In the coordinate plane, line p has slope 1/3 and y-intercept (0, 2). Line r is the result of dilating line p by a factor of 3 centered at the origin. What are the slope and y-intercept of line r?.
The line r has a slope 1/3 and y-intercept (0,5)
What is the Dilation?
Math definition of dilation Resizing an object is accomplished through a change called dilation. The objects can be enlarged or shrunk via dilation. A shape identical to the source image is created by this transformation. The size of the form does, however, differ.
Given
The slope of the line and its intercept (0,2)
The slope of the line r will not change.
And intercept is the addition of their ordinate will be.
Intercept = 2+3
Intercept = 5
So, the line r has slope 1/3 and y-intercept (0,5).
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A farmer buys a tractor for 50,000. If the tractor depreciates 10% per year, what is the value of the tractor in 7 years? :)))
Answer:
In order to complete the equation we need to use this method :
Remaining Amount = I(1-r)^tI=Initial AmountR=DECAY rateT=Time periods(Exponential Decay btw if you didnt know is when a population or group of something is declining, and the amount that decreases is proportional to the size of the population)
Now that we know that Time for Some Exponential Decay fun :D *sarcasm* :p
The farmer purchased a tractor for 50,000 so you start with that:
Remaining Amount = 50,000(1-r)^t
Decay rate would be 0.10 because you have to CONVERT 10% to decimal form.
Remaining Amount = 50,000(1-0.10)^t
Now time period would be 7 of course:
Remaining Amount = 50,000(1-0.10)^7
TIME TO SOLVE:
Answer 23914.845 BUT you have to round to nearest cent so then the answer would be:
23914.85Step-by-step explanation:
I learned this in my math class. ~Good------Night
Answer:
$23,914.85 (nearest cent).
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]
The given scenario can be modelled as an exponential equation.
The initial value (a) is the purchase cost of the tractor.
As the tractor depreciates by 10% each year, the value of the tractor is 90% of the previous year's value. Therefore, the base (b) is 0.9.
Therefore, the equation is:
[tex]\boxed{y=50000(0.9)^x}[/tex]
where:
x is time (in years).y is the value of the tractor (in dollars).To find the value of the tractor in 7 years, substitute x = 7 into the equation:
[tex]\implies y=50000(0.9)^7[/tex]
[tex]\implies y=50000 \times 0.4782969[/tex]
[tex]\implies y=23914.845[/tex]
Therefore, the value of the tractor in 7 years is $23,914.85 (nearest cent).
On the horizontal number line, -62 is located to the right of
-90. Enter an inequality that represents this statement
Inequality that represents this statement is -90 < -62
What is inequality?Inequality simply means that two things aren't equal. One of the items might be inferior to, superior to, greater than, or equivalent to the other things.P ≠ q denotes that p and q are not equal.When p < q, p is less than q.When p > q, p is bigger than q.If p is smaller than or equal to q, the expression is "p ≤ q".If p and q are equal and p is greater than q, then "p ≥ q".
Hence, the if on the horizontal number line, -62 is located to the right of
-90. The inequality that represents this statement is -90 < -62
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Please help
I don’t understand
The expression for the perimeter of the rectangle is 34u - 10 centimeters.
Perimeter of the rectangle:
Perimeter is known as the total length or distance of its boundary on all sides.
The formula that is used to calculate the perimeter of a rectangle is, perimeter of a rectangle = 2(l + w),
where 'l' is the length and
'w' is the width of the rectangle.
Given,
The width of the rectangle is (10u + 3) and the length of the rectangle is (7u - 8)
Now, we need to find the perimeter of the rectangle.
We know that the formula of the rectangle is
Perimeter = 2(l + w)
where l refers the length that is (7u - 8) and w refers the width that is (10u + 3).
Now, we have to apply these values on the formula, then we get,
=> Perimeter = 2((7u -8) + (10u + 3)
When we simplify the equation, then we get,
=> Perimeter = 2((10u + 7u) + (-8 +3))
=> Perimeter = 2(17u - 5)
=> Perimeter = 34u - 10
Therefore, the perimeter of the rectangle is 34u - 10 centimeters.
