There are four possible values of C if there exist distinct complex numbers.
A complex number is an element of a number system that extends the real numbers with a specific element denoted i is called the imaginary unit . the equation every complex number can be expressed as,
a + bi
where a and b are real numbers.
Let p(z) denote the cubic on the left-hand side; the right-hand side is then c3p(z/c). Write p(z)=z3+Az2+Bz+C so
z3 + Az2 + Bz + C ≡ z3+ cAz2 + c2Bz + c3C
⟹ (c−1)A = (c2−1)B = (c3−1)C = 0.
Solving this we can find the possible values of C.
A real number can be said as a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature. continuous means that values can have arbitrarily small variations. Every real number can be almost uniquely represented by an infinite decimal expansion.
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Question is incomplete. The complete question is:
Let c be a complex number. Suppose there exist distinct complex numbers r, s, and t such that for every complex number z, we have
(z−r) (z−s) (z−t) = (z−c r) (z−c s) (z−c t).
Compute the number of distinct possible values of c.
Hongbo sold x cell phones in 2013. The number of cell phones he sold in 2014 was 128% greater than in 2013, and the number of cell phones he sold in 2015 was 29% greater than in 2014. Which of the following expressions represents the number of cell phones Hongbo sold in 2015? A) (0.29)(1.28x) B) (0.29) (2.28x) C) (1.29)(1.28x) D) (1.29) (2.28x)
The number of cell phones sold in 2015 is (0.29)(1.28x)
The correct answer is A) (0.29)(1.28x).
What is a linear equation?
A linear equation is an equation in which the highest power of the variable is 1. Linear equations can be written in the form ax + b = 0, where a and b are constants and x is the variable. Linear equations are called "linear" because they represent a straight line when plotted on a graph.
We are told that the number of cell phones Hongbo sold in 2014 was 128% greater than in 2013, which means that he sold 128/100 = 1.28 times as many cell phones in 2014 as he did in 2013. This can be represented by the equation x * 1.28 = number of cell phones sold in 2014.
We are also told that the number of cell phones Hongbo sold in 2015 was 29% greater than in 2014, which means that he sold 29/100 = 0.29 times as many cell phones in 2015 as he did in 2014. This can be represented by the equation (number of cell phones sold in 2014) * 0.29 = number of cell phones sold in 2015.
Substituting the first equation into the second equation, we get:
(x * 1.28) * 0.29 = number of cell phones sold in 2015
This simplifies to:
(0.29)(1.28x) = number of cell phones sold in 2015
Hence, the number of cell phones sold in 2015 is (0.29)(1.28x)
the correct answer is A) (0.29)(1.28x).
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The concept of best-, worst-, and average-case analyses extends beyond algorithms to other counting problems in mathematics. Recall that the height of a binary tree is the number of edges in the longest path from the root to a leaf. Find the best-case height of a binary tree with seven nodes.
Using the 22n rule, determine the number of classes needed for the following data set sizes.
a) n = 50
b) n = 250
c) n = 1000
d) n = 3000
a) The number of classes needed when n = !
= 50 is
...
Can someone help me answer this
The two relations that are also functions are:
S = { (-1, 0), (3, 2), (5, 4), (8, 9), (15, 12)}R = {(0, -1), (2, 1), (5, 4), (7, 9), (14, 12)}Which of the following relations represent functions?A relation is a function if and only if each point in the domain is mapped into a single value of the range.
So for example, the following relation:
{ (a, b), (a, c), (d, f)}
The input a is mapped into two different outputs, thus, this is not a function.
Then from the given options the ones that can be functions are:
S = { (-1, 0), (3, 2), (5, 4), (8, 9), (15, 12)}
R = {(0, -1), (2, 1), (5, 4), (7, 9), (14, 12)}
In all the other relations we can see inputs mapped into more than one output.
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given that is a matrix with eigen pairs , and . find the matrix where . let , then , , ; , , ; , , .
a matrix is a collection of integers that have been put in rows and columns to make a rectangular array. The entries of the matrix are the integers, which are referred to as its elements.
