Joseph wants to factorise the following algebraic expression 3x squared + 6x + 4x + 8 provide yourself with a three-step guide on how to factorise the expression​

Answer:B

Step-by-step explanation:

The speed of the boat in still water is 3 times the speed of the river current.

To find the speed of the boat in still water, we can use the concept of relative motion and the given information about the boat's speed while traveling upstream and downstream.

Let's assume the speed of the boat in still water is "v" km/h, and the speed of the river current is "c" km/h.

When the boat is traveling upstream, it moves against the current, so its effective speed is reduced.

The boat's speed relative to the ground is given by (v - c) km/h.

Similarly, when the boat is traveling downstream, it moves with the current, so its effective speed is increased.

The boat's speed relative to the ground is given by (v + c) km/h.

According to the problem, the boat can travel 40 km upstream in the same time it would take to travel 80 km downstream.

Since time is constant in both cases, we can set up the following equation:

40/(v - c) = 80/(v + c)

To solve this equation, we can cross-multiply and simplify:

40(v + c) = 80(v - c)

40v + 40c = 80v - 80c

40c + 80c = 80v - 40v

120c = 40v

Dividing both sides by 40, we get:

3c = v.

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To convert the vertex form back to standard form, simply square the binomial, distribute a, and add the constants.

Example :

[tex]y=3(x+1)^2+5[/tex]

[tex]y=3(x^2+2x+1)+5[/tex]

[tex]y=3x^2+6x+3+5[/tex]

[tex]y=3x^2+6x+8[/tex] , This is the original standard form of the equation.

The vertex form of a quadratic equation is written as [tex]y = a(x - h)^2 + k[/tex] , where (h, k) represents the coordinates of the vertex.

To convert from vertex form to standard form, expand the equation using the distributive property:

[tex]y = a(x - h)^2 + k[/tex]

[tex]y = a(x^2 - 2hx + h^2) + k[/tex]

[tex]y = ax^2 - 2ahx + ah^2 + k[/tex]

Next, combine like terms by grouping the x^2 and x terms:

[tex]y = ax^2 - (2ahx) + (ah^2 + k)[/tex]

[tex]y = ax^2 - (2ahx) + (ah^2 + k)[/tex]

Finally, rearrange the terms in standard form:

[tex]y = ax^2 - (2ahx) + (ah^2 + k)[/tex]

[tex]y = ax^2 - 2ahx + ah^2 + k[/tex]

The resulting equation is in standard form, which is written as y = ax^2 + bx + c, where a, b, and c are constants. In this case, a = a, b = -2ah, and c = ah^2 + k.

By converting from vertex form to standard form, we express the quadratic equation in a different but equivalent format, allowing for different types of analysis and calculations.

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Answer:

Step-by-step explanation:

(x^3 - 10x + K)/(X+3) = 6 GIVEN

for different values of x there are many possible values of k some i will show

when we substitute x=1

we get k=33

at x=2

weget k=42

so many values are possible for k

because there is no intervel in question which restrics us from taking different values of x or k so you take any value of x you will get different values of k

┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈

✦ The number is - 5

┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈

[tex]\begin{gathered} \; \sf{\color{pink}{Let \; the \; other \; number \; be \; (x)::}} \\ \end{gathered}[/tex]

Atq,,

[tex]\begin{gathered} \; \color{skyblue} :\dashrightarrow \: \tt{3 \times \bigg \lgroup \: x + ( - 7) \bigg \rgroup = - 36} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \; \color{skyblue} :\dashrightarrow \: \tt{3 \times \bigg \lgroup \: x - 7 \bigg \rgroup = - 36} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \; \color{skyblue} :\dashrightarrow \: \tt{3x - 21 = - 36} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \; \color{skyblue} :\dashrightarrow \: \tt{3x = - 36 + 21} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \; \color{skyblue} :\dashrightarrow \: \tt{3x = - 15} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \; \color{skyblue} :\dashrightarrow \: \tt{x = \dfrac{\cancel{ - 15}}{\cancel{ \: 3}}} \qquad \bigg \lgroup \sf{Cancelling \: by \: 3} \bigg \rgroup \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \; \color{pink} :\dashrightarrow \underline{\color{pink}\boxed{\colorbox{black}{x = - 5}}} \: \pmb{\bigstar} \\ \\ \end{gathered}[/tex]

The answer is:

Work/explanation:

The product means we multiply two numbers.

