The solution to the system of equations is (-1, 2, 4), which is equal to choice (c) (-1, 2, 4).
What is the system of equations?One or many equations having the same number of unknowns that can be solved simultaneously are called simultaneous equations. And the simultaneous equation is the system of equations.
To solve the system of equations, we can represent it in an augmented matrix and use row operations to find its reduced row-echelon form.
The augmented matrix for the system is:
[ 2 1 4 | 16 ]
[ 5 -2 2 | -1 ]
[ 1 2 -3 | -9 ]
We want to get the matrix in reduced row-echelon form.
We can start by using row operations to get a 1 in the upper left corner:
R(1/2) -> R1:
[ 1 1/2 2 | 8 ]
[ 5 -2 2 | -1 ]
[ 1 2 -3 | -9 ]
Now we want to get zeros in the first column below the pivot element (1). We can do this by subtracting 5 times the first row from the second row, and subtracting the first row from the third row:
-5R1 + R2 -> R2:
-R1 + R3 -> R3:
[ 1 1/2 2 | 8 ]
[ 0 -9/2 -8 | -41 ]
[ 0 3/2 -5 | -17 ]
R2 + R3 -> R3:
[ 1 1/2 2 | 8 ]
[ 0 -9/2 -8 | -41 ]
[ 0 -3 -13 | -58 ]
We can continue with row operations to get a 1 in the second row, second column:
(-2/9)R2 -> R2:
[ 1 1/2 2 | 8 ]
[ 0 1 16/9 | 82/9 ]
[ 0 -3 -13 | -58 ]
3R2 + R3 -> R3:
[ 1 1/2 2 | 8 ]
[ 0 1 16/9 | 82/9 ]
[ 0 0 -23/3 | -92/3 ]
Finally, we can get a 1 in the third row, third column:
(-3/23)R3 -> R3:
[ 1 1/2 2 | 8 ]
[ 0 1 16/9 | 82/9 ]
[ 0 0 1 | 4 ]
Now the matrix is in reduced row-echelon form.
We can read the solution directly from the last column:
x = 8 - (1 + 8) = -1
y = 82/9 - (16/9)(4) = 2
z = 4
Therefore, the solution to the system of equations is (-1, 2, 4).
To learn more about the system of equations;
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Mme. Giselle's boutique in Cleveland, Ohio is planning to sell a Parisian frock. If the public view it as being the latest style, the frocks will be worth $10 comma 000. However, if the frocks are viewed as passe, they will be worth only $2 comma 000. If the probability that they are stylish is 10%, what is the expected value of the frocks? The expected value of the frocks (EV) is EVequals$ nothing. (Enter your response rounded to two decimal places.)
Answer:
the expected value of the frocks (EV) is 2800
Step-by-step explanation:
the expected value of the frocks= (probability of stylish* worth)+(probability of passe* worth)
If the public view it as being the latest style, the frocks will be worth $10,000.
if the frocks are viewed as passe, they will be worth only $2,000.
If the probability that they are stylish is 10%
probability of stylish = 10000
worth = 10%
probability of passe = 2000
[tex]=10 \%*10000+(1-10 \%)*2000\\\\=0.1\times 10000+(1-0.1)\times2000\\\\=1000+(0.9)\times2000\\\\=1000+1800\\\\=2800[/tex]
Therefore, the expected value of the frocks (EV) is 2800
The proportion of items in a population that possess a specific attribute is known to be 0.40. If a simple random sample of size 100 is selected and the proportion of items in the sample that contain the attribute of interest is 0.46, what is the sampling error?
