Answer:
[tex]x=\dfrac{\pi }{3}+2\pi n, \quad x=\dfrac{5\pi }{3}+2\pi n,\quad x=2\pi n,\quad x=\pi+2\pi n[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.5 cm}\underline{Trigonometric Double Angle Identities}\\\\$\sin (A \pm B)=\sin A \cos B \pm \cos A \sin B$\\\\$\cos (A \pm B)=\cos A \cos B \mp \sin A \sin B$\\\\$\tan (A \pm B)=\dfrac{\tan A \pm \tan B}{1 \mp \tan A \tan B}$\\\end{minipage}}[/tex]
Given equation:
[tex]\tan (x + \pi) + \sin(x + \pi) + \sin(x - \pi)=0[/tex]
Simplify using the double angle identities:
[tex]\implies \dfrac{\tan x + \tan \pi}{1 -\tan x \tan \pi} + \sin x \cos \pi+\cos x \sin \pi + \sin x \cos \pi -\cos x \sin \pi=0[/tex]
[tex]\implies \dfrac{\tan x + 0}{1 -\tan x(0)} + \sin x (-1)+\cos x (0) + \sin x(-1) -\cos x (0)=0[/tex]
[tex]\implies \dfrac{\tan x}{1} -\sin x - \sin x=0[/tex]
[tex]\implies \tan x-2\sin x =0[/tex]
Use the tan identity to rewrite tan(x) in terms of sin(x) and cos(x):
[tex]\implies \dfrac{\sin x}{ \cos x}-2\sin x=0[/tex]
Multiply both sides by cos(x):
[tex]\implies \dfrac{\sin x\cos x}{ \cos x}-2\sin x\cos x=0(\cos x)[/tex]
[tex]\implies \sin x-2\sin x \cos x=0[/tex]
Factor out sin(x) from the left side of the equation:
[tex]\implies \sin x(1-2 \cos x)=0[/tex]
Apply the zero-product property.
Case 1
[tex]\implies \sin x=0[/tex]
[tex]\implies x=\sin^{-1}(0)[/tex]
[tex]\implies x=2\pi n, \; \pi+2\pi n[/tex]
Case 2
[tex]\implies 1-2 \cos x=0[/tex]
[tex]\implies 1=2 \cos x[/tex]
[tex]\implies \cos x=\dfrac{1}{2}[/tex]
[tex]\implies x= \cos ^{-1} \left(\dfrac{1}{2}\right)[/tex]
[tex]\implies x=\dfrac{\pi }{3}+2\pi n, \;\dfrac{5\pi }{3}+2\pi n[/tex]
Solution
[tex]x=\dfrac{\pi }{3}+2\pi n, \quad x=\dfrac{5\pi }{3}+2\pi n,\quad x=2\pi n,\quad x=\pi+2\pi n[/tex]
Amir want to proportionally increae the ize of a photo to create a poter for hi room. The ize of the original photo i hown. Complete the tatement and then anwer the quetion to repreent way that Amir can increae the ize of hi photo
The height of the poster is 20 inches.
The original width of the poster was 6 inches. The original height of the poster was 4 inches. The size of the poster is scaled up. This is a transformation of the size of the poster. The width of the scaled-up poster is 30 inches. We need to find out the height of the scaled-up poster.
The scaling transformation preserves the shape of the object. This means the sides must still be in the same proportion. Let the constant of proportionality be represented by the variable "k".
30 = k*6
k = 30/6
k = 5
Hence, the poster is scaled up by a factor of five.
H = k*4
H = 5*4
H = 20
Hence, the height of the scaled-up poster is 20 inches.
The complete question is given below.
Amir wants to scale up a photo to create a poster for his room. The original picture is 6 inches in width and 4 inches in height. What will be the height of the poster if its width is 30 inches?
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The Tran family and the Campbell family each used their sprinklers last summer. The water output rate for the Tran family's sprinkler was 35 L per hour. The water output rate for the Campbell family's sprinkler was 25 L per hour. The families used their sprinklers for a combined total of 65 hours, resulting in a total water output of 1925 L. How long was each sprinkler used?
The time in hours for the Tran family's sprinkler will be 30 hours.
