Answer:
[tex]1[/tex]
Step-by-step explanation:
The gist of modular arithmetic in a nutshell: the numbers [tex]a[/tex] and [tex]b[/tex] are considered to be congruent by their modulus [tex]m[/tex] if [tex]m[/tex] is a divisor of their difference.
In mathematics: [tex]a \equiv_{m} b \Leftrightarrow (a - b) \vdots m[/tex]
Exemplifying this: [tex]6 \equiv_{7} -1[/tex] because [tex]6 - (-1) = 6 + 1 = 7[/tex], [tex]7 \vdots 7[/tex].
Let us have following equivalences: [tex]a \equiv_{m} b[/tex] and [tex]c \equiv_{m} d[/tex], then: [tex](a - b) \vdots m[/tex] and [tex](c - d) \vdots m[/tex] by definition.
Properties:
1. [tex]a + c \equiv_{m} b + d \Leftrightarrow ((a + c) - (b + d)) \vdots m \Leftrightarrow (a + c - b - d) \vdots m \Leftrightarrow ((a - b) + (c - d)) \vdots m[/tex].
2. [tex]a - c \equiv_{m} b - d \Leftrightarrow ((a - c) - (b - d)) \vdots m \Leftrightarrow (a - c - b + d) \vdots m \Leftrightarrow ((a - b) - (c - d)) \vdots m[/tex].
3. [tex]ac \equiv_{m} bd \Leftrightarrow (ac - bd) \vdots m \Leftrightarrow (ac - bc - bd + bc) \vdots m \Leftrightarrow (c(a - b) + b(c - d)) \vdots m[/tex].
4. What if we have [tex]a \equiv_{m} b[/tex] twice? If we abide by property 3, we can come to the conclusion that [tex]a^2 \equiv_m b^2[/tex]. It is fair enough that there is room for the equivalence [tex]a^n \equiv_{m} b^n[/tex].
[tex]2001 * 2002 * 2003 + 2004^3 = 2002 * (2001 * 2003) + 2004^3 \equiv_{7} 0 * (2001 * 2003) + 2^3 \equiv_{7} 0 + 8 \equiv_{7} 8 \equiv_{7} 1[/tex]
Notice that [tex]2002 \vdots 7[/tex] already. There is no need to consider the rest multipliers because the product is [tex]0[/tex] anyways, we can cut corners in this regard.
We used property 4.
Recapitulating this: our remainder is [tex]1[/tex].
Which of the following lines will have a negative slope? Select all that apply
Answer:
1, 5
Step-by-step explanation:
-16/4=-4
10/5=2
1/2=1/2
-1/-3=1/3
-1/4/1/2=-1/2
The negative ones are your answer.
For the following exercises, find the x- and y-intercepts of the graphs of each function.
26. f(x) = 4| x − 3 | + 4
For the function f(x) = 4|x - 3| + 4, we have that:
The function has no x-intercepts.The y-intercept is of y = 16.What is the x-intercept of a function?The x-intercept of a function is the value of x when y = f(x) = 0, hence:
0 = 4|x - 3| + 4
4|x - 4| = -4
|x - 4| = -1
The absolute value cannot be negative, hence the function has no x-intercepts.
What is the y-intercept of a function?The x-intercept of a function is the value of y = f(x) when x = 0, hence:
f(0) = 4|0 - 3| + 4 = 12 + 4 = 16.
The y-intercept is of y = 16.
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In order to compute the area of a particular circle, Juan first measures the length of its diameter. The actual diameter is 20 cm, but Juan's measurement has an error of up to $20\%$. What is the largest possible percent error, in percent, in Juan's computed area of the circle
The largest possible error in the area of the circle is of 44%.
