Write an expressions that is equivalent to 6c-2/2 +2c+11 in simplest form

The number of ways of selecting the four students out of nine students for attending the conference is equals to the 126 from using the combination formula.

The number of combinations of n things taken r at a time is determined by the combination formula. It is the factorial of n, divided by the product of the factorial of r and the factorial of the difference of n and r respectively. Mathematically, it can be written as \(ⁿCᵣ= \frac{ n!}{r! ( n - r)!}\)

Now, we have number of students majoring in Mathematics = 4

Number of students majoring in chemistry = 5

So, total number of students majoring = 9

Four students are selected to attend conference. Here, n = 9, r = 4 so,

Number of ways to any four can attend =

\( 9C_4 = \frac{ 9!}{4! ( 9 - 4)!}\)

\(= \frac{ 9×8×7×6×5!}{4! 5!}\)

\(=\frac{ 9×8×7×6}{4×3×2}\)

= 18× 7 = 126

Hence, required value is 126.

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The amount of megabytes left to download is 6.8 mb

Mathematical operations include addition, subtraction, multiplication, and division. The expression x + y, for instance, consists of the terms x and y with an addition operator in between them.

In this situation, John wants to download an two applications that are 10 MB and the second application, 3.2 MB has been downloaded.

The application left to download will be:

= Total mb - mb download

= 10 - 3.2

= 6.8 mb

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Complete question

John wants to download an two applications that are 10 MB. For the second application, 3.2 MB has been downloaded. How much is left to download?

Answer:

(-2,14) Hope this helps! Have a great day!!!

The method of reduction of order is a technique used to find a second solution to a homogeneous linear differential equation when one solution is already known.

However, it cannot be directly used for nonhomogeneous linear differential equations. In nonhomogeneous equations, the method of undetermined coefficients or variation of parameters is typically used to find a particular solution.

Therefore, the statement "the method of reduction of order can also be used for the nonhomogeneous equation" is false. It is important to understand the different techniques for solving differential equations, and to choose the appropriate method based on the type of equation and boundary conditions given.

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According to the given statement of the Nolan bought 5 pounds of turnips.

To find out how many pounds of turnips Nolan bought, we need to calculate the weight of the turnips. We are given that the bag of parsnips weighed 2 1/2 pounds.
The weight of the turnips is 5 times the weight of the parsnips. To find the weight of the turnips, we can multiply the weight of the parsnips by 5.
2 1/2 pounds can be written as 2 + 1/2 pounds.
To multiply a whole number by a fraction, we multiply the whole number by the numerator and divide by the denominator.
So, 2 * (1/2) = 2/2 = 1
Therefore, the parsnips weigh 1 pound.
Now, we can calculate the weight of the turnips by multiplying the weight of the parsnips (1 pound) by 5.
1 pound * 5 = 5 pounds.
Therefore, Nolan bought 5 pounds of turnips.

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The weight of the parsnips that Nolan bought is 2 1/2 pounds. To find out how many pounds of turnips Nolan bought, we need to multiply the weight of the parsnips by 5, since the turnips weigh 5 times as much as the parsnips. Nolan bought 12 1/2 pounds of turnips.

First, we need to convert the mixed number 2 1/2 to an improper fraction. To do this, we multiply the whole number (2) by the denominator (2) and add the numerator (1). This gives us 5 as the numerator, and the denominator remains the same (2). So, 2 1/2 is equal to 5/2.

Now, let's multiply the weight of the parsnips (5/2 pounds) by 5 to find the weight of the turnips. When we multiply a fraction by a whole number, we multiply the numerator by the whole number and keep the denominator the same.

So, 5/2 multiplied by 5 is (5 * 5) / (2 * 1) = 25/2 = 12 1/2 pounds.

Therefore, Nolan bought 12 1/2 pounds of turnips.

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True, Monte Carlo simulation is used for statistical sampling where larger number of trials are used for the precise result.

Step by Step Explanation:

Therefore, it is true to have more number of trials in Monte Carlo simulation  statistical sampling for precise result.

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Answer:you could do

You would need to rile a two and a one together though

The statistical technique used to estimate future values by successive observations of a variable at regular intervals of time that suggest patterns is called trend analysis.

