21
Find the perimeter of the isosceles triangle
7 ft.
48 ft.
A. 98 feet
B. 24 feet
C. 48. 5 feet
D. 200 feet

Step-by-step explanation:

7 natural

- sqrt(36) = -6 integer

-36/12 = -3 integer

pi irrational

6.48 rational

-2 integer

sqrt(10) irrational

0 whole

2 1/6 = 13/6 rational

-0.77777 rational (= -77777/100000)

e irrational

Answer:

40 times

Step-by-step explanation:

Number of known species of beetles: 4 × \(10^{5}\) = 400,000

Number of known species of caddis flies: about  \(10^{4}\) =  10,000

To compare how many times more species of beetles there are than caddies flies, you could divide 400,000 by 10,000, which gives you 40.

Therefore, there are 40 times more of beetle species than caddies flies.

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Answer:

Here's an example:

convert 2.5 into a mixed number.

Make the denominator less than the original.

The easy way for this is to do 25/10

when you put it through a calculator it ends up being 2.5

(essentially the mixed number and the decimal are the SAME numbers.)

Hope this clarified. :)

To convert a decimal to a mixed number, follow these steps:

Step 1: Identify the whole number part of the decimal. This is the part of the decimal before the decimal point.

Step 2: Identify the decimal part. This is the part of the decimal after the decimal point.

Step 3: Express the decimal part as a fraction by using the place value of the last digit.

Step 4: Simplify the fraction, if possible, by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by it.

Step 5: Combine the whole number part, the fraction, and simplify if necessary.

Here's an example:

Let's say we have the decimal 2.75.

Step 1: The whole number part is 2.

Step 2: The decimal part is 0.75.

Step 3: To express 0.75 as a fraction, we write it as 75/100. Since 75 and 100 have a common factor of 25, we can simplify it to 3/4.

Step 4: The fraction 3/4 is already in its simplest form.

Step 5: Combining the whole number part and the fraction, we have 2 3/4.

So, the decimal 2.75 can be written as the mixed number 2 3/4.

Remember to always simplify the fraction part if possible.

Answer:

x=113

Step-by-step explanation:

because 95 + 84 + 68 is 247 360 - 247 = 113

Answer:

The answer is "0.7616".

Step-by-step explanation:

Using formula:

\(\text{P( at least one de-fective) = 1 - P( all calculators work )}\)

                                          \(= 1-(\frac{34}{48}\times \frac{33}{47}\times \frac{32}{46}\times \frac{31}{45})\\\\= 1-(\frac{34}{1}\times \frac{11}{47}\times \frac{1}{23}\times \frac{31}{45})\\\\=1-(\frac{11594}{48647})\\\\=\frac{48647-11594}{48647}\\\\=\frac{37051}{48647}\approx 0.7616\)

Thus, the area of ΔHIJ using the Heron's formula is found as 580.47 square centimeter.

Heron of Alexandria (c. 62 ce) is credited with developing the Heron's formula, which determines the area of a triangle in regards of the lengths of its sides. If the side lengths are represented by the symbols a, b, and c: √s(s - a)(s - b)(s - c)

where s = half the perimeter,

s = (a + b + c)/2.

given data:

In ΔHIJ,

semi -perimeter s = (i + j + h) / 2

s = (33 + 61 + 39) / 2

s = 66.5

Now,

s - h = 66.5 - 33 = 33.5

s - i = 66.5 - 61 = 5.5

s - j = 66.5 - 39 = 27.5

area of ΔHIJ = √s(s - h)(s - i)(s - j)

area of ΔHIJ = √66.5*33.5*5.5*27.5

area of ΔHIJ = √336947.1875

area of ΔHIJ = 580.47

Thus, the area of ΔHIJ using the Heron's formula is found as 580.47 square centimeter.

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Answer:

what grade are you in that requieres this type of math

Step-by-step explanation:

Answer: the first one is 7/9 and the second one is option 2

Step-by-step explanation:

4+7 = 11

< or> = open dot

Answer

56 - 28 = 28 (2 - 1)

Explanation

The distributive property is used to open brackets or put an equation inside a bracket.

