Make x the subject of the formula where x is positive
b= x -6 / x + 2

(a) The fundamental matrix for the given system of equations is Φ(t) = e^(At).

Let's denote the given coefficient matrix as A:

A = [ -1 -4

      1 -1 ]

The fundamental matrix Φ(t) for the system is given by the matrix exponential of the coefficient matrix A multiplied by t:

Φ(t) = e^(At)

(b) The fundamental matrix φ(t) satisfying φ(0) = I is the identity matrix.

Finding the fundamental matrix φ(t) satisfying φ(0) = I:

To find the fundamental matrix φ(t) satisfying φ(0) = I, we substitute t = 0 into Φ(t):

φ(0) = Φ(0) = e^(A * 0) = e^(0) = I

So, the fundamental matrix φ(t) satisfying φ(0) = I is the identity matrix.

In summary, for the given system:

(a) The fundamental matrix Φ(t) is e^(At).

(b) The fundamental matrix φ(t) satisfying φ(0) = I is the identity matrix, denoted as φ(t) = I.

To know more about fundamental matrix refer here:

https://brainly.com/question/31981855?#

#SPJ11

Answer:

7.81

Step-by-step explanation:

The scalar multiplication of -3w, where w = (-2, 4), is (-6, -12).

Scalar multiplication involves multiplying a vector by a scalar, which is simply a number. In this case, we are multiplying the vector w by the scalar -3. To do this, we multiply -3 by each component of w, giving us (-3 * -2, -3 * 4) = (6, -12).

Geometrically, scalar multiplication stretches or shrinks a vector by a factor of the scalar. If the scalar is positive, the vector will be stretched or shrunk in the same direction. If the scalar is negative, the vector will be stretched or shrunk in the opposite direction (i.e., it will be flipped around the origin).

In this case, because the scalar is negative, the resulting vector is flipped around the origin. We can visualize this by drawing the vector w = (-2, 4) on a coordinate plane and then drawing the vector -3w = (6, -12) starting from the same point. We'll see that -3w is a reflection of w across the origin.

It's important to note that scalar multiplication is a fundamental operation in linear algebra, and it has many applications in fields such as physics, engineering, and computer graphics. It allows us to scale and transform vectors, which are often used to represent physical quantities like forces, velocities, and displacements.

To learn more about scalar multiplication, click here: brainly.com/question/30221358

#SPJ11

To find the probability that x is between 17 and 27, we need to standardize the values using the standard normal distribution, with a mean of 0 and a standard deviation of 1.

First, we standardize 17 and 27 as follows:

z = (x - μ) / σ

For x = 17:

z = (17 - 22) / 5 = -1

For x = 27:

z = (27 - 22) / 5 = 1

We can then look up the area under the standard normal distribution curve between z = -1 and z = 1 using a standard normal distribution table or a calculator. The area between these values represents the probability that x is between 17 and 27.

Using a standard normal distribution table, we find that the area between z = -1 and z = 1 is approximately 0.6827.

Therefore, the probability that x is between 17 and 27 is approximately 0.6827.

To learn more about probability refer below:

https://brainly.com/question/32004014

#SPJ11

To solve the problem we will calculate the amount of food consumed by Deon's dog in 2.5 weeks.

The new bag of food will last for 2.5 weeks.

Given to us

To know the amount of food consumed by Deon dog in 2.5 weeks, we will multiply the food consumed by Deon dog in 1-week by the Number of weeks for which food is been consumed.

Food consumed by Deon dog in 2.5 weeks

= Food consumed by Deon dog in 1-week x Number of weeks

= 62 cups of dog food x 2.5

= 155 cups of dog food

Thus, the food consumed by Deon's Dog is 155 cups.

As we can see the Dog will consume 155 cups of dog food in 2.5 weeks, therefore, the new bag of food will last for 2.5 weeks.

Learn more about Multiplication:

https://brainly.com/question/19943359

Answer:

60 minutes

Step-by-step explanation:

Given that Employee I can finish washing a car in 30 minutes. and

employee 2 can finish washing a car in 20 minutes.

Assuming that both will wath the car together after n minutes.

So, n must be the integral multiple of 30 as well as 20.

For niminum value of n,  n must be the lowest common factor of 30 and 20.

\(\Rightarrow n = LCM(30,20) \\\\\Rightarrow n = 60.\)

Hence, after 60 minutes, they will wash a care togethre.

Answer:

Lesser x = -4/3

Greater x = -1

Step-by-step explanation:

By the Zero Product Property, the roots are found by setting each factor equal to 0:

x+1 = 0

x = -1

3x+4 = 0

3x = -4

x = -4/3

So, the lesser x is -4/3 and the greater x is -1.

Answer:

how do you want me to help you?

