Answers
As a result of the sequences, the numbers for the first equation are 31,37,43, 64,128,256, and 37,42,47 for the second and third equations, respectively.
What is Arithemetic Progression?An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6. An arithmetic progression is another name for an arithmetic sequence.
What is Geometric Progression?A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.
so for the first equation:
we see the common difference is constant :
second term/third term - first term/second term =7-1 or 13-7
=6
the next three terms in this series would be calculated by adding the common difference to consecutive last terms =31,37,43
for the third equation
the common difference is a constant:
second term-first term=5
the next three terms in this series would be calculated by adding the common difference to consecutive last terms =37,42,47
for the second equation we don't see a constant value as a common difference ,then we conclude that it is a Geometric progression
difference in series = second term/first term
=4/2
=2
so for the three consecutive terms we will multiply the last consecutive terms by 2=64,128,256
Therefore the numbers for First equation are 31,37,43 for the second equation are 64,128,256 and third equation are 37,42,47
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Related Questions
Need to know what goes in the 4 boxes above, and the last box
Answers
Given that Owen moves half the number of boxes moved by Ariana.
So you can put 2 in the left side upper box, and 1 in the left side lower box.
Now, it is mentioned that Owen mobes 12 boxes. So the corresponding number of boxes moved by Arianna is to be obtained.
So you have to put 12 in the right side lower box. And a variable (say 'x') in the right side upper box.
The vaue of 'x' is to be calculated.
Cross multiply the terms,
[tex]\begin{gathered} 1\cdot x=2\cdot12 \\ x=24 \end{gathered}[/tex]Thus, the value of 'x' is 24.
Therefore, Arianna can move 24 boxes in the time when Owen moves 12 boxes.
Which of the following numbers could not be used to describe a distance walked? O 19 feet 0-140 feet 0 -125 feet 12 feet
Answers
NSWER
140 Ffeet
EXPLANATION
istance is an absolute value wquantity, so it is expressed either as a positive value or an absolute value of a negative number.
Solve simultaneously:y = 5x + 210y - 50x = 20
Answers
ANSWER
Infinitely many solutions (0 = 0)
EXPLANATION
We have the two equations and we are to solve them simultaneously.
We have:
y = 5x + 2 ___(1)
10y - 50x = 20 ___(2)
Put (1) in (2):
We have that:
10(5x + 2) - 50x = 20
50x + 20 - 50x = 20
=> 50x - 50x = 20 - 20
=> 0 = 0
This kind of solution implies that there are infinitely many solutions to this equation.
Exponential Growth and Decay : Growth Formula : y = a(1 + r)', Decay Fórmula: y = a(1 – r) 1. Suppose you deposited $5,500.00 at a bank with an annual interest rate of 5%. What would be the amount in the bank after 20 years?
Answers
in this case we have that it is growth formula, so we have that r= 0.05 and a =5500. Therefore the formula is
[tex]y=5500\cdot(1.05)^t[/tex]we only need to replace t by 20 and calculate
[tex]y=5500\cdot1.05^{20}=14593.13[/tex]so after 20 years we hace $14593.13 in our bank account
how could you use a graph of a proportional relationship to find any ratio in the the proportional relationship why does this work?
Answers
It should be emphasized that a connection is proportional if its graph is a line that passes through its origin.
How should the information be illustrated?If the graph of a connection is a line passing through the origin, the connection is proportionate. If it is not a line or ray that fails to achieve this, the ratio is not proportional.
The equation for the proportionality constant is K = y/x. This is the same equation used to get the slope of a straight line with respect to the origin.
If the graph of a connection is a line or ray that goes through the origin, the relationship is proportional. If the line or ray does not pass through the origin, it is not proportional.
Additionally, if anything is not linear, it is not proportional.
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(b)A sight-seeing ship is stopped in the water for an hour, miles from the shore. Then the captain heads the ship back to the shore at a constant rate. The ship docks at shore for awhile, then returns to the open sea
Answers
Solution:
Given that a sight-seeing ship is stopped in the water for an hour, miles from the shore. Then the captain heads the ship back to the shore at a constant rate. The ship docks at shore for awhile, then returns to the open sea.
