The composition of f and g, as (fog)(x) = f(g(x)) for functions f and g. g should be applied to x. If fog(x) = x and gof (x) = x for all x values in the domain of f and g, then they are inverse functions.
What is meant by function composition?In mathematics, function composition is an operation in which two functions, f and g, generate a new function, h, in such a way that h(x) = g(f(x)). This means that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.
Define fog, the composition of f and g, as (fog)(x) = f(g(x)) for functions f and g. g should be applied to x. If fog(x) = x and gof (x) = x for all x values in the domain of f and g, then they are inverse functions.
In math, the domain (the x-values) of one function becomes the range (the y-value answers) of the next function. Composition notation is as follows: (f o g)(x) = f(g(x)) and exists read “f composed with g of x” or “f of g of x”.
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if the work required to stretch a spring 3 ft beyond its natural length is 12 ft-lb, how much work (in ft-lb) is needed to stretch it 9 in. beyond its natural length?
The answer is 3 ft-lb.
What is the natural length of a spring?The spring's length without any attached mass is its natural length. Assuming the spring abides with Hooke's law The spring exerts a force Fs=kL if its length is altered by an amount L from its normal length, where k is a positive quantity known as the spring constant.W = 12kx2 is the amount of work required to stretch a spring x distances from its equilibrium point. Calculation information: (a) The formula is as follows: F = mg = (4 kg)(9.8 m/s2) = 39.2 N. x = 0.025 m.The spring's length at equilibrium is the length it has when no external forces are exerting any force on it. This is how spring naturally exists.
Beyond its natural length:
Work done to strech the spring to a lentgh x = 0.5 * k * x^2
Now;
12 = 0.5 * k * 9
k = 8/3 = 2.667
9 in = 1.5 ft
Work needed to stretch it 9 in. beyond its natural length = 0.5 * 2.667 * 1.5*1.5 = 3 ft-lb
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Please help no links tho
Michael is 10 years younger than Wanda. Linda is 5 years older than Wanda. The sum of
all their ages is 31 years. Which equation represents the sum of their ages in terms of
Wanda's age (w)?
A.
2w+15=31
B.
3w+15=31
C.
2w-5=31
D.
6
3w-5=31
Solve each equation.
log 5 x+3=3.7
After solving the given inequality the answer is x = 0.7/5log.
When we talk about inequality, what do we really mean?Inequality is a relationship in mathematics that results from a non-equal comparison of two numbers or other mathematical expressions.On a number line, it is most commonly used to compare the sizes of two numbers.So,
Given: log5x+3 = 3.7Then,
Log·5x+3 = 3.75logx+3 = 3.7(5logx+3)+(-3) = 3.7 + (-3)x = 0.7/5logTherefore, after solving the given inequality the answer is x = 0.7/5log.
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??? need this answer asap :,)
Answer:
[tex]\frac{1}{8b^6 a^12}[/tex]
Step-by-step explanation:
Hope this helps you :))
Solve using the Quadratic Formula. 3 x²+9 x=27
The correct answer of the question is 3{-1+√5}/ 2 or 3{-1-√5}/ 2 .
The given quadratic equation is 3 x²+ 9 x=27
To begin, we must transform the equation in the form
ax² + bx + c = 0, then apply the quadratic formula i.e.
x = {-b±√(b²- 4ac)}/ 2a .
Now,
3 x²+ 9 x=27
⇒ 3 x²+ 9 x - 27 = 0
⇒ 3(x²+ 3 x - 9 )= 0
⇒ x²+ 3 x - 9 = 0
Here, a = 1, b = 3 and c = --9
Now, applying quadratic formula
{-b±√(b²- 4ac)}/ 2a
= {-3±√(3²- 4 × 1 × -9)}/ (2 × 1)
= {-3±√(9 + 36)}/ 2
= {-3±√45}/ 2
= {-3±3√5}/ 2
= 3{-1 ±√5}/ 2
= 3{-1+√5}/ 2 or 3{-1-√5}/ 2
Therefore, the ultimate answer to the given equation is 3{-1+√5}/ 2 or 3{-1-√5}/ 2 .