;)

how can I help you help tell me

Answer:

A: r = d/t   B: 380,160  C: 216  D: miles/hour

Step-by-step explanation:

A: d = rt

Rearrange by dividing both sides by time(t)

d/t = r

B: d = 760,320 yards

t = 2 hours

r = d/t

r = 760,320 / 2

r = 380,160 yards/hr

C: 1 mile = 1760 yards

760,320 / 1760 = 432 miles

r = 432 / 2 = 216 miles/hour

D: It makes more sense to use miles per hour in this situation because it is the unit of measurement commonly used for measuring a vehicle's rate.

True, if V is a vector space with dimension n, then V has exactly one subspace with dimension 0 and exactly one subspace with dimension n.

A subspace of a vector space V is a subset of V that is also a vector space itself, under the same operations of vector addition and scalar multiplication as V. The dimension of a subspace is defined as the number of linearly independent vectors that span the subspace.

Now, let's consider the two cases:

Subspace with dimension 0:

A subspace with dimension 0 is a subspace that contains only the zero vector, denoted by {0}. Since the zero vector is always in any vector space, including V, there is exactly one subspace with dimension 0 in V, which is {0} itself.

Subspace with dimension n:

Since V has dimension n, it means that V is spanned by n linearly independent vectors. Therefore, the entire vector space V itself is a subspace of dimension n, as it satisfies all the properties of a subspace. Hence, there is exactly one subspace with dimension n in V, which is V itself.

Therefore, the statement is true, as there is exactly one subspace with dimension 0 and exactly one subspace with dimension n in a vector space V of dimension n

To learn more about vector space here:

brainly.com/question/13058822#

#SPJ11

The probability that a random sample of 12 second grade students results in a mean reading rate of more than 95 words per minute is 0.4582.

Given that the population mean, \(\mu\) = 90 wpm

The standard deviation of the population ,\(\sigma\) = 10

Sample size, n = 12

Sample mean, \(\bar x\) = 95

The reading rate of students follows the normal distribution.

Let z = \(\frac{\bar x - \mu}{\frac{\sigma}{\sqrt n} }\)

        = \(\frac{95 - 90}{\frac{10}{\sqrt 12} }\)

        = 1.732

Probability that the mean reading exceeds 95 wpm = P(\(\bar x\) >95)

                                                                                       = P(z>1.732)

                                                                                       = 1- P(z<1.732)

                                                                                       = 0.4582

[The value 0.4582 found from the area under the normal curve using tables].

Learn more about Normal Distribution at https://brainly.com/question/27701525

#SPJ4

Answer:

\(\huge\boxed{5p;\ (p+1)}\)

Step-by-step explanation:

\(5p^3+45p^2+40p=5p(p^2+9p+8)=5p(p^2+p+8p+8)\\\\=5p\bigg[p(p+1)+8(p+1)\bigg]=5p(p+1)(p+8)\\\Downarrow\\\boxed{5p};\ \boxed{(p+1)};\ \boxed{(p+8)}\)

the factors for the given expression are

\(5p, p+1, p+8\)

Given :

Given expression is \(5p^3 + 45p^2 + 40p\)

Lets factor the given trinomial by factoring out GCF that is greatest common factor

Lets find out GCF from the given expression

all the terms are divisible by 5  and also we have 'p' in common

so GCf is 5p

\(5p^3 + 45p^2 + 40p\\5p\left(p^2+9p+8\right)\\\)

Now we factor \(\left(p^2+9p+8\right)\)

Product is 8  and sum is 9

So factors are 8  and 1

\(5p\left(p^2+9p+8\right)\\5p\left(p+1\right)\left(p+8\right)\)

So the factors are

\(5p, p+1, p+8\)

Learn more : brainly.com/question/20127500

Answer:

Step-by-step explanation:

Idkkkkkkk

There is sufficient evidence to support the claim of a greater variance for machine 1

Given: n1=25 , n2​=22

The mean is the sum of all values divided by the number of values:

x1=2.95+3.45+...+3.35+3.12/25≈3.3284

x2​=3.22+3.30+...+3.16+3.33​/22≈3.2782

The variance is the sum of squared deviations from the mean divided by n−1. The standard deviation is the square root of the variance:

s1=√(2.95−3.3284)²+....+(3.12−3.3284)²/25−1≈0.2211

s1​=√25−1(2.95−3.3284)2+....+(3.12−3.3284)2​

​≈0.2211

s2=(3.22−3.3284)2+....+(3.33−3.3284)222−1≈0.0768

s2​=(3.22−3.3284)2+....+(3.33−3.3284)2²/22−1​≈0.0768

Determine the hypotheses:

H0=σ12≤σ22

H1​=σ12​>σ22​

Compute the value of the test statistic:

F=\(\frac{S^1_2}{S^2_2}\) =0.2211²/0.0768²≈8.288

The P-value is the probability of obtaining the value of the test statistic, or a value more extreme. The P-value is the number (or interval) in the column title of Table 4 containing the F-value with dfn=25−1=24 and dfd=22−1=21:

P<0.01

If the P-value is less than the significance level, reject the null hypothesis.

