Because in the first expression 4 was factored out to make it 4(2y-6). Before 4 was factored out the expressions were the same.
Dani wants to spend less than 1 hour at the gym. She will spend 20 minutes lifting weights and then will walk around the indoor track. It takes her 4.5 minutes to walk around the track. How many times can Dani walk around the track?
Dani can walk around the track 8 times.
What is an inequality?
In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
Dani wants to spend less than 1 hour at the gym.
She will spend 20 minutes lifting weights and then will walk around the indoor track.
It takes her 4.5 minutes to walk around the track.
The number of times that Dani can walk around the track,
< (60 - 40)/4.5
< 40/4.5
< 8.9
Therefore, she can walk around 8 times around the track.
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Consider the sequence defined recursively by a1=?2, a2=2, an+1=8an?1?2an. We can use matrix diagonalization to find an explicit formula for an.
a. Find a matrix that satisfiesn [an an+1] = M [an-1 an]
The matrix M is:
M = [8 -2]
[1 0]
This satisfies the relation [an] = [an-1] * M.
Matrix Diagonalization Sequence AnThe matrix M is determined by the recurrence relation. The first row of the matrix represents the coefficients of an and an-1 in the expression for an+1, and the second row represents the coefficients of an-2 and an-3.
Here, in the recurrence relation an+1 = 8an - 2an-1, the coefficient of an is 8 and the coefficient of an-1 is -2, so the first row of the matrix M is [8 -2].
Similarly, the second row of the matrix represents the coefficients of an-2 and an-3 in the expression for an-1. However, in the recurrence relation, there is no explicit expression for an-2 and an-3, so we set them to zero in the second row of the matrix, giving [1 0].
Thus, the matrix M is:
M = [8 -2]
[1 0]
This satisfies the relation [an] = [an-1] * M.
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which point best represents √10
Answer: Q is the answer.
Step-by-step explanation:
I need help with this someone exponents and exponential functions portfolio task 2 and task 3 for task 1 I have Growth Rate=5. A.The number of bacteria after 24 hours would be approximately 11 quadrillion.B. This table represents exponential growth because as the number gets bigger, so does the total number overall.C. Any non-zero number raised to a power of zero is equal to one becauseall the numbers that are raised to the zero power are equivalent and areequal to one. Also 0⁰is undefined.D. My rule for this table would be B x 5h+1+1E. If I started with 100 bacteria I would change my rule by cutting my hourly growth rate in half
The correct statement regarding the exponential function in this problem is given as follows:
B. This table represents exponential growth because as the number gets bigger, so does the total number overall.
How to model the situation?The situation is modeled with an increasing exponential function, which has the format presented as follows:
y = ab^x.
In which:
a is the initial value.b is the rate of change.The rate of change for this problem is given as follows:
b = 5.
As the absolute value of the rate of change is greater than 1, the exponential function is a growth function.
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translated 1 unit right and five units down
Answer:
y'=|x-5|-1
Step-by-step explanation:
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if a set of standardized test scores is normally distributed, having a mean of 85 and a standard deviation of 8, approximately 95 percent of the scores are somewhere between
In this case, with a standard deviation of 8 and a Z-score of 1.96 (which represents the 95th percentile), the interval would be from 85 - (8 * 1.96) to 85 + (8 * 1.96), or approximately 69 to 101.
A normal distribution of standardized test scores with a mean of 85 and a standard deviation of 8 has an approximately 95 percent of scores that fall between two points on the distribution. These points are commonly referred to as the "margin of error" and are used to create a confidence interval around the mean. To find the interval, we use the standard deviation and the Z-score to determine the number of standard deviations away from the mean the interval bounds lie. In this case, with a standard deviation of 8 and a Z-score of 1.96 (which represents the 95th percentile), the interval would be from 85 - (8 * 1.96) to 85 + (8 * 1.96), or approximately 69 to 101. This means that if the test scores are normally distributed, approximately 95 percent of the scores will fall between 69 and 101.