Here, we multiply 3 and a number increased by -7; let that number be z.

So we have

[tex]\sf{3(z+(-7)}[/tex]

simplify:

[tex]\sf{3(z-7)}[/tex]

This equals -36

[tex]\sf{3(z-7)=-36}[/tex]

[tex]\hspace{300}\above2[/tex]

[tex]\frak{solving~for~z}[/tex]

Distribute

[tex]\sf{3z-21=-36}[/tex]

Add 21 on each side

[tex]\sf{3z=-36+21}[/tex]

[tex]\sf{3z=-15}[/tex]

Divide each side by 3

[tex]\boxed{\boxed{\sf{z=-5}}}[/tex]

Answer: 98 This statement is true

Step-by-step explanation:

100-11=89

89-12=77

77+21=98

`Both Meg and Cassandra are incorrect in their assessments (option a).

Meg and Cassandra have both misunderstood the logical relationships between the statements. Let's analyze each statement and compare their claims:

Statement 1: "If she is stuck in traffic, then she is late."

Statement 2: "If she is late, then she is stuck in traffic."

Statement 3: "If she is not late, then she is not stuck in traffic."

Meg's claims: Meg states that Statement 3 is the inverse of Statement 2 and the contrapositive of Statement 1. However, this is incorrect. The inverse of Statement 2 would be "If she is not stuck in traffic, then she is not late," and the contrapositive of Statement 1 would be "If she is not late, then she is not stuck in traffic." So Meg's analysis is incorrect.

Cassandra's claims: Cassandra states that Statement 2 is the converse of Statement 1 and the inverse of Statement 3. However, this is also incorrect. The converse of Statement 1 would be "If she is late, then she is stuck in traffic," and the inverse of Statement 3 would be "If she is late, then she is stuck in traffic." So Cassandra's analysis is incorrect as well.

Therefore, both Meg and Cassandra are wrong in their assessments. The correct logical relationships are as follows:

- The contrapositive of Statement 1 is Statement 3.

- The converse of Statement 1 is Statement 2.

Hence, the correct answer is that both Meg and Cassandra are incorrect.

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The z-score for Brazil is given as follows:

Z = 0.87.

The z-score formula is defined as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In which:

The parameters for this problem are given as follows:

[tex]X = 6.24, \mu = 4.8, \sigma = 1.66[/tex]

Hence the z-score for Brazil is given as follows:

Z = (6.24 - 4.8)/1.66

Z = 0.87.

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The volume of revolution generated by revolving the region about the x-axis is -512π.

To find the volume of revolution using the washer method, we need to integrate the area of the cross-sections formed by rotating the region bounded by the graphs of y = 8√x, y = 16, and the y-axis about the x-axis.

Let's start by setting up the integral. We will integrate with respect to x since the region is bounded by the x-axis.

The lower limit of integration (x) is 0, and the upper limit is found by setting y = 8√x equal to y = 16 and solving for x:

8√x = 16

√x = 2

x = 4

So the integral setup is:

V = ∫[0, 4] π(R^2 - r^2) dx

To find the outer radius (R), we consider the distance between the curve y = 8√x and the x-axis. Since we are revolving around the x-axis, R is simply y = 8√x.

The inner radius (r) is the distance between the line y = 16 and the x-axis, which is simply 16.

Now we can set up the integral:

V = ∫[0, 4] π((8√x)^2 - 16^2) dx

= ∫[0, 4] π(64x - 256) dx

Integrating:

V = π(32x^2 - 256x) |[0, 4]

= π[(32(4)^2 - 256(4)) - (32(0)^2 - 256(0))]

= π[512 - 1024 - 0]

= -512π

The volume of revolution generated by revolving the region about the x-axis is -512π.

