solve the equation. (find only the real solutions. enter your answers as a comma-separated list.) 5x2 10x 4

10 mph more unusual.

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed over a larger range, a low standard deviation suggests that the values tend to be near to the mean (also known as the anticipated value) of the collection.

The lower case Greek letter (sigma), for the population standard deviation, or the Latin symbol s, for the sample standard deviation, are most frequently used in mathematical literature and equations to indicate standard deviation. Standard deviation may be written as SD.

EXPLANATION : The speed recordings follow an approximately normal distribution the mean of

100 readings was 2384 mph. with a standard deviation of 3.56mph

The speed limit read 20 mph

We have to find the number of standard deviations from the mean that the car going

under the speed hmit would be

Let the car going under the speed 20mph bey standard deviations away from mean

That is.

20 — 23.84 +y(3.56)

20—2384 —1.078651685

So the car going under the speed limit would be less than or equal to 107865 standard

A car traveling 34 mph

The number of standard deviations from the mean that the car is going at 34mph is given by

That is the car going at 34mph is 2.8539 standard deviations above the mean

A car traveling at 10mph

The number of standard deviations from the mean that the car going at 10mph is given by.

y= 2.8539

That is. the car going at 10mph is 3.8876 standard deviations

We know from the empirical nile that 99.7% of the observations he with in ±3 standard

deviations from the mean for a normally distributed data

But the speed of 10mph is not within these limits, where as 34 mph is within these limits

So the car is  travelling t 10mph is more unusual

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Answer:18

Step-by-step explanation:

2x=12

3x=?
2x/2=12/2= x=6

3(6)=18

Answer:

$10,240

Step-by-step explanation:

y = 20,000 (.80)^t

y = 20,000 (0.80)^3

0.8^3 = 0.512

0.512 x 20,000 = 10240

Your answer would be A. $10,240.

The line passing through (5, -2) and (-15, 14) is decreasing, based on the slope obtained from the previous problem.

To determine the nature of the line passing through the points (5, -2) and (-15, 14), we can utilize the slope obtained from the previous problem. The slope between two points is calculated by the change in the y-coordinates divided by the change in the x-coordinates.

Using the slope formula:

slope = (y2 - y1) / (x2 - x1)

Let's substitute the given coordinates into the formula:

slope = (14 - (-2)) / (-15 - 5)

slope = 16 / -20

slope = -4/5

Since the slope is negative (-4/5), the line is decreasing. This means that as we move from left to right along the line, the y-values decrease. Therefore, the line passing through points (5, -2) and (-15, 14) is decreasing.

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The number of days that it will take for there to be fewer than 1,500 tables in the warehouse is given as follows:

More 24 days.

The initial number of tables is given as follows:

2,100 tables.

They ship 25 tables daily, hence the function for the number of tables after n days is given as follows:

T(n) = 2100 - 25n.

There will be fewer than 1,500 tables after n days, for which;

T(n) < 1500

Hence:

2100 - 25n.< 1500

25n > 600

n > 600/25

n > 24.

Hence the time is more than 24 days.

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ΔXYZ will also be an equilateral triangle.

What is equilateral triangle?

An equilateral triangle in geometry is a triangle with equal-length sides on all three sides. In the well-known Euclidean space, an equilateral triangle also is equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others. It's also referred to it as a regular triangle because it is a regular polygon.

As X,Y,Z are the midpoints of sides of equilateral triangle so when we will join the X,Y,Z we will find that distances XY=YZ=XZ are three are equal because this is proved by similarity of triangles which in itself is a detailed and vast topic

Hence XYZ will also be an equilateral triangle

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Answer:

x = - 1 , x = 5

Step-by-step explanation:

- | x - 2 | + 3 = 0 ( subtract 3 from both sides )

- | x - 2 | = - 3 ( divide both sides by - 1 )

| x - 2 | = 3

the absolute value always gives a positive value, however, the expression inside the bars can be positive or negative, then

x - 2 = 3 or - (x - 2) = 3 ( solve both equations )

x - 2 = 3 ( add 2 to both sides )

x = 5

or

- (x - 2) = 3

- x + 2 = 3 ( subtract 2 from both sides )