The time in hours for the Campbell family's sprinkler will be 35 hours.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The water output rate for the Tran family's sprinkler was 35 L per hour.
The water output rate for the Campbell family's sprinkler was 25 L per hour.
And, The families used sprinklers for a combined total of 65 hours, which is resulting in a total water output of 1925 L.
Now,
Let time in hours for the Tran family's sprinkler = t
And, The time in hours for the Campbell family's sprinkler = 65 - t
So, We can formulate by the given condition,
⇒ 35t + 25 (65 - t) = 1925
Solve for t as;
⇒ 35t + 25 (65 - t) = 1925
⇒ 35t + 1625 - 25t = 1925
⇒ 10t + 1625 = 1925
⇒ 10t = 1925 - 1625
⇒ 10t = 300
⇒ t = 30
Thus, The time in hours for the Tran family's sprinkler = t
= 30 hours
And, The time in hours for the Campbell family's sprinkler = 65 - t
= 65 - 30
= 35 hours.
Therefore, we get;
The time in hours for the Tran family's sprinkler will be 30 hours.
The time in hours for the Campbell family's sprinkler will be 35 hours.
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My science class is pretty small. There are just 18 students in the class. My
teacher, Ms. Microbe, has an unusual system for pairing us up for labs. She
has given each of us a number from 1 through 18, and on lab days, she pulls
our numbers out of a bag to determine who is paired with whom. When we
did our last lab, I happened to notice that the sum of each person's number
with his/her lab, partner's number was a perfect square!
How were the partners assigned?
The partners are assigned in the form of (1, 15) (2, 14) (3, 13) (4, 12) (5, 11) (6, 10) (18, 7) (17, 8), and (16, 9).
Square numbers:A square number, also known as a perfect square, is an integer that is the square root of another integer, or the result of multiplying another integer by itself.
For example:
Square of 2 = 4
Square of 3 = 9
Square of 4 = 16
Here we have
A science class is pretty small
There are just 18 students in the class.
The teacher gave each of them numbers from 1 through 18 on lab days
Start from 1 and find by adding which number we will get a square number
Here 1 + 15 = 16
2 + 14 = 16
3 + 13 = 16
4 + 12 = 16
5 + 11 = 16
6 + 10 =16
After the above combinations, the remaining numbers are
7, 8, 9, 16, 17, 18
which can be added as given below to get square number 25
=> 18+7=25
=> 17+8=25
=> 16+9=25
Therefore,
The partners are assigned in the form of (1, 15) (2, 14) (3, 13) (4, 12) (5, 11) (6, 10) (18, 7) (17, 8), and (16, 9)
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Find the equation of the linear function represented by the table below in slope-
intercept form.
The equation of the linear function represented by the table would be y = 4x - 1.
What is the slope-intercept form of the line?
When you know the slope of the line to be examined and the point given is also the y-intercept, you can use the slope-intercept formula
y = mx + c.
The y value of the y-intercept point is represented by c in the formula.
By using the given table,
for x = 0 , y = -1
so by using the slope-intercept form of the line, we can write
y = mx + c
-1 = m(0) + c
c = -1 ----------(I)
Then for x = 1, y = 3
again by using the slope-intercept form of the line, we can write
y = mx + c
3 = m(1) + (-1) -----from (I)
3 = m - 1
⇒ m = 3 + 1
⇒ m = 4 -----------(II)
Now by using (I) and (II), we can make a linear function by using the slope-intercept form of the line
y = 4x - 1
Hence, the equation of the linear function represented by the table would be y = 4x - 1.
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a) 110⁰
b) 70⁰
c) 73⁰
d) 115⁰
Answer:I think is am B
Step-by-step explanation:
Step-by-step explanation:
(5x)°+(3x+4)°=180°
5x+3x+4=180
8x=176
x=22
D=5x
D=110°
answer this and u a big W if u dont ur a L
Answer:
Part A. (4,5)
Part B. (9,7)
Step-by-step explanation:
Look at the x an y. X is bottom numbers Y is the vertical numbers. Look at A then B and boom you would get what i got.
What is the value of 5.53?
The value of 3 in 5.53 is 3 hundredths.
