Answers
Answer:
y = 75; z = 75
Step-by-step explanation:
105 and z are a linear pair and that means they add up to 180
they are on a straight line which is why they are a linear pair
105 + z = 180
subtract 105 to both sides
z = 75
now add all of the remaining sides and subtract that from 360 because a quadrilaterals angles add to 360
75 + 89 + 95 = 259
360 - 259 = y
360 - 259 = 101
y = 101
these are your answer
Answer:
y=95
z=105
Step-by-step explanation:
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Related Questions
A forty-foot piece of wire was cut into two pieces. The length of one-
piece is 9 times the length of the other. What is the length of the
longer piece? System of equations
Answers
The length of the longer piece is 39.4 ft.
Given, a forty-foot piece of wire was cut into two pieces.
The length of one-piece is 9 times the length of the other.
Let the length of one piece be x,
and the length of the other piece be 9x
Now, according to the question
x + 9x = 44
10x = 44
x = 4.4
then, the length of the longer piece be 9×4.4 = 39.4
Hence, the length of the longer piece is 39.4 ft.
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(Lesson 9.8: Other Steady-State Methods.) Consider the following observations: 54 70 75 62 If we choose a batch size of 3, calculate all of the overlapping batch means for me. a. 65.25 b. 62.0, 68.5 c. 66.3, 69.0 d. 65.25 +3 e. None of the above
Answers
All of the overlapping batch means for me is (66.3, 69.0).
Given observations:
54 70 75 62
From the given data, if we choose a batch size of 3, then calculating all of the overlapping batch means for me in total
that is :
= 1/3 * (54 + 70 + 75)
= 66.3
and
= 1/3 * (70 + 75 + 62)
= 69.0
So often, the option c is correct from the given
that is 66.3, 69.0
Hence the answer is all of the overlapping batch means for me is (66.3, 69.0).
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a store has 24 saltwater fish. the store has 4 tanks for the fish. each tank has an equal number of fish. how many fish are in each tank
Answers
Answer:
Step-by-step explanation:
Answer: 6
there are 24 fish and 4 tanks so divide 24 by 4 and you'll have 6
Answer:
the number of fish in each tank is 6
Step-by-step explanation:
becuause 24 divided be 4 is 6
1. Mr. and Mrs. Ryan Miller bought a
refrigerator for $1,416. They agreed to
make 12 equal monthly payments. How
much more than $50 will each payment
be?
2. The $1,416 paid by the Millers (problem 1
to buy the refrigerator included an interest
charge of $188. What was the cash cost of
the refrigerator?
Answers
The monthly payment more than $50 is $68 and the original price of the refrigerator is $1228
Mr. and Mrs. Ryan Miller bought a refrigerator for $1,416.
They agreed to make 12 equal monthly payments
Monthly payment = 1416 / 12
The monthly payment is $118
more than $50 will each payment be = 118 - 50 = 68
The $1,416 paid by the Miller to buy the refrigerator included an interest charge of $188
The original price is 1416 - 188 = 1228
Therefore, the monthly payment more than $50 is $68 and the original price of the refrigerator is $1228
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You want to order posers to advertise your band. A company charges $109.95 for the first 100 posters and $65 for each additional 100 posters.
Write an equation that represents the cost (in dollars) of the posters of the number (in hundreds) of posters ordered (in slope- intercept form).
Answers
The equation that represents the total cost as a function of the number (in hundreds) of posters ordered, x is f(y) = 109.95 + 65x
let
y = total cost
x = numbers in hundreds
cost of first hundred = $109.95
Cost of additional hundred = $65
f(y) = 109.95 + 65x
The total cost of 1000 posters
1000 - first hundred = 900
additional hundreds = 900/100= 9
So,
f(y) = 109.95 + 65x
= 109.95 + 65(9)
= 109.95 + 585
= 694.95
f(y) = $694.95
Therefore, the total cost of 1000 posters is f(y) = $694.95
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Identify the sampling technique used (or to be used) in the following scenarios. Possible answers could be simple random, systematic random or stratified random sampling.
