (-1)I= 2 2 || x || = 0 1 || y ||

⇒2x+2y = 0y = -2x

Thus, the eigenvector corresponding to λ1 is:

x1= || 1 || and x2 = || -2 ||

The normalized eigenvector corresponding to λ1 is:

x1= || 1/√5 || and x2 = || -2/√5 ||

For λ2 = 2, A - 2I= -1 2 || x || = 0 -2 || y ||

⇒-x+2y = 0y = 1/2x

Thus, the eigenvector corresponding to λ2 is:

x1= || 2 || and x2 = || 1 ||

The normalized eigenvector corresponding to λ2 is:

x1= || 2/√5 || and x2 = || 1/√5 ||

Thus, the matrix P of eigenvectors is:

P= || 1/√5 -2/√5 || || 2/√5 1/√5 ||

Hence, the fundamental matrix of the homogeneous system is:

Φ(t)= P.D.[tex]P^{-1}[/tex]

where D= diagonal matrix of eigenvalues= || -1 0 || || 0 2 ||and [tex]P^{-1}[/tex] is the inverse of matrix P.

We will now find the inverse of matrix P.

b) Computation of inverse of matrix P

The inverse of matrix P is:

[tex]P^{-1}[/tex]= 1/√5 || 1 2 || || -2 1 ||

c) Multiplication by and integration

Multiplying Φ(t) by e

At, we have:e AtΦ(t)= PeDt.

[tex]P^{-1}[/tex].eAt= P.|| e-1t 0 || || 0 e2t ||.[tex]P^{-1}[/tex]

The solution to the system is:

x(t)= Φ(t)∫ Φ(t)-1.b(t) dt + Φ(t).[tex]x_0[/tex]

where b(t) is the vector of inhomogeneous terms, and [tex]x_0[/tex] is the initial condition.

d) Solution to the system

The nonhomogeneous system of equations can be written as:

X'=AX + b

where b= 1 [tex]e^{-t}[/tex]

The solution to the system is:

x(t)= Φ(t)∫ Φ(t)-1.b(t) dt + Φ(t).x0= P.|| e-t/√5 (e2t -1)/2√5 || || -2(e2t-1)/2√5 e-t/√5 ||.P-1 .|| 0 || || 1 ||+ P.|| 1/√5 -2/√5 || || e-t/√5 (e2t -1)/2√5 || || -2(e2t-1)/2√5 e-t/√5 ||.P-1 .|| -1/√5 || || 2/√5 ||= || 1/√5 -2/√5 || || e-t/√5 (1-e2t)/2√5 || || (e2t-3)/2√5 e-t/√5 ||.|| 0 || || 1 ||+ || 1/√5 -2/√5 || || e-t/√5 (e2t -1)/2√5 || || -2(e2t-1)/2√5 e-t/√5 ||.|| -1/√5 || || 2/√5 ||
The final answer is: x(t)= || e-t/√5 (1-e2t)/2√5 - (2e2t -3)/2√5 || || 1/√5 e-t/√5 +2/√5 (e2t-1)/2√5 ||

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Answer:

-1

Step-by-step explanation:

calculator

:)

The interpretation of a peak flow measurement obtained from bedside spirometry on a 35-year-old woman who is 5 feet 7 inches tall would suggest that her lung function is lower than what is predicted for her age and height, indicating some degree of airway obstruction or restriction.

To interpret the results of the spirometry test, we need to compare the obtained peak flow measurement to the predicted values based on the individual's age, height, gender, and race. This is because the normal lung function varies depending on these factors.

For instance, the predicted peak flow measurement for a 35-year-old woman who is 5 feet 7 inches tall is approximately 4.25 l/sec.

Therefore, an interpretation of the obtained peak flow measurement of 2.3 l/sec is that it is lower than the predicted value, indicating that the woman may have some degree of airway obstruction or restriction.

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Answer: 1.06 rounded

Step-by-step explanation:

7/6.58 = 1.06 rounded

Hope it helps I'm running out of time!!

Have a nice day!!!!

The total time taken to make combined 60 cookies by Larry and Mary is equal to 75.79 minutes.

Rate at which each person can make cookies

Time to make one batch of 3 cookies made by Larry = 8 minutes

⇒Number of cookies per minute = 3/8 cookies

Time to make one batch of 5 cookies made by Mary = 12 minutes

⇒Number of cookies per minute = 5/12 cookies

Combined rate at which they make cookies,

= 3/8 + 5/12

= 9/24 + 10/24

= 19/24 cookies per minute

Together they can make 19/24 cookies per minute.