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Answer: A. g(x) = 4∛x

Step-by-step explanation:

First, g(x) passes through the origin (0,0)

g(0) = 0

A,g(x) = ∛x+4,  g(0) = 4 ≠ 0

B,g(x) =  ∛x+4,  g(0) = ∛4≠0

So exclude A and B

Second, as can be seen in the figure,

The g(x) image is the magnification of the f(x) image on the y value.

f(x) = ∛x

So, Select A. g(x) = 4∛x quadruple the y value.

The answer is:

↬ f(x + 2) = 2x + 11

Work/explanation:

To evaluate the function, plug in x + 2 for x:

[tex]\boxed{\large\begin{gathered}\sf{f(x)=2x+7}\\\\\bf{distribute}\\sf{f(x+2)=2(x+2)+7}\\\\\bf{simplify}\\\sf{f(x+2)=2x+4+7}\\\\\sf{f(x+2)=2x+11}\end{gathered}}[/tex]

a. The interval of time between eruptions if the previous eruption lasted 4 minutes is 86.51 minutes.

b. The residual for this cycle is 2.07 minutes.

c. The interval of time between eruptions lasted for 2.07 minutes than the regression line equation predicted.

d. The slope of the regression line means that the interval of time between eruptions increases by 13.29 minutes for every additional minute of the previous eruption.

e. No, the value of the y-intercept doesn't have meaning in the context of the problem.

Based on the information provided above, the relationship between the duration of the previous eruption (x in minutes) and the interval of time between eruptions (y in minutes) is modeled by this regression line equation:

ÿ = 33.35 + 13.29x

Part a.

When x = 4 minutes, the value of is given by:

ÿ = 33.35 + 13.29(4)

ÿ = 86.51 minutes.

Part b.

The residual for the given cycle can be calculated as follows;

Residual = y - ÿ

Residual = 62 - (33.35 + 13.29(2))

Residual = 62 - 59.93

Residual = 2.07 minutes.

Part c.

Based on the calculation above, we can logically deduce that the interval of time between eruptions lasted for 2.07 minutes than the equation of regression line predicted.

Part d.

The slope of the regression line is equal to 13.29 and it implies that the interval of time between eruptions increases by 13.29 minutes for every additional minute of the previous eruption.

Part e.

In the context of the problem, we can logically deduce that the value of the y-intercept doesn't have any meaning because the duration of the previous eruption cannot be equal to 0 minutes.

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The net area of the curve represented by f(x) = ex - e on the interval [0, 2] is e2 - 1.

To find the net area of the curve represented by the function f(x) = ex - e on the interval [0, 2], we need to calculate the definite integral of the function over that interval. The net area can be determined by taking the absolute value of the integral.

The integral of f(x) = ex - e with respect to x can be computed as follows:

∫[0, 2] (ex - e) dx

Using the power rule of integration, the antiderivative of ex is ex, and the antiderivative of e is ex. Thus, the integral becomes:

∫[0, 2] (ex - e) dx = ∫[0, 2] ex dx - ∫[0, 2] e dx

Integrating each term separately:

= [ex] evaluated from 0 to 2 - [ex] evaluated from 0 to 2

= (e2 - e0) - (e0 - e0)

= e2 - 1

The net area of the curve represented by f(x) = ex - e on the interval [0, 2] is e2 - 1.

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The length of BD is 22.

In the given scenario, let's consider the following information.

AD = 8

AE = 6

EC is 12 more than BD.

To find the length of BD, we can utilize the Intercepted Arcs Theorem, which states that when two secants intersect outside a circle, the measure of an intercepted arc formed by those secants is equal to half the difference of the measures of the intercepted angles.

From the given information, we know that AD = 8 and AE = 6.

Since these are the lengths of the secants, we can use them to calculate the intercepted arcs.