What is the area of a circle?The area of a circle of radius r is given by:
[tex]A = \pi r^2[/tex]
With a diameter of 20 cm = radius of 10 cm, the area in cm² is given by:
[tex]A = \pi \times 10^2 = 100\pi[/tex]
With the error, with a diameter of 20 x 1.2 = 24 cm = radius of 12 cm, the area in cm² is given by:
[tex]A = \pi \times 12^2 = 144\pi[/tex]
The error is given by:
[tex]E = 144\pi - 100\pi = 44\pi[/tex]
The percent error is the error divided by the initial amount, multiplied by 100%, hence:
[tex]P = \frac{44\pi}{100\pi} \times 100\% = 44\%[/tex]
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Assuming the world population growth rate is 1% and the current population is about 7 billion, next year the population will be:
Assuming the world population growth rate is 1% and the current population is about 7 billion, next year the population will be 7.01 billion.
To calculate the percentage increase rate, use the fundamental increase charge formulation: subtract the original from the brand new cost and divide the results by way of the original cost. to show that right into a percent boom, multiply the results by 100.
The population of a given area is described as the range of humans generally residing in that vicinity, measured on 1 January in a given 12 months. The supply can be the most latest population census.
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what is the equation of the given line in the point -slope form
Answer:
E
Step-by-step explanation:
the equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 1) and (x₂, y₂ ) = (3, 4) ← 2 points on the line
m = [tex]\frac{4-1}{3-0}[/tex] = [tex]\frac{3}{3}[/tex] = 1
using (a, b ) = (3, 4 ) , then
y - 4 = 1 (x - 3) → E
The function g(x) is graphed.
On a coordinate plane, a curved line enters the plane at point (negative 2.3, 5), crosses the x- and y-axis at (0, 0), and leaves the plane at point (2.3, 5).
Which statements about the function are true? Choose three options.
The statements about the function that are true include:
g(0) = 0
g(1) = -1
g(-1) = 1
How to depict the function?From the information, the points include:
(x1, y1) = (-2, 2, 5).
(x2, y2) = (0, 0)
(x3, y3) = (2, 3, 5).
It should be noted that (x2, y2) implies that g(0) = 0. In this case, the statements about the function that are true include g(0) = 0, g(1) = -1, and g(-1) = 1. This is illustrated in the graph.
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. A housing down payment is money that a
prospective buyer provides up front when
purchasing a home and is usually a per-
cent of the purchase price of the home. A
lender typically requires private mortgage
insurance (PMI) when the buyer's down
payment is less than 20% of the purchase
price. To secure a mortgage, buyers also
need to have additional cash on hand
for closing costs and prepaid property
tax. Suppose a buyer wants to purchase
a $375,000 house and must have $7,200
on hand for closing costs and property
tax. Which of the following inequalities
represents the total funds (f) the buyer
must have on hand to secure the mortgage
without having to pay PMI?
A) f≤0.2(375,000) + 7,200
B) f≥0.2(375,000) +7,200
C) f≤0.2(375,000 +7,200)
D) f≥0.2(375,000 +7,200)
Answer:
B) f≥0.2(375,000) +7,200
Step-by-step explanation:
≥ means 'at least'
For how many values of x does the graph f(x)= x^2 -3 intersects the x-axis?
Answer:
cocomelon . 3/5 - 4
Step-by-step explanation:
Answer:
x=[tex]\sqrt3[/tex] and -[tex]\sqrt3\\[/tex]
Step-by-step explanation:
the roots(zeros) are the value of x where the graph intersects the x-axis.
to find the roots:
x^2-3=0
x^2=3
x=+-[tex]\sqrt3[/tex]
What is the value of (-5)^4
Answer:
-20
Step-by-step explanation:
-5-5-5-5=-20
an elevator has a maximum load restriction of 2.5 tons. is it safe for two tile layers weighing 175 ib and 240 ib plus 80 boxes of tile weighing 50 ib each
Using proportions, it is found that the elevator will be safe, as the total weight of 2.2075 tons is less than the maximum load restriction of 2.5 tons.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Each lb has 0,0005 tons. Hence the total weight in tons that we want to put in the elevator is:
T = (175 + 240 + 80 x 50) x 0.0005 = 2.2075 tons.
Hence, the elevator will be safe, as the total weight of 2.2075 tons is less than the maximum load restriction of 2.5 tons.
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Donna sells pencils for $2 and pens $3. She sold 11 items and made $30. How many pens did she sell ?
Donna sold 3 pencils and 8 pens solved using simultaneous equation
What is a simultaneous equation?