To make a total of 60 cookies,

Let 't' be the time in minutes required to make 60 cookies.

⇒ (19/24) t = 60

⇒ t = (60)/(19/24)

⇒ t  = 75.79 minutes (rounded to two decimal places)

Therefore, total time taken by  Larry and Mary approximately 75.79 minutes to make a combined total of 60 cookies.

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Answer:

Any line with the slope 1 or y = x + b

Step-by-step explanation:

Parallel lines by definition have the same slope

Value of the y-intercept or b doesn't matter in this case

You have to find the slope of the line through (3,6) and (5,8)

Slope equation is

Plug in values given

[tex]\frac{8-6}{5-3}[/tex]

Evaluate

[tex]\frac{2}{2} =1[/tex]

Any line with the slope of 1 (or no co-efficient in front of x) would be parallel to the line through (3,6) and (5,8)

Answer:

4

Step-by-step explanation:

Answer: w=4

Step-by-step explanation:

1).  5(3w)+2w=68

2). 15w+2w=68

3). 17w=68

4). 17w/17=68/17

5). w=4

When x = 3, y = 60 + 20(3) = 120. So, we can plot the point (3, 120).

An equation is a mathematical statement that uses symbols, numbers, and operations to show that two expressions are equal. It usually contains one or more variables, which represent unknown values that need to be solved for. Equations are used in a wide range of mathematical fields, such as algebra, geometry, calculus, and physics, to model real-world situations and solve problems. Some common examples of equations include:

Linear equation: y = mx + b

he total expenses for Myra's phone plan include the initial cost of buying the phone plus the monthly cost of the phone plan. Therefore, the total cost can be represented by the equation:

y = 60 + 20x

where y is the total cost and x is the number of months on the phone plan.

To graph this equation, we can plot a point at (0, 60) to represent the initial cost of buying the phone. Then, we can plot additional points by plugging in different values of x into the equation and finding the corresponding values of y. For example:

When x = 1, y = 60 + 20(1) = 80. So, we can plot the point (1, 80).

When x = 2, y = 60 + 20(2) = 100. So, we can plot the point (2, 100).

When x = 3, y = 60 + 20(3) = 120. So, we can plot the point (3, 120).

Connecting these points gives us a straight line, since the equation is linear.

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Answer:

The surface area would increase by a factor of 16.

Or you could also say:

Quadrupling the dimensions makes the surface area 16 times the original surface area.

Step-by-step explanation:

The surface area of a rectangular prism is calculated by adding the areas of all six faces. The formula for the surface area of a rectangular prism is 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height.

In this case, the surface area of the original rectangular prism with dimensions 3 ft by 6 ft by 5 ft would be: 2(3)(6) + 2(3)(5) + 2(6)(5) = 36 + 30 + 60 = 126 square feet.

If the dimensions of the box were quadrupled, the new dimensions would be 12 ft by 24 ft by 20 ft. The new surface area would be: 2(12)(24) + 2(12)(20) + 2(24)(20) = 576 + 480 + 960 = 2016 square feet.

So, if the dimensions of the box were quadrupled, the surface area would increase from 126 square feet to 2016 square feet. This represents an increase in surface area by a factor of 16.

The astronomer must rotate her telescope 86.829° to see star BBB. Rounding to the nearest degree, the astronomer must rotate her telescope 87°.

We can use the law of cosines to solve this problem. The law of cosines states that for a triangle with sides A, B, and C, A2 = B2 + C2 - 2BCcos(θ), where θ is the angle opposite side C.

In our case, A = 450450450, B = 400400400, and C = 909090. We know that angle θ is the angle we need to find, so we can rearrange the equation to solve for θ.

θ = cos-1(A2 - B2 - C2)/(-2BC)

θ = cos-1((450450450)2 - (400400400)2 - (909090)2)/(-2(400400400)(909090))

θ = cos-1(-9.65 × 10-12)/(-2.8 × 1012)

θ = cos-1(-3.4 × 10-13)

θ = 86.829°

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Answer:

The Answers

Step-by-step explanation:

Flag = 46

Clover = 46

Hat = 27

Acorridan thing = 198

Final answer = 317

Answer:

4 if x < 3

Step-by-step explanation:

First, find the equation of the line. From the graph we can tell the y-intercept is 4 and the slope is 0. Using y=mx+b, we find that y=(0)x+4 (same as y=4). f(x) is the same as y, so all you have to write is 4.

