Midpoint Definition: The point where a line is perfectly split in half
Coordinates exist in the form of ( x, y )
Generally, you find the midpoint by adding up the two numbers and dividing the sum by 2.
In other words,
Midpoint = ( [tex]\frac{x1+x2}{2} , \frac{y1+y2}{2}[/tex] )
You should get ( -22.5, 11 ) as your answer.
> Function g can be thought of as a translated (shifted) version of Y f(x) = x².
Using translation concepts, function g(x) is given as follows:
g(x) = x² - 3.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
Researching this problem on the internet, g(x) is a shift down of 3 units of f(x) = x², hence:
g(x) = x² - 3.
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Solve for m. 3/4m>−12 m>−16 m<−16 m>−9 m<−9
Answer: m > -16
Step-by-step explanation:
[tex]\frac{3}{4}m > -12\\\\m > -\frac{4}{3}(12)=-16[/tex]
can anyone help me solve these questions, please
Step-by-step explanation:
8.√128/√2
ans √64
10.3√81
3√3*3*3*3(find factor)
3 √3(this is cube root therefore we kept one out of three then we kept remaining inside of root.this is surds because one factor is inside the surds if factor is not remaining inside the surds then this is not surds)
Point One = (0, -2)
Point Two = (-3,-5)
Slope-Intercept Form
Answer:
y = x - 2
Step-by-step explanation:
The general structure of an equation in slope-intercept form is:
y = mx + b
In this formula, "m" represents the slope and "b" represents the y-intercept. Before writing our equation in this form, we first need to find the slope. The slope can be found using the point-slope formula:
y₁ - y₂ = m(x₁ - x₂)
In this formula, "m" represents the slope, "x₁" and "y₁" represent the values from Point One, and "x₂" and "y₂" represent the values from Point Two. You can find the slope by plugging the values from the points into the equation and then simplifying.
x₁ = 0 x₂ = -3
y₁ = -2 y₂ = -5
y₁ - y₂ = m(x₁ - x₂)
(-5 - (-2)) = m(-3 - 0)
-3 = m(-3)
1 = m
Now that we have a value for the slope, we can use the values from either one of the points to solve for the y-intercept (from the slope-intercept form equation).
m = 1
x = 0
y = -2
y = mx + b
-2 = (1)(0) + b
-2 = 0 + b
-2 = b
Therefore, the equation of the line in slope-intercept form is:
y = x - 2
Given: f(x) = x - 7 and h(x) = 2x + 3
Write the rule for f(h(x)).
f(h(x)) = 2x - 7
f(h(x)) = 2x - 4
f(h(x)) = 3x - 4
f(h(x)) = 3x - 7
Answer:
2nd option
Step-by-step explanation:
to find f(h(x)) substitute x = h(x) into f(x) , that is
f(h(x))
= f(2x + 3)
= 2x + 3 - 7
= 2x - 4
If you invested $4,500 for 8 months at an interest rate of 2.75%, how much interest would you earn?
Given the money invested and the interest rate, the value of the interest earned after 8 months is $82.50.
What is the value of the Interest?
From the equation of simple interest; I = PRT
Given that;
Principal P = $4,500Interest rate R = 2.75% = 2.75/100 = 0.0275Time T = 8 months = 8/12 yearsInterest I = ?I = PRT
I = $4,500 × 0.0275 × 8/12
I = $82.50
Given the money invested and the interest rate, the value of the interest earned after 8 months is $82.50.
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HELP ME WOTH THIS QUESTIONNN!!
Answer:
C
Step-by-step explanation:
For lines l and m and the transversal line that creates angles 6 and 18, angles 6 and 18 are corresponding angles of lines l and m. If they are congruent, lines l and m are parallel.
Answer: Choice C
look at the picture
[tex]\large\displaystyle\text{$\begin{gathered}\sf 9|x-8| < 36 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf Divide \ both \ sides \ by \ 9. \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{9(|x-8|)}{9} < \frac{36}{9} \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf |x-8| < 4 \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf Solve \ Absolute \ Value. \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf |x-8| < 4 \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf We \ know \ x-8 < 4 \ and \ x-8 > -4 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf x-8 < 4 \ (Condition \ 1) \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x-8+8 < 4+8 \ (Add \ 8 \ to \ both \ sides) \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x < 12 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf x-8 > -4 \ (Condition \ 2) \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x-8+8 > -4+8 \ (Add \ 8 \ to \ both \ \ sides) \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf x > 4 \end{gathered}$}[/tex]
[tex]\underline{\boldsymbol{\sf{Answer}}}[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf x < 12 \ and \ x > 4 \end{gathered}$} }[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf Therefore,\bf{\underline{the \ correct \ option}} \ \end{gathered}$}\large\displaystyle\text{$\begin{gathered}\sf is \ \bf{\underline{"A"}}. \end{gathered}$}[/tex]
Which is true regarding the system of equations?