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what is the difference? -8 - 3
Answer:
-11
Step-by-step explanation:
-8-3-(8+3)-11I think it helps you
if DM= 25 what is the value of r
please answer the questions listed below in the SS
The answer to the following listed algebra questions are below:
6 = a/4 + 2
substract 2 from both sides
6 - 2 = a/4
4 = a/4
cross product
4 × 4 = a
a = 16
-6 + x/4 = -5
x/4 = -5 + 6
x/4 = 1
x = 4 × 1
x = 4
9x - 7 = -7
Add 7 to both sides
9x = -7 + 7
9x = 0
x = 0/9
0 = 4 + n/5
0 - 4 = n/5
-4 = n/5
-4 × 5 = n
-20 = n
-4 = r/20 - 5
-4 + 5 = r/20
1 = r/20
1 × 20 = r
r = 20
How to solve algebraic expression-1 = (5+x) / 6
-1 × 6 = (5 + x)
-6 = 5 + x
-6 - 5 = x
x = -11
(v+9)/3 = 8
v + 9 = 8 × 3
v +9 = 24
v = 24 - 9
v = 15
2(n + 5) = -2
2n + 10 = -2
2n = -2 - 10
2n = -12
n = -12/2
n = -6
-9x + 1 = -80
-9x = -80 - 1
-9x = -81
x = -81/-9
x = 9
-6 = n/2 - 10
-6 + 10 = n/2
4 = n/2
4 × 2 = n
n = 8
-2 = 2 + v/4
-2 - 2 = v/4
-4 = v/4
-4 × 4 = v
-16 = v
144 = -12(x + 5)
144 = -12x - 60
144 + 60 = -12x
204 = -12x
x = 204 / -12
x = 17
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Which statements are true regarding the area of circles and sectors? Check all that apply.
A. The area of a circle depends on the length of the radius.
B. The area of a sector depends on the ratio of the central angle to the entire circle.
C. The area of a sector depends on pi.
D. The area of the entire circle can be used to find the area of a sector.
E. The area of a sector can be used to find the area of a circle.
ANSWER IS A, B, D, E
The statements are true regarding the area of circles and sectors are:
1). The area of a sector depends on the ratio of the central angle to the entire circle.
2) The area of the entire circle can be used to find the area of a sector.
3)The area of a sector can be used to find the area of a circle.
Option (B) ,(D) and (E) is correct.
What is circle?A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre”. The perimeter around the circle is known as the circumference.
Given:
The statements are true regarding the area of circles and sectors.
According to given question we have
WE know that
Area of a circle= π[tex]r^{2}[/tex]
So, area is dependent only on the radius.
The area of a sector depends on the ratio of the central angle to the entire circle is 1: 5.
The area of the sector of a circle is /360° *([tex]r^{2}[/tex]) where r is the radius of the circle and is the angle of the sector,.
Therefore, statements are true regarding the area of circles and sectors are:
1). The area of a sector depends on the ratio of the central angle to the entire circle.
2) The area of the entire circle can be used to find the area of a sector.
3)The area of a sector can be used to find the area of a circle.
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Select all the equations that represent the relationship between the amount of money, A, and the number of months, m.
From the given table, the equations that represent the relationship between the amount of money, A, and the number of months, m are:
C. A - 700 = 100mE. A = 700 + 100mHow to find the relationship between the variables?First, find the slope of the line:
= (1,300 - 1,200) / (6 - 5)
= 100 / 1
= 100
The slope is 100. We can use this to find the y-intercept:
y = mx + b
1,400 = 100(7) + b
b = 1,400 - 700
b = 700
The form of the relationship between the amount of money and the number of months is:
y = mx + b
y = 100x + 700
The variants of this equation are:
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a driver of a car took a day trip around the coastline driving at two different speeds. he drove 50 miles at a slower speed and 300 miles at a speed 20 miles per hour faster. if the time spent driving at the faster speed was thrice that spent driving at the slower speed, find the two speeds during the trip.
The slower speed is 20 miles per hour and the higher speed is 40 miles per hour.
time is calculated using the formula
[tex]Time=\frac{Distance}{Speed}[/tex]
In the given question
driver drove 50 miles at slower speed.
Let the slower speed be x miles per hour.