A factor of a number is a digit that can divide the number without leaving a remainder.

The greatest common factor of 56 and 28 is 28

56 = 28 × 2

28 = 28 × 1

56 - 28

= (28 × 2) - (28 × 1)

= 28 (2 - 1)

This is the factored simplification of this

If we then need to solve further,

28 (2 - 1) = 28 (1) = 28

Hope this Helps!!!

The point-slope form is given by:

Where m is the slope and (x1,y1) are the coordinate of one point of the line.

The given information is:

Slope m=13/11

Coordinates of the point: (16,20)

Replace these values in the formula:

That is the equation of the line.

By answering the presented question, we may conclude that She spends equation 40% of her time at work and 15% of her time on other hobbies. She spends 20% of her time napping.

In mathematics, an equation is an assertion that affirms the equivalence of two factors. An algebraic equation (=) separates two sides of an equation. For instance, the assertion  \("2x + 3 = 9"\) states that the word  \("2x + 3"\) Corresponds to the number "9".

The goal of solution solving is to figure out which variable(s) must still be adjusted for the equations to be true. It is possible to have simple or intricate equations, recurring or complex equations, and equations with one or more components.

For example, in the equations \("x2 + 2x - 3 = 0\)  ," the variable x is lifted to the powercell. Lines are utilized in many areas of mathematics, include algebra, arithmetic, and geometry.

Abby, according to the picture, spent:

She spends 25% of her time in school.

She spends 40% of her time at work and 15% of her time on other hobbies.

Therefore, Furthermore, she spends  \(20\) of her time napping.

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The algebraic expression for the price Ramon paid per share of Xerox stock is $40,000/x.

To express the price Ramon paid per share of Xerox stock algebraically, we can use the formula:

Price per share = Total cost / Number of shares

In this case, we know that Ramon bought x shares of Xerox stock for a total of $40,000

So we can substitute these values into the formula:

Price per share = $40,000 / x

Hence, the algebraic expression for the price is $40,000/x.

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The algebraic expression for the price Ramon paid per share of the Xerox stock is $40,000/x.

we can use the formula to determine the price paid per share of Xerox stock algebraically:

Price per share = Total cost of shares / Number of shares

Ramon bought x shares of Xerox stock for a total of $40,000

That is, total cost of shares = $40,000

Number of shares = x

Substitute these values into the formula:

Price per share = $40,000 / x

Therefore, the algebraic expression for the price is $40,000/x.

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(i) \(\lim_{x \to \pi/3}\) f(x) = 1 + √3.

(ii) \(\lim_{x \to \frac{\pi}{4}} f(x)\) does not exist.

For λ = 2.5, the function f(x) will be continuous at x = 0.

Given the function is,

f(x) = 1.5, when x = 0

    = 1 -2 sin x, when x < π/4

    = 1 + 2 sin x, when x > π/4

    = 1 + (sin λx/sin 5x)

Now,

\(\lim_{x \to \pi/3}\) f(x) = \(\lim_{x \to \pi/3}\) (1 + 2 sin x) [Since, π/3 > π/4]

                    = 1 + 2 sin (π/3)

                    = 1 + 2√3/2 = 1 + √3

Hence, \(\lim_{x \to \pi/3}\) f(x) = 1 + √3.

Now left hand limit is,

\(\lim_{x \to \frac{\pi^+}{4}}\) f(x) = \(\lim_{x \to \frac{\pi^+}{4}}\) (1 + 2sin x) = 1 +2 sin(π/4) = 1 + 2*(1/√2) = 1 + √2

and right hand limit is,

\(\lim_{x \to \frac{\pi^-}{4}}\) f(x) = \(\lim_{x \to \frac{\pi^-}{4}}\) (1 - 2 sin x) = 1 - 2*(1/√2) = 1 - √2

Since left hand limit and right hand limit are not equal so value of \(\lim_{x \to \frac{\pi}{4}} f(x)\) does not exist.

