The value of ∠K is 46.2° as the definition of angle is "An angle is created by joining two line segments at one point, or we can say that an angle is the combination of two line segments at a common endpoint".
What is angle?An angle is created by joining two line segments at one point, or we can say that an angle is the combination of two line segments at a common endpoint. When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the word "angle" originates. Based on measurement, there are different kinds of angles in geometry. The names of fundamental angles include acute, obtuse, right, straight, reflex, and full rotation. A geometrical shape called an angle is created by joining two rays at their termini. In most cases, an angle is expressed in degrees.
Here,
Side i = 68.91521 cm
Side j = 66 cm
Side k = 53 cm
Angle ∠I = 69.8°
Angle ∠J = 64°
Angle ∠K = 46.2°
∠K= sin⁻¹(k·sin(J)/j)
=sin⁻¹(53.(sin 64°)/66)
=46.2°
Since the definition of an angle is "An angle is created by joining two line segments at one point, or we can say that an angle is the combination of two line segments at a common endpoint," the value of ∠K is 46.2°.
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What is the solution to the equation -6 = x/8
Given equation is
[tex]\frac{x}{8}=-6[/tex]Performing the cross multiplication,
[tex]\begin{gathered} x=(-6)\times8 \\ =-48 \end{gathered}[/tex]Hence, the solution of the given equation is x=-48.
I need help with a math homework0.25kg=______g
We know that 1 kilogram is equivalent to 1,000 grams. This our conversion factor, knowing this, we transform 0.25 kg.
[tex]0.25\operatorname{kg}\cdot\frac{1,000gr}{1\operatorname{kg}}=250gr[/tex]Therefore, the answer is 250 grams.An ostrich ran 4,200 meters to the west at a constant velocity. it ran that distance in 1,200 seconds. what was it's velocity?
distance : 4,200 meters
time : 1,200 seconds
To find the velocity we have to apply the next formula:
Velocity = Distance / time
Replacing with the values given:
Velocity = 4,200 m / 1,200 sec = 3.5 meters per second
Velocity = 3.5 m/sec
Hello! I got -560 just want to confirm my answer. Thanks!
Explanation
We are given the following series:
[tex]12+4-4-12-20-...[/tex]We are required to determine the sum of the first 14 terms of the given series.
This is achieved thus:
We know that the sum of n terms of a series is given as:
[tex]\begin{gathered} S_n=\frac{n}{2}[2a+(n-1)d] \\ where \\ a=first\text{ term} \\ d=common\text{ difference} \\ n=number\text{ of terms} \end{gathered}[/tex]Therefore, we have:
[tex]\begin{gathered} S_n=\frac{n}{2}[2a+(n-1)d] \\ where \\ a=12 \\ d=4-12=-8 \\ n=14 \\ \\ \therefore S_{14}=\frac{14}{2}[2\cdot12+(14-1)-8] \\ S_{14}=7[24+(13)-8] \\ S_{14}=7(24-104) \\ S_{14}=7\cdot-80 \\ S_{14}=-560 \end{gathered}[/tex]Hence, the answer is:
[tex]S_{14}=-560[/tex]Celine is playing a game at the school carnival. There is a box of marbles, and each box has a white, a green, a blue, and an orange marble. There is also a fair 12-sided die labeled with the numbers 1 through 12. How many outcomes are in the sample space for pulling a marble out of the box and rolling the die?4832168
Multiply the number of possible outcomes of pulling a marble out times the number of possible outcomes o rolling the die to find the total amount of outcomes in the sample space.
There are 4 different possibilities of pulling a marble out of a box: white, green, blue and orange. Since the die has 12 outcomes, then the total amount of outcomes in the sample space is:
[tex]4\times12=48[/tex]I need help with a graph problem please that I am stuck on.
Solution:
First we have to derive the equation of the graph plot.
The general equation of an absolute value function is expressed as
[tex]\begin{gathered} y=a|x-h|+k\text{ --- equation 1} \\ \text{where} \\ (h,k)\text{ is the coordinate of the vertex of the function } \end{gathered}[/tex]step 1: Determine the coordinates (h,k) of the vertex of the graph.
The vertex of the function is the point at which the graph changes direction.
In tha above plot, the vertex of the plot is (-3,4).