This implies that that:
During the month, Fisher Company's Work in Process inventory account was credited for $120,500, which represented the Cost of Goods Manufactured for the month. Only one job remained in process on May 31; this job had been charged with $9,600 of applied overhead cost. The amount of direct materials cost in the unfinished job would be:
Answers
The amount of direct materials cost in the unfinished job would be $97600.
What is direct material cost?The price of direct materials is directly related to the unit of production and is immediately identifiable. For instance, the price of glass is a direct material expense in the production of light bulbs. The primary component needed for the production of commodities or products was material. Costs of raw materials or components used directly in the production of goods are referred to as direct material costs. For instance, if Company A manufactures toys, the cost of the plastic used to build the toys would be an example of a direct material cost.
Given Data
Work in Process inventory account was credited for $120,500.
charged with $9,600 of applied overhead cost.
Direct material cost = Work in progress - Overhead cost - Direct labor
Direct labor = 9600 ×[tex]\frac{100}{75}[/tex]
Direct labor = 12800
Direct material cost = 120000 - 9600-12800
Direct material cost = 97600
The amount of direct materials cost in the unfinished job would be $97600.
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When $\dfrac{2}{13}$ is written as a decimal, what is the $2000^\text{th}$ digit after the decimal point?
Answers
The 2000th digit after the decimal point is 5. See the explanation below.
What is the explanation that resolved the above problem?
First, we divide the fraction to get the decimal number.
2/13 = 0.15384615384
Paying close attention, you'd notice that after the 6th number forms the decimal point, the number forms a loop that repeats again. That is:
0.153846 153846 154...
Hence, to detect the 2000th number,
we divide 2000/6
we are left with 2
(that is 333 x 6 = 1998)
Hence we count two from the decimal and that gives us the 2000th digit.
That is: 5
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Full Question:
[tex]When $\dfrac{2}{13}$ is written as a decimal, what is the $2000^\text{th}$ digit after the decimal point?[/tex]
Gary is buying a $1,250 computer on the installment plan. He makes a down payment of $150. He has to make monthly payments of $48.25 for 2 years. What is the total finance charge?
Answers
The total finance charge on the computer purchased on finance by Gary is $58.00
What is finance charge?
The finance charge on the computer purchase is the excess of the total payments over the principal of the loan, where the principal is the purchase price of $1,250 minus the down payment of $150
principal=purchase price-down payment
principal=$1,250-$150
principal=$1,100
total payments=monthly payment*number of months in 2 years
total payments=$48.25
total payments=$48.25*24
total payments=$1,158.00
total finance charge=total payments-principal
total finance charge=$1,158.00-$1,100.00
total finance charge=$58.00
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Solve the following equation.
x
5
+
64
x
2
=
0
x
5
+64x
2
=0
Answers
The value of x in the equation x⁵ + 64x² = 0 is x = 0 or x = -8 after taking common.
What is a polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
It is given that the polynomial equation is:
x⁵ + 64x² = 0
x²(x³ + 64) = 0
x² = 0 or x³ + 64 = 0
x = 0 or x³ = -64
x = 0 or x = -8
Thus, the value of x in the equation x⁵ + 64x² = 0 is x = 0 or x = -8 after taking common.
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A catering service offers 8 appetizers, 9 main courses, and 3 desserts. A customer is to select 6 appetizers, 6 main courses, and 2 desserts for a banquet. Inhow many ways can this be done?
Answers
Given:
Number of appetizers offered = 8
Number of appetizers customer is to select = 6
Number of main courses offered = 9
Number of main courses customer is to select = 6
Number of desserts offered = 3
Number of desserts the customer is to select = 2
Let's determine how many ways this can be done.
This is a combination problem.