Answer:
The sampling error = 0.06
Step-by-step explanation:
From the given information:
Let represent [tex]\beta[/tex] to be the population proportion = 0.4
The sample proportion be P = 0.46 &
The sample size be n = 100
The population standard duration can be expressed by the relation:
Population standard duration [tex]\sigma = \sqrt{\dfrac{\beta(1- \beta)}{n}}[/tex]
[tex]\sigma = \sqrt{\dfrac{0.4(1-0.4)}{100}}[/tex]
[tex]\sigma = \sqrt{\dfrac{0.4(0.6)}{100}}[/tex]
[tex]\sigma = 0.049[/tex]
The sample proportion = 0.46
Then the sampling error = P - [tex]\beta[/tex]
The sampling error = 0.46 - 0.4
The sampling error = 0.06
A recent survey was conducted to compare the cost of solar energy to the cost of gas or electric energy. Results of the survey revealed that the distribution of the amount of the monthly utility bill of a 3-bedroom house using gas or electric energy had a mean of $143 and a standard deviation of $8. If the distribution can be considered mound-shaped and symmetric, what percentage of homes will have a monthly utility bill of more than $135? Write your answer exclude the percentage. (Exp. if your answer is 12%, then input as 12)
Answer:
84.13.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
For this question:
[tex]\mu = 143, \sigma = 8[/tex]
What percentage of homes will have a monthly utility bill of more than $135?
This is 1 subtracted by the pvalue of Z when X = 135. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{135 - 143}{8}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a pvalue of 0.1587
1 - 0.1587 = 0.8413
84.13% of homes will have a monthly utility bill of more than $135. Excluding the percentage, the answer is 84.13.
A 0.143-Henry Inductor is connected in series with a variable resistor to a 208-volt 400-cycle source. For what value of capacitance will the current be (a) 1.04 ampere lagging and (b) 1.04 ampere leading?
Answer:
A.)359.2, B.)2.5 uf
Step-by-step explanation:
E / I = R
208 / 1.04 = 200 ohms
2*pi*f*L = Xl
6.28*400*.143 = 359.2 ohm
1 / (2*pi*f*Xc) = c
1 /(6.28*400*159.2) = 2.5 uf
) Solve the equation 3x²-7x-6=0 by completing the square method
Answer:
x=3
Step-by-step explanation:
[tex]3x^{2}[/tex]-7x-6=0
9x-7x-6=0
=9x-7x=0+6=6
2x=6
x=6/2=3
Please answer this math question im desperate!! Will give brainliest!!
Answer:
Step-by-step explanation:
a ) the graph for a) is attached
y= -2x+5
when x=0, y=5 and when y=0, x=2.5
b) 4x-3y+9=0
-3y= -9-4x
y= 4/3 x+3
The perimeter of a rectangle whose sides are lengths(3z+2) units and(2z+3)units
Answer:
P = 10z + 10 units.
Step-by-step explanation:
To find the perimeter of a rectangle, you can use the formula P = 2l + 2w.
If one side is '3z + 2' and the other is '2z + 3', we can plug these into the equation:
P = 2(3z + 2) + 2(2z + 3).
Distributing the 2's gives us:
P = 6z + 4 + 4z + 6
Combine like terms, resulting in the final answer:
P = 10z + 10 units.
The base of a rectangular prism has an area of 12 square cm. The height of the rectangular prism is 3. What is the volume in cubic cm of this rectangular prism
Answer:
volume = 36 cm³
Step-by-step explanation:
The volume of a rectangular prism = lwh
where
w = width
l = length
h = height
The base of a rectangular prism is a rectangle and the area of a rectangle is the product of length and width. Therefore,
base area of the rectangular prism = length × width
base area = lw
Base area of the rectangular prism = 12 cm²
Recall, the formula of the volume of a rectangular prism is the product of the length, width and height.
volume = lwh
substitute lw value in the formula above
volume = 12 × 3
volume = 36 cm³
[Pic] The figure shows the location at which a slice is taken of a prism with base of an equilateral triangle. What will be the shape of the two-dimensional slice obtained?
A. Hexagon
B. Triangle
C. Square
D. Rectangle
Answer:
It would be B = Triangle because look where it’s cut sliced in half in a piece on top , it has three angles and a triangle has three angles so it’s B , Hope this helped :) brainliest will be appreciated
Help ASAP
Jamal and Diego both leave the restaurant at the same time, but in opposite directions. If Diego travels 7 mph faster than Jamal and after 4 hours they are 68 miles apart, how fast is each traveling?