Answers
a)
This sampling technique is simple random sampling, since the students are selected at random by drawing their names from a piece of paper.
b)
Since there is a condition to select a resident (being the sixth resident of the list), this technique is classified as systematic random sampling.
c)
The 20 students were selected by using a table of random numbers without any criteria. Therefores, this is a simple random sampling technique.
d)
Since, among the 100 selected random people, there was a pre determined subgroup of 5 barangays, this is a stratified random sampling technique.
e)
Since everyone in the sample was selected at random by dwaring lots, this is a simple random sampling technique.
If x>0, then x^(3/4)/x^(-¼)
HELPP PLEASEEE
Answers
Answer:
x
Step-by-step explanation:
using the rule of exponents
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex]
given
[tex]\frac{x^{\frac{3}{4} } }{x^{-\frac{1}{4} } }[/tex]
= [tex]x^{\frac{3}{4}-(-\frac{1}{4}) }[/tex]
= [tex]x^{(\frac{3}{4}+\frac{1}{4}) }[/tex]
= [tex]x^{1}[/tex]
= x
Answer:
[tex]\large\text{$\dfrac{x^{\left(\frac{3}{4}\right)}}{x^{\left(-\frac{1}{4}\right)}}=x$}[/tex]
Step-by-step explanation:
Given expression:
[tex]\large\text{$\dfrac{x^{\left(\frac{3}{4}\right)}}{x^{\left(-\frac{1}{4}\right)}}$}[/tex]
[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]
[tex]\implies \large\text{$x^{\left(\frac{3}{4}-\left(-\frac{1}{4}\right)\right)}$}[/tex]
Simplify:
[tex]\implies \large\text{$x^{\left(\frac{3}{4}+\frac{1}{4}\right)}$}[/tex]
[tex]\implies \large\text{$x^{\left(\frac{4}{4}\right)}$}[/tex]
[tex]\implies \large\text{$x^{1}$}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^1=a:[/tex]
[tex]\implies \large\text{$x$}[/tex]
Cole scored 18 points in his team's last game. That was 36% of the team's total points for the
game. How many total points did the team score?
Answers
The team's total points for the game was 50.
According to the question,
We have the following information:
Cole scored 18 points in his team's last game. That was 36% of the team's total points for the game.
Now, let's take the score points of the team in the game to be x points.
So, we have the following expression:
36% of x = 18
36x/100 = 18
Multiplying by 100 on both sides of the equation:
36x = 1800
Dividing by 36 on both sides of the equation:
x = 1800/36
x = 50
Hence, the team's total points for the game was 50.
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use the unit circle to find sec(7/6)
Answers
Step 1
Draw the unit circle required
Step 2
Find the value sec(7π/6) in cosine
[tex]\begin{gathered} \sec (\frac{7\pi}{6})=\frac{1}{cos(\frac{7\pi}{6})} \\ \sec (x)=\frac{1}{cos(x)} \end{gathered}[/tex]Step 3
Find cos(7π/6)
The trigonometric unit circle and a trigonometric table gives;
[tex]\begin{gathered} \cos (\frac{7\pi}{6})=\cos (\frac{\pi}{6}+\pi) \\ \cos (\frac{7\pi}{6})=\text{cos}(\frac{\pi}{6})\cos (\pi)-\sin (\frac{\pi}{6})sin\pi=-\cos (\frac{\pi}{6}) \\ \cos (\frac{7\pi}{6})=\frac{\sqrt[]{3}}{2}(-1)-(\frac{1}{2})(0)=-\frac{\sqrt[]{3}}{2} \\ \cos (\frac{7\pi}{6})=-\frac{\sqrt[]{3}}{2} \end{gathered}[/tex]Step 4
Find sec(7π/6)
[tex]\begin{gathered} \sec (x)=\frac{1}{cos(x)} \\ \text{sec}(\frac{7\pi}{6})=\frac{1}{\cos (\frac{7\pi}{6})} \\ \text{sec}(\frac{7\pi}{6})=\frac{1}{-\frac{\sqrt[]{3}}{2}} \\ \text{sec}(\frac{7\pi}{6})=-\frac{2}{\sqrt[]{3}} \end{gathered}[/tex]Step 5
Rationalize the denominator
[tex]\begin{gathered} \sec (\frac{7\pi}{6})=-\frac{2}{\sqrt[]{3}}\times\frac{\sqrt[]{3}}{\sqrt[]{3}} \\ \sec (\frac{7\pi}{6})=-\frac{2\sqrt[]{3}}{\sqrt[]{9}} \\ \sec (\frac{7\pi}{6})=-\frac{2\sqrt[]{3}}{3} \end{gathered}[/tex]Hence,
[tex]\sec (\frac{7\pi}{6})=-\frac{2\sqrt[]{3}}{3}[/tex]z ÷ 12 = 9
PLS NEED HELP FAST
STEP BY STEP
Answers
Answer:
z = 108
z/12 = 9
12 x z/12 = 12 x 9
12 x z/12 = 12 x 9
z = 12 x 9
= 108
Answer:
z = 108
Step-by-step explanation:
z / 12 = 9
Multiply 12 and 9
z = 12 * 9
12 * 9 = 108
z = 108
Hope I helped <3
On the prior screen, you sketched `ΔMJN` on the graph with vertices `M(16,-8)`, `J(16,2)`, and `N(4,0)`. What is the area of `ΔMJN`?