What is matrix?Linear algebra is a subfield of mathematics that mostly uses matrices. When you start solving linear equation systems, linear algebra first starts to seem good. You may concentrate on the figures and greatly simplify the procedure by condensing all the information into a single large chart and leaving out the rest.
Which 4 types of matrices are there?Almost as their name implies, square, symmetric, triangular, and diagonal matrices. All-zero identity matrices except along the major diagonal, where the values are
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if the simple interest on 3,000 for 10 years is 1,500 then what is the interest rate?
Answer:
5%
Step-by-step explanation:
Interest = deposit * annual rate * years
1500 = 3000 * rate * 10 yrs
1500/(3000*10) = rate in decimal form = .05 = 5 %
What is the smallest positive integer n, such that there exist positive integers a and b, with b obtained from a by a rearrangement of its digits, so that a–b=11…1 (The number of '1's equal to n)?
The smallest n is n=9.
What is an integer, and what are some examples of them?
A full number (not a fraction) that can be positive, negative, or zero is called an integer (pronounced IN-tuh-jer).
-5, 1, 5, 8, 97, and 3, 043 are some examples of integers.
-1.43, 1 3/4, 3.14,.09, and 5,643.1 are a few examples of numbers that are not integers.
Formally, the set of integers, designated Z, is defined as follows:
Z = {..., -3, -2, -1, 0, 1, 2, 3, ...}
Since b=DigitsRearranged(a)
→ a and b have the same remainder when divided by 9
→ a−b is divisible by 9
→ n≥9
And this is sufficient because there is a solution for this n:
a=812,345,709b=701,234,598a−b=111,111,111
So the smallest n is n=9.
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the limit of a function exists at a cluster point c if and only if the left- and right-handed limits both exist at c and are equal.
By using ε - δ definition of limit, the proof of
The limit of a function exists at a cluster point c if and only if the left- and right-handed limits both exist at c and are equal
has been shown below.
What is ε - δ definition of limit?
Let the function be f(x), cluster point be c and the limit be l. Then
the limit of a function exists at a cluster point c if
For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that |x − c |< δ ⟹ |f(x) − l| < ε
Let the limit exist at a cluster point c. Let the limit be l
For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that |x − c |< δ ⟹ |f(x) − l| < ε
For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that 0 < c - x < δ ⟹ |f(x) − l| < ε or
0 < x - c < δ ⟹ |f(x) − l| < ε
For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that c - δ < x < c ⟹ |f(x) − l| < ε or
c < x < c + δ ⟹ |f(x) − l| < ε
For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that c - δ < x < c ⟹ |f(x) − l| < ε and
For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that c < x < c + δ ⟹ |f(x) − l| < ε
So the left hand and right hand limit exist and are equal.
Let the left hand and right hand limit exist and are equal.
For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that c - δ < x < c ⟹ |f(x) − l| < ε and
For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that c < x < c + δ ⟹ |f(x) − l| < ε
Let [tex]\delta_3 = min\{\delta_1, \delta_2\}[/tex]
For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that c - [tex]\delta_1[/tex] < x < c ⟹ |f(x) − l| < ε and
For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that c < x < c + [tex]\delta_2[/tex] ⟹ |f(x) − l| < ε
For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that c - [tex]\delta_1[/tex] < x < c or c < x < c + [tex]\delta_2[/tex]⟹ |f(x) − l| < ε
For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that |x - c| < [tex]\delta_3[/tex] ⟹ |f(x) − l| < ε
The limit of a function exists at a cluster point c and the limit is l
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Part A: Given the function g(x) = |× + 31, describe the graph of the function, including the vertex, domain, and range. (5 points) Part B: If the parent function f(x) - |×] is transformed to h(x) = |× - 2, what transformation occurs from f(x) to h(x)? How are the vertex and range of h(x) affected?
A. The graph of the absolute value function is V-shaped, with the features given as follows:
Vertex: (-3,0).Domain: All real values.Range: [0, ∞).B. The transformation is that the function was shifted right two units, hence the features are given as follows:
Vertex: (2,0).Domain: All real values.Range: [0, ∞).What is the absolute value function?The absolute value function, with vertex (h,k), is defined as follows:
y = |x - h| + k.