\(\lim_{x \to 0}\) f(x) = \(\lim_{x \to 0}\) (1 + (sin λx/sin 5x)) = 1 + \(\lim_{x \to 0}\) ((sin λx/λx)/(sin 5x/5x))*(λ/5) = 1 + λ/5

Since f(x) is continuous at x = 0.

So, \(\lim_{x \to 0}\) f(x) = f(0)

1 + λ/5 = 1.5

λ/5 = 1.5 - 1 = 0.5

λ = 2.5

Hence the value of λ will be 2.5.

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Answer:

To find the roots of 4x² - 12x + 9 = 0 graphically, we need to plot the equation on a graph and find the x-intercepts, which are the roots.

Here are the steps to graph the equation:

Plot the x-axis and y-axis on the graph

Plot the points (x, 4x² - 12x + 9) for several values of x within the range of -1 to 4.

Connect the points to form a smooth curve.

Find the x-intercepts, where the curve intersects the x-axis. These points represent the roots of the equation.

After finding the x-intercepts, we can use the x-value of each intercept to substitute back into the original equation to find the corresponding y-value. This confirms that the x-intercepts are indeed the roots of the equation.

Note: The above steps can also be done using a graphing calculator or software.

Answer:

112 ft squared

Step-by-step explanation:

Answer:

time all of them together

Step-by-step explanation:

A percentage is a way to describe a part of a whole. The relative change from last year to this year is 3.7%.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

28.6% of city employees ride the bus to work, therefore, the final value is 28.6. While Last year, 29.7% of city employees rode the bus to work, therefore, the initial value is 29.7.

Since relative change means change with respect to some value. Thus, the relative value with respect to last year is,

Relative value = (29.7-28.6)/29.7 = 0.037 = 3.7%

Hence, the relative change from last year to this year is 3.7%.

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Step-by-step explanation:

we don't see the complex numbers.

so, we cannot check their distances.

a suspicion, though.

sqrt(45) a distance between 2 complex numbers is

sqrt(a² + b²).

so,

a² + b² = 45

a nice combination of whole square numbers would be 6 and 3.

6² + 3² = 36 + 9 = 45

if that is the case, then that would mean one of the following committed numbers

6 + 3i

3 + 6i

-6 + 3i

6 - 3i

-6 - 3i

-3 + 6i

3 - 6i

-3 - 6i

one of these numbers must be the result of the subtraction of the 2 provided complex numbers.

remember

(a + bi) - (c + di) = a-c + (b-d)i

We want to write a slope-intercept equation for the line with characteristics: m passes through (2,3) and the gradient, m is -4/9.

To write the equation of the line, we write it in the form:

Answer: Reflexive Property

Step-by-step explanation:

Hence, The Transitive property is used in the step4.

Given that ,

Alternate Interior Angles Theorem, using parallel lines a and b with transversal m,

We have to prove,

Using parallel lines m is transversal by using transitive property.

Suppose that, a and b are two parallel lines and m is the transversal that intersects a and b.

We know that,

If a transversal intersects any two parallel lines,

The corresponding angles and vertically opposite angles are congruent.

Transitive Property: if A = B and B = C, then A = C.

Therefore,

∠1 = ∠5 ………..(i) [Corresponding angles]

∠3 = ∠1 ………..(ii) [Vertically opposite angles]

From equations (i) and (ii), we get-

By transitive property,

∠3 = ∠5

Hence, it is proved it is a transitive property.

Hence , Transitive property is the steps 4.

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The slope, y-intercept, and equation of the line shown in each graph are as follows;

Slope = 3

y-intercept = -2.

Equation = y = 3x - 2.

Slope = 3

y-intercept = 1.

Equation = y = -1/2(x) + 1.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is represented by this mathematical expression;

y = mx + c

Where:

Slope of first graph = (1 - (-2))/(1 - 0)

Slope of first graph = (1 + 2)/(1 - 0)

Slope of first graph = 3

For the equation of the first graph, we have:

y = mx + c

y = 3x + (-2)

y = 3x - 2.