Answers
The triangle has an area of 60 square units.
How to determine the area of the triangle based on the location of its vertices
Herein we find the case of a triangle whose vertices are set on a Cartesian plane and whose area can be determined by means of the Heron's formula:
A = √[s · (s - MJ) · (s - JN) · (s - MN)]
s = (MJ + JN + MN) / 2
Where MJ, JN and MN are the side lengths of the triangle and s is the semiperimeter of the triangle.
First, determine the side lengths:
MJ = √[(16 - 16)² + [2 - (- 8)]²]
MJ = 10
JN = √[(4 - 16)² + (0 - 2)²]
JN = √[(- 12)² + (- 2)²]
JN = 2√37
MN = √[(4 - 16)² + [0 - (- 8)]²]
MN = √[(- 12)² + 8²]
MN = 4√13
Second, determine the semiperimeter:
s = (1 / 2) · (10 + 2√37 + 4√13)
s ≈ 18.294
Third, calculate the area of the circle:
A = √[18.294 · (18.294 - 10) · (18.294 - 2√37) · (18.294 - 4√13)]
A ≈ 60.002
The area of the triangle is approximately equal to 60 square units.
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pls help guyssssssssss
Answers
What are the coordinates of point A? ES 2 (8,6) (-6, 8) (-5.7) Save and Exit
Answers
To write the coordinates of a point in a x - y plane you:
1. Find the distance in x-axis:
The given point A is 7 units distance in x-axis
2. Find the distance in y- axis
The given point A is -5 units distance in y-axis
You write the coordinates in form (x,y)
As x=7 and y=-5
Point A is (7, -5)Answer: -5,7
Step-by-step explanation:
Biologists notice an alarming trend in the walleye population in Lake Erie. Despite efforts, the population is decreasing by 15% each year. They estimate the walleye population was 26 million at the beginning of the current year. Write a sequence that lists the population for the first 4 years using 26 million as the first term.
Answers
Given:
The initial population is p = 26 million.
The decreasing percentage is r = 15% each year = 0.15.
The objective is to write the sequence of population after 4 years.
Explanation:
The general formula of population decrease is,
[tex]A=P(1-r)^t\text{ . . . . .(1)}[/tex]The population in the 1st-year can be calculated by substituting t=1 in equation (1).
[tex]\begin{gathered} A_1=26(1-1.15)^1 \\ =26(0.85) \\ =22.1\text{million} \end{gathered}[/tex]The population in the 2nd year can be calculated by substituting t=2 in equation (1).
[tex]\begin{gathered} A_2=26(1-0.15)^2 \\ =26(0.85)^2 \\ =18.785million \end{gathered}[/tex]The population in the 3rd year can be calculated by substituting t=3 in equation (1).
[tex]\begin{gathered} A_3=26(1-0.15)^3 \\ =26(0.85)^3 \\ =15.967255million \end{gathered}[/tex]Hence, the population for the first 4 years will be,
26million,
22.1million,
18.785million,
15.967255million.