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If a vehicle is going 60 mph, how many feet does it travel in one second?
The vehicle going at 60 mph travelled 88 feet in one second
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.
Speed is the ratio of distance to time taken. It is given by:
Speed = distance / time
If a vehicle is going 60 mph.
1 second = 1/3600 hr
Therefore in one second:
Speed = distance / time
60 mph = distance / (1/3600)
distance= 60 * 1/3600 = 1/60 miles
1 mile = 5280 feet
1/60 miles = 1/60 miles * 5280 feet per mile = 88 feet
The vehicle travelled 88 feet
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Laura and Sean find the product of 3x4 using different methods.
Laura: It's 2 thirds of 4.
²×4 = 3 +
Use words, pictures, or numbers to compare their methods in the space below.
Sean: It's 4 groups of 2 thirds.
2|3
+
= 4x
8
83 this is also worth 100 points
Both Laura and Sean arrive at the same answer of 8/3 by using different methods.
Laura starts by multiplying 2/3 by 4 to find the total amount of 2/3 in 4 units.
Sean starts by finding the total amount of 2/3 in one group and then multiplying that amount by the number of groups, 4.
Both methods lead to the same answer, so it doesn't matter which method is used. The important thing is that the answer is correct.
41. MODELING - Wild Mustangs According to the Bureau of Land Management, the wild mustang population of Nevada in 2004 was 2515 more than six times the wild mustang population in Utah. The total number of wild mustangs in Nevada and Utah was 21,730. Determine the number of wild mustangs in each state in 2004.
The number of wild mustangs in Utah and Nevada are 2745 and 18985
respectively.
What is a linear equation?An equation of degree one is known as a linear equation.
A linear equation of two variables can be represented by ax + by = c.
From the given information let the number of wild mustangs in Utah be 'x'
So, The number of wild mustangs in Nevada is 6x + 2515.
Therefore, x + 6x + 2515 = 21730.
7x = 21730 - 2515.
7x = 19215.
x = 19215/7.
x = 2745.
So, The number of wild mustangs in Utah is 2745 and hence the number of wild mustangs in Nevada is 6×2745 + 2515 = 18985.
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Maria has 12 gallons of lemonade. She wants to give each of her friends 1/3 gallon of lemonade. How many friends can receive 1/3 gallon of lemonade?
Try This question out and I’ll give you brainliest
Answer:
$168.75
Step-by-step explanation:
If you need this for 7 and a half hours, start off by multiplying 22.50 by 7.
22.50 x 7 = 157.5
Now find half of 22.50 to account for the half.
22.50/2 = 11.25
Finally, add 157.5 and 11.25, and that should be your answer. :)
157.5 + 11.25 = $168.75
I hope this helped!! :)
consider the following correct implementation of the selection sort algorithm: public static arraylist selectionsort(arraylist arr) { int currentminindex; //line 3 int counter
The call to selection causes the statement of algorithms of the elements[minded] = temp; in line 19 of the method to be executed three times.
The declared array is 30 40 10 50 20; int [] err; The selection Sort method would be used to sort the array shown above. Flip the numbers 10 and 30 around. Move the numbers 20 and 40 around. exchange the new position of 40 for the number 50. Consequently, line 19 of the selection Sort algorithm would be run three times. Anyone static can access the method because it has the access specifier public. Accessing static members in this situation is independent of the object. This means that the method returns a void or nothing at all. A grouping of homogeneous (same type) components is known as an array. Option "B" is the appropriate way to provide a two-dimensional array into a function in the computer language; the following options are incorrect:
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state the sampling method being used.
A manufacture has to check the product being made. He decides to randomly state taking items from the finished product convener belt and after he starts he samples every 15th item off the belt
The sampling method being used is given as follows:
Systematic sampling.