Trend analysis is a statistical technique that helps identify patterns and tendencies in a variable over time. It involves analyzing historical data collected at regular intervals to identify a consistent upward or downward movement in the variable.

By examining the sequential observations of the variable, trend analysis aims to identify the underlying trend or direction in which the variable is moving. This technique is particularly useful when there is a time-dependent relationship in the data, and past observations can provide insights into future values.

Trend analysis typically involves plotting the data points on a time series chart and visually inspecting the pattern. It helps in identifying trends such as upward or downward trends, seasonality, or cyclic patterns. Additionally, mathematical models and statistical methods can be applied to quantify and forecast the future values based on the observed trend.

This statistical technique is widely used in various fields, including finance, economics, marketing, and environmental sciences. It assists in making informed decisions and predictions by understanding the historical behavior of a variable and extrapolating it into the future.

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The equation of the tangent line to the curve y = ln(x^2 - 5x + 1) at the point (5,0) is y = 0.

To find the equation of the tangent line to the curve y = ln(x^2 - 5x + 1) at the point (5,0), we need to find the slope of the tangent line at that point.

The derivative of y = ln(x^2 - 5x + 1) is:

y' = (2x - 5)/(x^2 - 5x + 1)

At the point (5,0), we have:

y' = (2(5) - 5)/(5^2 - 5(5) + 1) = 0

So the slope of the tangent line at (5,0) is 0.

The equation of the tangent line can be written as:

y - y1 = m(x - x1)

where (x1, y1) is the point of tangency and m is the slope.

Since the slope is 0, we have:

y - 0 = 0(x - 5)

which simplifies to:

y = 0

Therefore, the equation of the tangent line to the curve y = ln(x^2 - 5x + 1) at the point (5,0) is y = 0.

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Therefore , the solution of the given problem of function comes out to be the duckweed to grow a mass triple the original size will be 45 hours.

The mathematics curriculum involves examining numbers, the equation the environment we live in, structures, and both actual and hypothetical locations. A function is a variable representation of the relationship between the quantities of intake and the corresponding outputs for each. Simply explained, a function is a collection of inputs that, when combined, provide unique outputs for each input.

Here,

Given :

mass of a population of duckweed is 500g

=>  function m(t)= 500x³^t/45

So,

=> t = 45 hours

Since it is given that the mass of the population of the duckweed triples every 45 hours

it is clear that the time taken for the duckweed to grow a mass triple the original size will be 45 hours .

Therefore , the solution of the given problem of function comes out to be the duckweed to grow a mass triple the original size will be 45 hours.

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Answer:

Step-by-step explanation:

35-original drill set price

25% or .25-the additional price

markup in decimal form- 0.25

markup in percent form- 25%

Equation-35 + 25% or 0.25

35 + 25% = 43.75

Answer:

a.

\(f(t) = 21000( {.918}^{t} )\)

b.

\(f(4) = 21000( {.918}^{4}) = 14913.86\)

I believe the answer is 200.

The total sales in dollars for n tickets is 6.50n if all tickets are sold for $6.50 each.

It is defined as the combination of constants and variables with mathematical operators.

It is given that:

At a movie theater, all tickets are sold for $6.50 each.

Let n be the total number of tickets sold.

Each ticket cost = $6.50

Total ticket cost = $6.50n

Or

The total sales in dollars for n tickets = 6.50n

The above expression is a linear expression in one variable and the variable is n.

Thus, the total sales in dollars for n tickets is 6.50n if all tickets are sold for $6.50 each.

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Answer:

2.1

Step-by-step explanation:

This involves trigonometry. Since we need to find the value of a, we need to find a trig equation with a as the numerator. Luckily, we have one, tan. So, tan(20) is equal to a/6, right. So, using a calculator, tan(20) is approximately equal to 0.363. This times 6 should equal a. This is approximately around 2.1. Thus our answer is 2.1

The weighted average of the numbers 1 and 6, with a weight of 2/3 on the first number and 1/3 on the second number is 3.5. The correct option is A.