What is place value?It is important to note that place values can be defined as the value that's represented by a digit based on the position that it takes. In mathematics, place value refers to the position or location of a digit in a number.
Each digit has a specific place in a number. The position of each digit will be expanded when we represent the number in general form. Those positions begin with a unit place, also known as one's position.
In this case, we want to know the value of 3 in 5.53. It should be noted that the first 5 is 5 ones, the second 5 is 5 tenths and the 3 is 3 hundredths.
Therefore, it's 3 hundredths.
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Complete question
What is the value of 3 in 5.53?
point A is located at (-2,-6) on the coordinate plane. Point A is reflected over the y-axis to create point A’. What ordered pair describes the location of A’?
The ordered pair coordinates of A' are (2, -6) if A is reflected over the y-axis.
What are transformations?The transformation, or f: X → X, is the name given to a function, f, that maps to itself. After the transformation, the pre-image X becomes the picture X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation. A function can be moved in one way or another using translation, rotation, reflection, and dilation. A function can also be scaled using rotation around a point.
The coordinates of A are (-2, -6).
Point A is reflected over the y- axis to create point A'
(x, y) → (-x,y)
A (-2, -6) → A' (- (-2), -6))
So, the coordinates of A' are (2, -6).
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The map shows a portion of downtown Mapledale. Main Street and 2nd Avenue are parallel. Use the map to answer each question. Question Angle Which angle is an alternate exterior angle to angle 8? Which angle is a same-side interior angle to angle 2? Which angle is a corresponding angle to angle 3?
a. Angle 4 is an alternate exterior angles to angle 8.
b. Angle 3 is same-side interior angle to angle 2.
c. Angle 1 is corresponding angles to angle 3.
What are Corresponding Angles?Corresponding angles are located on the same corner and on the same side of a transversal.
For example, in the given image below, angles 1 and 3 are corresponding angles.
What are Alternate Exterior Angles?Alternate exterior angles are any two exterior angles that lie on two different parallel lines but on alternate sides of the transversal that crosses the two parallel lines.
For example, in the image given, angles 8 and 4 are alternate exterior angles.
What are Same-side Interior Angles?Same-side interior angles are interior angles that are located on the same side of the transversal but on different parallel lines that the transversal cuts across.
For example, angles 2 and 3 are same-side interior angles as seen in the given image.
What are Corresponding Angles?Corresponding angles are located on the same corner and on the same side of a transversal.
For example, in the given image below, angles 1 and 3 are corresponding angles.
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Which of The following Best describes the transformation of Y=x^2 so that the resulting equation is as follows?
Y=(x-3)^2+4
By using the concept of translation, it can be inferred that
The graph of the equation is translated 3 units to the left and 4 units down
What is translation?
Translation is a transformation which changes the position of a figure without changing the shape and size of the figure.
The given equation is
[tex]y = (x +3)^2 + 4[/tex]
This means the parabola [tex]y = x^2[/tex] is first translated 3 units to the left and then translated 4 units up.
So the first option is correct.
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During a bean bag toss, Abby threw the bean bag 2.2 meters. Which of the following values are not equivalent to 2.2
The values are not equivalent to 2.2 include
2.6 - 0.6
1.8 + 2.5
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.
In this case, 2.6 - 0.6 will be:
= 2.6 - 0.6
= 2.0
Also, 1.8 + 2.5 will be:
= 1.8 + 2.5
= 4.3
Therefore, they're not equivalent to 2.2
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Complete question
During a bean bag toss, Abby threw the bean bag 2.2 meters. Which of the following values are not equivalent to 2.2
1.2 + 1.0
2.6 - 0.6
0.9 + 1.3
1.8 + 2.5
Will give brainliest. Please it needs to be correct. Refer to the image
Answer: D
PLEASE GIVE BRAINLIEST THANK YOU!!!
a group of 350 people includes 187 play the flute, 172 play the clarinet, and 47 both the flute and the clarinet. a person is selected at random. 1. what is the probability that he/she plays the clarinet but not the flute? a. 0.4213 b. 0.3571 c. 0.7812 d. 0.4587 e. 0.2743 2. what is the probability that he/she plays exactly one of these types of instruments? a. 0.7821 b. 0.2457 c. 0.5057 d. 0.7571 e. 0.3645 3. what is the probability that he/she plays at most one of these instruments? a. 0.7514 b. 0.9245 c. 0.5151 d. 0.2486 e. 0.8657
Using probability concepts, we calculated that the likelihood that the person plays the clarinet but not the flute is 0.2743.