Mr. Jones' age is 3 years more than 4 times Mahelet's age. If the sum of their ages is 73, how old is Mahelet?
Answers
Mahelet's age is found to be 14 years by solving the simultaneous equations using the given data.
What exactly is a simultaneous equation?A collection of two or more equations, each having two or more variables, whose values can concurrently fulfil one, more, or all of the equations in the collection, with the number of variables being equal to or fewer than the collection's equations.
Given: Mahelet is four times older than Mr. Jones, who is three years older than Mahelet. The total of their ages is 73.
Let, x = Mahelet's age
y = Mr. Jones's age
We know that,
y = 4x +3
x + y = 73
Solving these equations simultaneously we get,
y = 4(73-y) +3
y = 292 - 4y + 3
5y = 295
y = 59
x = 73 - y = 73 - 59 = 14
Therefore, Mahelet's age is found to be 14 years by solving the simultaneous equations.
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Determine whether a relation is a function.
Answers
During a snowstorm, Amelia tracked the amount of snow on the ground.When the storm began, there was 1 inch of snow on the ground. For the first 2hours of the storm, snow fell at a constant rate of 3 inches per hour. Thestorm then stopped for 3 hours and then started again at a constant rate of 1inch every 2 hours for the next 6 hours. Make a graph showing the inches ofsnow on the ground over time using the data that Amelia collected.
Answers
First, let's write on a table the information about the snow on the ground for the 11 hours it snowed:
period of time in hours amount of snow in inches
0 1
from 0 to 2 1 + t * 3 (initial amount plus 3 in/h * number of hours)
from 2 to 5 1 + 2*3 = 7 (the same amount as when it stopped raining)
from 5 to 11 7 + (t-5)/2 (amount at t = 5 plus 1 in/2h * number of
hours since hour 5)
Now, using this information on a graph, we obtain:
Using the function F(x)= 3x-1 solve for the following values F(-2)=
Answers
For the function F(x)=3x-1, the value for F(-2) will be (-7).
How to tackle this type of question of function?
Put value of variable in the given function.
Here,
x=-2
then, F(-2) = 3(-2) - 1
F(-2) = -6 - 1
F(-2) = -7
Hence, F(-2) = (-7)
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What is the equation of the line that passes
through the point (-8, -8) and has a slope
of o?
Answers
Answer: y+8=m(x+8)
Step-by-step explanation: because you follow the form y-y1=m(x-x1)
A circular dartboard has diameter 40cm. Its bull’s eye has diameter of 8 cm. if an amateur throws a dart and it hits the board, what is the probability that the dart hits the bull’s eye.
Answers
Answer:
a value of is required in the following exercises, use
A circular dartboard has diameter 40 Its bull's eye has diameter 8
a. If an amateur throws a dart and it hits the board. What is the probability that the dart hits the bull's eye?
b. After many throws, 75 darts have hit the target. Estimate the number hitting the bull's eye.
Step-by-step explanation:
hope it helps! please mark brainlets
Find the number of different ways that an instructor can choose 4 students from a class of 23 students for a field trip.
Answers
We have to find how many ways we can group 23 students in groups of 4.
This can be calculated as a combination of 23 in 4, as order does not matter and there is no repetition.
We can calculate it as:
[tex]\begin{gathered} C(n,r)=\frac{n!}{r!(n-r)!} \\ C(23,4)=\frac{23!}{4!(23-4)!} \\ C(23,4)=\frac{23!}{4!19!} \\ C(23,4)=\frac{23\cdot22\cdot21\cdot20}{4\cdot3\cdot2\cdot1} \\ C(23,4)=\frac{212520}{24} \\ C(23,4)=8855 \end{gathered}[/tex]Answer: there are 8855 ways.