So the time taken to cover 50 miles at slower speed = [tex]\frac{50}{x}[/tex] ...(i)
driver drove 300 miles at faster speed.
given speed is 20 miles per hour faster i.e. speed = (x+20) miles per hour So the time taken to cover 300 miles at (x+20) mph speed = [tex]\frac{300}{(x+20)}[/tex]....(ii)
According to the question
the time spent driving at the faster speed was thrice that spent driving at the slower speed.
From equation (i) and (ii) we get
[tex]3*(\frac{50}{x} )=\frac{300}{x+20}[/tex]
[tex]\frac{150}{x} =\frac{300}{x+20}[/tex]
Cross Multiplying we get
[tex]150(x+20)=300x\\ \\ 150x+3000=300x\\ \\ 300x-150x=3000\\ \\ 150x=3000\\ \\ x=20[/tex]
Slower speed = x = 20mph.
Faster speed = (x+20) = 20+20 = 40mph.
Therefore , The slower speed is 20 miles per hour and the higher speed is 40 miles per hour.
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What value (s) of x will make [tex]x^{2}[/tex] =9 true?
Suppose you invest a dollars to earn an annual interest rate of r percent (as a decimal). After t years, the value of the investment with interest compounded yearly is A(t)=a(1+r) t . The value with interest compounded continuously is A(t)=a . e rt
c. For each situation find the unknown quantity, such that continuous compounding gives you an $ 1 advantage over annually compounded interest. Show your work.
- How much must you invest for 1 year at 2 % ?
- At what interest rate must you invest $ 1000 for 1 year?
- For how long must you invest $ 1000 at 2 % ?
The sum a = 4966.7 is invested at a rate of r = 4.439% for a period of t=4.621 years.
What exactly is a continuous compounding formula?The continuous compounding formula should be used when an issue expressly states that the amount is "constantly compounded."This formula makes use of the mathematical constant "e," which has a value of approximately 2.7182818.The continuous compounding formula is as follows:
A = Pe^rtWhere P represents the starting sum, A represents the total sum, r represents the interest rate, t represents time, and e is a mathematical constant.So,
According to the first point, we know that atr = 0.02, and t = 1.
a(e^rt) - a(1+r)^t = a[ e^(0.02) - 1.02]= 0.00020134 aThus for advantage > 1$ we need is as follows:
0.00020134 a > 1a > 1/ 0.00020134a~4966.7According to the second point, we got that:
t1= 1, a= 1000Then,
1000[e^r-1-r]> 1>> e^r-1-r > 0.001>>e^r-1-r - 0.001 > 0 ......(1)Now we hold that r > 0.04439:
r~ 0.04439 r~ 4.439%According to the third point, we got to know that:
a = 1000, r = 0.02,1000[e^0.02t - (1.02)^t] > 1>>e^0.02t - (1.02)^t > 1 ......(2)Now 2nd equation holds t > 4.621.
Therefore, the sum a = 4966.7 is invested at a rate of r = 4.439% for a period of t=4.621 years.
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FIRST PERSON TO ANSWER BRAINLIEST!!
Quadrilateral ABCD is rotated 90 degrees CCW about the origin THEN reflected across the x - axis.
What will be coordinate of C''? (no spaces in answer, use parentheses)
=======================================================
Explanation:
CCW = counter-clockwise
The rule for a 90 degree CCW rotation is this
[tex](\text{x}, \text{y})\to(-\text{y}, \text{x})[/tex]
it only works if the center of rotation is the origin.
The x and y coordinates swap places. Then you change the sign of the first coordinate after the swap occurred.
Applying that rotation rule to point C(5, 6) gets us to C ' (-6, 5).
Then to reflect over the x axis, we flip the sign of the y coordinate. The x coordinate stays the same. The notation would be [tex](\text{x}, \text{y})\to(\text{x}, -\text{y})[/tex]
So we go from C ' (-6, 5) to C '' (-6, -5)
The price of gasoline is currently $3.11, this is a 14% increase from a year ago. What was the price of gas a year ago.