Answer:
Jamal travels at a speed of 5 mph and Diego travels at a speed of 12 mph.
Step-by-step explanation:
Jamal's speed is of x mph.
Diego's speed is of (x + 7) mph.
Opposite directions.
This means that each hour, they will be x + x + 7 = 2x + 7 miles apart.
After 4 hours they are 68 miles apart, how fast is each traveling?
Using a rule of three.
1 hour - 2x + 7 miles apart.
4 hours - 68 miles apart.
[tex]4(2x + 7) = 68[/tex]
[tex]8x + 28 = 68[/tex]
[tex]8x = 40[/tex]
[tex]x = \frac{40}{8}[/tex]
[tex]x = 5[/tex]
Jamal travels at a speed of 5 mph and Diego travels at a speed of 12 mph.
Awnser on the lowest terms 2 hours 45 minutes + 3 hours 35 minutes
Step-by-step explanation:
2 hrs 45 min + 3 hrs 35 min
= 5 hrs 80 min
60 min = 1 hr
*80 min = 1 hr + 20 min
5hrs 80 min
= 5 hrs + 1 hr + 20 min
= 6 hrs 20 min
Answer:
6 hour 20 minutes
Step-by-step explanation:
Add the two time measurements separately.
2 hours + 3 hours = 5 hours
35 minutes + 45 minutes = 80 minutes
Now, simplify the measurements to the lowest terms. You can simplify the minutes by subtracting 60 from the value. 60 minutes is 1 hour. The number you get after subtracting is how many minutes there are.
80 - 60 = 20
80 minutes = 1 hour 20 minutes
Now add the two measurements together.
5 hours + 1 hour 20 minutes = 6 hour 20 minutes
Of 375 randomly selected students, 30 said that they planned to work in a rural community. Find 95% confidence interval for the true proportion of all medical students who plan to work in a rural community.
Answer:
The 95% confidence interval for the true proportion of all medical students who plan to work in a rural community is (0.0525, 0.1075).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 375, \pi = \frac{30}{375} = 0.08[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.08 - 1.96\sqrt{\frac{0.08*0.92}{375}} = 0.0525[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.08 + 1.96\sqrt{\frac{0.08*0.92}{375}} = 0.1075[/tex]
The 95% confidence interval for the true proportion of all medical students who plan to work in a rural community is (0.0525, 0.1075).
Suppose that the probability of a drought in any independent year is 20%. Out of those years in which a drought occurs, the probability of water rationing is ten percent. However, in any year, the probability of water rationing is five percent.
Which of the following is true?
a. 0.01
b. 0.05
c. 0.30
d. 0.02
Answer:
the correct option is d. 0.02
Step-by-step explanation:
We have the following events:
x: A drought occurd
y: Water rationing.
Therefore, according to the plaster we have:
P [x] = 0.20
P [y | x] = 0.10
Now P [it is a drought and water rationing happens] =
P [x n y] = P [y | x] * P [x] = 0.10 * 0.20 = 0.02
Which means that the correct option is d. 0.02
The number of 6th graders in RSM summer camp to that of 7th graders was 4 to 11, while the number of 5th graders to that of the 6th graders was 13 to 9. By what percent did the number of 7th graders exceed that of the number of 5th and 6th graders taken together ?
Answer:
The number of 7th graders exceed that of the number of 5th and 6th graders taken together by 5.88%.
Step-by-step explanation:
I am going to say that:
x is the proportion of 5th graders.
y is the proportion of 6th graders.
z is the proportion of 7th graders.
The number of 6th graders in RSM summer camp to that of 7th graders was 4 to 11
This means that:
[tex]\frac{y}{z} = \frac{4}{11}[/tex]
So
[tex]11y = 4z[/tex]
[tex]y = \frac{4z}{11}[/tex]
The number of 5th graders to that of the 6th graders was 13 to 9.
