Using the arrangements formula, it is found that there are 12 ways for the dragons to go on stage.
What is the arrangements formula?The number of possible arrangements of n elements is given by the factorial of n, that is:
[tex]A_n = n![/tex]
In this problem, we have that:
For the first dragon, either the green or the blue dragon, hence two outcomes.For the remaining dragons, there are 3! possible ways.Hence the number of ways by which they can go on stage is:
N = 2 x 3! = 12.
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Answer:
Using the arrangements formula, it is found that there are 12 ways for the dragons to go on stage.
What is the arrangements formula?
The number of possible arrangements of n elements is given by the factorial of n, that is:
A_n = n!A
n
=n!
In this problem, we have that:
For the first dragon, either the green or the blue dragon, hence two outcomes.
For the remaining dragons, there are 3! possible ways.
Hence the number of ways by which they can go on stage is:
N = 2 x 3! = 12.
2.3. Use the following subtraction strategies to calculate 884-597: 2.3.1. breaking up the second number 2.3.2. adding on to the smaller number until you reach the bigger number 2.4. Design a real life activity for the Intermediate Phase in which learners will be required to apply the associative property of multiplication over addition. (4) (3) (3) 2.5. Suppose you want to have the activity in 2.4 marked by peers. Give a marking guideline according to which learners can score each other's work. (2) 2.6. Draw a diagram by which you can visually explain to learners in the Intermediate Phase why the sum of five consecutive numbers is equal to the fifth multiple of the middle number. Choose any set of five consecutive numbers to illustrate your statement. Write down your explanation in four powerful sentences. (5) OW a 2.3 . Use the following subtraction strategies to calculate 884-597 : 2.3.1 . breaking up the second number 2.3.2 . adding on to the smaller number until you reach the bigger number 2.4 . Design a real life activity for the Intermediate Phase in which learners will be required to apply the associative property of multiplication over addition . ( 4 ) ( 3 ) ( 3 ) 2.5 . Suppose you want to have the activity in 2.4 marked by peers . Give a marking guideline according to which learners can score each other's work . ( 2 ) 2.6 . Draw a diagram by which you can visually explain to learners in the Intermediate Phase why the sum of five consecutive numbers is equal to the fifth multiple of the middle number . Choose any set of five consecutive numbers to illustrate your statement . Write down your explanation in four powerful sentences . ( 5 ) OW a
It should be noted that the value of 597 subtracted from 884 is 287.
How to illustrate the subtraction?The information is simply that we should subtract 884 and 597 and also illustrate it.
This will be:
884 - 597 = 287.
A word problem illustrating this is that a man had 884 pens and gave 597 pens to his friends. How many pens does he have left?
This will be:
= 884 - 597 = 287
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Consider the following data on the estimated cost (in millions of dollars) resulting from traffic congestion for different urban areas. The following are the data for the 13 largest U.S. urban areas.
The mean is $5.769 million and the standard deviation is $3.905 million.
What is the mean?The mean is the average of a data set.
What is the standard deviation?The standard deviation shows the measure of the dispersion from the mean.
Data and Calculations:Urban Area Total Cost Squared Difference
(millions of dollars) (x - u)²
New York 16 104.65
Los Angeles 13 52.27
Chicago 7 1.51
Washington, D.C. 5 0.59
Houston 5 0.59
Dallas, Fort Worth 4 3.13
Detroit 4 3.13
Miami 4 3.13
Phoenix 4 3.13
Philadelphia 4 3.13
San Francisco 3 7.67
Boston 3 7.67
Atlanta 3 7.67
13 Total 75 198.27
Mean = 5.769 (75/13) 15.251 (198.27/13)
Standard Deviation = 3.905 (square root of 15.251)
Question Completion:Urban Area Total Cost
(millions of dollars)
New York 16
Los Angeles 13
Chicago 7
Washington, D.C. 5
Houston 5
Dallas, Fort Worth 4
Detroit 4
Miami 4
Phoenix 4
Philadelphia 4
San Francisco 3
Boston 3
Atlanta 3
Calculate the mean and standard deviation for this data set (in millions of dollars). (Round your answers to three decimal places.) mean $ million standard deviation $ million
Thus, the mean is $5.769 million and the standard deviation is $3.905 million.
