Answer:
Pythagorean identity: sin²Ф + cos²Ф = 1
Step-by-step explanation:
The sine, cosine, and tangent values of an angle in a right-angled triangle are related by the Pythagorean identity, a fundamental trigonometric identity: sin²Ф + cos²Ф = 1
Given: cos(a) = 0.4 (we can use this to identify sin(a) ),
sin²(a) + (0.4)² = 1
sin²(a) = 1 - (0.4)²
sin²(a) = 1 - 0.16
sin²(a) = 0.84
Taking sq. roots on both sides will give,
sin(a) = ±√0.84
Sine is positive in the first and second quadrants, which leads us to the following conclusion:
sin(a) = +√0.84
Thus, rounding to two decimal places, sin(a) is almost equal to 0.917 or 0.92.
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Find the equation of the line
make sure its in standard form
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above
[tex]y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{4}{3}}x+10\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
so we're really looking for the equation of a lline whose slope is 4/3 and it passes through (4 , -8) in standard form
standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{-8})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{4}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-8)}=\stackrel{m}{ \cfrac{4}{3}}(x-\stackrel{x_1}{4}) \implies y +8 = \cfrac{4}{3} ( x -4)[/tex]
[tex]y+8=\cfrac{4}{3}x-\cfrac{16}{3}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3(y+8)=3\left( \cfrac{4}{3}x-\cfrac{16}{3} \right)}\implies 3y+24=4x-16 \\\\\\ 3y=4x-40\implies -4x+3y=-40\implies {\Large \begin{array}{llll} 4x-3y=40 \end{array}}[/tex]
For the graph, name the parent function and write an equation of the graph.
This is a transformation of the parent square root function, and it can be written as:
f(x) = √(-x + 4) - 2
Which is the parent function graphed?
It is ratter easy to identify the shape of the general square root function:
f(x) = √x
The only difference is that now it opens to the left, and it starts at the point (4, -2)
Then:
The sign of the x must be negative.
And with the known vertex we can write the equation:
f(x) = √(-x + 4) - 2
That is the graphed function.
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The solid below is dilated by a scale factor of
1
2
2
1
. Find the surface area of the solid created upon dilation.
The surface area of the solid created upon dilation is equal to 57.5 units².
In Mathematics and Geometry, the surface area (SA) of a cuboid can be calculated by using this mathematical equation (formula):
SA = 2(lb + bh + hl)
Where, h represents the height.
r represents the radius.
By substituting the given parameters into the formula for the surface area (SA) of a cuboid , we have the following;
SA = 2(lb + bh + hl)
SA = 2(9 x 5 + 5x 5 + 9 x 5)
SA = 2(45 + 25 + 45)
SA = 2 (90 + 25)
SA = 230 units²
After applying a dilation with a scale factor of 1/2, the surface area of the cuboid is given by;
Surface area = 230 × (1/2)²
Surface area = 230 × 1/4
Surface area = 57.5 units²
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1. Alex practices his guitar 5/8 of an hour on Wednesday and 3 3/4 hours on Thur a. Write an equation that can be used to determine how many hours Alex practiced his guitar on Wednesday and Thursday.
The Equation that can be used to determine how many hours Alex practiced his guitar on Wednesday & Thursday is H=5/8 + 33/4
In the equation,
H= Hours Alex played his Guitar
To calculate the total hours Alex played guitar, the basic addition of the hours given for that particular day is added. With this simple formula, the total Hours Alex played the guitar can be calculated.
In this case,
Total time Alex played Guitar on Wednesday = 5/8 Hours
Total time Alex played Guitar on Thursday = 3 3/4 Hours
Therefore, the equation for total hours Alex practiced his guitar on Wednesday & Thursday is H=5/8 + 33/4
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A researcher conducts a survey of 230 wives and 230 husbands and the counts of spouses who had affairs within
certain numbers of years of marriage were reported. Is there enough evidence at alpha = 0.05 to conclude that the count of husbands who
have had affairs differ significantly from the count of wives who have had affairs in each category of years of marriage? The count of wives
who had affairs is used as comparison (expected) for the husbands.
Categories Husbands affairs Wives affairs
Before 2 yrs 99 108
Between 2-10 yrs 50 44
After 10 yrs 12 18
No Affair 60 60
Step 1. Indicate the correct formulation of the hypotheses.
Option A:
H0: The proportion of husbands who have had affairs does not differ from the proportion of wives who have had affairs.
Ha: The proportion of husbands who have had affairs differs from the proportion of wives who have had affairs.
Option B:
H0: The proportion of husbands who have had affairs differs from the proportion of wives who have had affairs.
Ha: The proportion of husbands who have had affairs does not differ from the proportion of wives who have had affairs.
Answer:
Step 2. What is the number of husbands expected to have affairs between 2 and 10 years of marriage? Round to two decimals if required.
Answer:
Step 3. Find the value of the test statistic. (Round your answer to 3 decimals.)
Answer:
Step 4. Find the degrees of freedom associated with the test statistic for this problem.
Answer:
Step 5. Find the critical value of the test statistic from the table for p < 0.05. (Round your answer to 3 decimals.