Answer:
2.97%
Step-by-step explanation:
Answer:
2.72807 (aprox)
Step-by-step explanation:
14% = 14/100 = 0.14
100% = 100/100 = 1
It was a increase
then 14% = 100% + 14% = 1 + 0.14 = 1.14
3.11 / 1.14 = 2.72807 (aprox)
Check:
2,72807 + (2.72807*0.14) = 2.72807 + 0.38193 = 3.11
14. Evaluate the expression
17 ÷ (6.5-1-21)-(-5)² - 53
4 12
Answer: 53412
Step-by-step explanation:
17
6.5−1−21
−(−5)2−
Hi! i have this question thats on my homework, and its due tomorrow. im no sure if its correct, can you double check for me? if you earn a manager point every 30 minutes, how many minutes would you need to work for 50 manager points?
If you earn a manager point every 30 minutes, then the number of minutes you would need to work for 50 manager points is equal to 1500.
The number of minutes needed to work for 50 manager points can be calculated using multiplication. Multiplication is one of the arithmetic parts and is thought to be the opposite of division. It represents the basic idea of the repeated addition of groups of equal sizes.
As,
one manager point = 30 minutes
50 manager points = x
Here x represents the number of minutes required to earn 50 manager points
Cross multiplying,
30 × 50 = x
x = 1500
Hence the number of minutes required to earn 50 manager points if a manager point is earned every 30 minutes is calculated to be 1500 minutes.
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what property of integer is this?
The expression given as -15 + 0 is a representation of the identity property of integer
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the property of integer?The expression is given as
-15 + 0
The identity property of integer states that
x + 0 = x
This means that
-15 + 0 is a representation of the identity property of integer
Hence, the expression given as -15 + 0 is a representation of the identity property of integer
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Need help now pleaseeeeeeeee
What is the probability that a boy selected at random is a Junior?
P( Answer
J | B
)= Answer
Please begging of some help to finish this due today
What is the probability of randomly choosing a student who is a Junior and a boy?
P(J Answer
∩
B)= Answer
The probability that a boy selected at random is a Junior is 0.23 and the probability of randomly choosing a student who is a Junior and a boy is 0.14
What is probability?The probability of an event is the chance or the likelihood that the event would occur.
Note that the chance or the likelihood is represented as a numerical value
How to determine the probability that a boy selected at random is a Junior?The table that completes the question is added as an attachment
From the table, we have the following values
n(Boys and Junior) = 65
n(Boys) = 285
So, the probability that a boy selected at random is a Junior is
P = n(Boys and Junior)/n(Boys)
This gives
P = 65/285
Evaluate
P = 0.23
How to determine the probability of randomly choosing a student who is a Junior and a boy?From the table, we have the following values
n(Boys and Junior) = 65
Total = 465
So, the probability of randomly choosing a student who is a Junior and a boy is
P = n(Boys and Junior)/Total
This gives
P = 65/465
Evaluate
P = 0.14
Hence, the probability of randomly choosing a student who is a Junior and a boy is 0.14
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Simplify each expression.
(-3)¹/₃ . (-3)¹/₃ . (-3)¹/₃
The result of simplifying each number (-3)¹/₃ . (-3)¹/₃ . (-3)¹/₃ using the exponent rules is -3
To solve this exercise we have to resolve algebraic operations following the exponent rules.
(-3)¹/₃ . (-3)¹/₃ . (-3)¹/₃
Using the product rule that indicates that: the exponent result will be the addition of these exponents, we have:
(-3)¹/₃⁺ ¹/₃ ⁺ ¹/₃
(-3)³/₃
(-3)¹
-3
What is an exponent?In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.
Example: 3² = 3*3 = 9
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20 plants were measured and their heights recorded in cm.
