factorise 7e(6f-2) +5(6f-2)

A sequence is (recursively) defined as a1 = 0, a2 = 1, n>2, \(a_n = a_{n-1} - 3a_{n-2}\). The first seven terms are 0, 1, 1, -2, -5, 1, 16.

A recursive sequence is a sequence in which terms are defined using one or more previous terms which are given.

a1 = 0

a2 = 1

\(a_n = a_{n-1} - 3a_{n-2}\)

a3 = a2 - 3*a1 = 1 - 0 = 1

a4 = a3 - 3*a2 = 1 - 3 = -2

a5 = a4 - 3*a3 = -2 - 3 = -5

a6 = a5 - 3*a4 = -5 + 6 = 1

a7 = a6 - 3*a5 = 1 +15 = 16

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The resulting expression is (14/150) multiplied by the conjugate of the denominator, (√108 + √96 - √192 + √54).

To rationalize the denominator of the expression 14 / (√108 - √96 + √192 - √54), we need to eliminate the square roots from the denominator by multiplying both the numerator and denominator by the conjugate of the denominator. The conjugate of the denominator is (√108 + √96 - √192 + √54).

Multiplying the numerator and denominator by the conjugate, we get:

14 * (√108 + √96 - √192 + √54) / ((√108 - √96 + √192 - √54) * (√108 + √96 - √192 + √54))

Expanding both the numerator and denominator, we have:

14 * (√108 + √96 - √192 + √54) / (108 - 96 + 192 - 54)

Simplifying further, we get:

14 * (√108 + √96 - √192 + √54) / 150

Now, we have successfully rationalized the denominator, and the expression becomes:

(14/150) * (√108 + √96 - √192 + √54)

In summary, to rationalize the denominator of the given expression, we multiplied the numerator and denominator by the conjugate of the denominator, which eliminated the square roots from the denominator.

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Answer: B

Step-by-step explanation:

Answer:

The common difference between each term in the sequence is 3. To find the 21st term, we can use the formula for the nth term of an arithmetic sequence:

a_n = a_1 + (n - 1)d

where a_1 is the first term, d is the common difference, and n is the term number we want to find.

Substituting the given values, we get:

a_21 = 15 + (21 - 1)3

a_21 = 15 + 60

a_21 = 75

Therefore, the answer is (c) a^21=75.

Answer:

-10 is the answer

Step-by-step explanation:

\(xy + 2y \\ putting \: the \: value \: of \: x \: and \: y \\ 3 \times ( - 2) + 2 \times ( -2 ) \\ - 6 - 4 \\ = - 10\)

Answer:

20

Step-by-step explanation:

the inverse of

y=1/2x + 10

is

x=1/2y+10

from here you just solve for y

x-10 = 1/2y

2(x-10) = y

2x-20 = y

1) Two linearly independent solutions for the homogeneous part of the given inhomogeneous differential equation (DE) are \(y1(x) = e^{(-x)\) and \(y2(x) = e^{(4x)\).

2) The trial functions u1(x) and u2(x) for the particular solution (P.S.) Yp(x) using the method of variation of parameters are \(u1(x) = -2e^{(-x)}sin(x)\) and \(u2(x) = 2e^{(4x)}sin(x)\).

3) The general solution (G.S.) for the original DE is \(y(x) = c1e^{(-x)} + c2e^{(4x) }- 2e^{(-x)}sin(x) + 2e^{(4x)}sin(x)\), where c1 and c2 are constants.

1) To find two linearly independent solutions for the homogeneous part of the given inhomogeneous DE y" + y = 2sin(x), we consider the corresponding homogeneous DE, which is y" + y = 0. The characteristic equation is r^2 + 1 = 0, which yields r = ±i. Therefore, the two solutions for the homogeneous DE are \(y1(x) = e^{(-x)\)and \(y2(x) = e^{(4x)\).