First, let's find the intercepted arc corresponding to AD:

Intercepted Arc ADB = 2 [tex]\times[/tex] AD = 2 [tex]\times[/tex] 8 = 16

Similarly, we can find the intercepted arc corresponding to AE:

Intercepted Arc AEC = 2 [tex]\times[/tex] AE = 2 [tex]\times[/tex] 6 = 12

Now, we know that EC is 12 more than BD.

Let's assume the length of BD as x.

BD + 12 = EC

Now, let's consider the intercepted arcs theorem:

Intercepted Arc ADB - Intercepted Arc AEC = Intercepted Angle B - Intercepted Angle C

16 - 12 = Angle B - Angle C

4 = Angle B - Angle C.

Since Angle B and Angle C are vertical angles, they are congruent:

Angle B = Angle C.

Therefore, we can say:

4 = Angle B - Angle B

4 = 0

However, we have reached an inconsistency here.

The equation does not hold true, indicating that the given information is not consistent or there may be an error in the problem statement.

As a result, we cannot determine the length of BD based on the given information.

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Answer:

Step-by-step explanation:

To find the number of antiviral proteins injected into the person, we can set up a proportion:

2 mL contains 2.3 × 10^3 antiviral proteins

x mL contains how many antiviral proteins?

The proportion can be written as:

2 mL / 2.3 × 10^3 = x mL / (unknown number of antiviral proteins)

We can solve this proportion by cross-multiplication:

2 mL * (unknown number of antiviral proteins) = 2.3 × 10^3 antiviral proteins * x mL

x = (2.3 × 10^3 antiviral proteins * x mL) / 2 mL

Simplifying, we get:

x = 1.15 × 10^3 * x mL

Therefore, the number of antiviral proteins injected into the person is 1.15 × 10^3.

The total number of cells in the person's body is approximately 1 × 10^14. If 8% of the person's cells are infected with the virus, we can calculate the percentage of cells that can be affected by the medication:

Percentage of cells affected = (Number of infected cells / Total number of cells) * 100

Number of infected cells = 8% of 1 × 10^14 cells

Number of infected cells = (8/100) * 1 × 10^14

Number of infected cells = 8 × 10^12

Percentage of cells affected = (8 × 10^12 / 1 × 10^14) * 100

Percentage of cells affected = 8 × 10^-2 * 100

Percentage of cells affected = 8%

Therefore, the administered medication can affect 8% of the person's cells.

To find the amount of medication needed to have 1 antiviral protein for every infected cell, we can set up a proportion:

2.3 × 10^3 antiviral proteins in 2 mL

1 antiviral protein in x mL

The proportion can be written as:

2.3 × 10^3 antiviral proteins / 2 mL = 1 antiviral protein / x mL

We can solve this proportion by cross-multiplication:

(2.3 × 10^3 antiviral proteins) * x mL = 2 mL * 1 antiviral protein

x = (2 mL * 1 antiviral protein) / (2.3 × 10^3 antiviral proteins)

Simplifying, we get:

x = 0.8696 mL

Therefore, to have 1 antiviral protein for every infected cell, approximately 0.8696 mL of medication needs to be administered. This is equivalent to 0.0008696 liters.

Answer:

Step-by-step explanation:

To find the value of x, we can use the Angle Bisector Theorem, which states that in a triangle, a line segment that bisects an angle divides the opposite side into segments that are proportional to the other two sides.

In this case, segment AD bisects angle A, so we can set up the following proportion:

BD/DC = AB/AC

Plugging in the given values, we have:

14/DC = 28/25

To solve for DC (segment CD), we can cross-multiply:

28 * DC = 14 * 25

Simplifying further:

DC = (14 * 25) / 28

DC ≈ 12.5

Therefore, the length of segment CD is approximately 12.5.

Answer:

The correct answer is D. The graph of f(x) = 3(4)² - 5 + 3 is a transformation of the parent function. The parent function is y = x², which is a simple quadratic function.