Simultaneous equation refers to related equations that are solved at the same to derive answers to the unknown variables
Let assume that X pencils were sold and Y pens were sold
The total revenue is the sum of the prices multiplied by the quantities sold.
2X+3Y=30 (equation 1)
The sum of X and Y sold is 11
X+Y=11 (equation 2)
multiply the second equation by 2
2*(X+Y=11)
2X+2Y=22 (equation 3)
subtract equation 3 from 1
(2X+3Y=30)-(2X+2Y=22)
Y=8
Substitute for Y in equation 2
X+8=11
X=11-8
X=3
Which means he sold 3 pencils and 8 pens.
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Answer:
8
Step-by-step explanation:
Evaluate the expression using x=-1 and y=3 (6^4y^3)
The value of the expression when evaluated is: 162.
How to Evaluate an Expression?To evaluate the expression, 6x^4y^3, substitute x = -1 and y = 3 into the expression and solve.
6(-1^4) × 3^3
6(1) × 27
6 × 27
162
The value of the expression, 6x^4y^3, is: 162.
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Find the equation of the line that passes through (0, -3) and is parallel to
the line joining the points (9, 2) and (3, -5).
Answer:
y = [tex]\frac{7}{6}[/tex] x - 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (9, 2 ) and (x₂, y₂ ) = (3, - 5 )
m = [tex]\frac{-5-2}{3-9}[/tex] = [tex]\frac{-7}{-6}[/tex] = [tex]\frac{7}{6}[/tex]
• Parallel lines have equal slopes , so
m = [tex]\frac{7}{6}[/tex] is the slope of the parallel line
the line crosses the y- axis at (0, - 3 ) ⇒ c = - 3
y = [tex]\frac{7}{6}[/tex] x - 3 ← equation of parallel line
Hey there!
[tex] \\ [/tex]
Answer:[tex] \green{\boxed{\red{\bold{\sf{y = \dfrac{7}{6}x - 3}}}}}[/tex]
[tex] \\ [/tex]
Explanation:To find the equation of a line, we first have to determine its slope knowing that parallel lines have the same slope.
Let the line that we are trying to determine its equation be [tex] \: \sf{d_1} \: [/tex] and the line that is parallel to [tex] \: \sf{d_1} \: [/tex] be [tex] \: \sf{d_2} \: [/tex] .
[tex] \sf{d_2} \:[/tex] passes through the points (9 , 2) and (3 , -5) which means that we can find its slope using the slope formula:
[tex] \sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{y_2} - \orange{y_1}}{\red{x_2} - \blue{x_1 }}} [/tex]
[tex] \\ [/tex]
⇒Subtitute the values :
[tex] \sf{(\overbrace{\blue{9}}^{\blue{x_1}}\: , \: \overbrace{\orange{2}}^{\orange{y_1}}) \: \: and \: \: (\overbrace{\red{3}}^{\red{x_2}} \: , \: \overbrace{\green{-5}}^{\green{y_2}} )} [/tex]
[tex] \implies \sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{-5} - \orange{2}}{\red{ \: \: 3} - \blue{9 }} = \dfrac{ - 7}{ - 6} = \boxed{ \bold{\dfrac{7}{6} }}}[/tex]
[tex] \sf{\bold{The \: slope \: of \: both \: lines \: is \: \dfrac{7}{6}}} [/tex].