Slope of second graph = (0 - 1)/(2 - 0)

Slope of second graph = -1/2

For the equation of the second graph, we have:

y = mx + c

y = -1/2(x) + 1

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Part 1

a.  In function notation, we have that R(3) > D(3)

b. In function notation, we have that R(0) - D(0) = 25

Part 2

The drone is 20 feet above the ground when the rocket hit the ground.

Part 3

a. R(t) = D(t) when the graphs intercept at t = 4.75 s

b.  It tell us that the drone and rocket are at the same height at that time.

A function notation is the representation of a statement as a mathematical equation using symbols.

Part 1

a. To write the statement at 3 seconds the toy rocket is higher than the drone in function notation.

Since

At t = 3, the toy rocket is higher than the drone.

So, in function notation, we have that R(3) > D(3)

b. To write the statement at the start the toy rocket is 25 feet above the drone.

At the start t = 0, and the toy rocket is 25 feet above the drone.

So, in function notation, we have that R(0) - D(0) = 25

Part 2.

To find the height of the drone when the rocket hit the ground,

Since

We find R(t) = 0 and find the time t, where it intercepts the height of the drone.

So, from the graph R(t) = 0 at t = 5. And at t = 5, D(t) = 20

So, the drone is 20 feet above the ground when the rocket hit the ground.

Part 3.

a. The value of t at which R(t) = D(t) is where the graphs intercept.

The graphs intercept at t = 4.75 s

b. Since R(t) = D(t) at t = 4.75 s, it tell us that the drone and rocket are at the same height at that time.

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Using Maxwell's equations, we can determine the magnetic flux density. One of the Maxwell's equations is:

\(\displaystyle \nabla \times \mathbf{H} = \mathbf{J} + \frac{\partial \mathbf{D}}{\partial t}\),

where \(\displaystyle \nabla \times \mathbf{H}\) is the curl of the magnetic field intensity \(\displaystyle \mathbf{H}\), \(\displaystyle \mathbf{J}\) is the current density, and \(\displaystyle \frac{\partial \mathbf{D}}{\partial t}\) is the time derivative of the electric displacement \(\displaystyle \mathbf{D}\).

In this problem, there is no current density (\(\displaystyle \mathbf{J} =0\)) and no time-varying electric displacement (\(\displaystyle \frac{\partial \mathbf{D}}{\partial t} =0\)). Therefore, the equation simplifies to:

\(\displaystyle \nabla \times \mathbf{H} =0\).

Taking the curl of the given magnetic field intensity \(\displaystyle \mathbf{R} =2\cos( 10^{10} t-600x)\hat{a}_{z}\, \text{Am}\):

\(\displaystyle \nabla \times \mathbf{R} =\nabla \times ( 2\cos( 10^{10} t-600x)\hat{a}_{z}) \, \text{Am}\).

Using the curl identity and applying the chain rule, we can expand the expression:

\(\displaystyle \nabla \times \mathbf{R} =\left( \frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial y} -\frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial z}\right) \mathrm{d} x\mathrm{d} y\mathrm{d} z\).

Since the magnetic field intensity \(\displaystyle \mathbf{R}\) is not dependent on \(\displaystyle y\) or \(\displaystyle z\), the partial derivatives with respect to \(\displaystyle y\) and \(\displaystyle z\) are zero. Therefore, the expression further simplifies to:

\(\displaystyle \nabla \times \mathbf{R} =-\frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial x} \mathrm{d} x\mathrm{d} y\mathrm{d} z\).

Differentiating the cosine function with respect to \(\displaystyle x\):

\(\displaystyle \nabla \times \mathbf{R} =-2( 10^{10}) \sin( 10^{10} t-600x)\hat{a}_{z} \mathrm{d} x\mathrm{d} y\mathrm{d} z\).