Thus,
[tex]\begin{gathered} h=-3 \\ k=4 \end{gathered}[/tex]step 2: Substitute the respective values of -3 and 4 for h and k into equation 1.
Thus,
[tex]\begin{gathered} y=a|x-h|+k \\ \Rightarrow y=a|x-(-3)|+4\text{ ---- equation 2} \\ \end{gathered}[/tex]step 3: Select any point (x,y) on the graph plot, to evaluate a.
Thus, using the point (1,0), we have
[tex]\begin{gathered} y=a|x+3|+4 \\ x=1,\text{ y=0} \\ \Rightarrow0=a|1+3|+4 \\ -4=|4|a \\ \Rightarrow a=-1 \end{gathered}[/tex]step 4: Substitute the obatined value of a into equation 2.
Thus,
[tex]y=-|x+3|+4\text{ ----- equation 3}[/tex]Thus, the equatioin of the graph is evaluated to be
[tex]y=-|x+3|+4[/tex]A) Evaluate f(4).
To evaluate f(4), substitute the value of 4 for x into the derived equation.
Thus,
[tex]\begin{gathered} y=-|x+3|+4 \\ x=4 \\ \Rightarrow y=-|4+3|+4 \\ \therefore y=-3 \end{gathered}[/tex][tex]f(4)=-3[/tex]B) Solve for f(x)=2.
To solve, we have
[tex]\begin{gathered} -|x+3|+4=2 \\ \text{subtract 4 from both sides of the equation} \\ -|x+3|+4-4=2-4 \\ -|x+3|=-2 \\ \text{divide both sides by -1} \\ \frac{-|x+3|}{-1}=-\frac{2}{-1} \\ \Rightarrow|x+3|=2 \\ \text{When }x+3=-2 \\ x=-2-3 \\ \Rightarrow x=-5 \\ \text{when }x+3=2 \\ x=2-3 \\ \Rightarrow x=-1 \end{gathered}[/tex]Thus, we have
[tex]x=-5;-1[/tex]The shaded area is 120T cm?, and the radius is 24 cm. Find X.
We will have the following:
[tex]A=(\frac{x}{2})\cdot r^2\Rightarrow120\pi=(\frac{x}{2})(24)^2[/tex][tex]\Rightarrow\frac{x}{2}=\frac{5\pi}{24}\Rightarrow x=\frac{5\pi}{12}[/tex][tex]\Rightarrow x\approx1.31[/tex]So, the value of x is approximately 1.31.
Pressure (torr)Volume (mL)Which statement accurately represents the relationshipbetween pressure and volume ?75030O As pressure increases, volume increases.As pressure decreases, volume decreases.95022O As pressure increases, volume decreases.As pressure increases, volume stays constant.115019135015150013165010
The equation that describes the relationship between pressure and volume is
[tex]P=\frac{n\cdot R\cdot T}{V}[/tex]As you can observe, the pressure and the volume are inversely proportional, which means, as pressure increases, volume decreases.
Therefore, the answer is As pressure increases, volume decreases.which statement is true?6 is 4 times as many as 26 is 3 times as many as 26 is 2 times as many as 26 is 12 times as many as 2
6 is 3 times as many as 2, because:
[tex]\begin{gathered} 6=3+2 \\ 6=3+3 \end{gathered}[/tex]Factor completely 6x^2 -7x-20
Solution:
Given the expression;
[tex]6x^2-7x-20[/tex][tex]\begin{gathered} 6x^2-7x-20=6x^2-15x+8x-20 \\ \\ 6x^2-7x-20=3x(2x-5)+4(2x-5) \\ \\ 6x^2-7x-20=(2x-5)(3x+4) \end{gathered}[/tex]FINAL ANSWER:
[tex]\begin{equation*} (2x-5)(3x+4) \end{equation*}[/tex]Which problem could be solved with the expression 5 (2 + 4) = 6?Choose 1 answer:Hayden made 2 bracelets before school and 4 after school each day for 5 days. Then he split thebracelets into 6 equal groups. How many bracelets did Hayden have in each group?(вShadi is building a new back deck. He puts 2 nails and 4 screws in each board. He did this to 5boards. How many total screws and nails did he use?Khai, the dog, ate 2 bones on Monday, 4 bones on Tuesday and 6 bones on Wednesday. OnThursday, she ate 5 times more bones than the other days combined. How many bones did Khai eaton Thursday?Stuck? Review related articles/videos or use a hint.Report a problem
Let us attempt to solve the options to check which one will give the expression
[tex]5\times(2+4)\div6[/tex]OPTION A:
If Hayden makes 2 bracelets before school and 4 after school daily, then the bracelets she makes daily is gotten by
[tex]2+4[/tex]In 5 days, the number of bracelets will be the expression above multiplied by 5:
[tex]5\times(2+4)[/tex]If she breaks the total bracelets into 6 groups, this means that we divide the expression above by 6:
[tex]5\times(2+4)\div6[/tex]This tallies with the expression in the question.