To determine the number of ways this can be selected, apply the combination formula below:
[tex]_nC_r=\frac{n!}{r!(n-r)!}[/tex]Thus, we have:
[tex]_nC_r=_8C_6\ast_9C_6\ast_3C_2[/tex]Solving further, let's apply the formula and combine:
[tex]\begin{gathered} _8C_6\ast_9C_6\ast_3C_2=\frac{8!}{6!(8-6)!}\ast\frac{9!}{6!(9-6)!}\ast\frac{3!}{2!(3-2)!} \\ \\ _8C_6\ast_9C_6\ast_3C_2=\frac{8!}{6!(2)!}\ast\frac{9!}{6!(3)!}\ast\frac{3!}{2!(1)!} \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} _8C_6\ast_9C_6\ast_3C_2=\frac{8\ast7\ast6!}{6!(2\ast1)}\ast\frac{9\ast8\ast7\ast6!}{6!(3\ast2\ast1)}\ast\frac{3\ast2!}{2!(1)} \\ \\ _8C_6\ast_9C_6\ast_3C_2=\frac{8\ast7}{2\ast1}\ast\frac{9\ast8\ast7}{3\ast2\ast1}\ast\frac{3}{1} \\ \\ _8C_6\ast_9C_6\ast_3C_2=\frac{56}{2}\ast\frac{504}{6}\ast\frac{3}{1} \\ \\ _8C_6\ast_9C_6\ast_3C_2=28\ast84\ast3 \\ \\ _8C_6\ast_9C_6\ast_3C_2=7056 \end{gathered}[/tex]herefore, there are
I need help with the 16
Answers
NSWER
EXPLANATION
In a isometry the distances between points are conserved, so the image of segment PQ has to have the same length as segment PQ.
When we have a translation defined by a vector the x-coordinate of the vector tells the horizontal translation and the y-coordinate the vertical translation.
For this problem, if the vector is <3, 5>, we have to translate each point 3 units to the right and 5 units up.
[tex]Q(-2,-2)\to Q^{\prime}(-2+3,-2+5)=(1,3)[/tex][tex]P(-4,-4)\to P^{\prime}(-4+3,-4+5)=(-1,1)[/tex]The endpoints of the image segment are Q'(1, 3) and P'(-1, 1)
A cylindrical bucket contains 314 cubic inches of water. the height of the water is 4 inches. What is the radius of the bucket, to the nearest whole number
Answers
The radius of the cylindrical bucket which contains 314 cubic inches of water and 4 inch height of water is 5 inches.
What is the radius of the cylindrical bucket?A cylinder is simply a 3-dimensional shape having two parallel circular bases joined by a curved surface.
The volume of a cylinder is expressed as;
V = π × r² × h
Where r is radius of the circular base, h is height and π is constant pi ( π = 3.14 )
Given the data in the question;
Volume V = 314 in³Height h = 4 inRadius r = ?To determine the radius r, plug the given values into the volume formula above and solve r.
V = π × r² × h
314 in³ = 3.14 × r² × 4
314 in³ = r² × 12.56 in
Divide both sides by 12.56 in
r² = 314 in³ / 12.56 in
r² = 25 in²
Take the square root of both sides
r = √( 25 in² )
Radius r = 5 in
Therefore, the radius r of the cylindrical bucket is 5 inches.
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Factor 8mn2 + 12mn completely. A 42mn’ +3mn) B 4mn(2 + 3n) C 4mn(2mn + 3) D 4mn(2n + 3)
Answers
Question 1Step 1: Problem
[tex]\text{Factor 8mn}^2\text{ + 12mn}[/tex]Step 2: Concept
Factor the highest common factor out.