We know that the formula to calculate the weighted average is: weighted\ average=\frac{w_1x_1+w_2x_2+...+w_nx_n}{w_1+w_2+...+w_n} Where, $x_1,x_2,..x_n$ are the values, and $w_1,w_2,...,w_n$ are the weights. To find the weighted average of the numbers 1 and 6, with a weight of 2/3 on the first number and 1/3 on the second number, we substitute the values in the above formula as follows.

Weighted\ average=\frac{\frac{2}{3}\times 1+\frac{1}{3}\times 6}{\frac{2}{3}+\frac{1}{3}}\implies weighted\ average=\frac{\frac{2}{3}+2}{1}\implies weighted\ average=\frac{8}{3}\implies weighted\ average=2.67 approx 3.5 Therefore, the weighted average of the numbers 1 and 6, with a weight of 2/3 on the first number and 1/3 on the second number is 3.5.

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Answer:

see explanation

Step-by-step explanation:

if the denominator of a rational expression is zero then the expression will be undefined.

the numerator is the part of the rational expression that makes it zero.

solve the numerators in each to find values of x

1

\(\frac{x+6}{x-4}\)

x + 6 = 0 ( subtract 6 from both sides )

x = - 6 ← value that makes expression equal to zero

2

\(\frac{(x+4)(x-2)}{x+6}\)

(x + 4)(x - 2) = 0

equate each factor to zero and solve for x

x + 4 = 0 ⇒ x = - 4

x - 2 = 0 ⇒ x = 2

x = - 4 and x = 2 make the expression equal to zero

3

\(\frac{2x+10}{3x-12}\)

2x + 10 = 0 ( subtract 10 from both sides )

2x = - 10 ( divide both sides by 2 )

x = - 5 ← value that makes expression equal to zero

Answer:

1)  x = -6

2)  x = -4  and  x = 2

3)  x = -5

Step-by-step explanation:

A rational expression is undefined when the denominator equals zero.

A rational expression equals zero when the numerator equals zero.

Given rational expression:

\(\dfrac{x+6}{x-4}\)

Set the numerator to zero and solve for x:

\(\implies x+6=0\)

\(\implies x=-6\)

Given rational expression:

\(\dfrac{(x+4)(x-2)}{x+6}\)

Set the numerator to zero:

\(\implies (x+4)(x-2)=0\)

Apply the zero-product property and solve for x:

\(\implies x+4=0 \implies x=-4\)

\(\implies x-2=0 \implies x=2\)

Given rational expression:

\(\dfrac{2x+10}{3x-12}\)

Factor the numerator and denominator:

\(\dfrac{2(x+5)}{3(x-4)}\)

Set the numerator to zero and solve for x:

\(\implies 2(x+5)=0\)

\(\implies x+5=0\)

\(\implies x=-5\)

1. Objective Function and Constraints:

Maximize 2x1 + 3x2 + 5x3 subject to x1 + x2 + x3 ≤ 1500, x1 + x2 ≤ 1100, x2 ≤ 800, x3 ≤ 400.

2. Using Excel Solver, find the optimal allocation of funds.

3. The maximum value of the objective function is reported by Excel Solver.

We have,

Objective Function and Constraints:

Let:

x1 = amount spent on food

x2 = amount spent on shelter

x3 = amount spent on entertainment

Objective Function:

Maximize: 2x1 + 3x2 + 5x3 (since each dollar spent on food has a satisfaction value of 2, each dollar spent on shelter has a satisfaction value of 3, and each dollar spent on entertainment has a satisfaction value of 5)

Constraints:

Subject to:

x1 + x2 + x3 ≤ $1,500 (maximum disposable income)

x1 + x2 ≤ $1,100 (amount spent on food and shelter combined must not exceed $1,100)

x2 ≤ $800 (amount spent on shelter alone must not exceed $800)

x3 ≤ $400 (entertainment cannot exceed $400)

Using Excel Solver:

In Excel, set up a spreadsheet with the following columns:

Column A: Variable names (x1, x2, x3)

Column B: Objective function coefficients (2, 3, 5)

Column C: Constraints coefficients (1, 1, 1) for the first constraint (maximum disposable income)

Column D: Constraints coefficients (1, 1, 0) for the second constraint (amount spent on food and shelter combined)

Column E: Constraints coefficients (0, 1, 0) for the third constraint (amount spent on shelter alone)

Column F: Constraints coefficients (0, 0, 1) for the fourth constraint (entertainment limit)

Column G: Right-hand side values ($1,500, $1,100, $800, $400)

Apply the Excel Solver tool with the objective function and constraints to find the optimal allocation of funds.