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In a relatively pointless survey, the following data was collected on cars in a Costco parking lot: there were 94 white cars; 44 purple cars; 41 dark gray cars; 27 light blue cars; 46 green cars; 19 cars of some other color.
If you were to construct a Pareto chart (using the rule suggested in the book), how would the second bar in the graph be labeled?
color =
If I am to to construct a Pareto chart based on the rule of the chart, the second bar color in the graph be labeled light blue.
What is a Pareto chart?A Pareto chart is known to be a form of a bar graph.
It is made up of different lengths of bars that stands for frequency or cost ( e.g. time or money, and are said to be placed with longest bars on the left and then the shortest are placed to the right.
Since there are 27 light blue cars and this is the first one among the shortest, one can make it to be in the second bar and as such, If I am to to construct a Pareto chart based on the rule of the chart, the second bar color in the graph be labeled light blue.
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Draw u – v + w. please help !!!!!!!!!!
Here, we have to perform a sum of vectors and draw the resultant vector and the resultant vector will be <4, 0>.
How to illustrate the vector?If we see the image, we can write the vectors as:
w = <3, 3>
u = <-3, -4>
v = <-4, -1>
Now we want to sum:
u - v + w
u - v + w
= <-3, -4> - <-4, -1> + <3, 3>
= <-3 + 4 + 3, -4 + 1 + 3>
= <4, 0>
The graph of the resultant vector can be seen below.
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QUESTION IS DOWN BELOW 30 points for answer
Answer: a) 25:16 and b) 125:64
Step-by-step explanation:
For simplicity, assume that two spheres have diameters of 5 and 4.
a) 4pi(5^2) and 4pi(4^2)
= 100pi:64pi
= 100:64
= 25:16
b. 4/3 pi(5^3) and 4/3 pi(4^3)
= 166.67pi and 85.33pi
= 500:256
= 125:64
please help me asap thank you so so so much u are the most amazing
The smallest angle would be 19 degrees. So option D is correct.
What is the sum of the octagon?The sum of exterior angles of the regular octagon is 360 degrees.
Given;
The angles
x + 13 + 2x - 1 + 2x + 6 + 2x + 12 + 2x - 17 + 3x - 4 + 3x - 10 + 4x = 360
19x - 1 = 360
19x = 359
x = 18.89
The smallest angle would be
2x - 17 = 2(18.89) - 17 = 19
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Geometry
Help pls list steps so I can learn :)
Answer: [tex]\frac{25\pi}{4}[/tex]
Step-by-step explanation:
The area of the entire circle is [tex]\pi(5^2)=25\pi[/tex].
The area of a quarter of the circle is thus [tex]\frac{25\pi}{4}[/tex]
Choose the equation for the graph.
a) y = -x - 4 + 1
b) y=-x-4) - 1
c) y = -x + 4 + 1
d) y = -x + 4) - 1
e) y =
|x4| +1
Answer:
a
Step-by-step explanation:
The vertex is at (4,1).
Eliminate b, c, dAlso, the graph opens down, so this eliminates e.
So, the answer is a.
HELP ASAP!!!!GIVING BRAINLIEST!!!!!!
If f(x)=2x^2+2 and g(x)=x^2-1, find (f-g)(x).
Answer: B. x^2 + 3
Step-by-step explanation:
2x^2 + 2 -(x^2 - 1)
2x^2 + 2 - x^2 + 1
x^2 + 3
The table below gives recommended weight ranges for the balls from five different sports. (Hint: Find the average of each weight.)