6 x + 2 y = 46. 3 x + y = 23.
The system results in a false statement.
The system results in an intersection at one point.
The system results in parallel lines.
The system results in a true statement because they are the same line.
Answer:
they are the same line
Step-by-step explanation:
if you divide the first line by 2 you'll get:
2(3x)+2y=2(23)===> 3x+y=23
George plans to cover his circular pool for the upcoming winter season. The pool has a diameter of 20 feet and the cover extends 12 inches beyond the edge of the pool. A rope runs along the edge of the cover to secure it in place.
A. What is the area of the pool cover?
B. What is the length of the rope?
For the circular cover we have:
A) The area is 379.94 ft²
B) The length of the rope must be 68.2 ft
How to get the area of the cover?Remember that the area of a circle of radius R is given by the formula:
[tex]A = pi*R^2[/tex]
Where pi = 3.14
In this case, the diameter of the pool is 20ft, then the radius is:
R = 20ft/2 = 10ft
And it must extend 12 inches beyond, then the radius of the cover must be:
R = 10ft + 12in
Now, we know that 1ft = 12 in, then we can rewrite the radius as:
R = 10ft +1ft = 11ft
Then the area of the cover is:
[tex]A = 3.14*(11ft)^2 = 379.94 ft^2[/tex]
B) now we want to get the length of the rope, we know that the rope runs along the cover, then the length of the rope must be equal to the circumference of the cover.
Remember that the circumference of a circle of radius R is:
[tex]C = 2*pi*R[/tex]
Then the length of the rope will be:
[tex]C = 2*3.14*11ft = 68.2ft[/tex]
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You make a scale drawing of a tree using the scale 5 inches. = 27 feet. If the tree is 67.5 feet tall, how tall is the scale drawing?
Answer:
12.5 inches
Step-by-step explanation:
We use proportion to calculate the scale drawing
27 feet = 5 inches, so
67.5 feet = more inches (we know that it would be bigger than 5 inches)
We then put the bigger number on top and crossmultiply by saying:
67.5 over 27 × 5
Your answer should come out as 12.5 inches.
Two angles in a triangle have measures of 42 and 82. (Degrees)
What is the measure of the third angle?
Answer:
angles of the triangle are equal 180
so 42+82=124
180-124=56
so the answer is 56
Step-by-step explanation:
1. Solve x² +5x+3=0
Give your solutions correct to 2 decimal places.
Answer:
Step-by-step explanation:
hello :
x² +5x+3=0
delta = b²-4ac when : a =1 and b=5 c=3
delta =5²-4(1)(3) =13
X1 =(-b-sqrt(delta))/2a
X2 =(-b+sqrt(delta))/2a
continu.....
Which of the following polynomials has an even degree and a negative leading coefficient?
Polynomial going down from the left and passing through the point negative 6 comma 0 and going to a local minimum and then going up through the point negative 2 comma 0 to a local maximum and then going down through the point 3 comma 0 to a local minimum and then going up to the right through the point 5 comma 0
Polynomial going up from the left and passing through the point negative 6 comma 0 and going to a local maximum and then going down through the point negative 1 comma 0 to a local minimum and then up through the point 2 comma 0 to a local maximum and then down to the right through the point 4 comma 0
Polynomial going up from the left and passing through the point negative 6 comma 0 and going to a local maximum and then going down through the point negative 2 comma 0 and 0 comma negative 6 to a local minimum and then up to the right through the point 5 comma 0
Polynomial going down from the left and passing through the point negative 7 comma 0 and going to a local minimum and then going up through the point negative 3 comma 0 and 0 comma 8 to a local maximum and then down to the right through the point 4 comma 0
Using limits, the polynomial that has an even degree and a negative leading coefficient is:
Polynomial going down from the left and passing through the point negative 7 comma 0 and going to a local minimum and then going up through the point negative 3 comma 0 and 0 comma 8 to a local maximum and then down to the right through the point 4 comma 0.
What is a limit?A limit is given by the value of function f(x) as x tends to a value.