Once the Excel Solver completes, it will report the maximum value of the objective function, which represents the optimal satisfaction value achieved within the given budget constraints.

Thus,

Objective Function and Constraints: Maximize 2x1 + 3x2 + 5x3 subject to x1 + x2 + x3 ≤ 1500, x1 + x2 ≤ 1100, x2 ≤ 800, x3 ≤ 400.

Using Excel Solver, find the optimal allocation of funds.

The maximum value of the objective function is reported by Excel Solver.

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Answer:

\(\dfrac{2m -1}{5}\)

Step-by-step explanation:

Since we have common denominators inside the parentheses, we can combine the denominators. Then, we get the following expression:

\(2\huge\text{(}\dfrac{1}{5} m - \dfrac{2}{5} \huge\text{)} + \dfrac{3}{5}\)

\(2\huge\text{(}\dfrac{m - 2}{5} \huge\text{)} + \dfrac{3}{5}\)

Now, we can multiply the expression inside the parentheses by 2.

\(\huge\text{(}\dfrac{2m - 4}{5} \huge\text{)} + \dfrac{3}{5}\)

Since the expression inside the parentheses cannot be simplified further, we can open the parentheses and simplify the expression.

\(\dfrac{2m - 4}{5} + \dfrac{3}{5}\)

We can combine the denominators as the denominators are the same.

\(\dfrac{2m - 4 + 3}{5}\)

Finally, we can simplify -4 + 3.

\(\dfrac{2m -1}{5}\)

Therefore, the simplified expression is (2m - 1)/5.

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Thus, minimum of 3 usual smokers out of 22 adults is found when using the Range Rule of Thumb.

Using the Range Rule of Thumb, we can estimate the minimum number of usual smokers in a sample of 22 adults by considering the expected proportion of smokers in the population and applying it to the sample size.

According to this rule, the range of a distribution can be approximated as six times the standard deviation.

To estimate the minimum number of usual smokers we can expect to get out of 22 adults, we first need to find the standard deviation.

Given that 14% of the population smokes, we can express this proportion as a decimal: 0.14.

To determine the expected number of smokers in the sample, we simply multiply the proportion by the sample size: 0.14 * 22 = 3.08.

Since we cannot have a fraction of a person, we round the result to the nearest whole number.

In this case, we can expect a minimum of 3 usual smokers out of 22 adults when using the Range Rule of Thumb.

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The velocity of the top of the ladder is 20.62 feet per second.

We can use the Pythagorean theorem to relate the distance between the wall and the base of the ladder to the height of the ladder. Let h be the height of the ladder, then we have:

h² + 7² = 25²

h² = 576

h = 24 feet

We can then use the chain rule to find the velocity of the top of the ladder. Let v be the velocity of the base of the ladder, then we have:

h² + (dx/dt)² = 25²

2h (dh/dt) + 2(dx/dt)(d²x/dt²) = 0

Simplifying and plugging in h = 24 and dx/dt = -2, we get:

(24)(dh/dt) - 2(d²x/dt²) = 0

Solving for (d²x/dt²), we get:

(d²x/dt²) = (12)(dh/dt)

We can find (dh/dt) using the Pythagorean theorem and the fact that the ladder is sliding down the wall at a rate of 2 feet per second:

h² + (dx/dt)² = 25²

2h(dh/dt) + 2(dx/dt)(d²x/dt²) = 0

Substituting h = 24, dx/dt = -2, and solving for (dh/dt), we get:

(dh/dt) = -15/8

Finally, we can find (d²x/dt²) by plugging in (dh/dt) and solving:

(d²x/dt²) = (12)(dh/dt) = (12)(-15/8) = -45/2

Therefore, the velocity of the top of the ladder is 20.62 feet per second.

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Answer:

x = 13

Step-by-step explanation:

Given: f ( x ) = 4.5 x 2 − 3 x + 2 To determine the critical points, we must first calculate the first derivative of the function.