The average weights of each ball are 270 grams, 625 grams, 425 grams, 145.5 grams and 14.5 ounces
How to determine the average weights?The range is given as:
Sport Weight range of ball used
Volleyball 260-280 grams
Basketball 600-650 grams
Water Polo 400-450 grams
Lacrosse 142-149 grams
Football 14-15 ounces
The average of each weight is calculated as:
Average = (Max + Min)/2
So, we have:
Volleyball = (260+280)/2 = 270 grams
Basketball = (600+ 650)/2 = 625 grams
Water Polo = (400+450)/2 = 425 grams
Lacrosse = (142+149)/2 = 145.5 grams
Football = (14+15)/2 = 14.5 ounces
Hence, the average weights of each ball are 270 grams, 625 grams, 425 grams, 145.5 grams and 14.5 ounces
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Missing information in the question
Sport Weight range of ball used
Volleyball 260-280 grams
Basketball 600-650 grams
Water Polo 400-450 grams
Lacrosse 142-149 grams
Football 14-15 ounces
PLEEEEEEEEEEASSEEEEEEE ANSWER QUESTION IS DOWN BELOW WORTH 15 POINTS each
A ratio shows us the number of times a number contains another number. The ratio of the volume of the model to the volume of the original is 27/2744.
What is a Ratio?A ratio shows us the number of times a number contains another number.
Given that the scale factor is 3:14. Therefore, the ratios can be written as,
(a) The ratio of the surface area of the model to the surface area of the original is,
Surface area Ratio = (3/14)² = 9/196
(b) The ratio of the volume of the model to the volume of the original.
Volume Ratio = (3/14)³ = 27/2744
(c) The ratio of the width of the model to the width of the original.
Width Ratio = 3/14
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On July 1, 20x5, Augusta Enterprises issued bonds with a face value of $1,000,000. The bonds carry a face interest rate of 10 percent that is payable each July 1 and January 1.
a. Prepare the entry in journal form without explanation for the issuance assuming the bonds are issued at 97.
b. Prepare the entry in journal form without explanation for the issuance assuming the bonds are issued at 102.
Based on the price that Augusta Enterprises issued the bonds, the journal entries would be:
Date Account title Debit Credit
July 1, 20x5 Cash $97,000
Discount on Bonds payable $3,000
Bonds payable $1,000,000
Date Account title Debit Credit
July 1, 20x5 Cash $1,020,000
Premium on Bonds payable $20,000
Bonds payable $1,000,000
How are bonds recorded at premium and discount?The cash received from the discounted bond is:
= 1,000,000 x 97%
= $970,000
The cash received from the premium bond is:
= 1,000,000 x 102/100
= $1,020,000
The premium is:
= 1,020,000 - 1,000,000
= $20,000
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Which expression is equivalent to the following complex fraction?
-2/x + 5/y / 3/y - 2/x
Answer: [tex]\frac{5x-2y}{3x-2y}[/tex]
Step-by-step explanation:
[tex]\frac{-\frac{2}{x}+\frac{5}{y}}{\frac{3}{y}-\frac{2}{x}}[/tex]
Multiplying the numerator and denominator by xy,
[tex]=\frac{-2y+5x}{3x-2y}\\\\=\frac{5x-2y}{3x-2y}[/tex]
Find the measure of the angle indicated in bold
The measure of the angles in bold are as follows;
25. 90° and 90°
26. 60° and 60°
How to find angles?When two parallel lines are cut by a transversal , angle relationship are formed. They are alternate angles, corresponding angles etc.
Therefore,
x + 96 + x + 96 = 180
2x = 180 - 192
2x = -12
x = -6
Hence, the angles are 90 and 90 degrees.
6x = 5x + 10(corresponding angles)
6x - 5x = 10
x = 10
Therefore, the angles are 60 degrees and 60 degrees
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On a number line 1.77 would be located.
On a number line 1.77 would be located between 1 and 2 but it would be closer to 2 than 1.
Where would 1.77 be located?A number line is used to show the positioning of numbers. 1.77 is between 1 and 2. So, it would be located between 1 and 2 on the number line. Because 1.77 can be rounded off to 2, it would be closer to 2.