Here are the heights:
8.5
12.6
13.2
17 11.1
7.7
4.8 9.9 13.5
15.6 17.4
14
12 14.7 9.5
9.8
10
11.3
5
10
15
6.9
5
please answer :
a)
and
b)
Answer:
[tex]\begin{array}{| c | c | }{ \rule{3cm}0cm}&{ \rule{3cm}0cm} \\ \bf Height, h cm& \bf Frequency\\{ \rule{3cm}0cm}&{ \rule{3cm}0cm}\\ \\ 0 < h \leqslant 5 & 2 \\{ \rule{3cm}0cm}&{ \rule{3cm}0cm} \\5 < h \leqslant 10& 7 \\{ \rule{3cm}0cm}&{ \rule{3cm}0cm} \\ 10 < h \leqslant 15&8 \\{ \rule{3cm}0cm}&{ \rule{3cm}0cm} \\ 15 < h \leqslant 20&3 \\ { \rule{3cm}0cm}&{ \rule{3cm}0cm}\end{array}[/tex]
Step-by-step explanation:According to the topic,
We know the number of following height, h cm :-
The number of 0 < h ≤ 15 are 4.8 , 5The number of 5 < h ≤ 10 are 8.5 , 9.8 , 7.7 , 10 , 9.9 , 6.9 , 9.5The number of 10 < h ≤ 15 are 13.2 , 12.6 , 11.1 , 13.5 , 11.3 , 14 , 14.7 , 12The number of 15 < h ≤ 20 are 17, 15.4 , 17.4Qwhat is the value of 2x^2-10x+13
The value of the quadratic equation 2x^2 - 10x + 13 when x = 2 is 1
What are quadratic equations?Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
How to determine the value of the quadratic equation?The quadratic equation is given as
2x^2 - 10x + 13
When the value of x is 2, the quadratic equation becomes
2x^2 - 10x + 13 = 2 x 2^2 - 10 x 2 + 13
Evaluate the exponent
So, we have
2x^2 - 10x + 13 = 2 x 4 - 10 x 2 + 13
Evaluate the product
So, we have
2x^2 - 10x + 13 = 8 - 20 + 13
Evaluate the difference
So, we have
2x^2 - 10x + 13 = -12 + 13
Evaluate the sum
So, we have
2x^2 - 10x + 13 = 1
Hence, the value of the quadratic equation 2x^2 - 10x + 13 when x = 2 is 1
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Complete question
What is the value of 2x^2-10x+13 when x = 2
Please estimate 11% of 17.
Answer:
1.87
Step-by-step explanation:
The first step in this problem is to get rid of the percent by making it a number. The way you do this is divide by 100.
11%/100=0.11
The "of" after 11% means multiply, so you multiply 0.11 and 17
0.11*17=1.87
A rectangle has a perimeter of 64 cm. If the length is 6cm more than the width of the rectangle,
what are the dimensions of the rectangle? SHOW ALL work
Answer:
the length is 19
the width is 13
Step-by-step explanation:
well since a rectangle has two even sides the width have to be the same and the lengths have to be the same
perimeter is all the sides added together
since the length is the bigger size choose a sensible number (for example 15) and add another 15 to get the length and since it's 6cm smaller take 6 away from 15 which is 9 and add the two 9s together but 15+15+9+9 isn't 64 so you try again with a higher number until you each a total of 64
[tex]\huge\mathcal{\fcolorbox{aqua}{azure}{\red{Answer:-}}}[/tex]
To solve this problem, let's denote the width of the rectangle as $w$ (in cm).
According to the given information, the length of the rectangle is 6 cm more than the width, so the length can be represented as $w + 6$ (in cm).
The perimeter of a rectangle is given by the formula:
$$\text{{Perimeter}} = 2(\text{{length}} + \text{{width}})$$
Substituting the values, we have:
$64 = 2((w + 6) + w)$
Now, let's solve for $(w)$:
$64 = 2(2w + 6)$
$64 = 4w + 12$
$4w = 64 - 12$
$4w = 52$
Dividing both sides of the equation by 4, we get:
$w = \frac{{52}}{{4}}$
$w = 13$
So, the width of the rectangle is 13 cm.
Substituting the value of $w$ back into the expression for the length:
$$\text{{Length}} = w + 6 = 13 + 6 = 19$$
Therefore, the dimensions of the rectangle are 13 cm (width) and 19 cm (length).
what is the correct set of ordered pairs
What is the equation of the line that passes through the point (4,-8) and has a slope of -3/4
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{y = -3/4x - 5}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{Slope = -3/4 and passes through (4, -8)}[/tex]
Find: [tex]\textsf{Determine the equation of the line that fits the criteria}[/tex]
Solution: The first thing that we need to do is plug the information that was provided into the point-slope formula, distribute, and solve for y.