To find the domain, you must look at where the function is defined. It is only defined to the left of the point (3,4), where x < 3. We know its only defined there because the arrow and line only go in that direction. We know that it should be a < not a ≤ because the point at (3,4) is hollow, so (3,4) is not a point in the function and not included in the domain.

Answer:

Step-by-step explanation:

smelly a becasue

Answer:

60 and 100 degrees.

Step-by-step explanation:

Sum of the other 2 angles = 180-20 = 160 degrees.

3 + 5 = 8

160 / 8 = 20

- so the other 2 angles are:

3*20 = 60 and

5*20 = 100 degrees.

The average cost per motorist on a highway governed by a use fee based on congestion, operation and maintenance is determined by dividing the total cost ([tex]5t^2[/tex]) by the total traffic (t). So, the average cost per motorist is 5t.

The average cost per motorist for a highway governed by a use fee based on congestion, operation and maintenance can be determined by dividing the total cost ([tex]5t^2[/tex]) by the total traffic (t).

So, the average cost per motorist is 5t.

To better understand how this works, let's look at an example.

Suppose the total traffic is 20.

In this case,

the total cost is 5 × 202 = 2000.

Therefore, the average cost per motorist is 2000/20 = 100.

The cost per motorist is determined by the total traffic because the more cars there are on the highway, the more congested the highway will be.

Consequently, the more congested the highway, the more operation and maintenance is required, and thus the higher the use fee will be.

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The height of the right triangular prism is 84.3 cm.

To find the height of the right triangular prism, let's use the formula for the volume of a right triangular prism.

Volume of the right triangular prism = 1/2 × base × height × length

Where, base = 25 cm and height is what we need to find.

We are given that the volume of the prism is 0.075 cubic meters. We first need to convert the volume into cubic cm as the other units are given in cm. 1 cubic meter = 100 cm × 100 cm × 100 cm= 1,000,000 cubic cm

So, 0.075 cubic meters = 0.075 × 1,000,000 = 75,000 cubic cm

Substituting all the known values into the formula, we get:

75,000 = 1/2 × 25 × height × length

Hence, height = 75,000 / (1/2 × 25 × length)

Now, we need to find the length of the prism. As the base of the right triangular prism is a right isosceles triangle, its hypotenuse is the length of the prism. Using the Pythagorean theorem to find the hypotenuse, we have:

Length² = 25² + 25²

Length² = 1,250

Length = √1,250

Length ≈ 35.36 cm

Substituting this length into the equation we found earlier, we get:

height = 75,000 / (1/2 × 25 × 35.36)height ≈ 84.3 cm

So, the height of the right triangular prism is approximately 84.3 cm.

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Therefore, according to the model, the balloon is losing air at a rate of 13% per second.

In mathematics, a function is a rule that maps each element in one set, called the domain, to a unique element in another set, called the range. A function can be represented by an equation, a graph, or a table. Functions are commonly used to describe relationships between variables, such as how the area of a square changes as its side length increases. They are a fundamental concept in calculus, linear algebra, and many other branches of mathematics.

Here,

The function A(t) = 1.48(0.87)ⁿ represents the amount of air in the balloon t seconds after the leak begins.

To find the percentage at which the balloon is losing air each second, we need to find the percentage decrease in the amount of air for every one second of time passing.

To do this, we can calculate the ratio of the amount of air at time t=1 second to the amount of air at t=0 seconds, and then find the percentage decrease:

A(1) / A(0) = [1.48(0.87)¹] / [1.48(0.87)⁰] = 0.87

The ratio is 0.87, which means that the balloon is losing 13% of its air each second (since 1 - 0.87 = 0.13, which is 13% expressed as a decimal).

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Answer:

4[tex]m^{3}[/tex] +13m² + 4m - 12

Step-by-step explanation:

Use FOIL type method:

(4m^2 +5m - 6)(m+2)

= (4m^2)(m) + (5m)(m) - (6)(m) + (4m^2)(2) + (5m)(2) - (6)(2)

= 4m^3 +5m^2 +8m^2 -6m +10m -12

combine like terms:

= 4m^3 +13m^2 + 4m -12

The lower and upper bounds of x + y are 1040 and 1058, respectively.

What are lower bounds and upper bounds?

Lower bounds and upper bounds are used to define the range of possible values for a given quantity or measurement.

A lower bound represents the smallest possible value that a quantity could have, based on the available information or constraints. This means that the actual value of the quantity must be greater than or equal to the lower bound. For example, if we know that a person's height is between 150cm and 170cm, then the lower bound of their height is 150cm.