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In a random sample of 1214 eligible voters younger than 40 years old, 461 reported that they planned to vote in the upcoming election. In a random sample of 1098 voters 40 and older,560 reported that they planned to vote in the election. Construct a 90% confidence interval for the difference between the percent of all voters younger than 40 and 40 and older who plan to vote in the upcoming election. What critical z-score will be used
Using the z-distribution, with a critical z-score of z = 1.645, the 90% confidence interval is (-16.4%, -9.66%).
What are the mean and the standard error for the distribution of the difference of proportions?For each sample, the mean and the standard error are given as follows:
[tex]p_y = \frac{461}{1214} = 0.3797, s_y = \sqrt{\frac{0.3797(0.6203)}{1214}} = 0.0139[/tex].[tex]p_o = \frac{560}{1098} = 0.51, s_o = \sqrt{\frac{0.51(0.49)}{1098}} = 0.0151[/tex].Hence, for the distribution of differences, they are given as follows:
[tex]p = p_y - p_0 = 0.3797 - 0.51 = -0.1303[/tex].[tex]s = \sqrt{s_y^2 + s_o^2} = \sqrt{0.0139^2 + 0.0151^2} = 0.0205[/tex]What is the confidence interval?
The interval is:
[tex]p \pm zs[/tex]
In this problem, we have a 90% confidence level, hence[tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.
Then the bounds of the interval are:
p - zs = -0.1303 - 1.645(0.0205) = -0.164.p + zs = -0.1303 + 1.645(0.0205) = -0.0966.As a percentage, the 90% confidence interval is (-16.4%, -9.66%).
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Draw a histogram and a box-and-whisker plot to represent the combined data, and answer the questions. Be sure to include the new graphs as part of your final submission.
How do the graphs of the combined data compare to the original graphs?
Compared to the original graphs, do the new graphs make it easier or more difficult to estimate the price of a book?
The new graphs would make it more difficult to estimate the price of a book.
How to create the combined graph?To do this, we simply combine the frequencies on Felix and Tyler's table.
When this is done, we have the following dataset
3,3,3,3,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7, 8,8,8,8,9,9,9,9,9,9,9,9,9,11,11,13,13,13,13,15,15,15,16,16,18,18,18,18,18,19,19,19,19,19,19,29,32,32,36,36,36,38,38,64,64,66,66,66,68,68,69,75,75,76,76,76,76,76,78,78,79,82,82,86,86,86,89,96,96,97,97,99
Next, we create the box & whisker plot and the histogram using the new dataset
(see attachment for the graphs)
The new graphs would make it more difficult to estimate the price of a book.
This is so because the dataset used to create the graphs do not come from the same source
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Bailey was practicing karate and kicked the target 6 out of 20 times. Express the number of times she kicked the target as a fraction of the total number of kicks , and reduce the fraction to the lowest terms.
Answer:
ok so here we know that Baily kicked the target 6 times out of 20 that is 6/20 and then you just reduce the fraction dividing it by 2 so it will be 3/10
Step-by-step explanation:
hope it helps :)
The function g(x) = p sin x +q, where p>0, has a maximum value of 10 and a minimum value of -4. Find the value of p and of q.
Answer: [tex]p=7, q=3[/tex]
Step-by-step explanation:
The midline of the function is
[tex]\frac{10-4}{2}=3 \implies q=3[/tex]
This means that to obtain a maximum of 10, when [tex]\sin x[/tex] reaches it's maximum, 1, [tex]g(x)=p+q=10 \implies p=7[/tex]
Solve the logarithmic equation...
Answer:
x = 3
Explanation:
[tex]\sf Given \ equation: \ log_{10} (1000) = x[/tex]
Solving steps:
[tex]\rightarrow \sf log_{10} (1000) = x[/tex]
apply rule: logₐ(b) = c then b = aᶜ
[tex]\rightarrow \sf 1000 = 10^x[/tex]
rewrite following
[tex]\rightarrow \sf 10^3= 10^x[/tex]
cancel out bases
[tex]\rightarrow \sf x = 3[/tex]
Answer:
d.) x = 3
Step-by-step explanation:
you simply need to know 10 to power of how many makes 1000 , In case didn't know you can replace the value of x with the given options and see if it can be solved or not .