How are samples classified?Samples may be classified as:
A convenient sample is drawn from a conveniently available pool of options.A random sample is equivalent to placing all options into a hat and taking some of them.In a systematic sample, every kth element of the sample is taken.Cluster sampling divides population into groups, called clusters, and each element of the group is surveyed.Stratified sampling also divides the population into groups. However, an equal proportion of each group is surveyed.Hence in this problem we have a systematic sample with k = 15.
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How do i solve this?
Answer:
33
Step-by-step explanation:
The highest number is 50 and the lowest number is 17.
50 - 17 = 33
Fill in the blanks below with the correct units.
(a) Boris saw an elephant at the zoo. The elephant's mass was about 4000 ?
(b) In his shower, Greg used about 130 ? of water.
(c) The spacebar on the keyboard was about 11 ? long.
The respective units in the statements above are kg, L,cm
What are units?A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
Given here: Different quantities
a) Boris saw an elephant and its mass is mentioned.
Now we know,The Metric System of Measurements uses the mass units: gram (g), kilogram (kg) and tonne (t).
Thus the mass of the elephant is 4000 kg/tonne(t)
b) Greg used some volume of liquid in the shower
Now the units of liquid primarily used daily life is liters
Thus Greg used about 130 L of water
c) "The spacebar on the keyboard " in this statement the emphasis is on length and we know the units of length are m, cm etc.
Thus the length of the spacebar on the keyboard is 11 cm long.
Hence, The respective units in the statements above are kg, L,cm
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xa rectangular box is to have a square base and a volume of 40 ft3. rectangular box with a square base the material for the base costs 29 cents/ft2, the material for the top costs 24 cents/ft2, and the material for the sides costs 10 cents/ft2. if x denotes the length of one side of the base (in feet), find a function in the variable x giving the total cost of materials used in constructing the box in cents. total cost, as a function of x
The total cost of materials used in constructing the box in cents is given by the expression: Total Cost = [tex]1176/x2 + 960x[/tex].
Let x represent the length of the side of the square base, then the area of the base is given by [tex]x2[/tex]. If the volume of the box is given to be 40ft3, then the height of the box is given by [tex]40/x2[/tex]. The total cost of material used in constructing the box is given by the cost of the base, the cost of the top, and the cost of the sides. The total cost of material in cents is given by the expression:
Total Cost = [tex]29x2 + 24(40/x2) + 10(4x)(40/x2)[/tex]
The cost of the base is given by [tex]29x2[/tex], since the material for the base costs 29 cents/ft2. The cost of the top is given by [tex]24(40/x2)[/tex], since the material for the top costs 24 cents/ft2. The cost of the sides is given by [tex]10(4x)(40/x2)[/tex], since the material for the sides costs 10 cents/ft2.
Therefore, the total cost of materials used in constructing the box in cents is given by the expression:
Total Cost = [tex]29x2 + 24(40/x2) + 10(4x)(40/x2) = 1176/x2 + 960x[/tex]
The total cost of materials used in constructing the box in cents is given by the expression: Total Cost = [tex]1176/x2 + 960x.[/tex]
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(a) describe the relationship among the lengths of the segments formed by the two secants. you may use words and/or an equation.
The lengths of the segments formed by two secants are proportional to the distances of the points where the secants intersect the circle from the center of the circle.
If we denote the lengths of the two segments as x and y, and the distance between the center of the circle and the point of intersection of the secants as d, then x/y = d1/d2, where d1 and d2 are the distances between the center and the points of intersection of the secant with the circle.
When two secants intersect a circle at two distinct points, the lengths of the segments formed by the two secants are proportional to the distances between the center of the circle and the points of intersection. This is because the two segments are radii that connect the center of the circle to the points of intersection of the secants with the circle.
The proportionality between the lengths of the segments and the distances from the center can be expressed mathematically as x/y = d1/d2, where x and y are the lengths of the two segments, d1 and d2 are the distances between the center and the points of intersection of the secants with the circle, and x/y represents the ratio of the lengths of the two segments.