Assuming that we want to get the equation in Slope-Intercept Form, let's substitute m = 7/6:
Slope-Intercept Form:
[tex] \sf{y = mx + b} \\ \sf{Where \: m \: is \: the \: slope \: of \: the \: line \: and \: b \: is \: the \: y-intercept.} [/tex]
[tex] \implies \sf{y = \bold{\dfrac{7}{6}}x + b} [/tex] [tex] \\ [/tex]
We know that the coordinates of the point (0 , -3) verify the equation since it is on the line [tex] \: \sf{d_1} \: [/tex]. Now, replace y with -3 and x with 0:
[tex] \implies \sf{\overbrace{-3}^{y} = \dfrac{7}{8} \times \overbrace{0}^{x} + b} \\ \\ \implies \sf{-3 = 0 + b} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \sf{\boxed{\bold{b = -3}} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
Therefore, the equation of the line [tex] \: \bold{d_1} \: [/tex] is [tex] \green{\boxed{\red{\bold{\sf{y = \dfrac{7}{6}x - 3}}}}} [/tex]
[tex] \\ [/tex]
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Collect Data from Our Solar System
Fill in the table. To obtain each planet's distance from the sun
Answer:
jupiter, Saturn, Uranus, neptune are all distance from sun
Step-by-step explanation:
Answer:
AU:
Merc-0.39
Venus-0.72
Earth- 1
Mars- 1.52
Jupiter - 5.20
Uranus - 19.1
Neptune - 30
Years:
Merc-0.24
Venus-0.61
Earth- 1
Mars- 1.88
Uranus - 84?(maybe)
Neptune - 165
Step-by-step explanation:
Edge
50 POINTS HELP NOW
Find the logarithm base 10 of each number:
10
The logarithm base 10 of the number 10 is 1
How to solve logarithm ?We have to find logarithm base 10 of number 10.
Therefore, using logarithm rule
logₐ a = 1
Hence,
log₁₀ 10 = 1
Therefore, logarithm base 10 of the number 10 is 1
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Answer:
1
Step-by-step explanation:
The supplement of a 162 degree angle is an angle that measures
Answer:
18 degrees
Step-by-step explanation:
Supplementary angles are angles that when added together equal 180 degrees.
A + 162 = 180
- 162 -162
A = 18
Answer:
18
Step-by-step explanation:
When your are asked the supplement you minus 162 from 180. When you join SU from supplement and add a 1 behind SU you'll get 180. [1SU TO 180]
180-162
18
You are standing 22 feet from a tall building that has a glass elevator on the exterior wall facing you.
You watch the elevator as it ascends to the top of the building. The height h (in feet) of the elevator
above the ground can be modeled by / = 22 tan e, where © is the angle of elevation. Graph the
function. Describe what happens to © as h increases.
a. Find the graph in the attachment
b. As h increases, e tends to 90°
a. How to graph the function?
Since you are standing 22 feet from a tall building that has a glass elevator on the exterior wall facing you. You watch the elevator as it ascends to the top of the building.
The height h (in feet) of the elevator above the ground can be modeled by h = 22tane.
To plot the graph, we see that the function is the tangent function.
The tangent function has the value -∞ ≤ tanx ≤ +∞ for -90° ≤ x ≤ 90°
Since e is our angle of elevation and e ≥ 0, that is 0 ≤ e ≤ 90°. So, we choose the range of values for which tane ≥ 0. So, 0 ≤ tane ≤ +∞
So, we plot h = 22tane for 0 ≤ e ≤ 90°
Find the graph in the attachment
b. What happens to e as h increases?From the graph, we seet that at high h or as h increases, e tends to 90°
So, as h increases, e tends to 90°
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Solve the equation and provide all steps ¾ x+2¼ =9
Answer:
x=9
Step-by-step explanation:
3/4x+2 1/4=9
3/4x=9-2 1/4
3/4x=6 3/4
4(3/4x)=4(6 3/4)
3x=27
x=9
Answer:
x = 9
Step-by-step explanation:
3/4 x + 2 1/4 = 9 subtract 2 1/4 from both sides of the equation
3/4 x = 6 3/4 now divide both sides by 3/4
x = 9
Weekly wages at a certain factory are
normally distributed with a mean of
$400 and a standard deviation of $50.
Find the probability that a worker
selected at random makes between
$300 and $350.
[? ]%
Answer:
0.1359
Step-by-step explanation:
Emil is running a lemonade stand. He sells half of his lemonade in the morning, a quarter of what was left at lunchtime, and a third of what was left in the afternoon. When he closes for the day, he has 4 liters of lemonade left. How many liters of lemonade did he start the day with?
Answer:
16 Liters of the correct answer.
Emil started his lemonade stand with 12 litres of Lemonade.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
Given that:-Emil is running a lemonade stand. He sells half of his lemonade in the morning, a quarter of what was left at lunchtime, and a third of what was left in the afternoon.