Which of the following is equal to the rational expressions when x=2or1? (X-1)/(x+5)/(x-2)/(x-1)
Answer:
(x-2)/(x-1)
Step-by-step explanation:
(x-2)/(x-1)
Data was collected for a sample of organic snacks. The amount of sugar (in mg) in each snack is
summarized in the histogram below.
What is the sample size for this data set?
Explanation:
Add up the heights of each bar to get the sample size.
4+4+7+12+11+4+1 = 43
In the coin flipping lab, suppose that you simulated the flipping of a weighted coin 30 times and got 5 heads and 25 tails. What is your estimated probability for P(H)?
Answer:
1/6
Step-by-step explanation:
Out of 30 tosses, 5 come up heads. So the estimated probability of heads is 5/30, or 1/6.
Answer: 0.17
Step-by-step explanation:
just got it right on quiz
Determine if
16
x
2
−
25
y
2
=
1
16
x
2
-
25
y
2
=
1
is a hyperbola and if it is, which type it is. The transverse axis is
what is A and B
The values of a and b are 1/4 and 1/5 respectively
How to determine the true statement?The function is given as:
16x^2 - 25y^2 = 1
The above function is a horizontal hyperbola.
A horizontal hyperbola that passes through the origin is represented as:
[tex]\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1[/tex]
Rewrite 16x^2 - 25y^2 = 1 as
[tex]\frac{x^2}{1/16} - \frac{y^2}{1/25} = 1[/tex]
By comparison, we have:
[tex]a^2 = \frac{1}{16}[/tex]
[tex]b^2 = \frac{1}{25}[/tex]
Solve for a and b
[tex]a = \frac{1}{4}[/tex]
[tex]b = \frac{1}{5}[/tex]
Hence, the values of a and b are 1/4 and 1/5 respectively
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And a certain watery an urn contains balls number 1 to 34 from this are in five balls are chosen randomly without replacement for a one dollar bed a player chooses one set of phone numbers to Wayne all five numbers match match those shows it from the urn the order in which the balls or select it doesn’t matter what is the probability of winning the lottery with one ticket
The probability of winning the lottery with one ticket is mathematically given as
P(W)=2.99484408*10^{−8}
What is the probability of winning the lottery with one ticket?Generally, the equation for the probability is mathematically given as
P(1st ball)=1/34
one ball drawn remain
34-1=33
P(2nd ball)=1/33
In conclusion, the probability of winning the lottery with one ticket is
P(W)=1/34*1/33*1/32*1/31*1/30
P(W)=2.99484408*10^{−8}
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Complete the table below to solve the equation 2.5x − 10.5 = 64(0.5x).
x f(x) = 2.5x − 10.5 g(x) = 64(0.5x)
2
3
4
5
6
A newspaper started an online version of its paper 14 years ago. In a recent presentation to stockholders, the lead marketing executive stated, “The revenues for online ads are more than double that of the revenues for printed ads.”
Use the graph below to justify the lead executive’s statement.
Determine the approximate year that the two ad revenues were equal.
See Text Version
Two ocean beaches are being affected by erosion. The table shows the width, in feet, of each beach measured at high tide where 1995 is represented by year 0:
Year number Western Beach width (in feet) Dunes Beach width (in feet)
0 100 20
5 90 45
10 80 70
11 78 75
12 76 80
15 70 95
Describe the patterns shown by the erosion data measurements shown for each of the beaches in the table.
Between which years will the beaches have approximately the same width?
Assuming these rates remain constant, what can you do to get a better approximation of when the two beaches will have the same width?
The answers are as follows:
What is data?Data is information that has been translated into a form that is efficient for movement or processing.
1. By substituting the values x= 1, 2, 3..
We get the point where f(x)= g(x)
So, f(5)= g(5) =2
Hence, the value of x is 5.