- x = 1 ( multiply both sides by - 1 )

x = - 1

As a check

substitute these values into the equation and if both sides are equal then it is a solution.

x = - 1

left side = - | - 1 - 2 | + 3 = - | - 3 | + 3 = - | 3 | + 3 = - 3 + 3 = 0 = right side

x = 5

left side = - | 5 - 2 | + 3 = - | 3 | + 3 = - 3 + 3 = 0 = right side

solutions are x = - 1 , x = 5

Answer: y+5=3/8*(x-4)

Step-by-step explanation: Find the slope using m = y2-y1/x2-x2 which is the change of y over change of x, so the slope is m=3/8. Use the slope 3/8, and a given point (4, -5) to substitute for x1 and y1 in point slope form y -y1 = m(x-x1). So y-(-5)=3/8*(x-(4)). Now we simplify the equation so it's y+5=3/8*(x-4).

An expression that represents the measure of the third side is 4x.

A closed shape's perimeter is the sum of the lengths of its outside boundaries. The lengths of all the sides are added to determine the measurement.

Given:

The perimeter of the triangle is 3x² - 7x + 2.

And the measures of the two sides are x² - x - 4 and 2x² - 10x + 6.

The measure of the third side = the perimeter of the triangle - (the total measure of the two sides)

The measure of the third side = 3x² - 7x + 2 - (x² - x - 4 + 2x² - 10x + 6)

The measure of the third side = 3x² - 7x + 2 - (3x² - 11x +2)

The measure of the third side = 4x

Therefore, the measure of the third side = 4x.

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Playoffs are a competition where participants compete against specific opponents in a structured format, but it is not a requirement for every contestant to meet every other participant in turn.

No, it is not true that playoffs are a competition in which each contestant meets every other participant, usually in turn.

Playoffs typically involve a series of elimination rounds where participants compete against a specific opponent or team. The format of playoffs can vary depending on the sport or competition, but the general idea is to determine a winner or a group of winners through a series of matches or games.

In team sports, such as basketball or soccer, playoffs often consist of a bracket-style tournament where teams are seeded based on their performance during the regular season. Teams compete against their assigned opponents in each round, and the winners move on to the next round while the losers are eliminated. The matchups in playoffs are usually determined by the seeding or a predetermined schedule, and not every team will face every other team.

Individual sports, such as tennis or golf, may also have playoffs or championships where participants compete against each other. However, even in these cases, it is not necessary for every contestant to meet every other participant. The matchups are typically determined based on rankings or tournament results.

In summary, playoffs are a competition where participants compete against specific opponents in a structured format, but it is not a requirement for every contestant to meet every other participant in turn.

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The Taylor series for (a) f(x) = 1/(1 + 5) - 1/(1 + 5)^2(x - 5) + 2/(1 + 5)^3(x - 5)^2/2! - 6/(1 + 5)^4(x - 5)^3/3! + ... (b) f(x) = 2 ln 2 + (ln 2 + 1)(x - 2) + (1/2)(x - 2)^2/2! - (1/8)(x - 2)^3/3! + ...

(a) The Taylor series for the function f(x) = 1/(1 + x) centered at x = 5 can be expressed as:

f(x) = f(5) + f'(5)(x - 5) + f''(5)(x - 5)^2/2! + f'''(5)(x - 5)^3/3! + ...

To find the terms of the series, we need to calculate the derivatives of f(x) and evaluate them at x = 5. The derivatives are as follows:

f(x) = 1/(1 + x)

f'(x) = -1/(1 + x)^2

f''(x) = 2/(1 + x)^3

f'''(x) = -6/(1 + x)^4

...

Substituting these derivatives into the Taylor series formula and evaluating them at x = 5, we obtain:

f(x) = 1/(1 + 5) - 1/(1 + 5)^2(x - 5) + 2/(1 + 5)^3(x - 5)^2/2! - 6/(1 + 5)^4(x - 5)^3/3! + ...