Differentiate the given function with respect to x using the power rule of differentiation, d d x x n = n x n − 1.

f ′ (x) =    d        (4.5 x 2 − 3 x + 2)

        ______        

            d x  

Apply sum rule: d d x (f(x)) + g (x) = d d x f (x) + d d x g (x) } f ′ ( x) = d d x (4.5 x^2) + d d x (−3 x) + d d x (x) f ′ (x) = 9 x − 3

To determine the critical points, set f ′ (x) = 0 . 9 x − 3 = 0 9 x = 3 {∴ x = 13}

Therefore, the tangent line to f(x) is horizontal at the point x = 13

Hope this helps, have a nice day/night! :D

The area covered by the pool and the cement walkway is 304  square feet. The width of the walkway would be 5 feet

The area of the rectangle is the product of the length and width of a given rectangle.

The area of the rectangle = length × Width

Let x be represent the width of the walkway.

The pool measures 25 ft by 10ft . If the walkway must have a uniform width around the entire pool, then the total length of the pool and the walkway =  25+ x + x = 25 + 2x

The total width of the pool and the walkway = 10 + x + x = 10 + 2x

The area covered by the pool and the cement walkway is 304  square feet. This means that;

(25 + 2x)(10 + 2x) = 304

250 + 50x + 20x + 4x^2 = 304

4x^2 + 70x + 250 - 304 = 0

4x^2 + 70x - 54 = 0

x(x + 20) - 5(x + 20) = 0

(x - 5)(x + 20) = 0

x = 5 or x = - 20

Thus The width cannot be negative.

Therefore, the width of the walkway is 5 feet.

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Answer:

\(Probability = 0.198\)

Step-by-step explanation:

Given

Publish

\(Huge\ Success = 20\%\)

\(Modest\ Success = 30\%\)

\(Break\ Even = 30\%\)

\(Losers = 20\%\)

Favorable Reviews:

\(Huge\ Success = 99\%\)

\(Modest\ Success = 60\%\)

\(Break\ Even = 40\%\)

\(Losers = 30\%\)

Required

Determine the probability that a textbook is huge success and favorable

To do this, we simply multiply the probability of a textbook being huge success and being favorably reviewed. as follows;

\(Probability = 20\% * 99\%\)

\(Probability = 0.198\)

Answer:Let's denote the amount of Swiss francs as x. The conversion rate is £1 = 1.32 Swiss francs, so x = 1.32 pounds.

The bank charges £3 per transaction, so the amount of pounds after deducting the charge is 140 - 3 = 137 pounds.

The amount of Swiss francs is 1.32 * 137 = 180.44 francs.

So you would receive 180.44 Swiss francs if you exchanged £140 at this bank.

Step-by-step explanation:

Answer:

You would receive 106.0606 Swiss francs.

The conversion rate is 1.32 Swiss francs to 1 pound, so you would need to

exchange a total of 140 pounds in order to receive 106.0606

Swiss francs. But then, you would have to pay the £3 transaction

fee...which would leave you with only 103.0606 Swiss francs.

The value of \(M_x\) and \(M_y\) is 1083 and 484 respectively.

Also, the value of (x, y) is (24.2, 54.56).

We have,

y= x³ at y= 1 and x= 3

Then, we can write

Area =\(\int\limits^{3}_{1} {x^3} \, dx\)

= [x⁴/4]\(|_{1}^3\)

= 1/4 [ 81 - 1]

= 1/4 [80]

= 80/4

= 20

Now, X= 1/ A\(\int\limits^a_b {x(f(x) - g(x))} \, dx\)

= 1/20 \(\int\limits^3_1\) x(x³ - 0) dx

= 1/20 \(\int\limits^3_1\)x⁴ dx

= 1/20 [x⁵/5]\(|_1^3\)

= 1/100 [ 243 - 1]

= 1/100 [ 242]

= 24.2

Similarly, Y= 1/ A \(\int\limits^a_b 1/2{x(f(x)^2 - g(x)^2)} \, dx\)

= 1/40\(\int\limits^3_1\) (x⁶ - 0) dx

= 1/40 [x⁷/7]_1^3

= 1/40 [2187 - 1]

= 54.65

Now, M = ρ A = 20

So, y = Mx/M Mx

= 54.65

and, My= 484

Thus, the value of \(M_x\) and \(M_y\) is 1083 and 484 respectively.