Step 3: Method
[tex]8mn^2\text{ + 12mn = 4mn( 2n + 3)}[/tex]Step 4: Final answer
4mn(2n + 3)
Question 2
Step 1: Question
[tex]\text{Simplify }\frac{(1.24\text{ }\times10^2\text{ ) (3.6 }\times10^{-3})}{1.8\text{ }\times\text{ 10}}[/tex]Step 2: Concept
Apply laws of exponent
[tex]\begin{gathered} \text{Division law } \\ \frac{m^x}{m^y}=m^{x\text{ - y}}^{} \\ \text{Multiplication law} \\ m^x\text{ }\times m^y=m^{x\text{ + y}} \end{gathered}[/tex]Step 3: Method
[tex]\begin{gathered} =\text{ }\frac{(1.24\text{ }\times10^2\text{ )(3.6 }\times10^{-3})}{1.8\text{ x 10}} \\ =\text{ }\frac{1.24\text{ }\times\text{ 3.6 }\times10^{2\text{ + (-3)}}}{18} \\ =\text{ }\frac{4.464\text{ }\times10^{2\text{ - 3}}}{18} \\ =\text{ }\frac{4.464\text{ }\times10^{-1}}{18} \\ =\text{ }\frac{4.464}{18}\text{ }\times10^{-1} \\ =\text{ 0.248 }\times10^{-1} \\ =\text{ 2.48 }\times10^{-2} \end{gathered}[/tex]Step 4: Final answer
Option D is the correct answer
[tex]2.48\text{ }\times10^{-2}[/tex]
number of odd number outcomes when a die is rolled
Answers
Answer:
Explanation:
A die has 6 faces numbered 1 to 6.
The sample space when a die is rolled is:
[tex]\lbrace1,2,3,4,5,6\rbrace[/tex]Thus, the number of odd number outcomes when a die is rolled is:
ਦੀ ਲੋੜ ਹੀ I — I — Alls – PRAAT
Answers
The given polynomial is:
[tex]30x^3-13x^2-40x-12[/tex]Substitute x = -2/5 into the expression:
[tex]30\left(-\frac{2}{5}\right)^3-13\left(-\frac{2}{5}\right)^2-40\left(-\frac{2}{5}\right)-12=0[/tex]Therefore by the remainder theorem x = -2/5 is a root.
[tex]\begin{gathered} x=-\frac{2}{5} \\ multiply\text{ both sides by 5} \\ 5x=-2 \\ 5x+2=0 \end{gathered}[/tex]Hence, the factor is
5x + 2
A
Answer:
A
Step-by-step explanation:
[tex]{ \tt{ {30x}^{3} - {13x}^{2} - 40x - 12}}[/tex]
- For a value to be a factor of a function, the function range must be zero if the factor is substituted into it.
Testing with 5x+2
[tex]{ \tt{5x + 2 = 0}} \\ { \tt{x = - \frac{2}{5} }}[/tex]
Therefore;
[tex]{ \tt{ = 30( - \frac{2}{5}) {}^{3} - 13( - \frac{2}{5} ) {}^{2} - 40( - \frac{2}{5}) - 12 }} \\ \\ = { \tt{0}}[/tex]
hence 5x + 2 is a factor
3 to 5 men and total of 224 people how many are men
Answers
When there are 3 women to to 5 men and there is a total of 224 people, the number of men will be 140 men.
How to illustrate the information?From the information, it was stated that there are 3 women to to 5 men and a total of 224 people.
Therefore, it should be noted that the fraction for men that illustrates the information will be:
= 5/(3 + 5) × 224
= 5/8 × 224
= 5 × 28
= 140
Therefore, the number of men is 140 men.
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Set up a proportion and solve.
Find the cost of 3 scarves if 2 scarves cost $22.80.
Answers
Answer:
Proportion: 22.80/2=x/3
x= 34.20
Step-by-step explanation:
First find what the value of one scarf is:
22.80/2=11.40
Then multiple by 3 to get $34.20
Answer:
Proportion : 1 scarf = $11.40
Cost of 3 scarves = $34.20
Step-by-step explanation:
GIVEN: 2 SCARVES = 22.80
LET X = # OF SCARVES
2X=22.80
X=$11.40
$11.40(3) = cost of 3 scarves
$34.20 = cost of 3 scarves
A circular disc has a circumference of 141 meters. If we multiply the radius of the circular disc by 12, what will be the circumference of the new disc? OA) 168 m OB) 248 m OC) 4147 m OD) 352 m
Answers
Type a paragraph in which you use at least two linking commas, two semicolons, and one colon.