In the given equation, the number 4 inside the parentheses represents a horizontal compression or shrink of the graph. The factor of 3 outside the parentheses represents a vertical stretch or expansion. The constant term -5 represents a vertical translation down by 5 units, and the constant term 3 represents a vertical translation up by 3 units.

Therefore, the graph of f(x) = 3(4)² - 5 + 3 is a compressed version of the parent function y = x², shifted down by 5 units and then shifted up by 3 units.

Answer:

$248.00

Step-by-step explanation:

Hours worked on Friday:  6 hr and 30 min = 6.5 hr

Money earned on Friday:  $15.5/hr x 6.5 hr = $100.75

Hours worked on Saturday:  6.5 hr - 1.167 hr = 5.33   *10 min = 10/60 = 0.1667 hr

Money earned on Saturday:  $15.50 x 5.33 hr = $82.67

Hours worked on Monday:  4.167 hr

Money earned on Monday:  $15.50/hr x 4.167 hr = $64.58

Total money made:  100.75 + 82.67 + 64.58 = $248.00

Answer:

D.

Step-by-step explanation:

To find the number of customers Sam's Swimming Pool Cleaning has, we need to calculate the total revenue generated by the business and divide it by the weekly charge per customer.

Total revenue = 52 x $25 x number of customers

We know that the annual gross profit is $88,400. So, we can set up an equation to find the number of customers:

$88,400 = 52 x $25 x number of customers - $48,000

$88,400 + $48,000 = 52 x $25 x number of customers

$136,400 = $1,300 x number of customers

Number of customers = $136,400/$1,300

Number of customers = 105

Therefore, Sam's Swimming Pool Cleaning has 105 customers. The correct answer is D.

Sam’s Swimming Pool Cleaning have 105 customers.

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division. The structure of an expression is:

To get how many customers Sam has, write an equation that will relate to the gross profit. Let n be the customers. Since for 52 weeks, Sam charges $25 per week per person, multiply n by the number of weeks and the charge. The equation is written as $88,400 = 52 weeks x $25 per week x n persons. Divide $88,400 by the product of 52 weeks and the $25 charge. The answer will be 105.

Therefore, Sam’s Swimming Pool Cleaning have 105 customers.

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Answer:

f(3r - 1) = -6r + 6

Step-by-step explanation:

To find f(3r - 1), we substitute 3r - 1 for x in the expression for f(x) and simplify:

f(x) = 4 - 2x

f(3r - 1) = 4 - 2(3r - 1)

= 4 - 6r + 2

= -6r + 6

So, f(3r - 1) = -6r + 6.

Answer:

m = -3

Step-by-step explanation:

The slope-intercept form is y = mx + b

m = the slope

b = y-intercept

The equation is  y = -3x + 2

m = -3

So, the slope of the line is -3

Answer:

The slope is -3

Step-by-step explanation:

You were given the easiest form of linear equation, the slope-intercept form, because these are the ones that directly tell you the slope and       the y-intercept.

y=mx+b, Where m is the slope and b is the y-intercept.

The total amount to pay would be 8800 Ethiopian Birr.

To find the amount to pay including VAT, we need to know the applicable VAT rate. VAT, or Value Added Tax, is a consumption tax added to the value of goods and services. The VAT rate can vary from country to country or even within different regions.

Assuming a VAT rate of 10%, we can calculate the VAT amount by multiplying the net value of the shoes by the VAT rate. In this case, the net value of the shoes is 8000 Ethiopian Birr. Therefore, the VAT amount would be 8000 * 0.10 = 800 Ethiopian Birr.

To find the total amount to pay including VAT, we add the VAT amount to the net value of the shoes. Thus, the total amount to pay would be 8000 + 800 = 8800 Ethiopian Birr.

It's important to note that the VAT rate and regulations can vary, so it's always advisable to check the specific VAT rate applicable in a given country or region. Additionally, different goods and services may have different VAT rates or exemptions, so it's crucial to consider the specific rules governing the shoe industry in the relevant jurisdiction.