2) To determine the trial functions u1(x) and u2(x) for the particular solution (P.S.) Yp(x) using the method of variation of parameters, we assume that Yp(x) takes the form Yp(x) = v1(x)y1(x) + v2(x)y2(x), where v1(x) and v2(x) are unknown functions. Substituting this into the original DE, we obtain the following system of equations: v1'(x)y1(x) + v2'(x)y2(x) = 0 (homogeneous part), and v1'(x)y1'(x) + v2'(x)y2'(x) = 2sin(x) (particular part). Solving this system, we find \(v1'(x) = -sin(x)e^{(x)\)and \(v2'(x) = sin(x)e^{(-4x)\). Integrating these expressions yields \(v1(x) = -2e^{(-x)}sin(x)\)and \(v2(x) = 2e^{(4x)}sin(x)\).

3) The general solution (G.S.) for the original DE can be expressed as y(x) = Yh(x) + Yp(x), where Yh(x) is the homogeneous solution and Yp(x) is the particular solution. Therefore, the G.S. is given by \(y(x) = c1e^{(-x) }+ c2e^{(4x)} - 2e^{(-x)}sin(x) + 2e^{(4x)}sin(x)\), where c1 and c2 are arbitrary constants that can be determined from initial conditions or additional information, if provided. This solution satisfies both the homogeneous DE and the inhomogeneous DE, providing a complete solution to the given problem.

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Answer:

answer is mayonnaise duh

True, the Greek letter used to represent the probability of a Type I error is alpha ().

The Greek letter alpha (α) is indeed used in statistics, but it represents the level of significance chosen for a statistical test. The level of significance is the probability of rejecting the null hypothesis when it is actually true. The probability of making a Type I error (rejecting the null hypothesis when it is true) is equal to the level of significance (α) chosen for the test.

Therefore, alpha is not used to represent the probability of a Type I error directly, but it is related to it. The probability of a Type I error depends on the chosen level of significance and the specific hypothesis test being conducted.

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True. The Greek letter used to represent the probability of a Type I error is alpha

This is a statement and not a question. However, if you are asking whether the statement "the Greek letter used to represent the probability of a type i error is alpha (α)" is true or false, the answer is that it is partially true. While the Greek letter α is commonly used to represent the significance level (or the probability of a Type I error) in hypothesis testing, it is not the only letter that can be used.

Other letters such as β and γ may also be used in certain contexts. So the complete answer would be a long answer that explains the partial truth of the statement.

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Answer:

6.45

Step-by-step explanation:

Every part is 0.01 bigger or smaller

You can find it out by subtraction and then division

6.5 - 6.4 = 0.1

0.1 : 10 = 0.01

There are 10 parts that's why you divide it by 10.

If there will be 2 parts you will divide by 2

Location of F on the given decimal number line is \(6.45\) .

" Number line is defined as a straight line which represents the numbers on it with equal interval."

According to the question,

Given number line,

F is between two decimal numbers \(6.4\) and \(6.5\)

\(6.4\) and \(6.5\) divides into \(10\) equal parts.

On the number line distance between \(6.4\) and \(6.5\) is equals to \(0.1\)

Each part represents \(0.1 \over 10\) distance which is equals to \(0.01\).

F is on the \(5th\) location.

On the number line distance of F from \(6.4\) is \(0.01 \times 5 = 0.05\)

Therefore, location of F  

\(= 6.4 + 0.05\\\\= 6.45\)

Hence, location of F on the given decimal number line is \(6.45\) .

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Answer:

y=1/6x -1

Step-by-step explanation:

Use point-slope form to convert it to y=mx+b.

y-y1=m(x-x1)

y+2=1/6(x+6)

Distribute and simplify.

y+2=1/6x+1

y=1/6x-1

Answer:

$430

Step-by-step explanation:

Let the weekly income be x

Money spent on food= $86

% of weekly income spent on food = 20

20% of weekly income in terms = 20/100 * x = x/5

This, income is equal to $86 as given

thus,

x/5 = 86

x = 86*5 = 430

Thus, weekly income is $430.

Answer:

Reflection in the x-axis

Step-by-step explanation:

If the point (x, y) of the shape is rotated 180° about the origin, it will be transformed into the point (-x, -y).