This means that:
[tex]\frac{x}{y} = \frac{13}{9}[/tex]
[tex]9x = 13y[/tex]
[tex]x = \frac{13y}{9}[/tex]
All of them is 100%
This means that:
[tex]x + y + z = 1[/tex]
We need to find z.
[tex]y = \frac{4z}{11}[/tex]
[tex]x = \frac{13y}{9} = \frac{13*4z}{9*11} = \frac{52z}{99}[/tex]
Then
[tex]x + y + z = 1[/tex]
[tex]\frac{52z}{99} + \frac{4z}{11} + z = 1[/tex]
The lcm(least common multiple) between 11 and 99 is 99. Then
[tex]\frac{52z + 9*4z + 99z}{99} = 1[/tex]
[tex]187z = 99[/tex]
[tex]z = \frac{99}{187}[/tex]
[tex]z = 0.5294[/tex]
By what percent did the number of 7th graders exceed that of the number of 5th and 6th graders taken together ?
z(7th graders) is 52.94%.
x + y(5th and 6th graders) is 100 - 52.94 = 47.06%
52.94 - 47.06 = 5.88
The number of 7th graders exceed that of the number of 5th and 6th graders taken together by 5.88%.
what is the most abundant gas in the Earth's atmosphere?
Answer:
Nitrogen
Step-by-step explanation:
Nitrogen and oxygen are by far the most common; dry air is composed of about 78% nitrogen (N2) and about 21% oxygen (O2). Argon, carbon dioxide (CO2), and many other gases are also present in much lower amounts; each makes up less than 1% of the atmosphere's mixture of gases. Hope this helped!
What is the range of this function?
{-4,1,7,15}
{-1,4,8,18}
{-4,-1,1,4,7,8,15,18}
{-4,-1,15,18}
Answer:
{-4,-1,1,4,7,8,15,18}
Step-by-step explanation:
The range of this function is a universal set that contains all elements of each set
And is;
{-4,-1,1,4,7,8,15,18}
Answer: its actually (-4, 1, 7, 15)
Step-by-step explanation:
which expression is equivalent to (x^1/2y^-1/4z)^-2?
Answer:
y^1/2/xz^2 option 3
Step-by-step explanation:
(x^1/2 y^-1/4 z)^-2= x^(-1/2*2) y^(1/4*2) z^-2= x^-1 y^1/2 z^-2= y^1/2/xz^2
Answer: C y^1/2/xz^2
Step-by-step explanation:
I checked with my calculator.
How do I find x to the nearest tenth?
Answer:
x=24.8
Step-by-step explanation:
Find the product (4x^2+2)(6x^2+8x+5)
please see the attached picture for full solution
Hope it helps
Good luck on your assignment
Answer:
[tex]= 24 {x}^{4} + 32 {x}^{3} + 32 {x}^{2} + 16x + 10 \\ [/tex]
Step-by-step explanation:
[tex](4 {x}^{2} + 2)(6 {x}^{2} + 8x + 5) \\ 4 {x}^{2} (6 {x}^{2} + 8x + 5) + 2(6 {x}^{2} + 8x + 5) \\ 24 {x}^{4} + 32 {x}^{3} + 2 0{x}^{2} + 12 {x}^{2} + 16x + 10 \\ = 24 {x}^{4} + 32 {x}^{3} + 32{x}^{2} + 16x + 10 \\ [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Find the values of p for which the following integral converges:
∫[infinity]e 1/(x(ln(x))^p)dx
Input youranswer by writing it as an interval. Enter brackets or parentheses in the first and fourth blanks as appropriate, and enter the interval endpoints in the second and third blanks. Use INF and NINF (in upper-case letters) for positive and negative infinity if needed. If the improper integral diverges for all p, type an upper-case "D" in every blank.