The features of the function are given as follows:
Vertex: (h,k).Domain: All real values.Range: [k, ∞).For the first item, the function is |x + 3|, hence we just have to identify the features.
For the second function, the definition if h(x) = |x - 2|, with vertex at (2,0), meaning that the function was shifted two units right from the parent absolute value function y = |x|. The shift just changes the turning point of the graph, not altering domain and range.
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1) How much interest will you pay on a $43,000 car loan with a fixed APR of 4.9% if the loan is
for 5 years?
You pay the interest of 350 dollar on a $43,000 car loan with a fixed APR of 4.9% if the loan is for 5 years
What is APR?The term annual percentage rate of charge, sometimes referred to as a nominal APR and sometimes referred to as an effective APR, refers to the interest rate for the entire year, rather than just a monthly fee/rate, as applied to a loan, mortgage loan, credit card, and so on. It is a finance charge calculated on an annual basis.
We are given that it took out a car loan for $43,000 car loan with a fixed APR of 4.9% if the loan is for 5 years
We know that r = 4.9/12/100 = 0.0049
p = 43,000
Putting the values in formula we get;
= (43,000x 0.0049 x 2.767)/1.767
= $350
Therefore, the interest will be 350 dollar.
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-5 x -9 ddddddddddddd
Answer:
45
Step-by-step explanation:
two negative numbers multiplied equals a positive number
Zenith Investment Company is considering the purchase of an office property. It has done an extensive market analysis and has estimated that based on current market supply or demand relationships, rents, and its estimate of operating expenses, annual NOI will be as follows:
Year NOI
1 $ 1,210,000
2 1,210,000
3 1,210,000
4 1,270,000
5 1,320,000
6 1,370,000
7 1,409,000
8 1,449,170
A market that is currently oversupplied is expected to result in cash flows remaining flat for the next three years at $1,210,000. During years 4, 5, and 6, market rents are expected to be higher. It is further expected that beginning in year 7 and every year thereafter, NOI will tend to reflect a stable, balanced market and should grow at 3 percent per year indefinitely. Zenith believes that investors should earn a 12 percent return (r) on an investment of this kind.
Required:
a. Assuming that the investment is expected to produce NOI in years 1 to 8 and is expected to be owned for seven years and then sold, what would be the value for this property today? (Hint: Begin by estimating the reversion value at the end of year 7. Recall that the expected IRP = 12% and the growth rate (g) in year 8 and beyond is estimated to remain level at 3%.)
b. What would the terminal capitalization rate (RT) be at the end of year 7?
c. What would the going-in capitalization rate (R) be based on year 1 NOI?
The value of the property at the end of year 7 is 15,324,111$. for a detailed answer read below.
What is NOI?The net operating income (NOI) formula determines a company's revenue after operating costs have been subtracted, but before interest and taxes have been subtracted.
The net operating income of the property is given for years 1 to 8 in the question. Z Corporation wants to own the property for seven years and then sell the property in the 8th year. The growth rate in NOI is 3%, and the expected return on property is 12%.
The value of the property today is the present value of all the cash flow that the property can earn in the future. The terminal value of the property is the reversion value at the end of the eighth year. Compute the terminal value as follows. The value of the property at end of year 7 is $15,324,111. The current value of the property is the present value of all the cash inflow in terms of net operating income and the terminal value. In order to compute the present value of all future cash flows using the “NPV” function of the spreadsheet.The discount rate utilized to account for the property's growth rate while calculating the terminal capitalization rate is the perpetual cash flow from the asset. It is the gap between the growth rate in NOI (Net Operating Income) over an endless period of time and the IRR (the needed rate of return of the investor). The percentage return an investor will get on the property's worth is known as the "going-in" capitalization rate. It is calculated by dividing the property's first year's NOI by the property's current value.When comparing properties, the "going-in" capitalization rate is deceptive and useless. This is due to the fact that it disregards the property's overall NOI throughout all years. The first year's net operating income is divided by the property's current market value to get the going-in cap rate based on first-year NOI. The going-in cap rate = first-year NOI / Current value of the property.The "going-in" capitalization rate should be calculated as follows: So, using first-year NOI as the basis, the cap rate is. 8.29%
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I need help with my math homework
Choose all that apply when describing R^2. (Select all that apply.) Is used to determine the fit of a model. Can be inflated by adding more variables. Only describes the relationship between quantitative variables. Represents the percent of variability in y that can be explained by the model. Is only used in multiple linear regression. In simple linear regression, it is equal to the correlation coefficient r^2. Referred to as the coefficient of determination or coefficient of multiple determination. Can be inflated by removing variables.