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help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The amount owed by the debtor is $10865
How to determine the amount owed in six years?The given parameters about the compound interest are
Principal Amount, P = $5300
Interest Rate, R = 8%
Time, t = 6 years
To calculate the amount owed, we make use of the following formula
A = P + CI
Where
Compound interest, CI = P(1 + R)^t - P
So, the equation becomes
A = P + P(1 + R)^t - P
Evaluate the like terms
A = P(1 + R)^t
In this question, the formula is given as
A = P(1 + r/n)^nt
Where
n = 12, i.e compounded monthly
Substitute the known values in the above equation
A = 5300 * (1 + 8%/12)^(6*12)
Express 8% as decimal
A = 5300 * (1 + 0.08/12)^(6*12)
Evaluate the sum
A = 5300 * (1.01)^(6*12)
Evaluate the exponent
A = 5300 * 2.05
Evaluate the product
A = 10865
Hence, the value of the amount after 6 years is $10865
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You receive a gift certificate for a clothing store and plan to use it to buy T-shirts and sweatshirts. Describe a situation in which you can buy 9 T-shirts and 1 sweatshirt, but you cannot buy 3 T-shirts and 8 sweatshirts. Write and graph a system of linear inequalities that represents the situation.
A situation in which the person can afford 9 t-shirts and one 1-sweatshirts, but not 3 T-shirts and 8 sweatshirts are when the value of the gift card is $100 and the price of each t-shirt is $10.
What is inequality?The relation between two unequal expressions is defined as inequality.
Given that, the person can afford 9 T-shirts and 1 sweatshirt but not 3 t-shirts and 8 sweatshirts.
Let the value of the gift card be y.
Let the cost of one shirt and one sweatshirt be t and s respectively.
Then, the inequality for the condition that "the person can afford 9 T-shirts and 1 sweatshirt" is:
9t + s ≤ y
The inequality for the condition that " the person cannot afford 3 t-shirts and 8 sweatshirts" is:
3t + 8s > y
Now, let the person buys 1 sweatshirt in any situation, then from inequalities (1) and (2):
9t + 1 ≤ y
3t + 8 > y
Hence, the system of inequalities is:
9t + 1 ≤ y
3t + 8 > y
The graph of the inequalities is shown.
Let the value of the gift card be $100 and the price of each t-shirt is
t =$10, then
9(10) + 1 ≤ 100
91≤100, true
And,
3(10) + 8 > 100
38 > 100, false
Hence, a situation in which the person can afford 9 t-shirts and one 1-sweatshirts, but not 3 T-shirts and 8 sweatshirts are when the value of the gift card is $100 and the price of each t-shirt is $10.
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You and your friend are playing "Rock-Paper-Scissors." In this game, each of the two players chooses rock, paper, or scissors. Both players reveal their choice at the same time, and the winner is determined based on the choices. Rock beats scissors by smashing it, scissors beats paper by cutting it, and paper beats rock by covering it. If both players choose the same object, it is a tie. All the possible outcomes of the game are listed below. If we take outcomes 1,3,4,5,8,1,3,4,5,8,1, comma, 3, comma, 4, comma, 5, comma, 8, comma and 999 as a subset of the sample space, which of the statements below describe this subset?
As we already found, the probability of winning for any selection is 1/3 = 0.333.
What is probability?Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favourable outcomes / Number of samples
a) Let's suppose that player 1 chooses rock, and the selection of player 2 can be thought of as random.
If player 2 randomly selects rock, the result of the game is a draw.
if player 2 randomly selects papers, player 1 loses.
if player 2 randomly selects scissors, player 1 win.
Then we have 3 options with the same probability, that will be:
1/3
This is, the probability of winning is equal to the quotient between the number of outcomes that make player one win (1, in this case, scissors) and the total number of outcomes (3) = 1/3
the probability of a draw is equal to the quotient between the number of outcomes that make a draw (1, in this case, rock) and the total number of outcomes (3) = 1/3
The probability of losing is equal to the quotient between the number of outcomes that make player one lose (1, in this case, paper) and the total number of outcomes (3) = 1/3
The complete question is given below.
2. Almost everyone has played the rock-paper-scissors game at some point. Two players face each
other and, at the count of 3, make a fist (rock), an extended hand, palm side down (paper), or a
"V" with the index finger and middle fingers (scissors). The winner is determined by these rules:
rock smashes scissors, paper covers rock, and scissors cut paper. If both players choose the
same object, then the game is a tie. Suppose that Player 1 and Player 2 are both equally likely to
Choose rock, paper, or scissors.
a) Give a probability model for this change process.
b) Find the probability that Player 1 wins the game on the first throw.
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PLEASE HELP ANSWER CHOICES LESS THAN. GREATER THAN, THE SAME!!! WILL GIVE BRAINLYEST FOR CORRECT ANSWER AND IF YOU REMIND ME!!!!!!! HELP!
AnThe volume of prism is equal to volume of pyramid.
What is volume of prism?
The volume of a prism is defined as the total space occupied by the three-dimensional object.