Also, the value of (x, y) is (24.2, 54.56).

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The integral: S1 0 (-x³ - 2x² - x + 3)dx is -1/12

An integral is a mathematical operation that calculates the area under a curve or the value of a function at a specific point. It is denoted by the symbol ∫ and is used in calculus to find the total amount of change over an interval.

To evaluate the integral:

\($ \int_0^1 (-x^3 - 2x^2 - x + 3)dx $\)

We can integrate each term of the polynomial separately using the power rule of integration, which states that:

\($ \int x^n dx = \frac{x^{n+1}}{n+1} + C $\)

where C is the constant of integration.

So, we have:

\($ \int_0^1 (-x^3 - 2x^2 - x + 3)dx = \left[-\frac{x^4}{4} - \frac{2x^3}{3} - \frac{x^2}{2} + 3x\right]_0^1 $\)

Now we can substitute the upper limit of integration (1) into the expression, and then subtract the result of substituting the lower limit of integration (0):

\($ \left[-\frac{1^4}{4} - \frac{2(1^3)}{3} - \frac{1^2}{2} + 3(1)\right] - \left[-\frac{0^4}{4} - \frac{2(0^3)}{3} - \frac{0^2}{2} + 3(0)\right] $\)

Simplifying:

\($ = \left[-\frac{1}{4} - \frac{2}{3} - \frac{1}{2} + 3\right] - \left[0\right] $\)

\($ = -\frac{1}{12} $\)

Therefore,

\($ \int_0^1 (-x^3 - 2x^2 - x + 3)dx = -\frac{1}{12} $\)

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Answer:

6.0×10⁴mm

Step-by-step explanation:

A speck of dust in an electron microscope is 1.2 * 102 millimeters wide.The image is 5 * 102 times larger than the actual size. How many millimeters wide is the actual speck of dust?

Given

Length of microscope = 1.2×10²mm

If the image is 5×10² larger

Width of the image = 5×10²(1.2×10²)

Width of the image = 5×1.2(10⁴)

Width of the image = 6.0×10⁴mm

We can find the zeros of the given polynomial by setting it equal to zero and solving for x.

\({\texttt{{x}^{2} - \frac{3x}{2} - 7 = 0}}\)

To solve for x, we can use the quadratic formula:

\({\texttt{x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}}}\)

where a, b, and c are the coefficients of the quadratic equation.

In this case, a = 1, b = -3/2, and c = -7. Substituting these values in the quadratic formula, we get:

\({\texttt{x = \frac{-(-3/2) \pm \sqrt{(-3/2)^2-4(1)(-7)}}{2(1)}}}\)

Simplifying the expression inside the square root, we get:

\({\texttt{x = \frac{3/2 \pm \sqrt{9/4+28}}{2}}}\)

\({\texttt{x = \frac{3}{4} \pm \sqrt{\frac{121}{16}}}}\)

\({\texttt{x = \frac{3}{4} \pm \frac{11}{4}}}\)

\(\huge{\colorbox{black}{\textcolor{lime}{\textsf{\textbf{I\:hope\:this\:helps\:!}}}}}\)

\(\begin{align}\colorbox{black}{\textcolor{white}{\underline{\underline{\sf{Please\: mark\: as\: brillinest !}}}}}\end{align}\)

\(\textcolor{blue}{\small\texttt{If you have any further questions,}}\) \(\textcolor{blue}{\small{\texttt{feel free to ask!}}}\)

♥️ \({\underline{\underline{\texttt{\large{\color{hotpink}{Sumit\:\:Roy\:\:(:\:\:}}}}}}\\\)

Therefore, the zeros of the polynomial are:

\({\texttt{x_1 = \frac{3}{4} + \frac{11}{4} = 3}}\)

\({\texttt{x_2 = \frac{3}{4} - \frac{11}{4} = -\frac{8}{4} = -2}}\)

Hence, the zeros of the polynomial are 3 and -2.

Answer:

5.68*10⁵

Step-by-step explanation:

you can factor 10⁴ at the beginning too but I found it easier to explain what happens this way