Plug in the values
[tex]\textsf{y - y}_1 = \textsf{m(x - x}_1\textsf{)}[/tex][tex]\textsf{y - (-8) = -3/4(x - 4)}[/tex]Distribute and simplify
[tex]\textsf{y + 8 = (-3/4 * x) + (-3/4 * -4)}[/tex][tex]\textsf{y + 8 = -3/4x + (-3 * -4)/4}[/tex][tex]\textsf{y + 8 = -3/4x + (12)/4}[/tex][tex]\textsf{y + 8 = -3/4x + 3}[/tex]Solve for y
[tex]\textsf{y + 8 - 8 = -3/4x + 3 - 8}[/tex][tex]\textsf{y = -3/4x + 3 - 8}[/tex][tex]\textsf{y = -3/4x - 5}[/tex]Therefore, the final equation of the line that passes through the point (4, -8) and has a slope of -3/4 is [tex]\textsf{y = -3/4x - 5}[/tex]
2
Select the correct answer from each drop-down menu.
Statement 1: A number is prime if and only if it only has two unique factors.
Statement 2: A number has more than two unique factors if and only if it is not prime.
Statement 2 is true v The contrapositive of a biconditional statement is
Reset
never true
always true
sometimes true
Statement 2 is true. The contrapositive of a biconditional statement is always true.
What is a conditional statement?A conditional statement can be defined as a type of statement that can be written to have both a hypothesis and conclusion. This ultimately implies that, it typically has the form "if P then Q."
Where:
P and Q represent sentences.
What is a biconditional statement?A biconditional statement can be defined as a statement which combines a conditional statement with its converse. This ultimately implies that, a biconditional statement is generally created when a conditional statement is combined with its converse.
In Mathematics, a biconditional statement typically has the form "P if and only if Q." Therefore, the biconditional statement, "p if q," is true whenever the two statements have the same truth value. Otherwise, the biconditional statement is false.
In this context, we can reasonably infer and logically deduce that since statement 2 is true because the contrapositive of a biconditional statement is always true.
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7.) The height of a triangle is twice its base. The total area is 49 ft². Find the triangle's dimensions. Be sure to define
a variable, and write an equation.
Step-by-step explanation:
the area of a triangle is
baseline × height / 2
now we also know that
the height in that triangle is twice its baseline.
so,
height = 2×baseline
so, for the given area we have
49 = baseline × 2 × baseline / 2 = baseline²
baseline = 7 ft.
therefore,
height = 2×baseline = 2×7 = 14 ft.
and now we run into a problem. as we don't have any further information about the triangle, the lengths of the sides cannot be determined.
the reason is that the height can be placed anywhere on the baseline (from the left end point all the way over to the right end point). all these triangles created by the moving height have the same area (49 ft²), but different lengths of the legs.
the lengths of the legs are calculated via Pythagoras, because the height splits the main triangle into 2 smaller right-angled triangles.
so, if I assume e.g. an isoceles triangle (both legs are equally long), then I know that the height splits the triangle into 2 equal triangles and the baseline in half.
then I can calculate :
leg² = (baseline/2)² + height² = 3.5² + 14² =
= 12.25 + 196 = 208.25
(each) leg = 14.43086969... ft
if I assume the height is at an endpoint of the baseline then the whole triangle is by itself a right-angled triangle.
and the height is one leg and the other leg is again via Pythagoras
leg² = baseline² + height² = 7² + 14² = 49 + 196 = 245
leg = 15.65247584... ft
all the possible solutions for the leg lengths are between 14 ft (the height) and 15.65247584... ft.
What does |-5| + |7| equal?
Answer:
12
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
|-5|+|7|
|-5|=5
|7|=7
=5+7
=12
hope this helps u ; )
30 x 1/3=1 What is the property of this equation.
Answer:
[tex]x=\frac{1}{10}[/tex]
Step-by-step explanation:
[tex]\frac{30x^1}{3}=1[/tex]
Multiply both sides by 3
[tex]\frac{3\cdot \:30x^1}{3}=1\cdot \:3[/tex]
Simplify
[tex]30x=3[/tex]
divide both sides by 30
[tex]\frac{30x}{30}=\frac{3}{30}[/tex]
Simplify
[tex]x=\frac{1}{10}[/tex]