PLEASE HELP IT'S DUE NOW.. :(
Answers
Slope intercept form of equation of line f and line g is
Equation of line f
y = 1.75x + 3.5
Equation of line g
y = -4x - 8
First option is correct
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
Here,
For line f
The line passes through (2, 7) and (4, 10.5)
Slope =
[tex]\frac{10.5 - 7}{4 - 2}\\\frac{3.5}{2}\\\frac{7}{4}[/tex]
Equation of line =
[tex]y - 7 = \frac{7}{4}(x - 2)[/tex]
y = 1.75x - 3.5+7
y = 1.75x + 3.5
For line g
The line passes through (-3, 4) and (-2, 0)
Slope =
[tex]\frac{0-4}{-2-(-3))}\\-4[/tex]
Equation of line =
y - 4 = -4(x - (-3))
y - 4 = -4x-12\\
y =-4x-12+4\\
y = -4x-8
The first option is correct
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frequency The table and corresponding polygon show information about the waiting times of some patients at a dentist. Frequency What fraction of patients waited for more than 7 minutes? 10- 0- 5 6 7 8 Waiting time (x minutes) 9 10 x Waiting time (x minutes) 5< x≤6 6< x≤7 7< x≤8 8< x≤9 9< x≤ 10
Answers
The 31 minutes for the lowest quartile of the waiting times of patients at this surgery.
Given that,
The histogram displays statistics about the average patient wait time in dental offices, expressed in minutes. 3.24 frequency The table and related polygon display data regarding some patients' wait periods at a dentist.
We have to find frequency How many patients waited for longer than seven minute.
The frequency of a given data value is the number of times it happens. We use f to represent a data value's frequency. For instance, if five students received As in science, the grade A was said to have a frequency of five.
In the picture we can see the answer.
Therefore, The 31 minutes for the lowest quartile of the waiting times of patients at this surgery.
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From the graph , determine the value of x when F(x) = 4
Answers
for this we locate the point where y = 4, and find its ordered pair on the x-axis, and from the graph, x = - 3
answer: x = - 3
PLEASE HELP If each side has a scale factor of 1 in. to 5 ft., the actualperimeter is and the actual area isO 60 ft, 80 ftO 300 ft, 80 ft?80 ft, 60 ft280 ft, 300 ft
Answers
The perimeter is determine as the add of the sides of the figure. In this case:
[tex]P=(5+2+2+2+1+1+1+2)(5ft)[/tex][tex]P=16(1in5tf)=80ft[/tex]For the area we will divide the figure as follow:
The total area will be:
[tex]A=A_a+A_b[/tex]We find the are of a rectangle by:
[tex]A=h\cdot b[/tex]Where h is height and b is base
Then:
[tex]A_a=5\cdot2=10[/tex][tex]A_b=2\cdot1=2[/tex]Then the total area is:
[tex]A=10+2=12^{\doubleprime}[/tex]In feets:
[tex]12(5ft)=60ft^2[/tex]Isosceles triangle JKL has a perimeter of 36 units and the given vertices.
J (-3, -9)
K (-3, 7)
L (X, -1)
What is the possible x-coordinate for point L?
Answers
The possible x-coordinate for point L are x = (-16.85)(10.85)
What is perimeter?For geometry, the perimeter of the shape is defined as the total length of the boundary. The perimeter is determined by adding all the sides and side lengths that enclose the shape. It is measured in units such as centimeters, meters, feet and inches,
For the given question:
JK = [tex]\sqrt{(-3-(-3))^{2}+(-9-7)^{2} }[/tex]
JK = [tex]\sqrt{0^{2} +16^{2} }[/tex]
JK = 16
JL = [tex]\sqrt{(-3-x)^{2} +(-9-(-1))^{2} }[/tex]
JL = [tex]\sqrt{(-3-x)^{2} + 8^{2} }[/tex]
JL = [tex]\sqrt{(-3-x)^{2} + 64}[/tex]
KL = [tex]\sqrt{(-3-x)^{2} + (7-(-1))^{2} }[/tex]
KL = [tex]\sqrt{(-3-x)^{2} + 8^{2} }[/tex]
KL = [tex]\sqrt{(-3-x)^{2} + 64}[/tex]