(b) The Taylor series for the function f(x) = x ln x centered at x = 2 can be expressed as:

f(x) = f(2) + f'(2)(x - 2) + f''(2)(x - 2)^2/2! + f'''(2)(x - 2)^3/3! + ...

To find the terms of the series, we need to calculate the derivatives of f(x) and evaluate them at x = 2. The derivatives are as follows:

f(x) = x ln x

f'(x) = ln x + 1

f''(x) = 1/x

f'''(x) = -1/x^2

...

Substituting these derivatives into the Taylor series formula and evaluating them at x = 2, we obtain:

f(x) = 2 ln 2 + (ln 2 + 1)(x - 2) + (1/2)(x - 2)^2/2! - (1/8)(x - 2)^3/3! + ...

These series provide an approximation of the original functions around the given center points.

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Answer:

a) There are 4 terms.

b) 2 of them are negative

explanation:

Let's simplify step-by-step.

−3x^2+2y^2+5xy−2y+5x^2−3y^2

=−3x^2+2y^2+5xy+−2y+5x^2+−3y^2

Combine Like Terms:

=−3x^2+2y^2+5xy+−2y+5x^2+−3y^2

=(−3x2+5x^2)+(5xy)+(2y^2+−3y^2)+(−2y)

=2x^2+5xy+−y^2+−2y

Answer:

=2x^2+5xy−y^2−2y

Answer:

Step-by-step explanation:

A. There are 6 terms. Even if there is a variable onto the coefficient, it wouldn't be 2 terms but only 1, in this case, there are 6 terms.

B. If I simplify the number of negative terms, there would be 2 terms.-3x^2,-2y, and -3y^2 are all negative terms in this equation. I can't combine all because one has x as a variable and the other 2 has y. If I simplify both of the negative terms (-2, -3y^2) Ill get -5y^2. -2-3= -5 and just add my other values y and 2 square, and in that case, my final 2 negative terms are -3x^2 and -5y^2

For a step function input (u(t) = 1), the system's response can be obtained by finding the inverse Laplace transform of (s² + 30s + 369) / s². This will give the time-domain response of the system to a step function input. For a sine function input (x(t) = 22sin(5t)u(t)), the system's response can be obtained by finding the inverse Laplace transform of 5(s² + 30s + 369) / (s³ + 25s). This will give the time-domain response of the system to a sine function input.

To determine the response of a system with the transfer function H(s) = (s² + 30s + 369) / s to different input functions, we need to find the Laplace transform of the input function and multiply it by the transfer function H(s). Let's calculate the response for two cases:

Input: Step Function, u(t) = 1 (for t >= 0)

To find the Laplace transform of a step function, we use the formula:

L[u(t)] = 1/s

Multiplying the Laplace transform of the step function by the transfer function H(s), we get:

Y(s) = H(s) * L[u(t)]

= (s² + 30s + 369) / s * (1/s)

= (s² + 30s + 369) / s²

Now, we need to find the inverse Laplace transform of Y(s) to obtain the time-domain response.

The inverse Laplace transform of Y(s) will give us the time-domain response of the system to a step function input.

Input: Sine Function, x(t) = 22sin(5t)u(t)

To find the Laplace transform of a sine function, we use the formula:

L[sin(at)] = a / (s² + a²)

Multiplying the Laplace transform of the sine function by the transfer function H(s), we get:

Y(s) = H(s) * L[sin(5t)]

= (s² + 30s + 369) / s * (5 / (s² + 25))

Simplifying this expression, we have:

Y(s) = 5(s² + 30s + 369) / (s³+ 25s)

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Answer:

Step-by-step explanation:

The lengths of the two boards (234 inches and 246 inches) and adding them together, we find that the combined length of the boards is 480 inches.

To find the total length of the two boards, you need to add their individual lengths together.

Step 1: Identify the length of each board. The first board is 234 inches long, and the second board is 246 inches long.

Step 2: Add the lengths of the boards together.