What is conditional probability?The possibility of an event or outcome occurring based on the existence of a prior event or outcome is known as conditional probability. It is calculated by dividing the likelihood of the previous event by the likelihood of the subsequent, or contingent, event.
Here,
Finding people who can play the clarinet but not the flute is necessary. There are 172 people who can play the clarinet.
There are 47 people who can play both the clarinet and the flute.
As a result, 172-47=125 represents the number of people who can only play the clarinet and not the flute.
Probability(P),
P=( 125 / 350)
P=0.2743.
Therefore, the probability that a single person chosen at random can play clarinet but not flute is 0.2743.
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The area of a rectangle is given as 90 cm² and the length is 3 cm longer than its width. Find the length and the width of the rectangle.
Answer:
Step-by-step explanation:
Area of a rectangle is given by the formula :
A = L × W
Substituting 90 with A , x with W and (x+3) with L, we get :
90 = (x+3)×x
Simplifying the right side by expanding the bracket :
x(x+3) =
x²+3x
90=x²+3x
Now we can make a quadratic by subtracting both sides by 90 :
x²+3x-90 =0
I'm not sure about the rest
Segment RS is reflected over the line y = and then translated by (x +3, y + 4). The resulting segment
R" S" has coordinates R" (-1,4) and S" (-3,-2). What are the coordinates of the segment RS?
R=
S =
Answer:
-1,-2
Step-by-step explanation:
get the x and y value and combine the coordinates using the slope formula
If you rotate point A(-3,4) 180 degrees clockwise and then rotate it again 90 degrees counter clockwise what would be the coordinates of A"?
(3,-4)
(4,3)
(-4,-3)
(-3,-4)
The coordinates of A'', applying the two rotations, are given as follows:
A'' (4, 3).
What is a rotation?A rotation is one example of transformation that a function can undergo, in which the congruence and similarity of the images are kept but the orientation of the image changes.
The rules for each possible rotation are given as follows:
90° clockwise rotation: (x,y) -> (y,-x).90° counterclockwise rotation: (x,y) -> (-y,x).180° clockwise and counterclockwise rotation: (x, y) -> (-x,-y).270° clockwise rotation: (x,y) -> (-y,x).270° counterclockwise rotation: (x,y) -> (y,-x).The original coordinates are given as follows:
A(-3,4).
After the first 180º clockwise rotation, the coordinates are:
A'(3,-4).
(signals exchanged)
After the final rotation, the 90º counterclockwise rotation, the coordinates of A'' are given as follows:
A'' (4, 3).
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Evaluate -7(x - 4y) when x = -4 and y = -6.
A 140
B 52
C-28
D-140
Answer: D
Step-by-step explanation:
Take the equation and substitute the variables for the numbers given
-7(-4-4(-6))=-140
Hope this helps :)
PLEASE HELP!
3. In a survey of 1000 eligible voters selected at random, it was found that 8% had a college degree. Additionally it was found that 80% of those who had a college degree voted in the last presidential election. Whereas 55% of the people who did not have a college degree voted in the last presidential election. Assuming that the poll is representative of all eligible voters, find the probability that an eligible voter selected at random voted. Draw a diagram to represent this situation.
a) If you randomly chose an eligible voter from this group, what is that probability that they have a degree and did not vote?
b) If you randomly chose an eligible voter from this group, what is the probability that they voted?
c) If you randomly chose a person who voted in the presidential election, what is the probability that they had a college degree?
hello, i'm sorry but i can't graph the diagram but here are the answers for a-c :)
A. 8%
B. 39.6%
C. 58.4%
step by step:
A. Calculation to determine the probability of The voter had a college degree and voted in the last presidential election.