If the point (-x, -y) is reflected in the Y-axis, it will be transformed into the point (x, -y). This transformation is equivalent to the reflection of (x, y) in the x-axis.

Answer:

The residual value when x = 4 is 0.58

Step-by-step explanation:

The residual value of a fitted function is the difference between the actual value of the data for a given input and the result of the fitted function. On this problem for the actual values, when \(x = 4\) we have \(y_{data} = 7.3\) , although, for the fitted function on the same value of "x", we have a different value, which is calculated below:

\(y(4) = 2.78*4 - 4.4 = 6.72\)

The residual value is:

\(\text{residual value} = y_{data} - y_{function} = 7.3 - 6.72 = 0.58\)

The residual value when x = 4 is 0.58

Functions are written in terms of variables.  The residual value when the value of x is 4 is 0.58

Functions are written in terms of variables. Given the following function that represent the data in the table

y = 2.78x – 4.4

If the value of x is 4, the corresponding value of y is expressed as:

y = 2.78(4) – 4.4

y = 11.12 - 4.4

y = 6.72

Determine the residual value

Residual value = 7.3 - 6.72

Residual value = 0.58

Hence the residual value when the value of x is 4 is 0.58

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If Billy, who works 6 hours per day and is paid overtime at time and a half, works 7 hours one day, he earns $72.00.

The total earnings for the day by Billy is the addition of the normal earnings and the overtime earnings.

Overtime rates are based on a time and a half, which is 150% of the normal hourly rate of pay.

Normal hourly rate of pay = $9.60

Normal day work hours = 6 hours

The number of hours worked for the day = 7 hours

Overtime hours for the day = 1 hour (7 - 6)

Overtime rate = $14.40 ($9.60 x 1.5)

Normal earnings for the day = $57.60 ($9.60 x 6)

Overtime earnings for the day = $14.40 ($14.40 x 1)

Total earnings for the day = $72.00 ($57.60 + $14.40)

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Answer:

Let one no. be 1x

other be 4x

x+4x=60

5x=60

x=12

4x=4×12

48

hope it helps :)

The correct set of possible results would be (0, 1, 0, 0), (1, 2, 1, 0) and (1, 2, 0, 1).

Your approach seems to be correct, but there seems to be a minor mistake in your final list of possible solutions. Let's go through the steps to clarify.

Given the initial conditions z=t=0, you obtained a partial solution (0,1,0,0).

Next, you solved the homogeneous equations for z=1 and t=0, which resulted in a solution (1,1,1,0).

Similarly, solving the homogeneous equations for z=0 and t=1 gives another solution (1,1,0,1).

To find the general solution, you combine the partial solution with the solutions obtained in the previous step, using parameters a and b.

(0,1,0,0) + a(1,1,1,0) + b(1,1,0,1)

Expanding this expression, you get:

(0+a+b, 1+a+b, 0+a, 0+b)

Simplifying, you obtain the following set of solutions:

(0, 1, 0, 0)

(1, 2, 1, 0)

(1, 2, 0, 1)

Therefore, the correct set of possible results would be:

(0, 1, 0, 0)

(1, 2, 1, 0)

(1, 2, 0, 1)

Note that (0, 1, 1, 1) is not a valid solution in this case, as it does not satisfy the initial condition z = 0.

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Answer:

please see analysis

Step-by-step explanation:

You can do this with a proportion. It takes 5/6 of a gallon to paint 1 wall and you want to know how much of a wall can you paint with 1/2 gallon. So set up the proportion:

5/6 / 1 = 1/2 / x

cross multiplying gets you 5/6x = 1/2

multiply by the reciprocal of 5/6 to isolate x - which is 6/5. 1/2 times 6/5 = 3/5

Answer:

answer is a but please mark me brainliest if I m correct

The equation of the curve is y = Ceˣ - 1, where C is a constant. This can be answered by the concept of Slope.

The problem requires finding an equation for a curve whose tangent at any point (x,y) on it, except for the origin, has slope y + xy'. To do this, we can use the fact that the slope of the tangent to a curve y=f(x) at any point (x, y) is given by f'(x), where f'(x) is the derivative of f(x) with respect to x. Thus, we need to find f(x) such that f'(x) = y + xy'.