234 (length of first board) + 246 (length of second board) = 480

So, the total length of the two boards on the shelf is 480 inches. This means that if you were to place the two boards end-to-end, they would cover a distance of 480 inches.

In summary, by identifying the lengths of the two boards (234 inches and 246 inches) and adding them together, we find that the combined length of the boards is 480 inches. This calculation helps us understand the total amount of space the boards would occupy if placed side by side.

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The three characteristics required to properly describe a sampling distribution are mean, variance, and shape.

1. Mean: The mean, also known as the average, represents the central tendency of the sampling distribution. It is calculated by adding up all the sample means and dividing the sum by the total number of samples.

2. Variance: The variance is a measure of how much the sample means vary from the overall mean of the sampling distribution. It helps determine the spread or dispersion of the data.

3. Shape: The shape of a sampling distribution describes its general appearance. Common shapes include symmetrical (e.g., normal distribution) and skewed (e.g., positively or negatively skewed) distributions. The shape can give insights into the underlying population and the behavior of the data.

By considering the mean, variance, and shape, you can effectively describe the characteristics of a sampling distribution.

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Answer:

Step-by-step explanation:

Here you go mate

Step 1

12x-19=9x+5  Equation/Question

Step 2

12x-19=9x+5  Simplify

12x-19=9x+5

Step 3

12x-19=9x+5  Subtract 9x

3x-19=5

Step 4

3x-19=5  add 19

3x=24

Step 5

3x=24  Divide by 3

answer

x=8

Hope this helps

Answer:

3.06cm

Step-by-step explanation:

⁄(⁄ ⁄•⁄ω⁄•⁄ ⁄)⁄⁄(⁄ ⁄•⁄ω⁄•⁄ ⁄)⁄

Answer:3.06cm

Step-by-step explanation:

Answer:

x=1

Step-by-step explanation:

7x-1+2x-1=7

7x+2x-1-1=7

9x-2=7

9x=7+2

9x=9

9x/9=9/9

x=1

Answer: 5r-5s

Step-by-step explanation:

Hope this helps :)

Step-by-step explanation:

Example 1

Solve the equation x3 − 3x2 – 2x + 4 = 0

We put the numbers that are factors of 4 into the equation to see if any of them are correct.

f(1) = 13 − 3×12 – 2×1 + 4 = 0 1 is a solution

f(−1) = (−1)3 − 3×(−1)2 – 2×(−1) + 4 = 2

f(2) = 23 − 3×22 – 2×2 + 4 = −4

f(−2) = (−2)3 − 3×(−2)2 – 2×(−2) + 4 = −12

f(4) = 43 − 3×42 – 2×4 + 4 = 12

f(−4) = (−4)3 − 3×(−4)2 – 2×(−4) + 4 = −100

The only integer solution is x = 1. When we have found one solution we don’t really need to test any other numbers because we can now solve the equation by dividing by (x − 1) and trying to solve the quadratic we get from the division.

Now we can factorise our expression as follows:

x3 − 3x2 – 2x + 4 = (x − 1)(x2 − 2x − 4) = 0

It now remains for us to solve the quadratic equation.

x2 − 2x − 4 = 0

We use the formula for quadratics with a = 1, b = −2 and c = −4.

We have now found all three solutions of the equation x3 − 3x2 – 2x + 4 = 0. They are: eftirfarandi:

x = 1

x = 1 + Ö5

x = 1 − Ö5

Example 2

We can easily use the same method to solve a fourth degree equation or equations of a still higher degree. Solve the equation f(x) = x4 − x3 − 5x2 + 3x + 2 = 0.

First we find the integer factors of the constant term, 2. The integer factors of 2 are ±1 and ±2.

f(1) = 14 − 13 − 5×12 + 3×1 + 2 = 0 1 is a solution

f(−1) = (−1)4 − (−1)3 − 5×(−1)2 + 3×(−1) + 2 = −4

f(2) = 24 − 23 − 5×22 + 3×2 + 2 = −4

f(−2) = (−2)4 − (−2)3 − 5×(−2)2 + 3×(−2) + 2 = 0 we have found a second solution.