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The degree of f(x) is 5, and the leading coefficient is negative. There are 3 distinct real zeros and 2 relative maximum values.

From the graph of a function, the zeros of the function are the x-intercepts, that is, the values of x for which the graph crosses or touches the x-axis.

The function in this problem has three distinct zeros, given as follows:

Hence the degree of the function is given as follows:

2 x 2 + 1 = 5.

The leading coefficient is negative, as the function has an odd degree, but increases to left and decreases to right.

The relative maximums of the functions are the points where the function makes a downward turn, changing from increasing to decreasing, hence there are two points.

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Step-by-step explanation:

Parallel to the x-axis means it is just a horizontal line with the value being the y-coordinate of the point:

y = -2

Answer:

y=-2

and m=0 must be your answer

Step-by-step explanation:

as line is parallel to x axis its slope will be zero as it does not have any definite x coordinate

so

equation of line is y-y'=m(x-x')

so m=0 m is slope

y'=-2 and x'=4

so by substituting the values

y+2=0

so y=-2

and m=0 is your answer

The probability that a randomly student at the university has a commuting time between ​​​​ 55 and 70 mins is about 0.56. Given information:The commuting time (the average number of hours spent commuting each week) for students at a particular university is normally distributed with a mean of 63 mins and standard deviation of 9.61.

Find: We are to determine the probability that a randomly student at the university has a commuting time between ​​​​ 55 and 70 mins.

Here,μ = 63 min σ = 9.61 min. We have to find the probability of a random student has commuting time between 55 and 70 min. That is P(55 ≤ X ≤ 70).First, we need to convert the given range to Standard Normal Distribution form.i.e., z-score for X = 55 and X = 70.Z-score formula:z = (X - μ) / σFor X = 55z = (55 - 63) / 9.61z = -0.83For X = 70z = (70 - 63) / 9.61z = 0.73. We need to find the probability of a random student has a z-score between -0.83 and 0.73.P(-0.83 < z < 0.73)

Using standard normal table or calculator, we can find the probability P(-0.83 < z < 0.73) = P(z < 0.73) - P(z < -0.83)= 0.7665 - 0.2033≈ 0.56

Thus, the probability that a randomly student at the university has a commuting time between ​​​​ 55 and 70 mins is about 0.56.

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Answer:

The question isn't clear. Can you provide more information or context? What is A? Is it a set or a number? Without this information, I can't provide a meaningful answer.

Answer: The correct ratio to represent the ratio of paperback books to hardcover books is 5:3.

(a) The sum of the series 1+2+3+4+...+392 is 77,028.

(b) The sum of the series 1+2+3+4...x is (x/2)(1 + x).

(c) The sum of the series 546 + 547 + 548 + 549 is 2,190.

To solve the exercise using Polya's four-step problem-solving strategy, we will apply the procedures presented in the lesson.

(a) For the series 1+2+3+4+...+392:

Using the arithmetic series formula Sn = (n/2)(a + l), where n is the number of terms, a is the first term, and l is the last term, we can substitute the values: Sn = (392/2)(1 + 392) = 196(393) = 77,028.

(b) For the series 1+2+3+4...x:

To find the sum of this series, we need to know the number of terms (n) based on the value of x. Since the series follows a consecutive pattern, the number of terms will be equal to x itself. Thus, the sum of the series would be Sn = (x/2)(1 + x).

(c) For the series 546 + 547 + 548 + 549:

Using the arithmetic series formula Sn = (n/2)(a + l), we can determine the number of terms (n) by subtracting 546 from 549 and then adding 1: n = 549 - 546 + 1 = 4. Substituting the values into the formula: Sn = (4/2)(546 + 549) = 2(1095) = 2,190.

The final answer for each part is:

(a) The sum of the series 1+2+3+4+...+392 is 77,028.

(b) The sum of the series 1+2+3+4...x is (x/2)(1 + x).

(c) The sum of the series 546 + 547 + 548 + 549 is 2,190.

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