Since, JK + JL+ KL = 36 [Perimeter of triangle]
As we have already calculated, JK = 16
So, 16 + JL+ KL = 36
JL+ KL = 36 - 16
JL+ KL = 20
Since JKL is an isosceles triangle, JL= KL
So, let's replace KL by JK in the above equation:
JL+ JL = 20
2JL = 20
JL = 10
Now, substitute the value of JL in following equation:
JL = [tex]\sqrt{(-3-x)^{2} + 64}[/tex]
16 = [tex]\sqrt{(-3-x)^{2} + 64}[/tex]
Now square both sides,
256 = (-3-x)² + 64
256-64 = (-3-x)²
192 = (-3-x)²
13.85 = -3-x
x = -3 ± 13.85
x = (-3 - 13.85) (-3 + 13.85)
x = (-16.85)(10.85)
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1 months amren 5 movies and 3 video games for a total of $36. the next month he went 7 movies and 9 video games for a total of $78. find the rental cost for each movie in each video game.rental cost for each movie:rental cost for each video games:
Answers
Each movie cost $3.75 while each video game cost $5.75
Here, we want to get rental costs
We start by using variables to represent the costs of the movie and the video game
Let the cost of a movie be m and the cost of a video game be g
Thus, we have it that;
[tex]5m\text{ + 3g = 36}[/tex]and;
[tex]7m\text{ + 9g = 78}[/tex]So, we have two equations to solve simlutaneously
That would yield;
[tex]\begin{gathered} \text{From i;} \\ 5m\text{ + 3g = 36} \\ 3g\text{ = 36-5m} \\ we\text{ can have equation }ii\text{ as;} \\ 7m\text{ + 3(3g) = 78} \\ 7m\text{ + 3(36-5m) = 78} \\ 7m\text{ + 108-15m = 78} \\ 108-78\text{ = 15m-7m} \\ 8m\text{ = 30} \\ m\text{ = }\frac{30}{8} \\ m\text{ = \$3.75} \end{gathered}[/tex]Now, to get the value of g, we make a substitution into any of the equations;
[tex]\begin{gathered} 3g\text{ = 36-5m} \\ 3g\text{ = 36-5(3.75)} \\ 3g\text{ = 36-18.75} \\ 3g\text{ = 17.25} \\ g\text{ = }\frac{17.25}{3} \\ g\text{ = 5.75} \end{gathered}[/tex]Determine the solution to the inequality. |4x − 4| ≥ 8 x ≤ −1 or x ≥ 3 x ≤ −2 or x ≥ 3 x ≤ −3 or x ≥ 4 x ≤ −4 or x ≥ 4
Answers
The solution to the inequality will be -
x ≥ 3 or x ≤ -1
What is an Inequality? What is a expression? What is a mathematical equation?An inequality in mathematics compares two values or expressions, showing if one is less than, greater than, or simply not equal to another value.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.We have the given inequality as -
|4x − 4| ≥ 8
We have the inequality as -
|4x − 4| ≥ 8
4x - 4 ≥ 8 or 4x - 4 ≤ - 8
4x ≥ 12 or 4x ≤ - 4
x ≥ 3 or x ≤ -1
Therefore, the solution to the inequality will be -
x ≥ 3 or x ≤ -1
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if p=3x+4 and v=x+5, find pv-2p+v
Answers
Use substitution to simplify the expression.
pv - 2p + v
(3x + 4)(x + 5) - 2(3x + 4) + x + 5
3x² + 15x + 4x + 20 - 6x - 8 + x + 5
3x² + 15x + 4x + x - 6x + 20 + 5 - 8
3x² + 14x + 17
which exponential function has an x- intercept?(picture of functions below )
Answers
Question: which exponential function has an x-intercept?
Explanation:
Let the function:
[tex]f(x)=100^{x\text{ -5 }}\text{ - 1}[/tex]An x-intercept or zero of the function is when y= f(x)=0. In this case, notice that this occurs when x=5, since:
[tex]f(5)=100^{5\text{ -5 }}\text{ - 1= 100}^0\text{ - 1 = 1-1 =0}[/tex]thus, this function must cross the x-axis at the point x= 5. On the other hand, this function has a horizontal asymptote at y=-1, so the range of this function would be all y > -1. This fact further evidences that this function crosses the x-axis.
Answer: we can conclude that the correct answer is:
[tex]f(x)=100^{x\text{ -5 }}\text{ - 1}[/tex]