The two solutions we have found 1 and −2 mean that we can divide by x − 1 and x + 2 and there will be no remainder. We’ll do this in two steps.

First divide by x + 2

Now divide the resulting cubic factor by x − 1.

We have now factorised

f(x) = x4 − x3 − 5x2 + 3x + 2 into

f(x) = (x + 2)(x − 1)(x2 − 2x − 1) and it only remains to solve the quadratic equation

x2 − 2x − 1 = 0. We use the formula with a = 1, b = −2 and c = −1.

Now we have found a total of four solutions. They are:

x = 1

x = −2

x = 1 +

x = 1 −

Sometimes we can solve a third degree equation by bracketing the terms two by two and finding a factor that they have in common.

Step-by-step explanation:

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Commutative law under addition says- p + q = q + p. Commutative law under multiplication says p x q = q x p. Note- Rational numbers, integers and whole numbers are commutative under addition and multiplication. Rational numbers, integers and whole numbers are non commutative under subtraction and division.0

The relation 2 represents a function.

In order to determine which relation in the below table represents a function, we need to first understand what a function is.A function is a relationship in which each input value corresponds to exactly one output value.

To put it another way, each x-value has one and only one y-value. The most typical method to determine whether a relation is a function is to use the vertical line test.

The vertical line test is a way to determine if a relation is a function graphically. To test if a graph is a function, we draw a vertical line through each x-value on the graph. If a vertical line crosses the graph more than once, it is not a function.

If, on the other hand, the graph passes the vertical line test and no vertical line crosses the graph more than once, it is a function.Now let's look at the table below to determine which relation is a function.

We will first plot the x and y values of each relation on a coordinate system and then apply the vertical line test to each relation.

Relation 1: x | y0 | 10 | 11 | 22 | 23 | 34 | 35 | 4Relation 1 does not represent a function since we can draw a vertical line through x = 3 and the line will cross the graph more than once.

Relation 2: x | y2 | 33 | 34 | 45 | 46 | 57 | 5Relation 2 represents a function since we can draw a vertical line through each x-value on the graph and it will only cross the graph once.

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Answer:

\((x,y) \to (-y,x)\)

Step-by-step explanation:

Given

\(A = (0,1)\)

\(B = (1,0)\)

\(C = (2,4)\)

90 degrees counterclockwise rotation

Required

The algebraic representation

Let the coordinate point be \((x,y)\)

The rule of 90 degrees counterclockwise rotation is:

\((x,y) \to (-y,x)\)

So, we have:

\(A = (0,1)\) \(\to (-1,0)\)

\(B = (1,0)\) \(\to (0,1)\)

\(C = (2,4)\) \(\to (-4,2)\)

The  Bernoulli equation of given differential equation Xdydx + y = 1y² is ln (1 - x/y - x) = c

Any equation with one or more derivates and one or more terms of the dependent variable with respect to the independent variable is referred to as a differential equation (i.e., independent variable) dy/dx = f(x) (x)

-1/y = u

y¹/y² = u¹

xy¹ - (1 + x)y = xy²

now take the y² on other side,

xy¹/y² - (1 + x)/y = c

now replace the values by u¹,

xu¹ + (1 + x)u = x

xu¹ + u + ux = x

xu = s      ....[1]

Substitute the value of xu as s

u + xu¹ = s¹

s¹ + s = v

s - x  = t

s¹ - 1 = t¹

t¹ + 1 + t = 0

Now take the integration of both the sides,

dt/dx = - ( 1 + t)

-∫ dt/1+t =  ∫dx

-ln ( 1+ t ) = x + c

now ,put the value of t,

-in ( 1 + s - x ) = x + c

now put the value of s,

-ln ( 1 + xu - x ) = x + c

-ln ( 1 - x/y - x) = c.

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Answer:

10^-1*2.65

Step-by-step explanation:

two hundred sixty-five thousandths= 0.265

We need a number between 1 and 10, to do the multiplication in standard form, so 0.265 turns into 2.65.