When he closes for the day, he has 4 litres of lemonade left. Let the total lemonade he started with is x litres. Now we will form an expression from the given data to calculate the value of x.
x - (x/2) -(1/4)(x/2) - ( 1/4)(x/2)(1/3) = 4
x - ( x/2) - (x/8) - ( x/24) = 4
[ 24x -12x -3x - x][24] = 4
8x = 96
x = 12 liters
Therefore Emil started his lemonade stand with 12 liters of Lemonade.
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PLEASE HELP ME I WILL MARK CORRECT ANSWER BRAINLIEST
Answer:
36 units
Step-by-step explanation:
to do this you must first find the lengths of all the sides with pythagorean theorem
for a to b you use
3^2 + 4^2 = c^2
9 + 16 = c^2
25 = c^2
c = 5
5 is one of the lengths
b to c uses the same equation
so
5 is another one of the lengths
for d to c your equation is
5^2 + 12^2 = c^2
25 + 144 = c^2
169 = c^2
13 is another of the lengths
d to a has the same length as c to d so there is another 13 unit length
so
5 + 5 + 13 + 13 is your equation to find the perimeter
5 + 5 + 13 + 13 = 36
that is your answer
What type of triangle is shown below?
31°
28.5
19.2
109°
40%
991
Answer:
could u send a photo please
5. A bus covers a certain distance in 45 minutes if it runs at a Speed of 60km/hr. What must be the speed of the bus in order to reduce the time by 20 minutes.
Answer:
108 km/hr
Step-by-step explanation:
45 minutes = 3/4 hours
1) Distance = speed × time
= 60 × 3/4
= 45 km
2) 20 minutes = 1/3 hours. So, 3/4 - 1/3 = 5/12 hours.
speed = distance / time
= 45 / 5/12
= 108 km/hr
What polynomial function could be represented by the graph below
(A). F(X)=x^2+x-2
(B). F(X)=2x^2+2x-4
(C). F(X)=x^2-x-2
(D). F(X)=2x^2-2x-4
Answer:
(B). F(X)=2x^2+2x-4
Step-by-step explanation:
-4 means it passes through -4 at the y axis
B and D have -4
graph passes thru x axis at -2 and 1
if you enter x = -2 or 1 in the formula
(B). F(X)=2x^2+2x-4
you get 0
it's not D because when you enter -2 or 1 for x
you don't get 0
you get 8 and -4
Answer: (B). F(x) = 2x² + 2x - 4
Step-by-step explanation:
Let us think about the parent function F(x) = x² to pick our answer.
Options A and C have only shifted 2 units down (showed by the "-2" at the end) and the function graphed is shifted four units down.
Between options B and D, one is shifted 2 units to the right, and one is shifted 2 units to the left. We need the one shifted 2 units to the left. This is shown by the "+2x" in option B meaning it is our answer.
4.751 4.373 4.177 4.676 (a) Construct a confidence interval for the mean rate. Round the answer to at least four decimal places. A confidence interval for the mean rate is
98% confidence interval for the mean rate = [4.1437 , 4.4983]
We are given the interest rates (annual percentage rates) for a 30-year fixed rate mortgage from a sample of lenders in Macon, Georgia for one day ;
4.751, 4.373, 4.177, 4.676, 4.425, 4.228, 4.125, 4.251, 3.951, 4.192, 4.291, 4.414
Now, Firstly we will find the Mean of the above data, Xbar ;
Mean, Xbar = ∑ x ÷ n =
4.751 + 4.373 + 4.177 + 4.676 + 4.425 + 4.228 + 4.125 + 4.251 + 3.951 + 4.192 + 4.291 + 4.414 ÷ 12 = 4.321
Standard deviation, s = √ ∑(x - x bar)²÷ n-1 = 0.226.