Need two commas (,,)
two semicolons (;;)
one colon (:)
and not run on sentences and of course put period.
Answers
There are numerous advantages of involving oneself in sports. First and foremost, as known by all and very definitively, competitions increase the physical fitness of an individual. Additionally, sports also contribute to building stable mental well-being of a person. Various researchers show that people who are in the daily practice of sports in any form record better mental as well as physical health. Moreover, sports also eliminates the risk of a person catching diseases or facing any bodily interruptions. Competitions increase immunity and increase people’s stamina.
Kate paid 2.50 for 8 juice boxes how much should kate be expected to pay for 24 juice boxes
Answers
2.50 x 24= 60 for 24 juice boxes .
====================================================
Work Shown:
(2.50 dollars)/(8 juice boxes) = (x dollars)/(24 juice boxes)
2.50/8 = x/24
2.50*24 = 8x
60 = 8x
8x = 60
x = 60/8
x = 7.50
----------------
Another approach:
She paid $2.50 for 8 juice boxes. The unit price is 2.50/8 = 0.3125 dollars per juice box. Multiply this by 24 to get 24*0.3125 = 7.50
----------------
Yet another method:
We know the cost for 8 juice boxes is $2.50
We want to know the cost for 24 juice boxes.
The jump from 8 to 24 is "times 3". So we'll multiply the $2.50 cost by 3 to get 3*2.50 = 7.50
We can think of it like this
[tex]\frac{2.50 \ \text{dollars}}{8 \ \text{juice boxes}}=\frac{3*2.50 \ \text{dollars}}{3*8 \ \text{juice boxes}}=\frac{7.50 \ \text{dollars}}{24 \ \text{juice boxes}}[/tex]
Write an expression for the sequence of operations described below.
triple u, multiply v by the result, then multiply what you have by t
Answers
3u(v)(t)
What are the next two terms after -13, 8, -5, 3,-2
Answers
The next two terms in the sequence, -13, 8, -5, 3,-2 is 1 and -1.
What are the next two terms?The mathematical operations that would be used to determine the next two terms are addition and subtraction. Addition is used to determine the sum of two or more numbers. Subtraction is used to determine the difference between two or more numbers.
The first step is to determine the relationship between the numbers in the sequence. Looking at the numbers, it can be seen that the the difference between the first number and the second number gives the third number.
-13 + 8 = -5
-5 + 3 = -2
3 - 2 = 1
-2 + 1 = -1
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Renu's brother is 5 years younger than Renu. Now he is 30 years old. Connect their ages
Answers
The age of Renu and her brother is 35 and 30 years respectively.
Let the age of Renu be x
Then,
The age of her brother will be x-5
According to the question,
Age of Renu's brother is 35
So,
x-5 = 30
x = 30+5
x= 35
Hence, the age of Renu and her brother is 35 and 30 years respectively.
This question is related to the topic age problem. These problems aim is to find the age of certain people.
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Sonya drinks a 32 oz energy drink containing 80 calories per 12 oz how many calories did she drink
Answers
Answer:
213
Step-by-step explanation:
First we decide how many ounces 12 has in 32 (2.6)
Then we multiply 2.6 to 80 calories and get 213 calories
In a 7-card poker, played with a standard 52-card deck, 52C7, or 133,784,560, different hands are possible. The probability of being dealt various hands is the number of different ways they can occur divided by . Shown to the right is the number of ways a particular type of hand can occur and its associated probability. Find the probability of not being dealt this type of hand.
Answers
If the probability of being dealt this type of hand is 7654/133,784,560. the probability of not being dealt this type of hand is: 0.999944..