P = 80/1,000
P=0.08*100
P=8%
Therefore the probability of The voter had a college degree and voted in the last presidential election will be 8%
B. Calculation to determine the probability of The voter did not have a college degree and did not vote in the last presidential election.
P =396/1000
P=0.396*100
P=39.6%
Therefore the probability of The voter did not have a college degree and did not vote in the last presidential election will be 39.6%
C. Calculation to determine the probability if The voter voted in the last presidential election.
P = 584/1,000
P=0.584*100
P=58.4%
Therefore the probability if The voter voted in the last presidential election will be 58.4%
Given:-16=m-18;Prove:m=10
Answer:
m=2
Step-by-step explanation:
-16=m-18
-16+18=m
2=m
Ada lives 12 4/5 miles from her aunt's house. she lives 17 3/8 miles from her grandmother's house. how many more miles does jada live from her grandmother's house than her aunt's house?
Answer:
[tex]4 \frac{23}{40}\; \rm miles[/tex]
Step-by-step explanation:
To find how many more miles Ada lives from her grandmother's house than her aunt's house, we need to subtract the distance to her aunt's house from the distance to her grandmother's house.
Ada lives 17 3/8 miles from her grandmother's house.
Ada lives 12 4/5 miles from her aunt's house.
Convert both mixed numbers into improper fractions by multiplying the whole number by the denominator of the fraction, adding this to the numerator of the fraction, and placing the answer over the denominator:
[tex]17 \frac{3}{8}=\dfrac{17 \cdot 8+3}{8}=\dfrac{139}{8}[/tex]
[tex]12 \frac{4}{5}=\dfrac{12 \cdot 5+4}{5}=\dfrac{64}{5}[/tex]
As both improper fractions have a different denominator, we need to change both fractions into equivalent fractions with the same denominator. To do this, find the least common multiple (LCM) of the denominators, 8 and 5.
The LCM of 8 and 5 is 40. Therefore, convert the fractions into their equivalent fractions (with 40 as their denominator) by multiplying the numerator and denominator by the same number:
[tex]\dfrac{139}{8}=\dfrac{139 \cdot 5}{8 \cdot 5}=\dfrac{695}{40}[/tex]
[tex]\dfrac{64}{5}=\dfrac{64 \cdot 8}{5 \cdot 8}=\dfrac{512}{40}[/tex]
Now the fractions have the same denominator, we can carry out the subtraction by simply subtracting the numerators:
[tex]\dfrac{695}{40}-\dfrac{512}{40}=\dfrac{695-512}{40}=\dfrac{183}{40}[/tex]
Finally, convert the improper fraction into a mixed number by dividing the numerator by the denominator:
[tex]183 \div 40=4\;\rm remainder \;23[/tex]
The mixed number answer is the whole number and the remainder divided by the denominator:
[tex]4 \frac{23}{40}[/tex]
Therefore, Ada lives 4 23/40 miles more from her grandmother's house than her aunt's house.
What are the first 5 terms
The first five terms of the given sequence are a₁ = 50, a₂ = 25, a₃ = 12.5, a₄ = 6.25 and a₅ = 3.125.
What is a geometric sequence?In a geometric sequence the ratio of any two consecutive terms are equal. This ratio is known as the common ratio of the sequence.
Given that,
a₁ = 50 and aₙ = aₙ₋₁ ÷ 2
The first five terms are a₁, a₂, a₃, a₄ and a₅.
All the terms can be written using aₙ = aₙ₋₁ ÷ 2 as follows,
a₂ = a₁ ÷ 2
⇒ a₂ = 50 ÷ 2
⇒ a₂ = 25
a₃ = a₂ ÷ 2
⇒ a₃ = 25 ÷ 2
⇒ a₃ = 12.5
a₄ = a₃ ÷ 2
⇒ a₄ = 12.5 ÷ 2
⇒ a₄ = 6.25
a₅ = a₄ ÷ 2
⇒ a₅ = 6.25 ÷ 2
⇒ a₅ = 3.125
Hence, the first five terms are 50, 25, 12.5, 6.25 and 3.125 respectively.
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when the 171st even positive integer is subtracted from the 219th odd positive integer, the result is z. Find z.
a new car model is available with 5 choices of color, 3 choices of transmission and 4 types of interior. how many different variations of this model car are possible?