In this problem, to find the polynomial, we have to find the limits as x goes to infinity, hence:
[tex]\lim_{x \rightarrow -\infty} f(x) = [tex]\lim_{x \rightarrow -\infty} -a x^n[/tex]
Since n is even, we have that:
[tex]\lim_{x \rightarrow -\infty} -a (-\infty)^n = -a \times \infty = -\infty[/tex][tex]\lim_{x \rightarrow \infty} -a (\infty)^n = -a \times \infty = -\infty[/tex]Since it goes down to the left and down to the right, hence the function is:
Polynomial going down from the left and passing through the point negative 7 comma 0 and going to a local minimum and then going up through the point negative 3 comma 0 and 0 comma 8 to a local maximum and then down to the right through the point 4 comma 0.
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Which expression is equivalent to (z−3)4z−6 for all values of z where the expression is defined?
The equivalent of the expression [ (z−3)4z−6 ] is 4z² - 12z - 6.
What is the equivalent of the expression?
Given the expression; (z−3)4z−6
First, we apply distributive property.
(z−3)4z−6
(z−3)4z−6
z(4z) - 3(4z) - 6
We remove the parentheses
4z² - 12z - 6
Therefore, the equivalent of the expression [ (z−3)4z−6 ] is 4z² - 12z - 6.
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Find two positive numbers whose difference is 5 and the
sum whose squares is 557.
Answer: 19 and 14
Step-by-step explanation:
19^2+14^2= 557
What I did to start it is I tried 20 and 15 because I know the square roots of those and once I added them I saw that their sum was too big, so then I tried 19 and 14 because 19-14 is 5. It was really just guess and check :)
Write an equation for a line perpendicular to y=5x+1 and passing through the points (5,-2)
__________________________________________________________
[tex]\text{\textbf{Hello!} In this question, we are trying to find the equation of a line}\\\text{that is \underline{perpendicular} to our given equation}[/tex]
__________________________________________________________
[tex]\textbf{Explanation:}\\\\\text{To help us answer our question, we need to note some of our given info:}\\\\\text{Equation: y = 5x + 1}\\\\\text{Point passed through: (5, -2)}\\\\\text{We can use the above information to help us find our perpendicular equation.}\\\\\text{We will be using the slope-intercept form equation to help get us our answer:}\\\\\text{y = mx + b}[/tex]
[tex]\text{When a line is perpendicular to an equation, it means that its slope is }\\\text{\textbf{opposite} which results in the lines to meet at a \underline{90-degree} angle.}[/tex]
__________________________________________________________
[tex]\textbf{Solve:}\\\\\text{To get our perpendicular slope, we will use the formula:}\\\\\text{m1 = }-\frac{1}{m2}\\\\\text{m1 will be our given slope (5) and m2 will be our already provided slope. }\\\\\text{This is also known as a \underline{negative reciprocal}. }\\\\\text{Therefore: m1 = }-\frac{1}{5}\\\\\text{Since we now know our slope, we can plug it into our "m" variable in the}\\\text{slope intercept equation:}\\\\\text{y = }-\frac{1}{5}x+b\\[/tex]
[tex]\text{To find where the point is on the y-intercept, we will plug in our point}\\\text{(5, -2) to it's corresponding spots in our new equation above.}\\\\\text{Plug "5" to x and "-2" to y and solve:}\\\\\text{-2 = }-\frac{1}{5}(5)+b\\\\\text{-2 = }-1+b\\\\\text{Add 1 to both sides.}\\\\\text{-1 = }b\\\\\text{Therefore, our y-intercept is -1.}[/tex]
[tex]\text{When we plug -1 into our new equation, we get:}\\\\\text{y = }-\frac{1}{5}x-1\\\\\text{Therefore, our perpendicular equation is: }\boxed{y = -\frac{1}{5}x-1}[/tex]
__________________________________________________________
[tex]\textbf{Answer:}\\\\\boxed{y = -\frac{1}{5}x-1}[/tex]
__________________________________________________________
[tex]\textbf{Additional Info:}\\\\\text{You can learn more about \textbf{slope-intercept form} below:}[/tex]
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What is the card balance
Answer:
A card balance is the total amount of money that you currently owe on your credit card. The balance increases when purchases are made and decreases when payments are made. Purchases, balance transfers, foreign exchange, fees, and interest all factor into your credit card balance.
please brainlest and like
Solve the system of equations.
y = 2x+ 3
y=x^2+3x+3
Answer:
(0,3)
(-1,1)
Step-by-step explanation:
Hello!
Since both equations are equal to y, we can set the right-hand side of the equations equal to each other.
[tex]y = 2x + 3\\y = x^2 + 3x + 3[/tex][tex]y = y[/tex][tex]2x + 3 = x^2 + 3x + 3[/tex]Solve for x[tex]2x + 3 = x^2 + 3x + 3[/tex][tex]0 = x^2 + x[/tex][tex]0 = x(x + 1)[/tex][tex]x = 0, x =-1[/tex]X can either be 0 or -1. Remember, a solution to a system is not complete without a y-value. Plug in 0 and -1 for x in the first equation, and find the corresponding y-values.