Hence, OPTION A is correct.
Find the length of AB.6 in A30°BAB = [ ?Round your answer to the nearest hundredth.
At a flea market, used computer games are sold at the prices shown in the table below.Number of Games/Price ($)2/9.005/22.507/31.50Do the number of games and price form a proportional relationship?Choose the correct response.A.Yes. There is a constant of proportionality of $11.25.B.Yes. There is a constant of proportionality of $4.50.C.No. There is not a constant of proportionality.D.No. The slope is 4.5.
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y=kx
where k is the constant of proportionality
where k is the constant of proportionality
so
Verify
Let
x -----> numb
Find out the value of k in each case
er of games
y ----> price
Find out the value of k in each case
For x=2, y=9
k=y/x
k=9/2=$4.5 per game
For x=5, y=22.50
k=22.5/5=$4.50 per game
For x=7, y=31.50, because the value ok is the smaamef K
k=31.50/7=$4.50 per game
that means
Yes , Irs a proportional relationship
the answer is the option BJohn was asked to place the numbers shown below in order from greatest to least. 0.2 , -0.3, 1.6, 120%, -2%, 3.8, --33, 3.14 After ordering the numbers from greatest to least, what number would John have in the 3rd position?
Let's begin by listing out the information given to us:
0.2, -0.3, 1.6%, 120%, -2%, 3.8, -33, 3.14
In sorting the numbers from the greatest to the least, we must bear the following in mind:
I. Any number having a negative parenthesis is lower than zero
II. % means 100; any number having % means the real value of the number is multiplied by 100
0.2 = 0.2
-0.3 = -0.3
1.6% = 1.6 * 100 = 160
120% = 120 * 100 = 12000
-2% = -2 * 100 = -200
3.8 = 3.8
-33 = -33
3.14 = 3.14
Rearranging from the greatest to the least, we have it thus:
120%, 1.6%, 3.8, 3.14, 0.2, -0.3, -33, -200
The number in the third position is 3.8
The markings on the number line are evently spaced. Label the other markings on the number line. + + А B C -30 0 F 45 A= B = C = D = E = F=can someone please tell me the answers
The points are evenly spaced at a distance of 15 units between each other, then when we go to the right side of the graph from 0 we increase 15 units until we reach the point E, 15 units further we get to the point F, then we have the following labels:
E = 15
F = 15 + 15 = 30
As we got the left side from 0, we subtract 15 units for each marking, then we get:
D = 0 -15 = -15
C = -30 -15 = -45
B = -45 - 15 = -60
A = -60 - 15
It used to cost $33.00 to buy a case of 23 bottles of Sriracha. Because of the shortage, each case is now $50.00. How MUCH MORE is each bottle of Sriracha?
The amount of money that each bottle of sriracha would cost more would be = $0.82
What is product shortage?Product shortage is definitely as the decrease in the availability of a product in the market or decrease in its production.
The cost of a case of sriracha = $33.00
The amount of a case after the shortage = $50.00
The amount of bottles that is found in case = 23
The amount of each bottle before shortage = 23/33 = $0.70
The amount of each bottle after shortage = 50/33 =
$1.52
The amount of money that each bottle of sriracha would cost more = 1.52 - 0.70 = $0.82
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Use prime factorization to reduce each fraction 1. 22/165 2. 35/210
Lets find the prime factorization of 22, 165, 35 and 210. Prime factorization of a number is breaking a number down into the set of prime numbers which multiply together to result in the original number.