The volume of a Rectangular Prism = lbh cubic units.
Where
l = Base width of a rectangular prism
b = Base length of a rectangular prism
h = height of a rectangular prism
What is volume of pyramid?
A triangular pyramid has a base in triangle shape. As we know, the area of a triangle;
A = 1/2 b x h
where b is the base of the triangle and h is the altitude.
But we have rectangular pyramid,
volume of rectangular pyramid = 1/3lbh
Given,
The length of prism= 3a
breadth = 2b
height = c
Therefore, volume of prism = 3a(2b)(c)
= 6abc
Similarly, length of pyramid = a
breath = b
height = 18c
volume of pyramid = 1/3(a)(b)(18)c
=6abc, which is equal to volume of prism.
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if 50 lbs = 22.68 kg, what is 15/8 y pounds in kilograms
The kilograms equivalent of the given pound measurement as required in the task content is; 0.8505 kg.
What is the equivalent measure in kilograms of 15/8 y pounds?It follows from the task content that the equivalent measure of 15/8 y pounds is to be determined according to the given conversion factor.
Since it is given that; 50 lbs = 22.68 kg.
It follows by proportion that; 15/8 pounds is equivalent to; ( (15/8) × 22.68 ) / 50
= 0.8505 kilograms.
Therefore, the required equivalent kilogram measure is; 0.8505 kilograms.
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I WILL GIVE BRAINLYEST
Kim purchased some school supplies. She bought pencils that costs $9.57 and notebooks that cost $12.78. What was the total cost of her school supplies before tax?
Answer:$22.35
Step-by-step explanation:
What is the slope of a line perpendicular to the line whose equation is 3x+18y=108.
The slope of the line which is perpendicular to the given line 3x+18y=108 is (6).
We already know the equation of a line in slope intercept form y = mx + b and we also know that perpendicular lines that have slopes which are negative reciprocals of each other.
Given a line 13x + 18y=108, this slope intercept form can be written as,
3x + 18y = 108
18y = 108 - 3x
y = (108 /18) - (3/18)x.
y = (6) - 1x/6.
y = -(1/6)x + 6.
Hence the slope of the given line is (-1/6), thus the slope of the line which is perpendicular is (6).
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What is the value of the expression below when z=4z=4?
8z-6
8z−6
Answer:
80y-24z
Step-by-step explanation:
Find the area of the sas triangle with side lengths 29 and 36 and included angle 62 degrees.
The area of triangle is 460.89 unit square.
Given:
lengths of rod, a = 29 and b = 36 ,
angle between them (θ) = 62
We know that in a general triangle of side a,b,c and angles A,B,C ,
we can write area of triangle (Δ) is
Δ = absinθ/2
Δ = 29*36sin62/2
Δ = 460.89 unit square.
hence, the area of triangle is 460.89 unit square.
#123
The area of the SAS triangle is 460.89 cm³.
Given data;
Side length (a) = 29
Side length (b) = 36
With an angle of Ф = 62°
Here, it is stated that the triangle is a SAS triangle which is known as the Side Angle Side triangle.
Now, to calculate the area of a given triangle, we use the formula as;
Area = a*b*sinФ/2
From the above formula;
Area of the SAS triangle = a*b*sinФ/2
= [29*36*sin(62°)]/2
= 460.89 cm³
Hence, the area of the SAS triangle is 460.89 cm³.
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A nack company can pack 12 granola bar in a box. How many boxe are needed for 600 granola bar?
50 boxes are needed to pack 600 granola bar when 12 granola bar in a single bar.
Given, a nack company that sells snacks may fit 12 granola bars in a box.
We must determine the number of boxes required to hold 600 granola bars.
By using the unitary technique, we can calculate both the value of multiple units from the value of a single unit and the value of single unit from the value of multiple units. We typically utilize this technique for math calculations. This approach will be helpful to you while tackling problems involving ratio and proportion, algebra, geometry, etc.
Now, the number of boxes= 600/12
=50
Therefore, to pack 600 granola bars they need 50 boxes.
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The director of a local ballet company needs to print the programs for the next performance. Janet’s Print Shop charges $0.25 per program plus a $35 set-up fee. The Printing Press charges $0.15 per program plus a $50 set-up fee. Which printing company offers the better deal if 200 programs are printed? Explain your reasoning. Find the number of programs for which the total costs are the same. Explain how you determined the number of programs.