So, as the distances from the center to the points of intersection increase, the lengths of the segments will also increase in the same ratio. And if the distances from the center decrease, the lengths of the segments will decrease in the same ratio.
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Evaluate and simplify the following complex fraction. -2/-7|4/-9
The solution of the complex function is ( 71- 8i ) / (16 +8i).
What is a complex function?The area of mathematical analysis that studies functions of complex numbers are known as complex analysis, often known as the theory of functions of a complex variable.
Given that the function is ( 2 -7i) / ( 4 - 9i). The complex function will be solved as below:-
E = ( 2 -7i) / ( 4 - 9i)
E = ( 2 -7i) x ( 4 + 9i ) / ( 4 - 9i) x ( 4 + 9i )
E = ( 8 - 8i + 63 ) / ( 4 - 9i )²
E = ( 71 - 8i ) / ( 16 - 8i )
Therefore, the solution of the complex function is ( 71- 8i ) / (16 +8i).
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PLEASE HELP NOW! GRADPOINT
WHICH SYSTEM IS THE SOLUTION OF THE GRAPH?
The solution to the system of inequalities is following as y ≤ -4 ;y ≤ - x + 4
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
As per option (A), we have the system of inequality as follows:
y ≤ -4
y ≤ - x + 4
The region is above the graph, hence our inequality should be y ≤ - x + 4
The inequality sign part comes from visible the graph, the line is drawn using a dashed line, hence the line is included in the region.
Thus, this graph corresponds to a system of inequalities which is the correct answer that would be option (A).
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Bookwork code: F41 a) What is the frequency of the modal interval? b) What is the modal interval?
Modal interval is discussed below.
What is statistics?Statistics is the science concerned with developing and studying methods for collecting, analyzing, interpreting and presenting empirical data.
Given is the modal interval.
Modal interval →An interval of neighboring values for a measurement variable that occur noticeably more often than the values on each side of this interval.The frequency in the class interval is the highest in a continuous quantitative distribution where the values are grouped into classes with similar dimensions. Mode is not used as a measure of central tendency for continuous quantitative variables since it is more helpful for qualitative variables.The mode can be calculated by the formula -MODE = [tex]$L + h\frac{(f_{m} -f_{1}) }{(f_{m} -f_{1} ) + (f_{m} - f_{2} )}[/tex]
Therefore, Modal interval is discussed above.
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Solve the equation below. Show each step and check your work.
24n + 60 = 72
Answer:
n =1/2
Step-by-step explanation:
24n + 60 = 72
24n = 72 - 60
24n = 12 /24
n = 1/2
Answer:
n=1/2
Step-by-step explanation:
24n+60=72
24n=72-60
24n=12
n=12/24
n=1/2
A chemical company makes two brands of antifreeze. The first brand is 70% pure antifreeze, and the second brand is 95% pure antifreeze. In order to obtain 180 gallons of a mixture that contains 75% pure antifreeze, how many gallons of each brand of antifreeze must be used?
The antifreeze used by each brand will be V₁ = 72 gal. and V₂ = 108 gal.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that
ω₁ = 70% ÷ 100% = 0.7; 70% pure antifreeze.
ω₂ = 95% ÷ 100% = 0.95.
ω₃ = 85% ÷ 100% = 0.85.
V₁ = ?; volume of 70% antifreeze.
V₂ = ?; volume of 95% antifreeze.
V₃ = V₁ + V₂.
V₃ = 180 gal.
The quantity will be calculated as:-
V₁ = 180 gal - V₂.
ω₁ · V₁ + ω₂ ·V₂ = ω₃ · V₃.
0.70 · (180 gal - V₂) + 0.95 · V₂ = 0.85 · 180 gal.
126gal - 0.7V₂ + 0.95V₂ = 153 gal.
0.25V₂ = 27 gal.
V₂ = 27 gal ÷ 0.25.
V₂ = 108 gal.
V₁ = 180 gal - 108 gal.