The prime factorization of the number 22 is:
[tex]22=2\times11[/tex]Similarly, for 165, 35 and 210 we have
[tex]\begin{gathered} 165=3\times5\times11 \\ 35=5\times7 \\ 210=2\times3\times5\times7 \end{gathered}[/tex]Then, we can solve the given questions.
Question 1.
[tex]\frac{22}{165}=\frac{2\times11}{3\times5\times11}[/tex]so we can cancel out the number 11 and get
[tex]\frac{22}{165}=\frac{2}{3\times5}=\frac{2}{15}[/tex]Then, the answer is
[tex]\frac{2}{15}[/tex]Question 2.
[tex]\frac{35}{210}=\frac{5\times7}{2\times3\times5\times7}[/tex]and we can cancel out the number 5 and 7, then we obtain
[tex]\frac{35}{210}=\frac{1}{2\times3}[/tex]then, the answer is
[tex]\frac{1}{6}[/tex]Write the equation containing the points (-2,4) and (1,10).
Answer:
y=2x+8
Explanation:
Given the two points:
[tex]\begin{gathered} (x_1,y_1)=(-2,4) \\ \mleft(x_2,y_2\mright)=\mleft(1,10\mright) \end{gathered}[/tex]In order to find the equation of the line connecting them, we employ the use of the two-points formula given below:
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]Substitute the values:
[tex]\frac{y-4}{x-(-2)}=\frac{10-4}{1-(-2)}[/tex]Next, simplify:
[tex]\begin{gathered} \frac{y-4}{x+2}=\frac{6}{3}=2 \\ \implies y-4=2(x+2) \\ \implies y=2(x+2)+4 \\ \implies y=2x+4+4 \\ \implies y=2x+8 \end{gathered}[/tex]The equation containing the points (-2,4) and (1,10) is y=2x+8.
Which of the following would be the best equation for the function of the values for Janet’s reading?A) p = 6hB) p = 20hC) h = 20pD) 20 + p = h
In order to obtain the best equation for the function of the values for Janet’s reading, we will apply the equation of a straight line between two points.
The formula to calculate the equation of a line between two points is,
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]Let us now pick any two points from the table given
[tex]\begin{gathered} (x_1,y_1)=(1,20) \\ (x_2,y_2)=(6,120) \end{gathered}[/tex][tex]\begin{gathered} \text{where,} \\ p=y \\ h=x \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \frac{y-20}{x-1}=\frac{120-20}{6-1} \\ \end{gathered}[/tex]Simplify
[tex]\begin{gathered} \frac{y-20}{x-1}=\frac{100}{5} \\ \frac{y-20}{x-1}=20 \\ y-20=20(x-1) \\ y=20(x-1)+20=20x-20+20=20x \\ y=20x \\ \therefore p=20h \end{gathered}[/tex]Hence, the answer is
[tex]p=20h\text{ (OPTION B)}[/tex]During a job interview, Pam Thompson is offered a salary of $32,000. The company gives annual raises a 4%. What will be Pam’s salary during her fifth year on the job? (Round time value factor to three decimal places and final answer to the nearest whole number.)
We will have the following:
First, we construct the equation that describes the scenario:
[tex]P(x)=32000(1+0.04)^x[/tex]Now, we will determine her salary at the 5th year at her job:
[tex]P(x)=32000(1+0.04)^5\Rightarrow P(5)=38932.89288[/tex][tex]\Rightarrow P(5)\approx38932.893[/tex]So, her salary after 5 years would be approximately $38933.
9Find the percentage change from the first quantity to the second quantity:From 60 km/h to 45 km/h.Answer:%
To calculate the percentage change;
From 60km/h to 45km/h is a decrease
So we will calculate the decrease = 60 - 45 =15
Divide 15 by the original value which is 60 and then multiply by 100%
That is;
Percentage change = 15/60 x100%
=25%
suppose they are a T V cost in an election between three Canadians then who is Garza and we see to be decided by polarity of the first 55 votes are counted the Titleist are as followed
a) We have the votes for 55 people out of 80.
We have to find the minimum number of votes needed by Donahue to be sure that he will win the election.
There are 80 - 55 = 25 votes remaining.