Now, the pivotal quantity for the 98% confidence interval for the mean rate is;
P.Q = x bar - ц ÷ n - 1 ≈ tn - 1
where, Xbar = sample mean
s = sample standard deviation
n = sample size = 12
So, 98% confidence interval for the mean rate, μ is ;
P(-2.718 < t₁₁ <2.718) = 0.98
P(-2.718 <Xbar - μ σ√ⁿ < 2.718) = 0.98
P(Xbar - 2.718 * ₈÷ √ⁿ < μ Xbar + 2.718 * ₈÷ √ⁿ ) = 0.98
98% confidence interval for μ = (Xbar - 2.718 * ₈÷ √ⁿ < μ Xbar + 2.718 * ₈÷ √ⁿ ) = 0.98
[4.321 - 2.718 * 0.226 ÷ √₁₂ , 4.321 + 2.718 * 0.226 ÷ √₁₂
= [4.1437 , 4.4983]
Therefore, 98% confidence interval for the mean rate = [4.1437 , 4.4983]
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The main floor of Kinsey's home is 1,425 square feet. The upper level is 875 square feet with one unfinished bedroom that measures 150 square feet. The finished basement is 1,425 square feet with 7.5-foot ceilings. Kinsey's MLS listing includes below-grade square footage in livable area. What's the reportable square footage for Kinsey's home
The reportable square footage for Kinsey's home = 2150square feet.
The main floor of Kinsey's home is 1,425 square feet.
The upper level is 875 square feet with one unfinished bedroom that measures 150 square feet.
The finished basement is 1,425 square feet with 7.5-foot ceilings.
That means the square footage of the upper floor plus the main floor (minus the unfinished laundry area).
Kinsey should report square feet (1425+875- 150)
= 2150square feet.
Hence, The reportable square footage for Kinsey's home = 2150square feet.
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Points u, m, and d are collinear with m between u and d. given um=5x+30 md=3x+80 ud=10x+20
The lengths um, md and ud are 255 units, 215 units and 470 units respectively, when given that points u, m, and d are collinear with m between u and d and um=5x+30, md=3x+80, ud=10x+20. This can be obtained by adding um and md which is equal to ud. An equation is obtained and solve for x.
What is the required lengths ?Given that, um=5x+30
md=3x+80
ud=10x+20
We know that m is the midpoint of ud
Thus, um + md = ud
5x+30 + 3x+80 = 10x+20
5x+3x + 30+80 = 10x+20
8x + 110 = 10x+20 (taking terms with x to one side of equation)
10x - 8x = 110 - 20
2x = 90
⇒ x = 45
Therefore the lengths,
um=5x+30 = 5(45)+30 = 225 + 30 = 255
md=3x+80 = 3(45)+80 = 135 + 80 = 215
ud=10x+20 = 10(45)+20 = 450 + 20 = 470
Hence the lengths um, md and ud are 255 units, 215 units and 470 units respectively, when given that points u, m, and d are collinear with m between u and d and um=5x+30, md=3x+80, ud=10x+20.
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CAN SOMEONE HELP PLEASE
a = 3, b = 5, and c = 7. What is m&B° to the nearest tenth?
Answer: 38.2 degrees
Step-by-step explanation:
[tex]b^2 = a^2 + c^2 - 2ac \cos B\\\\5^2 = 3^2 + 7^2 - 2(3)(7) \cos B\\\\25 = 58-42 \cos B\\\\-42 \cos B=-33\\\\\cos B=\frac{33}{42}\\\\B \approx 38.2^{\circ}[/tex]
help me answer this table problem please
By using the concepts of relations and functions and based on the table given, the function presents the following relationship:
x → f(x)
7 → 95
How to evaluate a function according to a table
Functions are relations between an input set named domain (x) and an output set named range (f(x)), that is:
x → f(x)
After a quick observation, for x = 7, then f(7) = 95. In more graphically manner, the function present the respective relation:
7 → 95
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Can you help me please
Answer: Option D
[tex]\displaystyle d=\frac{C}{\pi}[/tex]
Step-by-step explanation:
To solve the formula for d, we will isolate the d variable.
Given:
C = πd
Divide both sides of the equation by π:
[tex]\displaystyle\frac{C}{\pi}=\frac{\pi d}{\pi}[/tex], [tex]\displaystyle\frac{C}{\pi}=d[/tex]
Reflexive property
[tex]\displaystyle d=\frac{C}{\pi}[/tex]