P<0.01⇒ Reject H0

Complete Question:

The variance in a production process is an important measure of the quality of the process. A large variance often signals an opportunity for improvement in the process by finding ways to reduce the process variance. Conduct a statistical test to determine whether there is a significant difference between the variances in the bag weights for the two machines. Use a .05 level of significance. What is your conclusion? Which machine, if either, provides the greater opportunity for quality improvements?

To learn more about the standard deviation, visit:

brainly.com/question/23907081

#SPJ4

There is sufficient evidence to support the claim of a greater variance for machine 1

Given: n1=25 , n2​=22

The mean is the sum of all values divided by the number of values:

x1=2.95+3.45+...+3.35+3.12/25≈3.3284

x2​=3.22+3.30+...+3.16+3.33​/22≈3.2782

The variance is the sum of squared deviations from the mean divided by n−1. The standard deviation is the square root of the variance:

s1=√(2.95−3.3284)²+....+(3.12−3.3284)²/25−1≈0.2211

s1​=√25−1(2.95−3.3284)2+....+(3.12−3.3284)2​

​≈0.2211

s2=(3.22−3.3284)2+....+(3.33−3.3284)222−1≈0.0768

s2​=(3.22−3.3284)2+....+(3.33−3.3284)2²/22−1​≈0.0768

Determine the hypotheses:

H0=σ12≤σ22

H1​=σ12​>σ22​

Compute the value of the test statistic:

F= \(\frac{S_2^1}{S_2^2}\) =0.2211²/0.0768²≈8.288

The P-value is the probability of obtaining the value of the test statistic, or a value more extreme. The P-value is the number (or interval) in the column title of Table 4 containing the F-value with dfn=25−1=24 and dfd=22−1=21:

P<0.01

If the P-value is less than the significance level, reject the null hypothesis.

P<0.01⇒ Reject H0

To learn more about Standard deviation:

brainly.com/question/23907081

#SPJ4

Complete Question:

The variance in a production process is an important measure of the quality of the process. A large variance often signals an opportunity for improvement in the process by finding ways to reduce the process variance. Conduct a statistical test to determine whether there is a significant difference between the variances in the bag weights for the two machines. Use a .05 level of significance. What is your conclusion? Which machine, if either, provides the greater opportunity for quality improvements?

Answer:

4 × (7 - 3)

Step-by-step explanation:

You first subtarct 3 from 7 and then multiply that answer by 4

Answer:

4 × (7 - 3)

Step-by-step explanation:

Answer:

18, 19(which has two) 20(has two)

Step-by-step explanation:

Just find the ones that appear more than one time.

Answer:

18

Step-by-step explanation:

Re-arrange

16 16,16,17,18,||18,18||,19,19,19,20,20

Find the middle number

i.e ( 18+18) /2

One of the factors is present in all of the items mentioned. The order of the value of the other factor will match the order of the value of the product.

To learn more about Multiplicative comparison refer to:

https://brainly.com/question/171046

#SPJ1

Answer:

i think its

Step-by-step explanation:

— 34 ∙ 2 = 36 34 + 2 = 36 36 + 34 = 2 34 – 2 = 36.

Answer:

34+2=36

Step-by-step explanation:

If 36-2=34, then it is the same the other way around meaning 34+2=36.

The measures of the angles in the completed table of the question can be presented as follows;

Angle AFB \({}\)        \({}\)Angle BFC      Angle DFE   Angle EFA

48          \({}\) \({}\)             42                    48                132

36 \({}\)                       54                    36                144

40\({}\)                        50                    40                140

An angle is a geometric figure formed by the opening (space) at the point where two rays meet.

The specified angle measurement indicates that we get;

Angle AFB and angle BFC are complementary angles

Angle AFB and angle DFE are vertical angles

Vertical angles are congruent

Angle EFA and angle BFD are vertical angles

Angle BFD = Angle BFC + Angle CFD

Therefore;

Angle EFA = Angle BFC + Angle CFD

Angle CFD = 90°

The completed table can be presented as follows;

Angle AFB \({}\)             Angle BFC         Angle DFE              Angle EFA

48 \({}\)                             42                          48                       132

AFB = DFE = 36 \({}\)    BFC=90-36 =54       36                        90 + 54 = 144

90-50 = 40\({}\)      \({}\)      140 - 90 = 50            40                        140

The possible question, obtained from a similar question on the internet can be presented as follows;