We can solve this differential equation by using separation of variables. Separating the variables and integrating both sides, we get:

∫(1/y + x) dy = ∫dx

This gives us the equation:

ln|y| + 1/2 x^2 = C

where C is a constant of integration. Solving for y, we get:

y = Ceˣ - 1

where C = ± e^(-1/2C'). Since y cannot be zero (otherwise the slope would be undefined), we take C = e^(1/2) in the positive case, and C = -e^(1/2) in the negative case.

Therefore, the equation of the curve whose tangent at any point on it, different from origin, has slope y+xy​ is y = Ceˣ - 1, where C = ± e^(1/2)

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Answer:

Your answer should be x = \(\frac{48}{7}\).

Hope this helps.

Answer:

x is about 6.857 or 48/7

Step-by-step explanation:

to do this we cross multiply

42/18=16/x

42x=18(16)

42x=288

x=6.857

Hopes this helps please mark brainliest

Answer:

Step-by-step explanation:

well i guess if the decimal is on the left you would move it to the right twice

because if you only moved it once it'd become 1.0

and if you moved it to the left once it would also become 1.0

and if you moved it twice to the left you would be left with .10

pls mark me brainliest

Answer:

5.575

Step-by-step explanation:

divide it by 2 its easy

The required number of seconds would it take to travel the the length of the building is 91.

The equation for speed is basic like distance partitioned by time. You take the distance voyaged (for instance 3 meters) and gap it when (three seconds) to get the speed (one meter each second) Thus, we can characterize Speed as the pace of progress of position of an article toward any path.

We have,

length of the building = 455 meter

speed of elevator = 5 m/s

We know,

speed = distance/time

5 = 455/time

Time = 455/5

Time = 91 seconds.

Thus,time take to travel the the length of the building is 91 seconds.

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Answer:

D. Reflect across the y-axis and then across x = 7

Step-by-step explanation:

A and B work because each transformed point is 12 to the right (x-value is 12 greater), and 3 left then 15 right is the same thing as just 12 right.

C. works because if you take each of the points and reflect them over the y-axis (make the x value positive) and then across the line x=6 (vertical line at 6 on the x-axis) it will map the points onto the correct image.

So, the answer is D. Reflect across the y-axis and then across x = 7.

Answer:

b

Step-by-step explanation:

end of life

edge 2020

Answer:

b

Step-by-step explanation:

Answer:

Option 1 -  7⁵

Step-by-step explanation:

When dividing numbers that have the same base number (7), you subtract bottom exponent from the top exponent.  So exponent  8 - 3 = 5

You keep the same base number and use the resultant exponent.

7⁵

The measure of the angle ∠DYW as per the quadrilateral in a circle postulate is = 111°

A quadrilateral that is encircled by a circle is referred to as a cyclic-quadrilateral.

This shows that a circle connects the four vertices of the quadrilateral.

Con-cyclic vertices are referred to as such.

Circumcenter and circumradius are terms used to describe the circle's center and radius, respectively.

The Greek word "kuklos," which meaning "circle" or "wheel," is where the word "cyclic" originates.

The name "quadrilateral" is derived from the old Latin word "Quadri", which meaning "four-side" or "latus".

Now, in the question we have:

∠W = (7x-2.9)°

∠R = (5x+5.5)°

∠D = (10x-33)°

Now we know the opposite angles of quadrilateral in a circle are supplementary.

So, (7x-2.9)° + (10x-33)° = 180°

⇒ 17x = 180 + 2.9 + 33

⇒ 17x = 215.9

⇒ x = 12.7

Now putting the value of x to get the values of the angles:

∠W = (7x-2.9)° = 86°

∠R = (5x+5.5)° = 69°

∠D = (10x-33)° = 94°

As per the quadrilateral angles rule, all the angles sum up to 360°.

∠W + ∠R + ∠D + ∠Y= 360°

Putting the values:

∠Y = 360 - 86 - 69 - 94

= 111°

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