V₁ = 72 gal.
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which of the following are examples of unethical statistical practices? check all that apply. representative sampling of a population accounting for all observations development of misleading graphs running multiple tests until a desired result is obtained
The receiving and giving money, gifts, and other types to get a favor from the government or from an institution or from an organization is amounts to bribe which is not an ethical practice.
The magnitude of the corruption in the form of a bribe may vary from the place of practice that is in situations where it has taken place.
This practice of taking bribe is considered to be an immoral act and it is punishable under the Foreign Corrupt Practices Act (FCPA) which became law in 1977 in the USA.
The main aim of the Act is to fight bribery and corruption from foreign countries and the US government as used by this law to control the unethical practice.
Types of bribery:
Active bribery
Passive bribery
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Please solve the initial value of the given problem
The solution of the initial value problem is y = -3x/(3㏑x - 1)
What an initial value problem?An initial value problem is a differential equation in which the initial value of the function is given.
How to solve the initial value problem?Since we have the initial value problem
y' = (xy + y²)/x² , y(1) = 3.
We see that it is a homogeneous differential equation.
What is a homogeneous differential equation?A homogeneous differential equation is a differential equation in which the powers of x and y are the same.
So, we proceed to solve the equation as folows.
Let y = vx.
So,
y/x = v and dy/dx = xdv/dx + vSo, substituting these two into the differential equation, we have that
y' = (xy + y²)/x²
dy/dx = (xy/x² + y²/x²
xdv/dx + v = y/x + (y/x)²
xdv/dx + v = v + v²
xdv/dx = v²
Now using the method of separation of variables, we have that
dv/v² = dx/x
Integrating both sides, we have that
∫dv/v² = ∫dx/x
-v⁻¹ = ㏑x + C
-1/v = ㏑x + C
Substituting v = y/x into the equation, we have that
- 1/y/x = ㏑x + C
-x/y = ㏑x + C
So, making y subject of the formula, we have that
y = -x/(㏑x + C)
Since y(1) = 3, we have that
3 = -1/(㏑1 + C)
3 = -1/(0 + C)
3 = -1/C
C = -1/3
So, y = -x/(㏑x + (-1/3))
y = -x/(㏑x - 1/3)
y = -x/(3㏑x - 1)/3
y = -3x/(3㏑x - 1)
So, the solution is y = -3x/(3㏑x - 1)
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Can anyone help me?
Due to length restrictions, we kindly invite to check the explanation for further detail on how to complete a maze with trigonometric functions.
How to complete sucessfully a trigonometric maze
In this question we must go through a maze formed by 16 squares, fifteen of them with cases of right triangles, we must apply trigonometric functions to complete the maze. To complete this task, we need to use the following trigonometric function:
sin θ = y / √(x² + y²)
cos θ = x / √(x² + y²)
tan θ = y / x
Where:
x - Adjacent legy - Opposite legNow we proceed to show how deal with the maze:
Step 1:
x = 19 · cos 28°
x = 16.78 (LEFT)
Step 2
x = 39 / tan 59°
x = 23.43 (LEFT)
Step 3:
x = 31 · sin 71°
x = 29.311 (RIGHT - DOWN)
Step 4:
x = 12 · tan 25°
x = 5.600 (RIGHT)
Step 5:
x = 27 / sin 48°
x = 36.332 (RIGHT)
Step 6:
x = 38 / cos 14°
x = 39.163 (DOWN - LEFT)
Step 7:
x = 16 · cos 54°
x = 9.405 (RIGHT)
Step 8:
x = 29 / tan 74°
x = 8.316 (DOWN)
Step 9:
x = 17 · sin 42°
x = 11.375 (LEFT)
Step 10:
x = 47 · tan 29°
x = 26.052 (LEFT)
Step 11:
x = 31 / sin 63°
x = 34.792 (LEFT)
Step 12:
x = 24 / cos 51°
x = 38.136 (UP)
Step 13:
x = 46 · tan 31°
x = 27.640 (RIGHT)
FINISH
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Please answer the attached question
Answer:
Option A.