The following statements are correct,
a.) Is used to determine the fit of a model.
b.) Can be inflated by adding more variables.
c.) Referred to as the coefficient of determination
d.) Represents the percent of variability in y that can be explained by the model.
e.) In simple linear regression, it is equal to the correlation coefficient r².
Define Regression Analysis
Regression analysis is a set of statistical processes for estimating the relationships between a dependent variable and one or more independent variables.
R² ≡ 1 - SS(res) / SS(tot)
SS(res) + SS(reg) = SS(tot)
R² = SS(reg) / SS(tot) = (SS(reg)/n) / ( SS(tot)/n )
Where,
The total sum of squares(proportional to the variance of the data),SS(tot) = ∑ (y - y(bar) )₂
The regression sum of squares, also called the explained sum of squares,SS(reg) = ∑ (f(i) - y(bar) )²
The sum of squares of residuals, also called the residual sum of squares,SS(res) = ∑ (y(i) - f(i) )² = ∑e²(i)
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At a video game store an animal game costs $45.00. If the sales tax is 5%, what is the total amount Blake will pay for the game?
Answer:
$47.25
Step-by-step explanation:
First we find how much the tax will be
45x0.05
2.25
and now we add to find the total
45+2.25
47.25
hopes this helps
Evaluate the algebraic expression for
the given values of x=
3 and y = 4.
7x - 2y - 1 = ?
Will give brainlest answer!!
Answer: 12
Step-by-step explanation:
7(3)-2(4)-1=12
Find the length of the mid segment of the trapezoid with the given vertices.
4. E(-3, 3), F(1, 3), G (3, -3), H(-5, -3)
The length of the mid-segment of the trapezoid is 6
What is a trapezium?The trapezium is a quadrilateral where 1 pair of sides are parallel and the sum of angle pairs between parallel lines is 180 degrees.
We have,
The vertices of a trapezoid:
E = (-3, 3)
F = (1, 3)
G = (3, -3)
H = (-5, -3)
The figure can be considered as,
E____________F
/ \
M / \ N
/ \
H/_____________________\G
MN is the mid-segment of the trapezoid.
MN = (EF + HG) / 2
EF = √(4² + 0) = 4
HG = √(8² + 0) = 8
MN = (4 + 8) / 2
MN = 12/2
MN = 6
Thus,
6 is the length of the mid segment of the trapezoid.
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Lime Scooter Rentals in San Diego charges $2 to start and
$0.10 per minute after. The price to rent a scooter for m
minutes from Spin Scooter Rentals is shown in the graph to
the right. For which time(s) are the prices the same at both
rental companies?
The time for which the cost is the same for both companies is given as follows:
10 minutes.
How to define the cost functions?As the cost per unit of time is constant for each company, the cost functions are linear functions.
The slope-intercept definition of a linear function is given as follows:
y = mx + b.
The coefficients and their meaning are given as follows:
m is the slope, representing the cost per minute.b is the intercept, representing the initial cost.Then the cost functions are given as follows:
Lime Scooter Rentals: y = 2 + 0.1x.Spin Scooter Rentals: y = 1 + 0.2x. (from the graph, in 10 minutes, the cost increased by $2, then the slope is of 0.2).Then the costs will be the same when:
1 + 0.2x = 2 + 0.1x
0.1x = 1
x = 1/0.1
x = 10 minutes.