Values of p are in the interval ,
For the values of p at which the integral converges, evaluate it. Integral =
Answer:
Step-by-step explanation:
Find the values of p for which the following integral converges:
∫[infinity]e 1/(x(ln(x))^p)dx
Input youranswer by writing it as an interval. Enter brackets or parentheses in the first and fourth blanks as appropriate, and enter the interval endpoints in the second and third blanks. Use INF and NINF (in upper-case letters) for positive and negative infinity if needed. If the improper integral diverges for all p, type an upper-case "D" in every blank.
Values of p are in the interval ,
For the values of p at which the integral converges, evaluate it. Integral =
Recall that
[tex]\int\limits^{\infty}_1 \frac{1}{x^p} dx[/tex]
converge if p > 1 and converge to [tex]\frac{1}{p-1}[/tex] and divertgent if p ≤ 1
Now, let u = Inx ⇒ du = 1/x dx
: e ≤ x ≤ ∞ ⇒ 1 ≤ u < ∞
⇒ [tex]\int\limits^{\infty}_e \frac{dx}{x(Inx)^p} = \int\limits^{\infty}_1 {x} \frac{du}{u^p}[/tex]
converge if p > 1 and converge to [tex]\frac{1}{p-1}[/tex] and divertgent if p ≤ 1
[tex]\text {Integral}=\frac{1}{p-1}[/tex]
The radius of the inscribed circle is cm, and the radius of the circumscribed circle is cm.
The complete question is;
Instructions:Select the correct answer from each drop-down menu.
The side length of the square in the figure is 8 cm.
The radius of the inscribed circle is [ (32)^(1/2), 16, 4, 32 ] cm, and the radius of the circumscribed circle is [ (32)^(1/2), 2(32)^(1/2), (128)^(1/2), 128 ] cm.
Image is attached.
Answer:
Radius of inscribed circle = 4 cm
Radius of circumscribed circle = 32^(1/2) cm
Step-by-step explanation:
The square has a side of 8cm.
Thus,the diameter of the inscribed circle would be same as a side of the square.
So, if diameter = 8cm, then, radius of inscribed = 8/2 = 4cm
Now, to the circumscribed circle, the diagonal of the square would be the diameter of the circumscribed circle. It can be calculated with Pythagoreas theorem.
So, d² = 8² + 8²
d² = 64 + 64
d² = 128
d = √128
Expressing it in surd form gives;
d = √32 x √4
d = 2√32 cm
So radius of circumscribed circle = (2√32)/2 = √32 cm or 32^(1/2) cm
Answer:
4 and 32^1/2
Step-by-step explanation:
i just did it on plato :))
Suppose the nightly rate for a hotel in Rome is thought to be bell-shaped and symmetrical with a mean of 138 euros and a standard deviation of 6 euros. The percentage of hotels with rates between 120 and 144 euros is
Answer:
The percentage of hotels with rates between 120 and 144 euros is 84%.
Step-by-step explanation:
We know that the distribution of the nightly rate for a hotel in Rome is bell shaped with a mean of 138 euros and a standard deviation of 6 euros.
We want to know the proportion of hotels between 120 and 144 euros.
We can approximate the distribution to a normal distribution and calculate the z-score for both boundaries:
[tex]z_1=\dfrac{X_1-\mu}{\sigma}=\dfrac{120-138}{6}=\dfrac{-18}{6}=-3\\\\\\z_2=\dfrac{X_2-\mu}{\sigma}=\dfrac{144-138}{6}=\dfrac{6}{6}=1[/tex]
Then, we can calculate the proportion as the probability of having rates between 120 and 144:
[tex]P=P(120<X<144)=P(-3<z<1)\\\\P=P(z<1)-P(z<-3)\\\\P=0.8413-0.0013\\\\P=0.8400[/tex]
Then, we can conclude that the percentage of hotels with rates between 120 and 144 euros is 84%.
A manufacturer of cheese filled ravioli supplies a pizza restaurant chain. Based on data collected from its automatic filling process, the amount of cheese inserted into the ravioli is normally distributed. To make sure that the automatic filling process is on target, quality control inspectors take a sample of 25 ravioli and measure the weight of cheese filling. They find a sample mean weight of 15 grams with a standard deviation of 1.5 grams. What is the standard deviation of sample mean
Answer:
[tex] \bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}}) [/tex]
And the standard deviation for the sample mean would be given by:
[tex] \sigma_{\bar X}= \frac{1.5}{\sqrt{25}}= 0.3[/tex]
Step-by-step explanation:
For this case we know that the amount of cheese inserted into the ravioli is normally distributed. And we have the following info given;
[tex] \bar X =15[/tex] the sample mean
[tex]s= 1.5[/tex] the sample deviation
[tex] n=25[/tex] the sample size
And for this case we know that the sample size is large enough in order to apply the central limit theorem and the distribution for the sample mean would be given by:
[tex] \bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}}) [/tex]
And the standard deviation for the sample mean would be given by:
[tex] \sigma_{\bar X}= \frac{1.5}{\sqrt{25}}= 0.3[/tex]
1
TIN
10
Which inequality represents the same ages?
The inequality graphed below represents the ages, a, of
players on a baseball team
10 11 12 13 14 15 16 17 18 19 20
0 12
0 12 sa < 18
0 12 >as 18
12 a < 18
Answer: the last 1/ 12 a < 18
Step-by-step explanation:
What is the value of y when x = 0? When x = 0, y =
Answer:
The point in which the graph crosses the x-axis is called the x-intercept and the point in which the graph crosses the y-axis is called the y-intercept.
Step-by-step explanation:
The x-intercept is found by finding the value of x when y = 0, (x, 0), and the y-intercept is found by finding the value of y when x = 0, (0, y).
There are 7 more black than red markers in a box. If the total number of markers is 63, how many black markers are there?
Answer: 35
Step-by-step explanation: Let me know if you need an explanation.
Answer:
37
Step-by-step explanation:
Split and fill the difference
33 black
30 red
there is only a difference of three so you'll need to add and take a total of 4. to make up for the needed difference for 7.
33+2=35 black
30-2=28 red
Prove the statement is true using mathematical induction: 2n-1 ≤ n! Use the space below to write your answer. To make the < symbol, you might want to use the < with the underline feature.
Step-by-step explanation:
Given that n! = n(n - 1)(n - 2)(n - 3)...2×1
We want to show that 2n - 1 ≤ n!
Since
n! = n(n - 1)(n - 2)(n - 3)...2×1
= n(n - 1)!
n! = n(n - 1)(n - 2)!
n! = (n² - n)(n - 2)!
From here obviously,
n! ≥ n
n! ≥ 2n
And
n! ≥ 2n - 1
Which implies
2n - 1 ≤ n!
does anyone know the answer for dis problem?
x = # of CDs Walter has
3x - number of CDs Brian has
144 - total
x + 3x = 144
4x = 144
x = 144/4
x = 36
Answer: D. 36
Answer:
D.36
Step-by-step explanation:
X+3X=144
4X=144 (THEN DIVIDE BOTH SIDES B 4)
X=144/4=36
f(x) = x2 + 1
g(x) = 5-x
(f+g)(x) =
O x2 + x-4
x²+x+4
O x2-x+6
O x2 + x + 6
Answer:
[tex] \boxed{(f + g)(x) = {x}^{2} - x + 6} [/tex]
Given:
[tex]f(x) = {x}^{2} + 1 \\ \\ g(x) = 5 - x[/tex]
To Find:
[tex](f + g)(x) = f(x) + g(x)[/tex]
Step-by-step explanation:
[tex] = > f(x) + g(x) = ({x}^{2} + 1) + (5 - x) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {x}^{2} + 1 + 5 - x\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {x}^{2} + 6 - x\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {x}^{2} - x + 6[/tex]