In 120 different variations of this model car are possible.
Define multiplication.One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of identical size. Let's use the ice creams as a multiplication example to help us comprehend. There are two such groupings, and each group has ice cream.
Calculating the sum of two numbers multiplied together is the process of multiplication. Simple tests in addition, subtraction, multiplication, and division will be given. 2. a noncount noun The process or occurrence of something of a certain kind multiplying occurs when their quantity or number increases.
Given,
There are five different ways to choose a car's color.
3 different car transmission selection options are available.
There are four different interior automobile selection options.
There are two different ways to pick a car's engine.
The potential number of car variations is thus:
Multiplying:
5 × 3 × 4× 2
120
In 120 different variations of this model car are possible.
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reduce with all steps
Use the diagram and the given angle measure to find the other three measures
The other three measures are:
∠1 = 159°∠2 = 21°∠4 = 21°What is Angle?An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.This, I assume, refers to two lines that cross and create four angles.
The sum of the additional angles 2 and 3 is 180°.Angles 2 and 3 equal 180°.159⁰ + angle 2 = 180⁰angle 2 = 180⁰ - 159⁰angle 2 = 21⁰The same applies to angles 2 and 4 since angles 1 and 3 are vertical angles.
Since vertical angles are congruent in measure, it is simple to determine their measurements.
Hence, the three measures are:
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Ms. Galindo’s class has adopted two equal sections of a highway to keep clean. The combined length of the two sections is
6/8
of a mile. How long is each section?
Each section of a highway has length of 1.5 miles.
In this question, Ms. Galindo’s class has adopted two equal sections of a highway to keep clean.
We need to find the length of each section.
Let each section measures x mile.
The combined length of the two sections is 6/8 of a mile.
So, we get an equation x + x = 6/8
We solve above equation to find the value of x.
2x = 6/8
x = (6/8) / 2
x = 6/4
x = 1.5
Therefore, each section of a highway has length of 1.5 miles.
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Find the equation of a line parallel to 6x + y = -8 that passes through the point (7, 7).
The equation of a line parallel to 6x + y = -8 that passes through the point (7, 7) is y = -6x + 49
The equation of the parallel line is given
6x + y = -8
y = -8 -6x
y = -6x - 8
The slope intercept form is
y = mx + b
Where m is the slope of the line
b is the y intercept
Comparing the equation
Slope of the line m = -6
The slope of the all the parallel lines will be equal
Then line is passing through the point (7, 7)
The point slope form is
[tex]y-y_1=m(x-x_1)[/tex]
Substitute the values in the equation
y-7 = -6(x-7)
y - 7 = -6x + 42
y = -6x +42 +7
y = -6x + 49
Hence, the equation of a line parallel to 6x + y = -8 that passes through the point (7, 7) is y = -6x + 49
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A fast food restaurant was selling 2 boxes of chicken nuggets for $4.52
A competing restaurant was selling 4 boxes of chicken fingers for $9.44
Which food has a higher unit price?
Answer: The competing restaurant
Step-by-step explanation:
If you divide the 4.52 by 2 you get 2.26 for the first restaurant's unit price
If you divide the 9.44 by 2 you get 2.36 for the second restaurant's unit price
Hope this helps :)
Chelsea has final exams in calculus, physics, and history.
She has up to 25 hours to study for exams. She plans to
study history for 2 hours. She needs to spend at least 7
hours studying for calculus, but over 14 is too much.
She hopes to spend between 8 and 12 hours on physics.
Write and graph a system of inequalities to represent
the situation.
Answer:
x-variable y-variable Inequalities
calculus physics 7≤x≤14
8≤y≤12
x+y≤23
Step-by-step explanation:
The table represents points on a line. What is the slope
X 1 4 7 10
Y 8 6 4 2
Answer:
slope = - [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (1, 8) and (x₂, y₂ ) = (10, 2) ← 2 ordered pairs from the table
m = [tex]\frac{2-8}{10-1}[/tex] = [tex]\frac{-6}{9}[/tex] = - [tex]\frac{2}{3}[/tex]