The rows in the following table represent a complete set of angle measurement in the attached drawing created with MS Excel

Make use of the drawing and the angle measurements in each row on the table to find the missing (required) angle measurement

Angle AFB \({}\)         Angle BFC             Angle DFE               Angle EFA

48                   \({}\)     42                           48                            132

                                                          36                                

\({}\)                                                                                           140

Learn more on vertical angles here: https://brainly.com/question/4282601

#SPJ1  

The Interval that is the approximate 95% confidence interval is 0.094 to 0.146

The Interval can be calculate as below:

α = 12%= 0.12  represent the proportion estimated

\(SE\) = 0.013 represent the standard error

The confidence interval for the true proportion is given by:

α ± \(z_{\alpha/2 } SE\)

And for 95% of confidence the critical value is \(z_{\alpha/2 }\) =1.96 and when we subtitute the value to the formula we got:

0.12± 1.96 x 0.013 =(0.094, 0.146)

The Interval that is the approximate 95% confidence interval is 0.094 to 0.146

Hence, the Interval that is the approximate 95% confidence interval is 0.094 to 0.146

Learn more about  confidence interval  here: https://brainly.com/question/14095092

#SPJ4

Given that, the parametric equations are x = t cos(t) and y = t sin(t), where t = pi.

The first derivative of x(t) is `dx/dt=cos(t)-t*sin(t)`The first derivative of y(t) is `dy/dt=sin(t)+t*cos(t)`Let (x, y) be the point on the curve where t = π.

So the coordinates of the point are `(x, y) = (π(-1), π(0))`.The slope of the tangent line is `dy/dx=dy/dt÷dx/dt`.

Therefore, `dy/dx=(sin(t)+t*cos(t))/(cos(t)-t*sin(t))`, and at `t = π`, we have `dy/dx = (0 + π(-1)) / (-1 - π(0)) = π/(1) = π`.So the slope of the tangent line is π when `t = π`.

Thus the equation of the tangent line at t = π is `y = π(x - π)`.

The derivative of a function measures the rate at which the function's value changes with respect to its input variable. It provides information about the slope or steepness of the function at a particular point. The derivative of a function f(x) is commonly denoted as f'(x) or dy/dx.

Visit here to learn more about derivative brainly.com/question/29144258

#SPJ11

Answer:

same, man. wish I could go back to elementary school where everything was easy and fun.

If x < 3, then the square root of  (x^2 - 6x + 9) can be simplified to (3-x).

First we factorise the quadratic expression:

x^2 - 6x + 9 = (x - 3)^2 ..(i)

(Since the expression is a perfect square trinomial, it can be factored as the square of a binomial.)

Then we will simplify the square root:

√(x^2 - 6x + 9) = √((x - 3)^2).

Now, since x - 3 is squared, taking the square root will eliminate the square, resulting in the absolute value of x - 3.

Final simplified form: √((x - 3)^2) = |x - 3|.

Therefore, the simplified square root expression is |x - 3| when x < 3 which equals to 3-x.

To learn more about polynomial factorisation,

https://brainly.com/question/26685427

Answer:

x=12/5

Step-by-step explanation:

x*5/12=1

x=1*12/5

x=12/5

Answer:

x = 12/5

Step-by-step explanation:

Combine multiplied terms into a single fraction

5x/12 = 1

Multiply all terms by the same value to eliminate fraction denominators

12 x 5x/12 = 12

Cancel multiplied terms that are in the denominator

5x = 12

x = 12/5

Answer:

5/9

Step-by-step explanation:

we add all of the values and divide by the total number in this case 9, all of them add to make 5 so we do 5÷9 to get 5/9

The important resonance structures for the given ion must be drawn, showing all lone pairs of electrons, formal charges, double bonds, and electron flow arrows.

Resonance structures are alternative representations of a molecule or ion that differ only in the placement of electrons. They are important in understanding the stability and reactivity of organic compounds. In this case, we are asked to draw the important resonance structures for a specific ion.

To start, we need to identify the ion and its molecular formula. Once we have that information, we can determine the possible resonance structures. Each resonance structure is a valid Lewis structure that obeys the octet rule and maintains the overall charge of the ion.

To draw the resonance structures, we begin by placing the atoms in their correct positions and adding lone pairs of electrons as needed. Next, we identify any double bonds or formal charges present in the original ion.

Using curved arrows, we show the movement of electrons to generate alternative resonance structures. The movement of electrons can involve breaking and forming bonds, as well as the shifting of lone pairs.

By drawing all the important resonance structures, we gain a better understanding of the electron distribution and the stability of the ion. This knowledge is crucial for predicting the reactivity and behavior of the compound.

Learn more about Resonance structures

brainly.com/question/14466514

#SPJ11

Answer:

-1/3 Is the coeff because y is multiplied by it