Donahue has 24 votes already. The second candidate in number of votes has 18 votes, which is a difference of 6 votes.
We can think of a situation where the remaining votes are given to this two candidates and both have the same votes.
This would mean an amount of 24 + 18 + 25 = 67 votes.
Then, they won't have the same votes but we can think of Donahue having 67/2 = 33.5 ≈ 34 votes, and Garza having 33.
Then, this is the most extreme situation where Donahue wins by one vote.
We can then calculate the difference of votes he needs as 34 - 24 = 10 votes.
b) We can think again the same situation, but with Garza having 34 votes and Donahue having 33 votes.
This the extreme situation where Garza wins by the minimum difference.
Then, Garza would have to add 34 - 18 = 16 votes at least to win in this situation.
Answer:
a) Donahue needs 10 more votes to be sure he wins the election.
b) Garza needs at least 16 votes to be sure he wins the election.
9) 59 is 93 percent of what?
93 Let the unknown number be X,
( 59/ X ) = 93 /100
Cross - multiply,
59 x 100 = 93 x x
x = ( 59 x100) divided by 93
x= 5900 / 93
x = 63.44 _
Answer:
Step-by-step explanation:
59 = 93%(X)
59 = 93/100*(x)
59*100 = 93(x)
5900/93 = x
63.44 = x
Hence 59 is 93 percent of 63.44
A recipe that uses 1/2 pound of almonds makes 5/6 cup of almond butter. Which is a reasonable estimate for the amount of almond butter the recipe makes per pound of almonds?What amout of almond butter does the recipe make per pound of almonds?____ cup(s) of almond butter per pound of almonds
The given information is:
1/2 pound of almonds makes 5/6 of almond butter.
Since 1 pound is double of 1/2 pound, we will need to multiply the amount of almond butter by 2 to find the almond butter that 1 pound can make.
Multiply the amount of almond butter by 2:
[tex]2\times\frac{5}{6}[/tex]The reason for this multiplication is that to find the amount of almond butter that 1 pound makes, we need double of what 1/2 can make.
Solving the multiplication:
[tex]2\times\frac{5}{6}=\frac{2\times5}{6}[/tex]Since 2x5 is equal to 10:
[tex]2\times\frac{5}{6}=\frac{10}{6}[/tex]1 pound of almonds makes 10/6 cups of almond butter.
Answer: 10/6 cups of almond butter per pound of almonds
PR = 9x -31 and QR = 43: Find xQ is the midpoint of PR
We can model the situation as:
Since Q is the midpoint of PR, QR and PQ have the same length, so PQ is also equal to 43.
Now, we can formulate the following equation:
PR = PQ + QR
So, replacing PR by 9x-31, PQ by 43 and QR by 43, we get:
9x - 31 = 43 + 43
9x - 31 = 86
Solving for x:
9x - 31 + 31 = 86 + 31
9x = 117
9x/9 = 117/9
x = 13
Answer: x = 13
Solve the equation x(x+6) = 91 using completing the square, finding the square root, and solving. Put the equivalent equations in the appropriate order. |x+3 = 10 7 x² + 6x = 91 x= 7 or x = -13 x² - 6x +9 = 91 +9 x + 3 = 10 or x + 3 = -10 (x+3)² = 100
Solution
Given the equation below:
[tex]x(x+6)=91[/tex]Using the completing the square:
[tex]\begin{gathered} x(x+6)=91 \\ x^2+6x-91=0 \\ half\text{ the coefficient of x, square and add to both side} \\ x^2+6x=91 \\ x^2+6x+(3)^2=91+(3)^2 \\ (x+3)^2=91+9 \\ (x+3)^2=100 \end{gathered}[/tex]Square root both side of the equation
[tex]\begin{gathered} (x+3)^2=100 \\ \sqrt{(x+3)^2}=\pm\sqrt{100} \\ x+3=\pm10 \\ x=\pm10-3 \\ x=7,x=-13 \end{gathered}[/tex]Therefore the equivalent equations in the appropriate order is
Given the following graph of f (x), what is f (4)?
*graph included*
When function of x is the line on the graph with the equation function of x =-3/2x+1, the value of f(4) is -5.
Given that,
In the picture we have graph with a line function of x.