Missing InformationThe graph for the cost for Spin Scooter Rentals is given by the image shown at the end of the answer.
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consider the functions given below. P(x)= 2/3x-1 Q(x)= 6/-3x+2 Match the expression with its simplified form
Answer:
P/Q = (-3x +2)/(3(3x -1))
PQ = 12/((3x -1)(-3x +2))
Step-by-step explanation:
You want the quotient and product of P(x) = 2/(3x -1) and Q(x) = 6/(-3x +2).
QuotientThe quotient is found by multiplying by the inverse of the denominator:
[tex]P(x)\div Q(x)=\left(\dfrac{2}{3x-1}\right)\div\left(\dfrac{6}{-3x+2}\right)=\left(\dfrac{2}{3x-1}\right)\times\left(\dfrac{-3x+2}{6}\right)\\\\\\\dfrac{2(-3x+2)}{6(3x-1)}=\boxed{\dfrac{-3x+2}{3(3x-1)}}[/tex]
ProductAs with multiplying any fractions, the numerator is the product of the numerators, and the denominator is the product of the denominators.
[tex]P(x)\times Q(x)=\left(\dfrac{2}{3x-1}\right)\times\left(\dfrac{6}{-3x+2}\right)=\dfrac{2\cdot 6}{(3x-1)(-3+2)}\\\\\\=\boxed{\dfrac{12}{(3x-1)(-3x+2)}}[/tex]
__
Additional comment
Usually the simplified form would contain no parentheses. The indicated products would be multiplied out.
Question The general form of a hyperbola is 6x2−5y2+12x+50y−149=0.
Answer:the general form of a hyperbola is 6x^2-5y^2+12x+50y-149=0 the answer is (x+1)^2/5 -((y-5)^2/6=1
Step-by-step explanation:
give an example of a continuous function and closed interval that do not satisfy the conclusion of the mean value theorem
A continuous function is the one in which the function is continuous is the interval given for the function.
A continuous function that does not satisfy the conclusion of the mean value theorem on a closed interval is the function f(x) = |x| on the interval [-1, 1].
This function is continuous on the interval [-1, 1], but it does not have a derivative at x = 0. Therefore, the mean value theorem does not apply at this point, and there is no value c in the interval [-1, 1] such that f'(c) = (f(1) - f(-1))/(1 - (-1)).
This is an example of a function that is continuous on a closed interval, but does not satisfy the conclusion of the mean value theorem.
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Determine if the following ratios form a proportion
a) 45 g to 60 g and 36 kg to 48 kg
b) 450 m to 3 km and 75 cm to 7 m
Answer:
a was ture
b was wrong
Step-by-step explanation:
a)
[tex]\frac{45}{60} =\frac{3}{4}[/tex]
[tex]\frac{36}{48} =\frac{3}{4}[/tex]
b)
[tex]\frac{450m}{3km} =\frac{450}{3000} =\frac{3}{20} \\[/tex]
[tex]\frac{75cm}{7m}=\frac{75}{700} =\frac{15}{140}[/tex][tex]=\frac{1}{7}[/tex]
Answer:
1. 45:60 = 36:48
(45:60)/15 = (36:48)/12 (divide by their GCF)
3:4 = 3:4
PROPORTION2. 4500:3 = 75:700
(4500:3)/3 = (75:700)/25
1500:1 = 3:28
NOT PROPORTIONStep-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-A window comprises a square with sides of length z and a semicircle with diameter x as shown in the figure. If the total area of the window is 463 square inches, estimate the value of x to the nearest hundredth of an inch.
The value of x nearest hundredth of an inch is 18.19 inches.
Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.
Given that total area of the window is 463 square inches
We will need to write an equation using area of a square an area of a semi circle to find the approximate value of x and we know the total area of the window.
Area of square = [tex]x^{2}[/tex]
The area of the semicircle = [tex]\frac{1}{2}[/tex]πr²
So the radius squared would be 1/4 X squared
And the total area is 463.
We've got to clean this up two times pi times 1/4 that would be 1/8 times pi .