An upper bound represents the largest possible value that a quantity could have, based on the available information or constraints. This means that the actual value of the quantity must be less than or equal to the upper bound. For example, if we know that a person's weight is between 50kg and 80kg, then the upper bound of their weight is 80kg.

In some cases, we may be able to determine a range of possible values for a quantity using both a lower bound and an upper bound. This range of possible values is sometimes referred to as an interval or a confidence interval.

To find the lower and upper bounds of x + y, we need to consider the possible values of x and y that would result in the maximum and minimum values of their sum when added together.

Let's start by considering the possible values of x and y that would round to 630 and 420, respectively, when rounded to the nearest 10:

x: Any number between 625 and 634 would round to 630 when rounded to the nearest 10.

y: Any number between 415 and 424 would round to 420 when rounded to the nearest 10.

To find the lower bound of x + y, we need to add the smallest possible values of x and y:

Lower bound = 625 + 415 = 1040

To find the upper bound of x + y, we need to add the largest possible values of x and y:

Upper bound = 634 + 424 = 1058

Therefore, the lower and upper bounds of x + y are 1040 and 1058, respectively.

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Nοne οf the given graphs match this descriptiοn, sο nοne οf them shοw the sοlutiοn tο the equatiοn.

Equivalent expressiοns are expressiοns that wοrk the same way despite their appearance. If twο algebraic expressiοns are equivalent, then the twο expressiοns have the same value when the variable is set tο the same value.

The equatiοn lοg Subscript 3 Baseline (x + 2) = 1 can be rewritten as 3^1 = x + 2. This simplifies tο x = 1. Therefοre, the sοlutiοn tο the equatiοn is x = 1.

On the cοοrdinate plane, this sοlutiοn is represented by a vertical line passing thrοugh x = 1.

Hence, Nοne οf the given graphs match this descriptiοn, sο nοne οf them shοw the sοlutiοn tο the equatiοn.

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Answer: A

Step-by-step explanation:

USE MATH   WAY IT HELPS ALOT

Answer:

An even function is symmetric about the y-axis. An odd function is symmetric about the origin. As the graphed function is neither symmetric about the origin, nor symmetric about the y-axis, it is neither even nor odd.

Step-by-step explanation:

Even and odd functions are special types of functions.

An even function is symmetric about the y-axis. An odd function is symmetric about the origin. As the graphed function is neither symmetric about the origin, nor symmetric about the y-axis, it is neither even nor odd.

[tex]\cfrac{89.40~~ - ~~\stackrel{ \textit{minus the tax of each} }{0.50-0.50-0.50-0.50-0.50-0.50}}{6}\implies \cfrac{86.40}{6}\implies \stackrel{ each }{14.40}[/tex]

Answer:

21

Step-by-step explanation:

[tex]\frac{x}{6}=\frac{7}{2} \\x=21[/tex]

Answer:

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

Let the number of glasses be g.

Then g glasses can be filled with 3 1/2 bottles of water.

Set up equation to represent this and solve for g:

Answer:

The cube's volume can be represented as 8y^3 when expressed in terms of y.

Step-by-step explanation:

The side length of a cube is given as 2y. To express the volume of the cube in y, we can use the formula for the volume of a cube which is given as V = s^3, where s is the length of one side of the cube.

Substituting 2y as the length of the side of the cube, we get:

V = (2y)^3

Simplifying, we get:

V = 8y^3

Therefore, the volume of the cube expressed in terms of y is 8y^3.

The probability that Babby gets the same number of heads that Abby gets is 1/8 + 1/8 = 1/4. To solve this problem, we need to consider all the possible outcomes of Abby and Babby's coin tosses.

There are four possible outcomes for Abby's toss: heads or tails, and two outcomes for Babby's toss: heads or tails. Therefore, there are a total of 4 x 4 = 16 possible outcomes for the two coin tosses.

To determine the probability that Babby gets the same number of heads as Abby, we need to identify the outcomes where this happens. Abby can get either 0 or 1 heads, so we need to consider the outcomes where Babby gets 0 or 1 heads as well.

The possible outcomes where Abby gets 0 heads are:

Abby: tails, Babby: tails tails

Abby: tails, Babby: heads tails

In both of these outcomes, Babby also gets 0 heads, so the probability of this happening is 2/16 = 1/8.

The possible outcomes where Abby gets 1 head are:

Abby: heads, Babby: tails heads or heads tails

Abby: tails, Babby: heads heads

In two of these outcomes, Babby also gets 1 head, so the probability of this happening is 2/16 = 1/8. Therefore, the probability that Babby gets the same number of heads that Abby gets is 1/8 + 1/8 = 1/4.

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