We are to maintain a constant mean distance of ( d-avg ) to qualify for the cross-country biking expedition.
The qualification for the expedition is to rirde an average distance of:
[tex]d_{avg}\text{ }\ge\text{ 35 miles each for 5 consecutive day }[/tex]We are already on target for 4 days. For which we covered a distance ( d ) for each day:
[tex]\begin{gathered} \text{\textcolor{#FF7968}{Day 1:}}\text{ 45 miles} \\ \text{\textcolor{#FF7968}{Day 2:}}\text{ 33 miles} \\ \text{\textcolor{#FF7968}{Day 3:}}\text{ 27 miles} \\ \text{\textcolor{#FF7968}{Day 4: }}\text{26 miles} \end{gathered}[/tex]We are to project how much distance we must cover atleast on the fifth day ( Day 5 ) so that we can qualify for the expedition. The only condition for qualifying is given in terms of mean distance traveled over 5 days.
The mean value of the distance travelled over ( N ) days is expressed mathematically as follows:
[tex]d_{avg}\text{ =}\sum ^N_{i\mathop=1}\frac{d_i}{N}[/tex]Where,
[tex]\begin{gathered} d_i\colon Dis\tan ce\text{ travelled on ith day} \\ N\colon\text{ The total number of days in consideration} \end{gathered}[/tex]We have the data available for the distance travelled for each day ( di ) and the total number of days in consideration ( N = 5 days ). We will go ahead and used the standard mean formula:
[tex]d_{avg}\text{ = }\frac{d_1+d_2+d_3+d_4+d_5}{5}[/tex]Then we will apply the qualifying condtion to cover atleast 35 miles for each day for the course of 5 days.
[tex]\frac{45+33+27+26+d_5}{5}\ge\text{ 35}[/tex]Then we will solve the above inequality for Day 5 - (d5) as follows:
[tex]\begin{gathered} d_5+131\ge\text{ 35}\cdot5 \\ d_5\ge\text{ 175 - 131} \\ \textcolor{#FF7968}{d_5\ge}\text{\textcolor{#FF7968}{ 44 miles}} \end{gathered}[/tex]The result of the above manipulation shows that we must cover a distance of 44 miles on the 5th day so we can qualify for the expedition! So the range of distances that we should cover atleast to qualify is:
[tex]\textcolor{#FF7968}{d_5\ge}\text{\textcolor{#FF7968}{ 44 miles}}[/tex]All covered distances greater than or equal to 44 miles will get us qualified for the competition!
The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day, 277 people entered the park, and the admission fees collected totaled 828.00 dollars. How many children and how many adults were admitted?
Given:
Let x be the number of children.
Let y be the number of adults.
In total, there were 277 people.
So,
[tex]x+y=277\ldots\ldots\ldots(1)[/tex]According to the question, the fee of $1.50 for children and $4 for adults and the total fees collected is $828.
So,
[tex]1.5x+4y=828\ldots\ldots\ldots(2)[/tex]Multiply by 4 in equation (1),
[tex]4x+4y=1108\ldots\ldots\ldots(3)[/tex]Subtracting the equation (2) from (3), we get
[tex]\begin{gathered} 2.5x=280_{} \\ x=112 \end{gathered}[/tex]Substitute x=112 in equation (1), we get
[tex]\begin{gathered} 112+y=277 \\ y=165 \end{gathered}[/tex]Thus,
• The number of children is x = 112.
,• The number of adults is y = 165.
the lines are perpendicular if the slope of one line is 4/7 what is the slope of the other line
if two lines are perpendicular, it is true that:
[tex]\begin{gathered} m1\cdot m2=-1 \\ Let\colon \\ m1=\frac{4}{7} \\ m2=other_{\text{ }}line \\ \frac{4}{7}\cdot m2=-1 \\ solve_{\text{ }}for_{\text{ }}m2 \\ m2=-1\cdot\frac{7}{4} \\ m2=-\frac{7}{4} \end{gathered}[/tex]Rewrite (4x4 + 8x2 + 3)/(4x2) in the form q(x) + r(x)/b(x) where q(x) = quotient, r(x) = remainder, and b(x) = divisor.
ANSWER
(x² + 2) + 3/4x²
EXPLANATION
Since the divisor is a single-term polynomial, to write the answer in the requested form, we can distribute the divisor into each of the terms of the dividend,
[tex]\frac{4x^4+8x^2+3}{4x^2}=\frac{4x^4}{4x^2}+\frac{8x^2}{4x^2}+\frac{3}{4x^2}[/tex]And simplify,
[tex]\frac{4x^4}{4x^2}+\frac{8x^2}{4x^2}+\frac{3}{4x^2}=(x^2^{}+2)^{}+\frac{3}{4x^2}[/tex]Hence, the answer is (x² + 2) + 3/4x².
18#Suppose that 303 out of a random sample of 375 letters mailed in the United States were delivered the day after they were mailed. Based on this, compute a 90% confidence interval for the proportion of all letters mailed in the United States that were delivered the day after they were mailed. Then find the lower limit and upper limit of the 90% confidence interval. Carry your intermediate computations to at least three decimal places. Round your answers to two decimal places. (If necessary, consult a list of formulas.)Lower limit:Upper limit:
ANSWER:
Lower limit: 0.77
Upper limit: 0.84
STEP-BY-STEP EXPLANATION:
Given:
x = 303
n = 375
We calculate the value of the proportion in the following way:
[tex]\begin{gathered} p=\frac{x}{n}=\frac{303}{375} \\ \\ p=0.808 \end{gathered}[/tex]For a 90% confidence interval we have the following:
[tex]\begin{gathered} \alpha=100\%-90\%=10\%=0.1 \\ \\ \alpha\text{/2}=0.1=0.05 \\ \\ \text{ For the normal table this corresponds to:} \\ \\ Z_{\alpha\text{/2}}=1.645 \end{gathered}[/tex]We calculate the limits of the 90% confidence interval using the following formula:
[tex]\begin{gathered} \text{ Lower limit: }p-Z_{\alpha\text{/2}}\cdot\sqrt{\frac{p\cdot(1-p)}{n}}=\:0.808-1.645\cdot\sqrt{\frac{0.808\cdot\left(1-0.808\right)}{375}}\:=0.77 \\ \\ \:\text{Upper limit: }p-Z_{\alpha\text{/2}}\cdot\sqrt{\frac{p\cdot\left(1-p\right)}{n}}\:=0.808+1.645\cdot\sqrt{\frac{0.808\cdot\left(1-0.808\right)}{375}}=0.84 \end{gathered}[/tex]Factor by grouping c^2-8c +16 -4d^2
INFORMATION:
We have the following expression
[tex]c^2-8c+16-4d^2[/tex]And we must factor it by grouping
STEP BY STEP EXPLANATION:
To factor it by grouping, we must:
1. group the first 3 terms of the expression
[tex](c^2-8c+16)-4d^2[/tex]2. factor the expression in the parenthesis
[tex](c-4)^2-4d^2[/tex]3. rewrite 4d^2 as unique exponential expression
[tex](c-4)^2-(2d)^2[/tex]4. factor by square difference
[tex]((c-4)+2d)((c-4)-2d)[/tex]5. simplify
[tex]=(c+2d-4)(c-2d-4)[/tex]ANSWER:
the factoring for c^2-8c +16 -4d^2 by grouping is
[tex](c+2d-4)(c-2d-4)[/tex]Grocery store A is selling bananas for $9.75 for 1/2 pound .Grocery store B is selling 5 pounds of Bananas for $3.75 which store us offering the best unit rate
Grocery Store B ($1.33 per pound of bananas)
1) With these data we can write the following, and ,
Grocery Store A:
$ pounds
9.75 1/2
x--------------- 1
1/2x=9.75 x 2
x =19.5
Cross multiplying it:
Grocery Store B
$ pounds
5 3.75
y 1
3.75y=5
y=5/3.75
y=1.33
2) The best unit rate is at Grocery Store B ($1.33 per pound of bananas)
sin38° = ? (Write the Trigonometic ratio as a fraction)
Solution
The trigonometric ratio of sin 38 =
[tex]\begin{gathered} \sin \text{ 38 =}\frac{opposite}{hypothenus} \\ \text{opposite = a} \\ hypothenuse\text{ = c} \\ Sin\text{ 38 =}\frac{a}{c} \\ \end{gathered}[/tex][tex]Sin38^o\text{ = 0.6157= }\frac{6157}{10000}[/tex]f(x) = 9x² + 5x +4
g(x) = - 8x² - 3x - 4
Find (f + g)(x).
Answer:
1x^2+2x
Step-by-step explanation:
Put into Equation
(9x^2 +5x+4)+(-8x^2-3x-4)
Distribute
9x^2+5x+4-8x^2-3x-4
Combine like terms
1x^2+2x
Hope this helped!
Write down the domain of f-1 according to the following figure. A. {4, 5, 6, 7} B. {4, 3, 2, 7} C. {1, 2, 4, 5} D. {1, 2, 3, 4}
given to find down the domain of f inverse of the function.
An inverse function is found interchanging the first and second coordinate of each ordered pair.
thus the answer is, option A. {4,5,6,7}
Use the pair of functions f and g to find the following values if they exist[tex] f(x) = \sqrt{x + 2} [/tex][tex]g(x) = 3x - 2[/tex]a. (f+g)(2)b.(f/g)(0)c.(f-g)(-1)
Question 1: Identify the vertex. *A. (-2, -1)B. (-2, 1)C. (2, -1)D. (2, 1)
The standard equation of parabola with vertex (h,k) is :
(x - h)² = 4a(y - k)
The given eqation is : (x + 2)² = 4(y - 1)
On comparing the given equation with the standard equation we get
h = -2, a = 1 and k = 1
Vertex is ( h,k)
So, the vertex of the given equation of parabola is (-2, 1)
Answer : B (-2, 1)
if I make 9.75 hour and work 30 hours a week. how much I make in a week? how much I make in a month? how much in a year?
Since you make $9.75 per hour and you work 30 hours a week that means that you make:
[tex]9.75\cdot30=292.5[/tex]Therefore you make $292.5 in a week.
A month has 4 1/3 weeks, then per month you earn:
[tex]292.5\cdot4\frac{1}{3}=1267.5[/tex]Therefore you earn $1267.5 in a month.
Finally since each year has 12 month you earn:
[tex]1267.5\cdot12=15210[/tex]Therefore you earn $15210 in a year.
If {an) is an arithmetic sequence where a1=-23 and the common difference is 6, find a79
Given:
The first term
[tex]a_1=-23[/tex]The common difference, d=6
To find
[tex]a_{79}[/tex]Using the nth term formula,
[tex]\begin{gathered} a_n=a+(n-1)d \\ a_{79}=-23+(79-1)6 \\ =-23+(78)6 \\ =-23+468 \\ =445 \end{gathered}[/tex]Hence, the answer is,
[tex]a_n=445[/tex]A random number generator is programmed to produce numbers with a Unif (−7,7) distribution. Find the probability that the absolute value of the generated number is greater than or equal to 1.5.
We are given the following uniform distribution:
The probability that the absolute value of the number is in the following interval:
[tex]\begin{gathered} -7The probability is the area under the curve of the distribution. Therefore, we need to add both areas. The height of the distribution is:[tex]H=\frac{1}{b-a}[/tex]Where:
[tex]\begin{gathered} a=-7 \\ b=7 \end{gathered}[/tex]Substituting we get:
[tex]H=\frac{1}{7-(-7)}=\frac{1}{14}[/tex]Therefore, the areas are:
[tex]P(\lvert x\rvert>1.5)=(-1.5-(-7))(\frac{1}{14})+(7-1.5)(\frac{1}{14})[/tex]Simplifying we get:
[tex]P(\lvert x\rvert>1.5)=2(7-1.5)(\frac{1}{14})[/tex]Solving the operations:
[tex]P(\lvert x\rvert>1.5)=0.7857[/tex]Therefore, the probability is 0.7857 or 78.57%.
Two mechanics worked on a car. The first mechanic charged $105 per hour, and the second mechanic charged $120 per hour. The mechanics worked for a combined total of 20 hours, and together they charged a total of $2175. How long did each mechanic work?
Solution
The first mechanic charged $105 per hour.
The second mechanic charged $120 per hour.
The mechanics worked for a combined total of 20 hours
Let the first mechanic work for x hours
Then
[tex]\begin{gathered} 105x+(20-x)120\text{ =2175} \\ 105x+2400-120x=2175 \\ \text{collect like terms} \\ 105x-120x=2175-2400 \\ -15x=-225 \\ \\ \text{Divide both sides by -15} \\ \frac{\text{-15x}}{\text{-15}}=-\frac{225}{\text{-15}} \\ \\ x=15 \end{gathered}[/tex]The first mechanic work for x hours which 15hours
The second mechanic work for (20-x ) hours which is 20-15=5hours
.
which description is correct for the polynomial[tex]4x {}^{2} + 3x - 2[/tex]a cubic trinomial b quartic trinomial c cubic trinomial d quadratic trinomial
4x² + 3x - 2
This is a quadratic trinomial
Explanation: A quadratic equation has 2 as its highest index power
Then a polynomial involving 3 terms is a trinomial equation.
Hence the expression
4x² + 3x - 2 has its highest index power as 2 (4x raised to the power of two) and it has three separate terms, and that makes it a quadratic trinomial.
I need quick answers please, is due soon. i need assistance finding 5 points. 2 to the left of vertex, i need the vertex, and 2 to the right of the vertex. the graph only goes up to 14. thank you!
We have to find 5 points of the parabola:
[tex]y=x^2+8x+11[/tex]and then graph it.
We can find the vertex by completing the square:
[tex]\begin{gathered} y=x^2+8x+11 \\ y=x^2+2\cdot4x+16-16+11 \\ y=(x+4)^2-5 \end{gathered}[/tex]As we now have the vertex form of the parabola, we can see that the vertex is at (x,y) = (-4,-5).
We can now calculate two points to the right of the parabola by giving values to x as x = 0 and x = -2:
[tex]y=0^2+8\cdot0+11=11[/tex][tex]\begin{gathered} y=(-2)^2+8\cdot(-2)+11 \\ y=4-16+11 \\ y=-1 \end{gathered}[/tex]We now know two points to the right of the parabola: (0, 11) and (-2, -1).
As the line x = -4 is the axis of symmetry, we will have the same value for y when the values of x are at the same distance from this line.
Then, we can write:
[tex]\begin{gathered} y(0)=y(-8)=11 \\ y(-2)=y(-6)=-1 \end{gathered}[/tex]Then, we have two points to the left: (-8, 11) and (-6, -1).
We can graph the parabola as:
What are the magnitude and direction of w = ❬–10, –12❭? Round your answer to the thousandths place.
The direction of a vector is the orientation of the vector, that is, the angle it makes with the x-axis.
The magnitude of a vector is its length.
The formulas to find the magnitude and direction of a vector are:
[tex]\begin{gathered} u=❬x,y❭\Rightarrow\text{ Vector} \\ \mleft\Vert u|\mright|=\sqrt[]{x^2+y^2}\Rightarrow\text{ Magnitude} \\ \theta=\tan ^{-1}(\frac{y}{x})\Rightarrow\text{ Direction} \end{gathered}[/tex]In this case, we have:
• Magnitude
[tex]\begin{gathered} w=❬-10,-12❭ \\ \Vert w||=\sqrt[]{(-10)^2+(-12)^2} \\ \Vert w||=\sqrt[]{100+144} \\ \Vert w||=\sqrt[]{244} \\ \Vert w||\approx15.620\Rightarrow\text{ The symbol }\approx\text{ is read 'approximately'} \end{gathered}[/tex]• Direction
[tex]\begin{gathered} w=❬-10,-12❭ \\ \theta=\tan ^{-1}(\frac{-12}{-10}) \\ \theta=\tan ^{-1}(\frac{12}{10}) \\ \theta\approx50.194\text{\degree} \\ \text{ Add 180\degree} \\ \theta\approx50.194\text{\degree}+180\text{\degree} \\ \theta\approx230.194\text{\degree} \end{gathered}[/tex]Therefore, the magnitude and direction of the vector are:
[tex]\begin{gathered} \Vert w||\approx15.620 \\ \theta\approx230.194\text{\degree} \end{gathered}[/tex]Which of the following are the xintercepts on the graph of the function shown below? f(x)=(x+2)(x-7)
Which of the following are the xintercepts on the graph of the function shown below? f(x)=(x+2)(x-7)
we have the function
f(x)=(x+2)(x-7)
This is a vertical parabola written in factored form
The zeros or x-intercepts of the function are
x=-2 and x=7
Remember that the x-intercepts are the values of x when the value of the function is equal to zero
therefore
the answer is
x=-2 and x=7kelly is knitting a scarf for her brother. it took her 1/3 hour to knit 3/8 foot of the scarf. How fast is Kelly's knitting speed, in feet per hour?A[tex]4 \frac{1}{2} [/tex]B[tex]3[/tex]C[tex]2\frac{1}{2} [/tex]D[tex]1 \frac{1}{8} [/tex]
We need to divide the number of foot of scarf knitted by the number of time, in hours, taken.
[tex]\frac{\frac{3}{8}\text{ ft }}{\frac{1}{3}\text{ hour}}=\frac{3}{8}\cdot3\frac{\text{ ft}}{\text{ hour}}=\frac{9}{8}\frac{\text{ ft}}{\text{ hour}}=\frac{8+1}{8}\frac{\text{ ft}}{\text{ hour}}=1\frac{1}{8}\frac{\text{ ft}}{\text{ hour}}[/tex]A university student is selecting courses for his next semester. He can choose from 8 science courses and 4 humanities courses. In how many ways can he choose 4 courses if more than 2 must be science courses
The number of ways which he can choose 4 courses if more than 2 must be science is; 224 ways.
Combination of outcomes;
He can choose from 4 humanities courses and 8 science courses.
If the condition requires that he chooses more than 2 science courses, it follows that;
He can only choose three science courses and only 1 humanities courses.
8C3 x 4C1 = 56x 4 = 224
On this note, the number of ways he can choose the required 4 courses is; 224 ways.
Learn more on combination here:
brainly.com/question/4658834
#SPJ1
2. FR has a midpoint M. Use the given information to find the missing endpoint. F(-2,3) and M(3,0)
ANSWER:
R(8, -3)
STEP-BY-STEP EXPLANATION:
We have that the midpoint formula is the following:
[tex]M(m_1,m_2)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]In this case, we know the midpoint M, that is, m1 and m2 and the startpoint F, that is, we know, x1 andy1, we replace to calculate the values of R, the endpoint:
[tex]\begin{gathered} 3=\frac{-2+x_2}{2} \\ 6=-2+x_2 \\ x_2=6+2=8 \\ \\ 0=\frac{3+y_2}{2} \\ 0=3+y_2 \\ y_2=-3 \\ \\ \text{Therefore, the missing endpoint is: (8,-3)} \end{gathered}[/tex]Part A: Clancey and Ethan are starting new books. So far, Clancey has read 1/4 of his book, which has 240 total pages and Ethan has read 2/5 of his book, which has 170 total pages. Who has read more pages so far, Clancey or Ethan?Of the combined total number of pages in both books, what fraction have clancey and ethan read combined?
In order to find who has read more pages, let's find the number of pages read by each one.
The number of pages read by Clancey is:
[tex]\frac{1}{4}\cdot240=\frac{240}{4}=60[/tex]The number of pages read by Ethan is:
[tex]\frac{2}{5}\cdot170=\frac{340}{5}=68[/tex]So Ethan read more pages.
The combined number of pages in both books is 240 + 170 = 410.
The combined number of pages read is 60 + 68 = 128
So the fraction is:
[tex]\frac{128}{410}=\frac{64}{205}[/tex]The Elkhart Athletic Departments sells T-shirts and Hats at a big game to raise money. They sale the T-shirts for $12 and the Hats for $5. At the last football game they sold a total of 32 items and raised $265. How many T-shirts and Hats were sold at the game?
Let x represent the number of T shirts that they sold
Let y represent the number of hats that they sold
They sold the T-shirts for $12 and the Hats for $5. This means that the cost of x T shirts and y hats would be
12 * x + 5 * y
= 12x + 5y
The total amount raised was $265. It means that
12x + 5y = 265 equation 1
Also, the total number of t shirts and hats sold was 32. It means that
x + y = 32
x = 32 - y
Substituting x = 32 - y into equation 1, it becomes
12(32 - y) + 5y = 265
384 - 12y + 5y = 265
- 12y + 5y = 265 - 384
7y = 119
y = 119/7
y = 17
x = 32 - y = 32 - 17
x = 15
15 T shirts and 17 hats
Which function has the following characteristics? • A vertical asymptote at x = 3 • A horizontal asymptote at y = 2 Domain: {** +3] 2x - 8 X - 3 y=x2-9 2 9 x² - 4 4 OB. V C. 2x2 - 18 x² - 4 4 2x2 - 8 O D. ** - 9
SOLUTION
To get this, note that the vertical asymptote can be gotten by setting the denominator to be equal to 0.
If we do this, we will notice that the vertical asymptote of option A and option D is x = 3
That is
for option A
[tex]\begin{gathered} y=\frac{2x-8}{x-3} \\ x-3=0 \\ x=3 \end{gathered}[/tex]For option D
[tex]\begin{gathered} y=\frac{2x^2-8}{x^2-9} \\ x^2-9=0 \\ x^2=9 \\ x=3 \end{gathered}[/tex]So, the answer is either option A or D.
But to get the correct answer, let us look at the graphs for both functions
Graph of A
[tex]y=\frac{2x-8}{x-3}[/tex]From the graph, you can see that the domain is defined at x = 3. Notice that the green line cut across x = 3.
Now let's check Graph of option D
[tex]y=\frac{2x^2-8}{x^2-9}[/tex]From the graph, you can see that the domain is defined at x = -3 and x = 3. Notice that the purple and green line cut across x = -3 and x = 3. So, the domain here is
[tex]x=\pm3[/tex]Hence
What is the midpoint of the line segment graphed below?10-(5,9)-10-10-(2,-1)10
Step 1
The midpoint formula is given as;
[tex]\begin{gathered} \frac{x_1+x_2}{2},\frac{y_1+y_2}{2} \\ =\frac{5+2}{2},\frac{9-1}{2} \\ =3.5,4 \end{gathered}[/tex]Answer;
[tex](\frac{7}{2},4)[/tex]You have the option of borrowing money from one source that charges simple interest or from another source that charges the same APR but compounds the interest monthly. Which would you choose, and why?
I would choose the source that charges simple interest. This is because simple interest is based only on the principal (The amount borrowed), but compound interest is based on the principal and also the interest that has been generated from it.
In the figure, k//l, find the values of z and y.
Answer:
• z=113°
,• y=67°
Explanation:
In the diagram below, by the principles of vertical and corresponding angles:
[tex](6y-113)\degree=67\degree\text{ (Corresponding angles)}[/tex]We solve for y:
[tex]\begin{gathered} 6y=67+113 \\ 6y=180 \\ y=\frac{180}{6} \\ y=30 \end{gathered}[/tex]Next, angles z and (6y-113) are on a straight line. Therefore:
[tex]z+(6y-113)\degree=180\degree[/tex]However, recall we stated earlier that (6y-113)°=67°, therefore:
[tex]\begin{gathered} z+67\degree=180\degree \\ z=180\degree-67\degree \\ z=113\degree \end{gathered}[/tex]The values of z and y are 113° and 67° respectively.
How to graph it I know others one but not this one
Answer: (0, 2)
Explanation
The coordinates are a set of values that show the exact position of a point. In graphs, it is usually a pair of points in the form (x, y), where x represents the value in the horizontal axis and y represents the value of the vertical axis.
As we can see from the image above, in our point x = 0 (marked in red) while y = 2 (marked in purple). Rearranging the coordinate we get (0, 2).
Solve by completing the square. x2 - 8x + 5 = 0
Answer:
[tex]\begin{gathered} x_1=4+\sqrt[]{11} \\ x_2=4-\sqrt[]{11} \end{gathered}[/tex]Step-by-step explanation:
Solve the following quadratic completing the square:
[tex]x^2-8x+5=0[/tex]Keep x terms on the left and move the constant to the right side:
[tex]x^2-8x=-5[/tex]Then, take half of the x-term and square it.
[tex](-8\cdot\frac{1}{2})^2=16[/tex]Now, add this result to both sides of the equation:
[tex]x^2-8x+16=-5+16[/tex]Rewrite the perfect square on the left.
[tex]\begin{gathered} (x-4)^2=-5+16 \\ (x-4)^2=11 \end{gathered}[/tex]Take the square root of both sides:
[tex]\begin{gathered} \sqrt[]{(x-4)^2}=\pm\sqrt[]{11} \\ x-4=\pm\sqrt[]{11} \\ x=\pm\sqrt[]{11}+4 \end{gathered}[/tex]Hence, the two solutions of the equation are:
[tex]\begin{gathered} x_1=4+\sqrt[]{11} \\ x_2=4-\sqrt[]{11} \end{gathered}[/tex]