Combine like terms which would be 1.4 x squared.
Divide both sides by 1.4 and take the positive square root.
182x=18
Round to the nearest 100th which would be 18.19.
So value of x which is diameter of semicircle nearest 100th is = 18.19
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Name the image of P(9,1.5) after being translated along the vector <3, -0.5>
Answer:
The coordinates would be (12,1)
Step-by-step explanation:
What is the correct solution for the system
{
x-3y = -12
5x - 3y = -48
Answer:
x = -9; y = 1
Step-by-step explanation:
x - 3y = -12
- 5x - 3y = -48
-------------------------
-4x = 36
x = -9
-9 - 3y = -12
-3y = -3
y = 1
of the five points $(3, 10),$ $(6, 20),$ $(12, 35),$ $(18, 40)$ and $(20, 50),$ what is the sum of the $x$-coordinates of the points that lie in the region above the line $y
The sum of the x-coordinates of the points that lie in the region above the straight line y = 2x + 7 in coordinate plane is thirty-eight.
A point lies above the straight line , y = 2x + 7 in co-ordinate plane . If its y -coordinate is greater than two times its x-coordinate plus 7. Now, we are checking the each ordered pair one by one ,
(i) plug x = 3 and y = 10
2x + 7 = 3×2 + 7 = 13 > 10
(ii) plug x = 6 in 2x+7
=> 2× 6 + 7 = 19 < 20
(iii) x = 12
=> 2x + 7 = 2× 12 + 7 = 31 < 35
(Iv) x = 18
=> 2x + 7 = 2× 18 + 7 = 43 > 40
(v) x = 20
2x + 7 = 2×20 + 7 = 47 < 50
We see (6, 20) , ( 12,35) and (20,50) satisfy this condition. Now, we determine the sum of x-coordinates . The sum of the x-coordinates of these points is 6 + 12 + 20 = 38 . So, required sum of x-coordinates is 38.
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Complete question:
Of the five points (3, 10), (6, 20),(12, 35), (18, 40)and (20, 50), what is the sum of the x-coordinates of the points that lie in the region above the line
y = 2x + 7 in coordinate plane.
the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length is
The segment joining the midpoints of two sides of a triangle is parallel to the third side and half as long as the third side.
According to Midpoint theorem, if the midpoints of two sides of a triangle are joined by the segment, then resultant segment is parallel to the third side of the triangle and is half of the length of the third side. Consider the triangle ABC, as shown in the figure. Let the midpoints of the sides AC and AB be given as E and D. Then the line DE is said to be parallel to the side BC, whereas the side DE is half of the side BC i.e., DE || BC and DE = (1/2 BC).
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what is the volume of a hemisphere with a radius of 6.4 ft, rounded to the nearest tenth of a cubic foot
Answer:
1,150 cubic feet.
Step-by-step explanation:
The volume of a hemisphere with a radius of 6.4 feet can be calculated using the formula 4/3 * pi * r^3, where r is the radius of the hemisphere. Plugging in the values, we get 4/3 * pi * 6.4^3 = approximately 1,153 cubic feet. Rounded to the nearest tenth, the volume of the hemisphere is 1,150 cubic feet.
how many 2/3 cup serving are in a 4 cup container of food?
Answer:
6
Step-by-step explanation:
Divide 4 by [tex]2/3[/tex]
[tex]\frac{4}{2/3}[/tex] =[tex]\frac{4*3}{2}[/tex]
=6
12, 18, 10, 20, 8, pattern
Answer:
The pattern is in the order of even number being added or subtracting (takes turns)
Step-by-step explanation:
12,18,10,20,8
12 to 18 is plus 6
18 to 10 is minus 8
10 to 20 is plus 10
20 to 8 is minus 12
[tex]12 + 6 = 18 \\ 18 - 8 = 10 \\ 10 + 10 = 20 \\ 20 - 12 = 8 \\ 8 + 14 = 22 \\ 22 - 16 = 6 \\ = 24 \\ = 4 \\ = 26 \\ = 2 \\ ..[/tex]