Step-by-step explanation:
CAN SOMEONE HELP WITH THESE QUESTIONS?
The population after seven years is 12301
The velocity is 194 m/s
The acceleration is 126 m/s^2
What is the population?We know that we need to use the equation that can be written by the value that says that;
P = Poe^rt
P = population at time t
Po = Initial population
t = time
r = population growth rate
We now have that;
3Po =Poe^11r
3 = e^11r
r = ln3/11
r = 0.0998
In the next seven years;
P = 6117e^0.0998* 7
P = 12301
Then we have the equation;
s(t) = 7t^3 + 5t + 9
v(t) = 21t^2 + 5
at t = 3
We have 194 m/s
Then also;
a(t) = 42t
At t = 3
We have 126 m/s^2
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find the coordinates of point $p$ along the directed line segment $ab$ so that the ratio of $ap$ to $pb$ is $1$ to $3$ .
The point $p$ has coordinates such that the ratio of the distances $ap$ to $pb$ is $1$ to $3$.
To find the coordinates of point $p$ along the directed line segment $ab$, we will use the ratio of $ap$ to $pb$ being $1$ to $3$. First, we need to find the length of $ap$ and $pb$. To do this, we will use the formula for the distance between two points: [tex]$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$[/tex]. We know the coordinates for points $a$ and $b$, so we can plug them into the formula to find the length of $ab$, which is $d_{ab}$. We can then use the ratio of $1$ to $3$ to find the lengths of $ap$ and $pb$. $d_{ap}=\frac{1}{4}d_{ab}$ and $d_{pb}=\frac{3}{4}d_{ab}$. We can then use the formula for the distance between two points again, this time with the coordinates of $a$ and $p$, to find the coordinates of $p$. Finally, we can plug the coordinates of $p$ back into the formula to check if the ratio of $ap$ to $pb$ is indeed $1$ to $3$.
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Fill in the blanks to follow the steps in solving the equation:
5x − 12 − 6x = −10x + 7 − 1
Answer:
see explanation
Step-by-step explanation:
5x - 12 - 6x = - 10x + 7 - 1
step 1 : combine like terms
- x - 12 = - 10x + 6
step 2 : collect x- terms on the left side of the equation
add 10x to both sides
9x - 12 = 6
step 3 : collect constants on the right side of the equation
add 12 to both sides
9x = 18
step 4 : isolate x by dividing both sides by 9
x = 2
To solve the equation 5x - 12 - 6x = -10x + 7 - 1, combine like terms and isolate the x term and we get x=2
Explanation:To solve the equation 5x - 12 - 6x = -10x + 7 - 1, we need to combine like terms on both sides of the equation. Let's start by combining the x terms on the left side:
(5x - 6x) - 12 = -10x + 7 - 1
Simplifying further:
-x - 12 = -10x + 6
Next, we want to get all the x terms on one side of the equation. We can do this by adding 10x to both sides:
-x - 12 + 10x = -10x + 6 + 10x
Simplifying further:
9x - 12 = 6
Now, we want to isolate the x term. Let's add 12 to both sides:
9x - 12 + 12 = 6 + 12
Simplifying further:
9x = 18
Finally, divide both sides of the equation by 9 to solve for x:
x = 2
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Answer the follwing. SLATE under "Assignments => Assignment Part A in Week 4, before class begins.
Personal Financial Statements
Lisa is trying to get her personal finances in order. She does not know how to organize the following information.
Mortgage Payment
House
Credit Card Balance
After-tax Income
Groceries Expense
Car
Clothing Owned
Car Loan Payment
Furniture
Car Loan
Car Maintenance
Utilities Expense
Cash in bank
Mortgage
1.410
350.000
11.160
3,600
288
18,000
540
532
14.000
12.000
280
120
600
217.200
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