We have to find what is the value of f(4).
By seeing the graph,
We have points (-2,4) and (-4,7)
We must determine the line's equation.
That is y=mx+b
Slope of the line m is rise/run
m=7-4/-4-(-2)
m=3/-2
m=-3/2
Now,
4=-3/2(-2)+b
4=3+b
b=4-3
b=1
The equation of the line is y=-3/2x+1
We can write as function of x =-3/2x+1
Then Take x=4
f(4)=-3/2(4)+1
f(4)=-6+1
f(4)=-5
Therefore, The value of f(4) is -5 when the function of x is the line on graph that is function of x =-3/2x+1.
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Hi i need some help on question 11 b and c. I have already done a
ANSWER:
a. 16.27 cm^3
b. 4.3 cm
c. 325.4 seconds
STEP-BY-STEP EXPLANATION:
The first thing is to calculate the value of the volume, which is the sum of the volume of each part, like this:
[tex]\begin{gathered} V=V_t+V_c+V_s \\ r=\frac{d}{2}=\frac{2.6}{2}=1.3 \\ V_t=A_b\cdot\frac{h}{3}=\pi\cdot(r)^2\cdot\frac{h}{3}=3.14\cdot(1.3)^2\cdot\frac{1.2}{3}=2.12cm^3 \\ V_c=A_b\cdot h=\pi\cdot(r)^2\cdot h=3.14\cdot(1.3)^2\cdot1.8=9.55m^3 \\ V_s=\frac{4}{6}\cdot\pi\cdot r^3=\frac{4}{6}\cdot3.14\cdot(1.3)^3=4.6cm^3 \\ V=V_t+V_c+V_s \\ V=2.12+9.55+4.6 \\ V=16.27cm^3 \end{gathered}[/tex]The volume of the upper container is 16.27 cm^3, and being symmetrical, it is the same for the bottom container.
At the moment that all the sand finishes going to the bottom container, the height will be the sum of the heights in each case.
Then:
[tex]\begin{gathered} h=1.2+1.8+1.3 \\ h=4.3\text{ cm} \end{gathered}[/tex]Therefore, the height is 4.3 centimeters
To reach that height, all the sand had to be passed from one side to the other, therefore, we can calculate the time as follows:
[tex]\begin{gathered} t=\frac{16.27cm^3}{0.05\frac{cm^3}{s}} \\ t=325.4\text{ sec} \end{gathered}[/tex]It would take a time of 325.4 seconds
The following is the cost function for natural gas for the city where Greg lives. Greg's natural gas bill last month was $51.54. How many therms did Greg use last month? Round the answer to the nearest tenth of a therm (one decimal place). Only input the number. Do not input any unit. Example: 89.3
Kauro, this is the solution:
This is the cost function for natural gas for the city where Greg lives:
• c (t) = 16.74 + 0.742t
Now we replace c (t) by 51.54 to solve for t, as follows:
51.54 = 16.74 + 0.742t
Subtracting 16.74 at both sides:
51.54 - 16.74 = 16.74 + 0.742t - 16.74
34.8 = 0.742t
Dividing by 0.742 at both sides:
0.742t/0.742 = 34.8/0.742
t = 46.9 therms
The correct answer is 46.9
I have been struggling with this problem for around 2 hours and can’t seem to get it
the quotient rule say:
[tex](\frac{f(x)}{g(x)})^{\prime}=\frac{g(x)\cdot f^{\prime}(x)-f(x)\cdot g^{\prime}(x)}{(g(x))^2}[/tex]now we defined:
[tex]\begin{gathered} f(x)=-4x^2+16 \\ g(x)=(x^2+4)^2 \end{gathered}[/tex]and the derivative:
[tex]\begin{gathered} f^{\prime}(x)=-8x \\ g^{\prime}(x)=2\cdot(x^2+4)\cdot2x \\ g^{\prime}(x)=4x(x^2+4) \end{gathered}[/tex]so now we can replace on the quotient rule:
[tex]\frac{(x^2+4)^2\cdot(-8x)-4x(x^2+4)\cdot(-4x^2+16)}{(x^2+4)^4}[/tex]now we can use properties, like:
[tex](x^2+4)^2=x^4+8x+16[/tex]