Answer:
Printing press
Step-by-step explanation:
Janet's print shop - 0.25*200=50+35=85
Printing press - 0.15*200=30+50=80
3 5/8 divided by 1/2
Answer:
7 1/4
Step-by-step explanation:
convert to improper fraction 3 5/8 = 3x8/8 + 5/8 = 24+5/8 =29/8
divide 29/8 divided by 1/2 = 58/8
simplify 7 1/4
Hope this helps! <3
I need to learn about algebra 1 how would i get help?
Answer:
Step-by-step explanation:
Firstly, you would need to have someone teach you unless you don't then I'm sure there are courses online and to be excellent at it, practice a lot of questions and do diagnostic questions for each topic.
What is this? Please help.
-3.2(2.6)
Answer: I believe the answer is -8.32
Answer:
Step-by-step explanation:−8.32
Dave opens a savings account that has an annual simple interest rate of 0.15%. If he initially deposits $10,000, find the amount in the savings account after 5 years. $
The total amount in his savings account after 5 years will be $10,075 if the annual simple interest rate is 0.15%.
According to the question,
We have the following information:
Dave opens a savings account that has an annual simple interest rate of 0.15%. He initially deposits $10,000 and the time given is 5 years.
We know that following formula is used to find simple interest:
Principal*rate*time/100
(10000*0.15*5)/100
100*0.15*5
$75
Now, the total amount will be the sum of interest and the principal amount:
10000+75
$10,075
Hence, the total amount in his savings account after 5 years will be $10,075 if the annual simple interest rate is 0.15%.
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Juan has three rain sticks measuring 8 inches 6 inches and 12 inches each. What is the least common multiple of 8, 6 and 12?
A. 12
B. 24
C. 48
D. 96
Answer:
24
Step-by-step explanation:
LCM 8 ,6 ,12 =24
by PRIME factorization
8 = 2 x 2 x 2
6 = 2 x 3
12 = 2 x 2 x 3
2 x 2 x 2 x 3 =24
write an equation of the line that passes through point p and is perpendicular to the line with the given equation.
The equation of the perpendicular line is y = (1/8)x + 15/4.
We are given the equation of a straight line. The equation is y = -8x - 3. The slope of the given line is -8. We need to find the equation of the straight line that is perpendicular to the given line and passes through the coordinates (2, 4).
The slope of the perpendicular line will be the negative reciprocal of the slope of the given line. Let the slope of the perpendicular line be represented by the variable "m".
m = -1/(-8) = 1/8
The equation of the perpendicular line using the slope-point form can be written as given below.
y = mx + c
y = (1/8)x + c
The line passes through the point (2, 4).
4 = (1/8)2 + c
4 = (1/4) + c
c = 4 - (1/4)
c = 15/4
Hence, the equation of the perpendicular line is y = (1/8)x + 15/4.
The complete question is given below.
Write an equation of the line that passes through point p and is perpendicular to the line with the given equation.
P (2, 4)
y = -8x - 3
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What’s the answer for 3(2x+5)+2x=7?
Answer:
x=5+1/2
Step-by-step explanation:
3(2x-5)-2x=7
We move all terms to the left:
3(2x-5)-2x-(7)=0
We add all the numbers together, and all the variables
-2x+3(2x-5)-7=0
We multiply parentheses
-2x+6x-15-7=0
We add all the numbers together, and all the variables
4x-22=0
We move all terms containing x to the left, all other terms to the right
4x=22
x=22/4
x=5+1/2
Step-by-step explanation:
3(2x-5)-2x=7
We move all terms to the left:
3(2x-5)-2x-(7)=0
We add all the numbers together, and all the variables
-2x+3(2x-5)-7=0
We multiply parentheses
-2x+6x-15-7=0
We add all the numbers together, and all the variables
4x-22=0
We move all terms containing x to the left, all other terms to the right
4x=22
x=22/4
x=5+1/2
cans of regular coke are labeled as containing . statistics students weighed the contents of randomly chosen cans, and found the mean weight to be ounces. assume that cans of coke are filled so that the actual amounts are normally distributed with a mean of and a standard deviation of . find the probability that a sample of cans will have a mean amount of at least .
the probability of the event that a sample of 5 cans will have a meaningful amount of at least 12.13 oz is 0.0078
We are provided with the information that cans of coke are filled in the account of having normal distribution, with the provided means which is 12.00 oz and the standard deviation of 0.12 oz and the sample size is
n= 5.
let X be the sample mean, so the probability will be :
P(X[tex]\geq[/tex] 12.13) = 1- P(X<12.13)
=1- P(X-(μ/(σ/[tex]\sqrt{n}[/tex])) < (12.13 -12.00)/(0.12/[tex]\sqrt{5}[/tex]))
= 1- P(z<2.42)
= 1-0.9922
=0.0078
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Cans of regular Coke are labeled as containing 12 oz. Statistics students weighted the content of 5 randomly chosen cans, and found the mean weight to be 12.13. Assume that cans of Coke are filled so that the actual amounts are normally distributed with a mean of 12.00 oz and a standard deviation of 0.12 oz. Find the probability that a sample of 5 cans will have a mean amount of at least 12.13 oz.