Because 2.65 becomes, smaller we use a negative power. We only move the decimal place once to the left, so we would multiply 2.65 by 10^1.

10^-1*2.65=0.265

The standard form of two hundred sixty-five thousandths is 265 × 10⁻³.

The number system is a way to represent or express numbers.

A decimal number is a very common number that we use frequently.

Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.

Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.

Given that,

Two hundred sixty-five = 200 + 65 = 265

Now,

Thousandths mean we need to divide it by thousand

So,

⇒ 265/1000

⇒ 265/10³

By the law of indices

⇒ 265 ×  10⁻³

Hence "The standard form of two hundred sixty-five thousandths is 265 × 10⁻³".

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Water hammer is defined as a surge in pressure or force caused when a fluid in motion is abruptly stopped or changes direction.

The correct answer is C

To calculate the maximum rise in pressure at the valve due to water hammer, the following formula is used is the Poisson's ratio of concrete,  is the diameter of the pipe,  is the thickness of the pipe,  is the length of the pipe, is the velocity of water in the pipe, and $g$ is the acceleration due to gravity.

Let's now plug in the given values in the formula: Therefore, the maximum rise in pressure at the valve due to water hammer is 2273 kPa, which is option C.

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The work done to lift a 1 kg object from the center of the Earth to its surface is approximately 2.041 x 10^13 Joules.

The force of attraction experienced by a particle of mass m when it is located at the point (x, 0) due to a mass M located at the origin is given by:

F = k(Mm / r^2)

where r is the distance between the two masses, and k is a constant of proportionality. Since only the magnitude of force is given in the question, the value of k is irrelevant. The direction of the force of attraction is towards the origin, so it is a radial force.

When a particle of mass m is located at (x, 0), the force experienced by the particle due to mass M is given by:

F = k(Mm / x^2) (since the distance from (x, 0) to the origin is x).

The mass of the particle is not given, so we will assume that it is 1 kg (this value is also irrelevant since we only need to calculate work done).

At x = b, the force of attraction is:

F = kM / b^2

At x = a, the force of attraction is:

F = kM / a^2 (since the particle will reach r = a, 0)

The work done to lift a 1 kg object from the center of the Earth to its surface is given by:

W = ∫(R to 0) F(r) dr

where F(r) = 0.0015r is the force of gravity experienced by a 1 kg object at a distance r from the center of the Earth, and R is the radius of the Earth.

Substituting the given values, we get:

W = ∫(6371000m to 0) 0.0015r dr

 = 0.00075r^2 |_6371000m

 = 0.00075(6371000)^2

Calculating this expression, we find that the work done is approximately 2.041 x 10^13 Joules (to three significant figures).

Therefore, the work done to lift a 1 kg object from the center of the Earth to its surface is approximately 2.041 x 10^13 Joules.

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The given improper integral ∫(pœ dx) may converge to a finite value, diverge to infinity, diverge to negative infinity, or diverge altogether.

The convergence or divergence of the integral depends on the value of the exponent p and the behavior of the integrand function as x approaches certain limits.

To determine the convergence or divergence of the improper integral ∫(pœ dx), we need more information about the integrand function and the limits of integration. The symbol "pœ" is not defined, so we cannot provide a specific evaluation for the integral.

However, we can discuss the possible scenarios. If the integrand function has a singularity or behaves in such a way that the integral becomes unbounded as x approaches a certain value, then the integral may diverge to infinity or negative infinity. If the integrand function approaches zero or remains bounded as x approaches the limits of integration, then the integral may converge to a finite value. Lastly, if the integrand function oscillates or does not have a well-defined behavior, the integral may diverge altogether.

Without further information about the integrand function and the limits of integration, it is not possible to determine the exact value or the convergence/divergence nature of the given improper integral.

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Answer:

ok so

-1/5x=w

w=1865

so -1/5x=1865

x=-9325

Hope This Helps!!!

Answer:

i a pretty sure for part E its 1865

Step-by-step explanation: