We operate as follows:
[tex]4(2x+3)=3x+3+2x\Rightarrow8x+12=5x+3[/tex][tex]\Rightarrow3x=-9\Rightarrow x=-3[/tex]The value of x is -3.
for the literal equation x^2+m=y, express x in terms of y and m
We have the equation of y as a function of x:
[tex]y(x)=x^2+m[/tex]To find x(y) we just need to solve for x, first by subtracting m from both sides
[tex]y-m=x^2[/tex]Now, we just have to take the square root on both sides
Taking the square root of a number it's actually raising it to the 1/2 power:
[tex]\sqrt[]{a}=a^{\frac{1}{2}}[/tex]Now, when we proceed to raise the square root of a number to two, we can arrange it like this:
[tex](a^{\frac{1}{2}})^2=a^{\frac{2}{2}}=a^1=a[/tex]When we take the square root of a number that is raised to two the result will be the number without any power, like this:
[tex]\sqrt[]{a^2}=a[/tex]Then:
[tex]\sqrt[]{x^2}=x=\sqrt[]{y-m}[/tex]Can anyone solve this?
The value of x for the given triangle is 2√5 units.
According to the question,
We have the following information:
We have two triangles joint together whose sides are given.
Now, we will use the Pythagoras theorem to find the value of x.
Let's denote the hypotenuse of the triangles with h, perpendicular with p and base with b.
First, we will use it in triangle other than the side x.
[tex]h^{2} =p^{2} +b^{2}[/tex]
[tex]p^{2} =9^{2} -6^{2}[/tex]
[tex]p^{2} =81-36[/tex]
[tex]p^{2} = 45[/tex]
p = √45
p = 3√5 units
Now, the perpendicular of this triangle will be the hypotenuse of another triangle.
[tex]h^{2} =p^{2} +b^{2}[/tex]
[tex]b^{2} =(3\sqrt{5}) ^{2} - 5^{2}[/tex]
[tex]b^{2} = 45-25[/tex]
[tex]b^{2} = 20[/tex]
b = 2√5 units
Hence, the value of x is 2√5 units.
To know more about value of x here
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Suppose that the local sales tax rate is 4% and you purchase a car for $18,000. How much tax is paid? What is the cars total cost?
Solution
Step 1:
Cost = $18000
Tax = 4% of $18000
Step 2
[tex]\begin{gathered} Tax\text{ = 4\% of \$18000} \\ \\ Tax\text{ = }\frac{4}{100}\text{ }\times\text{ \$18000} \\ \\ Tax\text{ paid = \$720} \end{gathered}[/tex]Step 3
[tex][/tex]I NEED HELPPP Which expression is equivalent to 34.3-97
-62.7
1) Solving that expression we'll find an equivalent number or expression.
34.3 -97=
2) Rewriting 97 as 97.0 to proceed with the subtraction:
Since -97 is the number whose absolute value is greater than 34.3 than the result is : -62.7
the radius of a circle is 15 what is the length of an arc that subtends an angle of Pi radians
The arc length of a circle is calculated by the formula
[tex]s=\theta\cdot r[/tex]replace the values of the angle and the radius into the formula
[tex]\begin{gathered} s=\pi\cdot15 \\ s=15\pi \end{gathered}[/tex]the arc length of the arc that subtends an angle of pi is 15pi.
Each vertex of a quadrilateral is dilated by a factor of 1/2 about the point P (-3,7). What will be the effect on the perimeter of the resulting figure.
Note that the perimeter of any quadrilateral is the sum of its sides.
[tex]P=\sum ^n_{i\mathop=1}a_i[/tex]So it is always proportional to the length of any side,
[tex]P\propto a_i[/tex]Note that the dilation either stretches of compresses the sides.
For the factor 1/2, each side of the quadrilateral will get multiplied by 1/2, which simply means that the sides will get halved.
So the new perimeter is given by,
[tex]P^{\prime}=\sum ^n_{i=1}(\frac{1}{2}a_i)=\frac{1}{2}\sum ^n_{i=1}(a_i)=\frac{1}{2}P[/tex]Thus, the perimeter will also get halved due to the dilation.
Therefore, option A is the correct choice.
How do you turn 2x+3y=12 into slope intercept form?
Answer:
y = -2x/3 + 4
Explanation:
The equation of a line in slope-intercept form is expressed as y = mx+c
Given the equation 2x+3y=12, you will have to make y the subject of the formula as shown:
Given
2x+3y=12
3y = 12 - 2x
3y = -2x + 12
Divide through by 3
3y/3 = -2x/3 + 12/3
y = -2x/3 + 4
Hence the expression in slope intercept form is y = -2x/3 + 4
The length of a rectangle is 2ft more than twice the width. The area is 144 ft squared. Find the length and width of the rectangle.
The formula for the area of a rectangle (A) is given as
[tex]A=\text{length}\times breadth[/tex]Given that
The length of a rectangle is 2ft more than twice the width,
Therefore,
length = 2 + 2width
where,
[tex]\begin{gathered} w=\text{width} \\ l=2+2w \\ A=144ft^2 \end{gathered}[/tex]Hence,
[tex]\begin{gathered} 144=(2+2w)\times w \\ 144=2w+2w^2 \\ 144=2(w+w^2) \\ \frac{144}{2}=\frac{2(w+w^2)}{2} \\ 72=w+w^2 \\ w^2+w-72=0 \end{gathered}[/tex]Factorizing the equation above
[tex]\begin{gathered} w^2+9w-8w-72=0 \\ w(w+9)-8(w+9)=0 \\ (w-8)(w+9)=0 \\ w-8=0\text{ or }w+9=0 \\ w=8\text{ or w=-9} \\ \therefore w=8or-9 \end{gathered}[/tex]Note that the width can never be negative, therefore the width of the rectangle is 8.
Recall that:
[tex]\begin{gathered} l=2_{}+2w=2+2(8)=2+16=18 \\ l=18 \end{gathered}[/tex]Hence,
[tex]\begin{gathered} \text{length = 18ft} \\ \text{width = 8ft} \end{gathered}[/tex]
A Distance Run (km) B Distance Run (km) 0 1 1 1 | 2 | 4 | 7 7 088 9 1 1|224 5 5 8 1 2 3 2 3 3 6 8 9 2 3 5 5 6 7 8 9 2 1 1 3 6 | 7 3 03 4 4 15 310 What is the DIFFERENCE in the ranges of the 2 sets of data?Type your answer without a label.
The range of a data set is said to be the difference between the highest value and the lowest value in the given set of data.
To find the difference in the ranges of the 2 sets of data, find the range of data set A, find the range of data set B, then subtract the range of A from B.
Thus, we have:
For data A:
Minimun data value = 08
Maximum data value = 35
Range of data set A = 35 - 08 = 27
For data set B:
Minimum data value = 01
Maximum data value = 30
Range of data set B = 30 - 01 = 29
Difference in the ranges = Range of set B - Range of set A = 29 - 27 = 2
Therefore, the difference in the ranges of the sets of data is 2
ANSWER:
2
Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin.Horizontal axis and passes through the point (9, −4)
Answer:
[tex]x=\frac{9}{16}y^2[/tex]Step-by-step explanation:
Since the vertex of the parabola at the origin (h,k) is (0,0). The standard form of the parabola is represented as:
[tex]\begin{gathered} x=a(y-k)^2+h \\ \end{gathered}[/tex]If the parabola passes through the point (9,-4), we can substitute for (x,y) and (h,k) and solve for ''a.'' and determine the equation:
[tex]\begin{gathered} 9=a(-4-0)^2+0 \\ 9=a(16)+0 \\ a=\frac{9}{16} \\ \end{gathered}[/tex]Then, the equation of the parabola in standard form would be:
[tex]x=\frac{9}{16}y^2[/tex]3 Check your notes! A container is shaped like a rectangular prism and has a volume of 72 cubic feet. Give two different sets of measurements that could be the dimensions of the container. Answers: a feet X feet x a feet feet X feet X feet >
Explanation:
The volume of the container = 72 cubic ft
The container is a rectangular prism.
The formula for volume of rectangular prism:
[tex]\text{Volume = length }\times\text{ width }\times\text{ height}[/tex]To get the posssible values of the containers dimention, we will find the factors of 72. Since the volume is a product of the dimensions
[tex]\begin{gathered} 72\text{ = 3 }\times\text{ 24} \\ 72\text{ = 3 }\times\text{ 4 }\times\text{ 6} \\ \text{The possible dimensions can be:} \\ 3\text{ ft }\times\text{ 4ft }\times\text{ 6ft} \end{gathered}[/tex][tex]\begin{gathered} 72\text{ = }2\text{ }\times\text{ 36} \\ 72\text{ = 2 }\times4\text{ }\times\text{ 9} \\ \text{The possible dimensions:} \\ 9ft\text{ }\times\text{ 4ft }\times\text{ 2ft} \end{gathered}[/tex]use the given conditions to write an equation for each line in the point-slope form and slope-intercept form (-3,2) with slope -6
Explanation
the slope-intercept form of a line has the form:
[tex]\begin{gathered} y=mx+b \\ where\text{ m is the slope} \\ and\text{ b is the y-intercept} \end{gathered}[/tex]when given the slope and a point of the line we can use the slope-point formula, it says.
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ where\text{ m is the slope} \\ (x_1,y_1)\text{ is a point of the line} \end{gathered}[/tex]so
Step 1
a)Let
[tex]\begin{gathered} slope=\text{ -6} \\ point\text{ \lparen -3,2\rparen} \end{gathered}[/tex]b) now, replace and solve for y
[tex]\begin{gathered} y-y_{1}=m(x-x_{1}) \\ y-2=-6(x-(-3)) \\ y-2=-6(x+3) \\ y-2=-6x-18 \\ add\text{ 2 in both sides} \\ y-2+2=-6x-18+2 \\ y=-6x-16 \end{gathered}[/tex]so, the equation of the line is
[tex]y=-6x-16[/tex]I hope this helps you
The center of a circle is at (8,-8). One point on the circle is at (8, -3). What is thearea of the circle? (Use 3.14 for pi.)A 15.7 unitsB 64 units?C 78.5 units?D 200.96 units2
The center of a circle is at (8,-8). One point on the circle is at (8, -3). Then the radius of the circle is -3 - (-8) = -3 + 8 = 5 units.
The area of a circle is computed as follows:
A = πr²
Replacing with π = 3.14 and r = 5:
A = 3.14(5)²
A = 3.14(25)
A = 78.5 units²
You have two spinners each with three sections of equal size, one labeled with the numbers 1,2,3 and the others 2,4,6. You spin both and observe the numbers. Let X be the sum of the two numbers. In the game you are playing, you win if you get a sum of at least a 600 in 100 spins. If not you lose, should I play?
From the table
[tex]\text{Total possible outcomes = 9}[/tex]we are to find the probability of getting a sum of at least 600 in 100 spins
This means, we need to get a sum of at least 6 in 1 spin
Hence
[tex]\begin{gathered} P(\text{getting a sum of at least }6\text{ in one spin)} \\ =\text{ }\frac{number\text{ of possible outcome}}{total\text{ possible outcome}} \end{gathered}[/tex]From the table
number of the possible outcome of getting a sum of at least 6 = 5
Therefore
[tex]\begin{gathered} P(\text{getting sum of at least 6 in one spin)} \\ =\text{ }\frac{5}{9} \\ \cong\text{ 0.56} \end{gathered}[/tex]Since the probability is more than 0.5 then
I can play the game
у = 3х – 7у = 3х + 1Are these equations, parallel, perpendicular or neither
A line equation can be written in slope-intercept form, which is
[tex]y=mx+b[/tex]Where m represents the slope and b represents the y-intercept.
If the slopes of two lines are equal they are parallel, if one slope is minus the inverse of the other they are perpendicular, otherwise they are neither.
Comparing our lines to the slope-intercept form, we can find their slopes.
[tex]\begin{gathered} y=3x-7\Rightarrow m=3 \\ y=3x+1\Rightarrow m=3 \end{gathered}[/tex]Since their slopes are equal, those lines are parallel to each other.
In right triangle ABC, angle c is a right angle and sin A= sin B. What is m
which
In plane trigonometry, the sine theorem or also known as the law of sines is a ratio between the lengths of the sides of a triangle and the sines of their corresponding opposite angles.
it is
[tex]\frac{a}{\sin A}=\frac{b}{\sin B}[/tex]According to the question Sin A=Sin B, so
[tex]a=b[/tex]wich means that this right traingle has two equal sides
if the two sides of a right triangle have the same length, then, they form the same angle with the hypotenuse
also, the question says that C=90 °
we know the sum of the internal angles on a triangle must be 180 °,then
[tex]\begin{gathered} A+B+C=180 \\ A=B \\ 2A+C=180 \\ A=\frac{180-C}{2} \\ A=\frac{90}{2} \\ A=45\text{ \degree} \\ B=45\text{\degree} \end{gathered}[/tex]so the answer is B)45 °
Solve the equation 2(8+4c)=32
c = 2
Explanation:
2(8+4c)=32
we open the bracket:
2×8 + 2×4c = 32
16 + 8c = 32
collect like terms:
8c = 32 - 16
8c = 16
Divide through by 8:
8c/8 = 16/8
c = 2
4. Principal Sanders wants to know if wearing school uniforms will help students improve theirmath test scores. She decides to conduct an experiment to find out She chooses two groups ofstudents to test One group will wear uniforms, the other will not.Part A. Define the variables and treatment for the experiment. (3 points)I1 What is the control variable? Why?
Note that:
The control variable is the variable that does not change (that is, constant ) in an experiment. It does not take part in the experiment
The response variable is the dependent variable that determines the outcome of the experiment.
The treatment of an experiment is the independent variable, and it determines the outcome of the experiment.
From the illustration given in this exercise, the control variable, the response variable, and the treatments are identified below with reasons.
1) The control variable = The mathematical abilities of the students
Reason: The students chosen for the experiment must have the same mathematical abilities to prevent bias in the results of the experiment.
2) The response variable = Math test scores
Reason: The maths test scores of the two groups of students are the outcomes of the experiment, hence the response variable.
3) The treatment for the experiment = Wearing of school uniforms
Reason: Wearing of school uniforms is the treatment that the two groups of students were subjected to in order to confirm if their will be any effects on their Maths test scores.
The product of 10 over 22 and 14 over 5 is equivalent to which of the following
Given
Product means multiplication
[tex]\frac{10}{21}\times\frac{14}{5}[/tex][tex]\begin{gathered} \frac{10}{21}\times\frac{14}{5}=\frac{140}{105} \\ \end{gathered}[/tex][tex]\begin{gathered} \frac{140\div5}{105\div5}=\frac{28}{21} \\ \\ \frac{28\div7}{21\div7}=\frac{4}{3} \\ \\ \frac{4}{3}=1\frac{1}{3} \end{gathered}[/tex]The final answer
[tex]\frac{10}{21}\times\frac{14}{5}=1\frac{1}{3}[/tex]one week a student exercise 3 hours at school and another 2/3 of an hour at home. If 1/4 of the student's total exercise came from playing soccer,how munch time did the students spend playing soccer that week? Enter your answer in hours ; do not include units in your answer.Enter your answer as a fraction in simplest terms using the / as the fraction bar
it is given that,
student exercise 3 hours at school,.
and 2/3 hours at home,
let he do exercise for total 'x' hours,
also,
1/4 of the student's total exercise came from playing soccer
so, exercise came from soccer is , x/4
now sum the hours,
3 + 2/3 + x/4 = x
11/3 = x - x/4
3x/4 = 11/3
[tex]x=\frac{11\times4}{3\times3}[/tex]x = 44/9 hours,
so, the time spend on soccer is,
x/4 =
[tex]\begin{gathered} \frac{\frac{44}{9}}{4} \\ =\frac{44}{36} \end{gathered}[/tex][tex]=\frac{11}{9}[/tex]thus, the answer is
time spend on soccer is, 11/9
A small town has two local high schools. High School A currently has 900 studentsand is projected to grow by 50 students each year. High School B currently has 500students and is projected to grow by 100 students each year. Let A represent thenumber of students in High School A in t years, and let B represent the number ofstudents in High School B after t years. Graph each function and determine whichhigh school is projected to have more students in 4 years.so i accidentally disconnected from my tutor and i am not sure if this graph is right or wrong. can you help me?
Answer:
High school A will have 200 more students than High school B.
Graphing the two equations;
Explanation:
Given that High School A currently has 900 students and is projected to grow by 50 students each year.
If t represent number of years, A represent the number of students in High School A in t years, and B represent the number of students in High School B after t years.
[tex]A=900+50t[/tex]High School B currently has 500 students and is projected to grow by 100 students each year.
[tex]B=500+100t[/tex]The number of student each high school is projected to have in 4 years is;
[tex]\begin{gathered} A=900+50(4)=900+200 \\ A=1100 \\ \\ B=500+100(4)=500+400 \\ B=900 \end{gathered}[/tex]Therefore, high school A will have 200 more students than High school B.
Graphing the two equations;
A translation 5 units right and 6 units down maps A onto A'. Write thetranslation as a vector.
A translation 5 units right and 6 units down maps A onto A'. Write the
translation as a vector.
we have that
the rule for the translation is
A(x,y) -------> A'(x+5, y-6)2. For each of the next dot plots, guess the approximate location of the mean by thinking aboutwhere the balance point for the data would be. Then check how close your guess was bycalculating the mean.0 1 2 3 4 5 6 7 8 9 1001235 6 7 89 10012569 10
ANSWER
1) The plot looks like the fulcrum would balance at point 4
After calculation, the mean is 4.
2) The plot looks like the fulcrum would balance at point 3;
After calculation, the mean is 3.8.
3) The plot looks like the fulcrum would balance at point 8;
After calculation, the mean is 7.2
EXPLANATION
From the given data;
1) The plot looks like the fulcrum would balance at point 4.
the mean
[tex]\begin{gathered} mean(x)=\frac{(2+2+2)+(7+7)}{5} \\ =\frac{20}{5} \\ =4 \end{gathered}[/tex]2) The plot looks like the fulcrum would balance at point 2;
The mean;
[tex]\begin{gathered} x=\frac{0+1+1+2+2+2+3+3+4+10}{10} \\ =\frac{38}{10} \\ =3.8 \end{gathered}[/tex]3) The plot looks like the fulcrum would balance at point 8;
[tex]\begin{gathered} x=\frac{0+6+7+7+8+8+8+9+9+10}{10} \\ =\frac{72}{10} \\ =7.2 \end{gathered}[/tex]David is running a fried chicken stand at fall music festivals. He sells fried chicken legs for $4 each and fried chicken tenders for $8/ cup. A festival costs $60 for a vendor license and supply costs are $1 for each chicken leg and $2 for each cup of tenders. David wants to make profit of more than $300 but he only has $110 to spend on costs ahead of time. Create a total profit and a cost equation to model the situation with x = # of chicken legs and y = # cups of tenders.
SOLUTION
From the question,
Chicken legs cost $1, but the selling price is $4
Chicken tender cost $2 per cup, but the selling price is $8
Now, a festival costs $60 and David has only $110 to spend.
Also number of chicken legs sold is represented as x and
number of chicken tenders sold is represented as y.
Hence the cost equation becomes
[tex]\begin{gathered} x\times1\text{ dollar for chicken legs + y}\times2\text{ dollars for chicken tender + 60 }\leq110 \\ x+2y+60\leq110 \end{gathered}[/tex]Note that profit = sales - cost
So we have to subtract the cost from the sales.
Now, David wants to make sales more than $300.
Hence the sales equation becomes
[tex]\begin{gathered} x\times4\text{ dollars for chicken legs + y}\times8\text{ }\times\text{dollars for chicken tender }\ge300 \\ 4x+8y\ge300 \end{gathered}[/tex]So, we will subtract the cost equation from the sales equation to get the profit equation. This becomes
[tex]\begin{gathered} 4x+8y-(x+2y+60)\ge300 \\ 4x+8y-x-2y-60\ge300 \\ 4x-x+8y-2y\ge300+60 \\ 3x+6y\ge360 \end{gathered}[/tex]Hence, the cost and profit equation is
[tex]\begin{gathered} 60+x+2y\leq110 \\ 3x+6y\ge360 \end{gathered}[/tex]But what we have as a correct choice in the answers is the cost and sales equation, which is
[tex]\begin{gathered} 60+x+2y\leq110 \\ 4x+8y\ge300 \end{gathered}[/tex]use the spinner shown find the probability the pointer lands on purple. A. 1/3 B. 3/8C. 30/180D. 1/6
The answer is B. 3/8
Find the next number 7.14.28.56, ?*
Answer: 112
Explanation:
The sequence we have is:
[tex]7,14,28,56[/tex]We can see that the numbers are all multiples of 7:
[tex]\begin{gathered} 7\times1=7 \\ 7\times2=14 \\ 7\times4=28 \\ 7\times8=56 \end{gathered}[/tex]In each step, the number we multiply 7 by, doubles.
So the next number must be 7 multiplied by double of 8 which is 16:
[tex]7\times16=112[/tex]Another way to see this sequence is that each number is twice the previous number:
14 is twice 7
28 is twice 14
56 is twice 28
So the next number must be twice 56:
[tex]56\times2=112[/tex]In any case, the next number is 112
Slope What is the slope of the line through (-4, 2) and (3,-3)?
We have the next formula in order to obtain the slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where
(-4, 2)=(x1,y1)
(3,-3)=(x2,y2)
we substitute the values
[tex]m=\frac{-3-2}{3+4}=\frac{-5}{7}=-\frac{5}{7}[/tex]the slope is -5/7
How do you determine the domain and range of a relation• when the relation is presented as a set of ordered pairs?• when the relation is presented in a mapping diagram?• when the relation is presented as a graph?B./UType your response here.
First item:
When a relation is presented as a set of ordered pairs (a,b) its domain is given by all the different values that appear in the first coordinate of the pairs. Analogously its range is given by all the different values that appear in the second coordinate. For example, if we have the following relation:
[tex]\mleft\lbrace(1,2\mright),(2,3),(2,4)\}[/tex]There are only two different values in the first coordinate of the pairs: 1 and 2. Then its domain is {1,2}.
There are three different values in the second coordinate of the pairs: 2, 3 and 4. Then its range is {2,3,4}.
Second item:
When the relation is presented in a mapping diagram we have something like this:
Each ellipse represents a set. The set from which the arrows come from is the domain and that at which the arrows arrive is the range. So for the relation shown in the picture its domain is {a,b,c,d} and its range is {x,y,z}
Third item:
When the relation is presented as a graph in a grid the domain will be given for all the values in the horizontal axis for which there's a corresponding value in the graph. If you draw a vertical line that passes through a value A in the horizontal axis you can find two cases:
- The line meets the graph at least once. Then A is part of the domain.
- The line never meets the graph. Then A is not part of the domain.
Something very similar happens with the range. The values that are part of the range are values in the vertical axis for which there's at least one corresponding value in the graph. If you draw a horizontal line that passes through a value B in the vertical axis you have:
- The line meets the graph at least once. Then B is part of the range.
- The line never meets the graph. Then B is not part of the range.
Write the 12.4% as simplified fractions. ANS. ___________ .
The Solution
The given percentage is
[tex]12.4\text{ \% =}\frac{12.4}{100}=\frac{\frac{124}{10}}{100}[/tex][tex]12.4\text{ \% =}\frac{124}{10}\times\frac{1}{100}=\frac{124}{1000}=\frac{31}{250}[/tex]Hence, the correct answer is 31/250
Help me please so i can see if i’m on the rights track. if csc (θ) = 13/12 and 0° < θ < 90°, what is cos (θ)? write the answer in simplified, rationalized form.
Given in the question is:
[tex]\csc (\theta)=\frac{13}{12}[/tex]Recall the trigonometric identity:
[tex]\csc (\theta)=\frac{1}{\sin (\theta)}[/tex]Therefore, we have that
[tex]\sin (\theta)=\frac{12}{13}[/tex]Recall the trigonometric ratio:
[tex]\begin{gathered} \sin (\theta)=\frac{\text{opp}}{\text{hyp}} \\ \cos (\theta)=\frac{\text{adj}}{\text{hyp}} \end{gathered}[/tex]and, using the Pythagorean Theorem:
[tex]hyp^2=opp^2+adj^2[/tex]From the sin value, we have:
[tex]\begin{gathered} opp=12 \\ hyp=13 \\ \therefore \\ 13^2=12^2+adj^2 \\ 169=144+adj^2 \\ adj^2=169-144=25 \\ adj=\sqrt[]{25} \\ adj=5 \end{gathered}[/tex]Therefore, the value of cos(θ) is:
[tex]\sin (\theta)=\frac{5}{13}[/tex]