[tex]y = 2(0) + 3\\y = 3[/tex]
And
[tex]y = 2(-1) + 3\\y = -2 + 3\\y = 1[/tex]
So the solutions to the system are (0,3) and (-1,1)
WILL GIVE BRAINLIEST!!! If [tex]\frac{a}{b} =2[/tex] what is the value of [tex]\frac{a}{a-b}[/tex]?
Could the answer be D) or is it C)?
A) -2
B) 1
C) 2
D) It cannot be determined from the given information
Considering the given proportion, the value of [tex]\frac{a}{a - b}[/tex] is:
C) 2
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The proportion between a and b is given by:
a/b = 2.
Then:
a = 2b.
The expression is:
[tex]\frac{a}{a - b} = \frac{2b}{2b - b} = \frac{2b}{b} = 2[/tex]
Hence option C is correct.
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Which graph best represents the solution to the system of equations shown below? y = -2x + 14 y = 2x + 2 A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on the ordered pair 3, 8. A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on ordered pair 8, 3. A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on ordered pair negative 8, negative 3. A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on ordered pair negative 3, 8.
The graph whuch best represents the solution to the system of equations is; A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on the ordered pair 3, 8.
What is the graphical solution of the system big equations?As an alternative, solving the system of equations algebraically, we have;
-2x +14 = 2x +2
x = 3 and by substitution;
y = 8.
On this note, the point (3,8) is a solution of the graph and hence, the answer choice with two lines intersecting at (3,8) is correct.
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what’s the equation for g(x)?
Answer:
Step-by-step explanation:
hello :
g(x) = (x+5)²
Someone please help I’m lost
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
There is one angle and an adjacent side of the triangle given equal to corresponding angle and side of the other triangle and if we observe the figure we can see that there's also a adjacent side XY common in both the Triangles.
Hence, the two triangles are congruent by SAS congruency criteria.
[tex] \qquad \large \sf {Conclusion} : [/tex]
SAS criteriaComplete the following table given this information: (Do not round intermediate calculations.) Cost of machine $ 94,000 Residual value $ 4,000 Useful life 5 years Estimated units machine will produce 100,000 Actual production: Year 1 60,000
Year 2 15,000 Use MACRS table.
Straight line method?
Units of production?
Declining balance?
MACRS (5-year class)
The completion of the following table under different depreciation methods is as follows:
Depreciation Expense:Method Year 1 Year 2
Straight line $18,000 $18,000
Units of production $54,000 $13,500
Declining balance $37,600 $22,560
MACRS (5-year class) $18,800 $30,080
Data and Calculations:Cost of machine = $94,000
Residual value = $4,000
Depreciable value = $90,000 ($94,000 - $4,000)
Estimated useful life = 5 years
Depreciation expense:
Straight-line method = $18,000 ($90,000/5)
Estimated units of produciton = 100,000
Unit depreciation rate = $0.90
Actual production Depreciation
Year 1 = 60,000 $54,000 ($0.90 x 60,000)
Year 2 = 15,000 $13,500 ($0.90 x 15,000)
Declining Balance:
Year 1 = $37,600 ($94,000 x 40%)
Year 2 = $22,560 ($94,000 - $37,600) x 40%
MACRS:
Year 1 = $18,800 ($94,000 x 20%)
Year 2 = $30,080 ($94,000 x 32%)
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n this equation, one-fourth is added to the variable y.
y+14=34
What is the value of y?
The value of y is = -------------
Answer:
I think its 19.75
PLEASE HELP PLEASE I DONT KNOW THIS QUESTION AND IVE BEEN STUCK ON THIS FOR A DAY
Answer:
A = -5
B = 1
Step-by-step explanation:
Hello!
You simply plug in the given x-value into the equation to find the missing y-value.
Solve for APlug in -1 for x into y = 2x - 3.
y = 2x - 3y = 2(-1) - 3y = -2 - 3y = -5Solve for BPlug in 2 for x into y = 2x - 3.
y = 2x - 3y = 2(2) - 3y = 4 - 3y = 1Write equation for horizontal line and vertical lines passing through the point of 0 and 7
Answer:
Step-by-step explanation:
for horizontal line slope m=0
eq. of horizontal line at (0,7) with slope 0 is
y-7=0(x-0)
y-7=0
or
y=7
slope of vertical line=∝
eq of vertical line through (0,7) is
y-7=∝(x-0)
or
x-0=0(y-7)
x-0=0
or
x=0
Need help ASAP
I will mark Brainleist
Need help part A, B and C
Roller Coaster Crew
Ray and Kelsey have summer internships at an engineering firm. As part of their internship, they get to assist in the planning of a brand new roller coaster. For this assignment, you help Ray and Kelsey as they tackle the math behind some simple curves in the coaster's track.