Setting this expression equal to zero according to \(\displaystyle \nabla \times \mathbf{H} =0\):

\(\displaystyle -2( 10^{10}) \sin( 10^{10} t-600x)\hat{a}_{z} \mathrm{d} x\mathrm{d} y\mathrm{d} z =0\).

Since the equation should hold for any arbitrary values of \(\displaystyle \mathrm{d} x\), \(\displaystyle \mathrm{d} y\), and \(\displaystyle \mathrm{d} z\), we can equate the coefficient of each term to zero:

\(\displaystyle -2( 10^{10}) \sin( 10^{10} t-600x) =0\).

Simplifying the equation:

\(\displaystyle \sin( 10^{10} t-600x) =0\).

The sine function is equal to zero at certain values of \(\displaystyle ( 10^{10} t-600x) \):

\(\displaystyle 10^{10} t-600x =n\pi\),

where \(\displaystyle n\) is an integer. Rearranging the equation:

\(\displaystyle x =\frac{ 10^{10} t-n\pi }{600}\).

The equation provides a relationship between \(\displaystyle x\) and \(\displaystyle t\), indicating that the magnetic field intensity is constant along lines of constant \(\displaystyle x\) and \(\displaystyle t\). Therefore, the magnetic field intensity is uniform in the given medium.

Since the magnetic flux density \(\displaystyle B\) is related to the magnetic field intensity \(\displaystyle H\) through the equation \(\displaystyle B =\mu H\), where \(\displaystyle \mu\) is the permeability of the medium, we can conclude that the magnetic flux density is also uniform in the medium.

Thus, the correct expression for the magnetic flux density in the given medium is:

\(\displaystyle B =6\cos( 10^{10} t-600x)\hat{a}_{z}\).

The graph of the given system of equations is shown below

From the question, we are to graph the given system of equations.

The given system of equations are

y − 2x = −1

x + 3y = 4

The graph of the given system of equations is shown below

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The true statements about the polynomial function graphed are:

Its leading coefficient is positive.

It has an odd degree.

None of the zeroes have even multiplicity.

From the given options, the true statements about the polynomial function graphed are:

Its leading coefficient is positive.

It has an odd degree.

None of the zeroes have even multiplicity.

Let's analyze each statement:

Its leading coefficient is positive:

The leading coefficient of a polynomial is the coefficient of the term with the highest degree.

From the graph, if the polynomial is going upwards on the right side, it indicates that the leading coefficient is positive.

It has an odd degree: The degree of a polynomial is the highest power of the variable in the polynomial expression.

If the graph has an odd number of "turns" or "bumps," it indicates that the polynomial has an odd degree.

None of the zeroes have even multiplicity:

The multiplicity of a zero refers to the number of times it appears as a factor in the polynomial.

In the given graph, if there are no repeated x-intercepts or no points where the graph touches and stays on the x-axis, it implies that none of the zeroes have even multiplicity.

The other statements (its leading coefficient is negative, it has an even degree, it has exactly two real zeroes, it has exactly three real zeroes, and none of the zeroes have odd multiplicity) cannot be determined based solely on the information given.

Therefore, the true statements about the polynomial function graphed are:

Its leading coefficient is positive.

It has an odd degree.

None of the zeroes have even multiplicity.

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The simplification of the given expression 3n²(n² + 4n - 5) - (2n² - n⁴ + 3) is; 4n⁴ + 12n³ - 17n² - 3

We want to simplify the polynomial expression;

3n²(n² + 4n - 5) - (2n² - n⁴ + 3)

Using distributive property of algebra, we expand the first bracket to get;

(3n⁴ + 12n³ - 15n²) - (2n² - n⁴ + 3)

Opening the brackets gives us;

3n⁴ + 12n³ - 15n²- 2n² + n⁴ - 3

Reorder the expression to group like terms to get;

3n⁴ + n⁴ + 12n³  - 15n²- 2n² - 3

= 4n⁴ + 12n³ - 17n² - 3

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Answer:

-2

Step-by-step explanation:

The initial value on a graph is the value of y when x = 0.

x is how far to the right or left a point on the graph is, so when x is not to the right or left at all, it is at the point 0.

y is how far a point is up or down, so, as shown on the graph, when x is 0, y is -2.

a) P((1/10)ΣH < 139) ≈ 0.2514, where H ~ N(140,7^2) and (1/10)ΣH is also normally distributed with mean 140 and standard deviation 7/√10.

b) P(F1 + F2 + F3 + F4 + F5 > 755) ≈ 0.4207, where F ~ N(150,5^2) and the sum F1 + F2 + F3 + F4 + F5 is also normally distributed with mean 750 and standard deviation 25.

c) P(F < H) ≈ 0.0185, where F ~ N(150,5^2), H ~ N(140,7^2), and their difference F - H is also normally distributed with mean 10 and standard deviation sqrt(5^2 + 7^2).

d) P(ΣH + ΣF < 1500) ≈ 0.2777, where ΣH denotes the total weight of 5 Honeycrisp apples and ΣF denotes the total weight of 5 Fuji apples. Both ΣH and ΣF are sums of i.i.d. normal variables and their sum is also normally distributed with mean 1450 and standard deviation sqrt(57^2 + 55^2).

e) Yes, it is necessary to use the Central Limit Theorem for questions b) and d) because we need to approximate the distribution of a sum of i.i.d. normal variables with a normal distribution.

a) We have H ~ N(140,7^2), and we want to find P((1/10)ΣH < 139). Since H is normally distributed, (1/10)ΣH is also normally distributed with mean 140 and standard deviation 7/√10. Therefore, we have

P((1/10)ΣH < 139) = P(Z < (139 - 140)/(7/√10)) = P(Z < -0.671) ≈ 0.2514,

where Z ~ N(0,1) is the standard normal distribution.

b) We have F ~ N(150,5^2), and we want to find P(F1 + F2 + F3 + F4 + F5 > 755), where Fi denotes the weight of the i-th Fuji apple. Since the Fi are i.i.d. normal variables, their sum is also normal with mean 5150 = 750 and standard deviation 55 = 25. Therefore, we have:

P(F1 + F2 + F3 + F4 + F5 > 755) = P(Z > (755 - 750)/25) = P(Z > 0.2) ≈ 0.4207,

where Z ~ N(0,1) is the standard normal distribution.

c) We want to find P(F < H), where F ~ N(150,5^2) and H ~ N(140,7^2). Since F and H are normal variables, their difference F - H is also normal with mean 150 - 140 = 10 and standard deviation sqrt(5^2 + 7^2) ≈ 8.602. Therefore, we have:

P(F < H) = P((F - H) < 0) = P(Z < -10/8.602) ≈ 0.0185,

where Z ~ N(0,1) is the standard normal distribution.

d) We want to find P(ΣH + ΣF < 1500), where ΣH denotes the total weight of the 5 Honeycrisp apples and ΣF denotes the total weight of the 5 Fuji apples. Since ΣH and ΣF are sums of i.i.d. normal variables, their sum is also normal with mean 5140 + 5150 = 1450 and standard deviation sqrt(57^2 + 55^2) ≈ 29.155. Therefore, we have:

P(ΣH + ΣF < 1500) = P(Z < (1500 - 1450)/29.155) ≈ 0.2777,

where Z ~ N(0,1) is the standard normal distribution.

e) Yes, it is necessary to use the Central Limit Theorem (CLT) for questions b) and d). In both cases, we are interested in the distribution of a sum of i.i.d. normal variables, which is not normal in general. However, by the CLT, if the sample size is large enough, the sum will be approximately normal regardless of the underlying distribution of the variables. Therefore, we can use the normal distribution to approximate the sum and calculate probabilities. For questions a) and c), we only need to consider the distribution of the sample mean or the difference between two normal variables, which are already normal and do not require the CLT.

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well, first off let's check which term has the highest degree, hmmm in this case it has to be the x³, so that's the leading term and its coefficient is 9.