Which statement shows 2, –4, –1, and 0 in order from least to greatest?
A. 2 < –4 < –1 < 0
B. –4 < 2 < 1 < 0
C. –4 < –1 < 0 < 2
D. 2 < 0 < –1 < –4
Answer:
C
Step-by-step explanation:
Sue has a crate, open at the top in the shape of a cuboid. The internal dimensions of the crate are 36cm long by 36cm wide by 60 cm high.
Sue has a stick of length 90cm. She places the stick in the crate so that the shortest possible length extends out from the crate.
Calculate the length of the stick that extends from the crate
Calculate the angle the stick makes with the base of the crate
Image has the answer for part A.
Part B)
47.9 degrees
Step-by-step explanation:
Pythagoras: a^2+b^2=c^2
36²+36²=C²
√2592=C
C=50.9cm
Used Trigonometry: SOH CAH TOA
Tan=Opposite/Adjacent
Tan=60/50.9
The angle stick makes when it meets the base: Tan^-1(60/50.9)
=49.7˚
The solution is, The angle stick makes when it meets the base is, 47.9 degrees.
What is Pythagorean theorem?Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.
here, we have,
Pythagoras: a^2+b^2=c^2
36²+36²=C²
√2592=C
C=50.9cm
Used Trigonometry: SOH CAH TOA
Tan=Opposite/Adjacent
Tan=60/50.9
The angle stick makes when it meets the base:
Tan^-1(60/50.9)
=49.7˚
Hence, The solution is, The angle stick makes when it meets the base is, 47.9 degrees.
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A plane took 5 hours to complete a 1500 mile trip while flying into the wind. Coming back it only took 3 hours. What was the speed (in miles per hour) of the plane and the wind?
Answer:
Step-by-step explanation:75mph
solve the system of equation using eliminations -x+9y=35 and 2x+2y=10 by combining the equations
The solution by Elimination Method of the given equations -x+9y=35 and 2x+2y=10 is given by, x=1,y=4.
Given the equations are,
-x+9y = 35 .............(i)
2x+2y = 10 ...........(ii)
From the equation (ii) we get,
2x+2y = 10
x+y = 5 ...............(iii)
Adding (i) and (iii) we get,
-x+9y+x+y = 35+5
10y = 40
y = 40/10
y = 4
Substituting the value of y in (i) we get,
-x+9*4 = 35
-x+36 = 35
-x = 35-36
-x = -1
x = 1
Hence the solution of the equations is, x=1,y=4.
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what other regression do you need to run to test the null hypothesis that, holding other factors fixed, age has no effect on sleeping?
The null we are interested in testing here is that the coefficients on age and age^2 are jointly zero. So, we would need to run a restricted version of the regression above where these two variables are omitted and calculate.
Given:
what other regression do you need to run to test the null hypothesis that, holding other factors fixed, age has no effect on sleeping.
The null we are interested in testing here is that the coefficients on age and age^2 are jointly zero.
[tex]F = R^2_{ur}-R^2_r / q / 1-R^2_{ur} (n-k-1)[/tex]
Therefore the null we are interested in testing here is that the coefficients on age and age^2 are jointly zero. So, we would need to run a restricted version of the regression above where these two variables are omitted and calculate.
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What formula is a 1/2 Bxh?.
Answer:
Area of a triangle
Step-by-step explanation:
Area of a triangle = (1/2)(b)(h)
Answer: It is used to find the area of a triangle
Write the phrase as an expression.
a number c divided by 25
expression:
I’m really confused… Please help
The given phrase written as an algebraic expression is c / 25 .
The given phrase is : a number c divided by 25
So if we consider any number 'c' , then the number when divided by c can be written as c ÷ 25
The required expression to represent this is given by c / 25.
Expressions are phrases used to describe statements in mathematics that contain variables, numbers, sometimes both, and at least two terms joined by an operator. Mathematical operations include addition, multiplication, and division.
The two types of expressions used in mathematics are numerical expressions, which only contain numbers, and algebraic expressions, which also contain variables.
A symbol with an unknown value is referred to as a variable. A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided. A number that has been further multiplied by a variable is referred to as a coefficient in an equation.
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