2. As per the given data, during year 14,
revenue from online ads is approximately $4.2 million, whereas revenue from online ads is double than revenue from printed ads.
Also, both line intersect inbetween 7 and 8th year and both online ads and printed ads generated an approximate revenue of $2.2 million.
3. Western Beach erodes from 100 ft to 70 ft.
So, rate of erosion = 30 ft/15 yr = 2 ft/yr.
and, Dunes Beach builds up from 20 ft to 95 ft.
So, rate of buildup = 75 ft/15 yr = 5 ft/yr.
Hence, Dunes beach gets 5 feet every year, and every 5 years the beach loses 25 feet.
b) From the table, beaches will have the same width sometime in year 11 (2006).
c) If the rate remains constant then there is no same width cause of decrease in western beach and increase dunes beach.
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A box with an open top is to be constructed from a 15 inch by 24 inch piece of cardboard by cutting squares of equal sides from the corners and folding up the sides. Find the dimensions of the box of the largest volume that can be constructed.
The dimensions of the box of the largest volume that can be constructed are
D=18,9,3
What are the dimensions?Generally, the equation for the lenght is mathematically given as
Lenght=(24-2x)
Widht= (15-2x)
Therefore
Volume =L*B*H
V=(24-2x)(15-2x)x
V=(360-48x-30x+4x)x
V=4x^3-78x^2+360x
Differnciating we have
dv/dx=12x^2-156x+360
put dv/dx=0
12(x^2-13x+30)=0
x^2-10x-3x+30=0
(x-10)(x-3)=0
root=10,3
Second diiferciation
d^v/dx^2=24x-156
[tex]lim _{x=3} =-84 < 0[/tex]
In conclusion,
L=24-2x
L=24-2x3
L=18in
w= 15-2x
w=15-2*3
w=9in
h=x
h=2in
Dimension=18,9,3
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A garden table and a bench cost $714 combined. The garden table costs $64 more than the bench. What is the cost of the bench?
Answer:
The bench costs $325
Step-by-step explanation:
let garden table = x
let bench = y
x = y+64
x+y = 714
y+y+64 = 714 (we know, x = y+64)
2y + 64 = 714
2y = 650
y = 325
Answer:
Bench: $325
Garden Table: $389
Step-by-step explanation:
g + b = 714 Eq. 1
g = b + 64 Eq. 2
g = cost of the garden table
b = cost of the bench
Replacing Eq.2 in Eq.1
(b+64) + b = 714
2b + 64 = 714
2b = 714 - 64
2b = 650
b = 650/2
b = 325
from the Eq. 2
g = b + 64
g = 325 + 64
g = 389
Check:
from the Eq. 1
g + b = 714
389 + 325 = 714
Question
Determine an angle between 0° and 360° that is coterminal to an angle with measure of 1524°.
Enter your answer below without a degrees symbol - just enter the numeric answer.
Answer: 84°
Step-by-step explanation:
On a unit circle, coterminal angles are angles that are in the opposite position of the asked angle. 1524° revolves around 127/15π times across the entire unit circle.
84° is the only positive coterminal angle between 0 and 360 that is in the opposite position of 1524°.
Keep in mind, that there are more coterminal angles, namely 444°, 804°, 1164°, and 1524° itself, but they are outside of the range of 0 and 360 degrees.
Which of the following are solutions to the equation below?
Check all that apply.
9x² - 6x + 1 =7
O A. x= 2√2
B. x = -√7+1
3
☐ C. X=
□ D. X=
√√7+1
3
+1
□ E. x = 2√2
3
O F. X= -√2+1
Answer: C and B
Step-by-step explanation:
[tex]9x^2 - 6x+1=7\\\\9x^2 - 6x-6=0\\\\x=\frac{-(-6) \pm \sqrt{(-6)^2 - 4(9)(-6)}}{2(9)}\\\\x=\frac{6 \pm \sqrt{252}}{18}\\\\x=\frac{1 \pm \sqrt{7}}{3}[/tex]