Part A
The first part of Ray and Kelsey's roller coaster is a curved pattern that can be represented by a polynomial function.
1. Ray and Kelsey are working to graph a third-degree polynomial function that represents the first pattern in the coaster plan. Ray says the third-degree polynomial has four intercepts. Kelsey argues the function can have as many as three zeros only. Is there a way for the both of them to be correct? Explain your answer.
2. Kelsey has a list of possible functions. Pick one of the g(x) functions below and then describe to Kelsey the key features of g(x), including the end behavior, y-intercept, and zeros.
g(x) = (x + 2)(x − 1)(x − 2)
g(x) = (x + 3)(x + 2)(x − 3)
g(x) = (x + 2)(x − 2)(x − 3)
g(x) = (x + 5)(x + 2)(x − 5)
g(x) = (x + 7)(x + 1)(x − 1)
3. Create a graph of the polynomial function you selected from Question 2.
Part B
The second part of the new coaster is a parabola.
4. Ray needs help creating the second part of the coaster. Create a unique parabola in the pattern f(x) = (x − a)(x − b). Describe the direction of the parabola and determine the y-intercept and zeros.
5. Create a graph of the polynomial function you created in Question 4.
Part C
6. Now that the curve pieces are determined, use those pieces as sections of a complete coaster. By hand or by using a drawing program, sketch a design of Ray and Kelsey's coaster that includes the shape of the g(x) and f(x) functions that you chose in the Parts A and B. You do not have to include the coordinate plane. You may arrange the functions in any order you choose, but label each section of the graph with the corresponding function for your instructor to view.
Answer:
Part A
1. A third degree polynomial has exactly three zeros. This is because its highest power (or degree) is 3. Ray would only be correct in saying that a polynomial can have 4 zeros if it is a 4th degree polynomial. Since in this case, a 4rd degree polynomial is being discussed, Kelsey is correct.
2. Function chosen: g(x) = (x + 2)(x - 1)(x - 2)
End behaviour: x —> ∞, g(x) —> ∞
x —> - ∞, g(x) —> -∞
Zeros/x intercepts of the function: -2, 1, 2
y intercept: g(x) = (x + 2)(x - 1)(x - 2)
g(x) = (0 + 2)(0 - 1)(0 - 2)
g(x) = (2)(-1)(-2)
g(x) = 4
3. See Graph 1
Part B
4. f(x) = (x + 5)(x + 3)
Direction: opens upward
Zeros/x intercepts: -5, -3
y intercept: 15
5. See graph 2
Part C
You can draw the roller coaster yourself using the graphs below
if the graph of f(x)=x^2 how will the graph be affected if the coefficient of x^2 is change to 1/3
The graph would be affected by horizontally stretching the curve of f(x) = x^2 when the coefficient is changed
How to determine the change?The function is given as:
f(x) = x^2
When the coefficient of x^2 changes to 1/3, we have:
f(x) = 1/3x^2
The above represents a stretch of the function
This means that the graph would be affected by horizontally stretching the curve of f(x) = x^2 when the coefficient is changed
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Mr. Carson washes his car every 8 days, checks the oil every 7
days, and checks the tire pressure every 9 days. He washed it Monday July 18,
2022, checked the oil on Wednesday and checked the tire pressure on Thursday
of that same week. When is the first day after that Monday on which he will
do all these activities on the same day? Find the number of days counted from
that Monday July 18, 2022.
The first day when he would do these activities on the same day is December 7, 2023.
When would he do these activities on the same day?In order to determine which day Mr. Carson would wash his car, check his oils and check the tire pressure, the multiple of 8, 7, and 9 have to be determined.
A multiple of a number is the product of an integer and that number. A common multiple is a number that is common to all three numbers. The lowest common multiple of 8, 7 and 9 is 504. So, in 504 days he would do all three activities on the same day.
In order to convert 504 days, take note of the following:
365 days = 1 year
12 month = 1 year
1 month = 4 weeks
30 days = 1 month
504 / 365 = 1 year 139 days
139 days / 30 days = 4 months 19 days
504 days = 1 year, 4 months and 19 days
1 year, 4 months and 19 days + July 18, 2022 = December 7, 2023
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