ProbabilityProbability of complement of the event A =P (Ac) = 1- P(A)
A = event of the particular type of hand
Probability of A :
P(A) = n (A) / n(S)
P(A) = 7480 / 133,784,560
Ac = event of not being dealt of this type of hand
Probability of Ac:
P (Ac) = 1- P(A)
P (Ac) = 1- 7480 / 133,784,560
P (Ac) = 133, 777,080 / 133,784,560
P (Ac) = 0.999944
Therefore the probability of not being dealt this type of hand is 0.999944.
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The complete question is :
In 7 card poker,played with a standard 52 card deck 52C7 or 133,784,560 different hands are possible. The probability of being dealt various hands is the number of different ways they can occur divided by 133,784,560. The probability of being dealt this type of hand is 7654/133,784,560. Find the probability of not being dealt this type of hand.
PLEASE HELP ASAP Solve for y, z, x, or t: z-a=z/b if b does not equal 1
Answers
On solving the equation z-a = z/b if b≠1 , for z we get z=ab/(b-1) .
in the question ,
the equation is given as
z-a = z/b
adding "a" to both the sides
we get
z-a+a = z/b + a
z = z/b + a
subtracting z/b from both the sides , we get
z - z/b [tex]=[/tex] z/b - z/b + a
z - z/b = a
taking z common
z(1-1/b) = a
taking LCM as b and solving further , we get
z (b-1)/b = a
on cross multiplication we get
z = ab/(b-1)
Therefore , on solving the equation z-a = z/b if b≠1 , for z we get z = ab/(b-1) .
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The cholesterol levels of an adult can be described by a normal model with a mean of 185 mg/dL and a standard deviation of 29. What percent of adults do you expect to have cholesterol levels over 190 mg/dL?
Answers
Given
mean = 185 mg/dL
standard deviation = 29
Required: The percent of adults that have cholesterol levels over 190 mg/dL
Step 1: Find the z-score for the given cholesterol level using the formula:
[tex]\begin{gathered} z\text{ = }\frac{x\text{ - }\mu}{\sigma} \\ Where\text{ }\mu\text{ is the mean} \\ and\text{ }\sigma\text{ is the standard deviation} \end{gathered}[/tex]Substituting the given values:
[tex]\begin{gathered} z\text{ = }\frac{190-\text{ 185}}{29} \\ z\text{ = 0.1724} \end{gathered}[/tex]Step 2: Using a normal distribution table, find the probability of a random value greater than 0.1724
[tex]P(x\text{ >}0.1724)\text{ = 0.43156}[/tex]Step 3: Convert to percent by multiplying by 100%
[tex]\begin{gathered} =\text{ 0.43156 }\times\text{ 100} \\ =\text{ 43.156}\% \\ \approx\text{ 43.2\%} \end{gathered}[/tex]Hence, the percent of adults that should have a cholesterol level greater than 190 mg/dL is 43,2%
Please help I’ll mark you as brainliest if correct!
Answers
Answer:
A is 729,2187,6561 and it would be geometric
B is 46,55,64 and is arithmetic
C is 32,36,40 and is arithmetic
What is the slope of a line perpendicular to the line whose equation is 3x-12y=-108
Answers
Answer:
-4
Step-by-step explanation:
Given:
Equation of line is 3x-12y = -108.To Find:
Slope of line perpendicular to the given line.Concept used:
For a line ax+by+c = 0 , the slope is equal to -a/b.Slope of a line perpendicular to a line say ax+by+c = 0 will be b/a.For the given equation, we have
a = 3, b = -12 and c = 108
So, Slope of line perpendicular to given line = -12/3 = -4
So, the slope of required line is -4.
The slope of a line perpendicular to the line whose equation 3x - 12y = - 108 will be negative 4.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The equation is given below.
3x - 12y = - 108
Convert the equation into a slope intercept, then we have
3x - 12y = - 108
12y = 3x + 108
y = (1/4)x + 9
The product of the slopes of the perpendicular line will be a negative one. Then we have
(1/4)m = -1
m = - 4
The slope of a line perpendicular to the line whose equation 3x - 12y = - 108 will be negative 4.
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