Table: Critical Values of the X2 Distribution
https://bsuonline.blackboard.com/bbcswebdav/pid-17666795-dt-content-rid-860559_1/xid-860559_1
Answer:
Step 6. At the 0.05 level of significance, determine whether to fail to reject or reject the null hypothesis.
A) Reject Null Hypothesis
B) Fail to Reject Null Hypothesis
Answer:
Step 7. Choose the correct conclusion at the 0.05 level of significance.
A) There is enough evidence to conclude that the proportions of husbands who have had affairs differ significantly from the proportions of wives who have had
affairs.
B) There is not enough evidence to conclude that the proportions of husbands who have had affairs differ significantly from the proportions of wives who have had
affairs.
Answer:
The answers are given below:
Option AExpected value is 44The test statistic is 2.068df= 3Critical value= 7.815Fail to reject the null hypothesisOption BThe null hypothesis is the assertion that there is no association between the two sets of data or variables being investigated in a scientific study.
The term "null" refers to the idea that any experimentally detected difference is purely accidental and that no underlying causal relationship exists.
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If f(x)=-12x what is f(12)
The correct answer is
f(12) = -12(12) = -144
A metallurgist has only one alloy containing 34% aluminum and another containing 69% aluminum. How many pounds of each alloy must he use to make 45 pounds of a third alloy containing 56% aluminum
To create 45 pounds of a third alloy containing 56% aluminum, the metallurgist has to employ around 16.71 pounds of the alloy containing 34% aluminum and roughly 28.29 pounds of the alloy containing 69% aluminum.
Let x be the number of pounds of the alloy containing 34% aluminum that the metallurgist needs to use, and let y be the number of pounds of the alloy containing 69% aluminum.
We can set up a system of two equations to represent the constraints in the problem:
[tex]x + y = 45[/tex]
Since the total amount of alloy produced is 45 pounds
[tex]0.34x + 0.69y = 0.56(45)[/tex]
Since the amount of aluminum in the final alloy is 56% of 45 pounds
Simplifying the second equation, we get:
[tex]0.34x + 0.69y = 25.2[/tex]
Now we have two equations in two unknowns that we can solve using any method of our choice. For this problem, we will use the substitution method.
From the first equation, we can express y in terms of x:
[tex]y = 45 - x[/tex]
Substituting this expression for y into the second equation, we get:
[tex]0.34x + 0.69(45 - x) = 25.2[/tex]
Simplifying and solving for x, we get:
[tex]0.34x + 31.05 - 0.69x = 25.2\\-0.35x = -5.85\\x = 16.71[/tex]
Therefore, the metallurgist needs to use approximately 16.71 pounds of the alloy containing 34% aluminum and approximately 28.29 pounds of the alloy containing 69% aluminum to make 45 pounds of a third alloy containing 56% aluminum.
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If I have a population of all the apples in an orchard, what would I call the subset of 1000 apples collected from the orchard knowing that the 1000 apples was less than the population of the apples? 50 points
I would call the subset of 1000 apples collected from the orchard knowing that the 1000 apples was less than the population of the apples as a sample
What is a sample?You should be aware that Set of all possible outcomes or results of a statistical trial or experiment is called a sample
The total outcome in the orchard is 1000 apples Which is the universal set.
So the sample is drawn from the universal set to give a sub set of 1000 apples.
Total population is the universal set is larger than the sample size which is the subset of 1000 apples
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Omar was collecting data for a statistics project.
He was asking people to write down the month
they were born. What type of data would this be
considered?
A
B
Categorical
Numerical
The data collected would be a categorized type.
Data refers to a collection of facts, observations, or measurements that have been gathered through various sources, such as experiments, surveys, observations, or other means. Data can be in various forms, including numbers, text, images, audio, or video, and it can be analyzed to gain insights, make predictions, or support decision-making processes.
Omar gathered what is known as categorical data, which is the month of each person's birth. Data that represents characteristics or qualities, such as categories or labels, is referred to as categorical data. The months of the year in this instance signify categories rather than quantifiable numerical values. As a result, the data gathered would be categorized.
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write an expression that has a value of 5 more than t
Answer:
t + 5
Step-by-step explanation:
its self explanatory
The history data of an airline company show that 5%
of the people that book a flight do not show up. If 42
people made a booking for a flight with a 40
-seat small plane, what is the probability that there will be a seat available for every passenger that shows up?
Give your answer as a percentage, rounded to the nearest unit, without giving the percentage symbol e.g. write 82 for 82.2%
The probability that there will be a seat available for every passenger that shows up is given as follows:
0.6276 = 62.76%.
What is the binomial distribution formula?The binomial distribution formula gives the probability of obtaining a specific number of successes in a fixed number of independent trials, where each trial has only two possible outcomes (success or failure) and the probability of success is constant throughout the trials.
The mass probability formula is given by the equation presented as follows:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters, along with their meaning, are listed as follows:
n is the fixed number of independent trials.p is the constant probability of a success on a single independent trial of the experiment.The parameters for this problem are given as follows:
n = 42, p = 0.95.
(p is the probability of a person showing up).
The probability of more than 40 people showing up is obtained as follows:
P(X > 40) = P(X = 41) + P(X = 42).
In which:
P(X = 41) = 42 x (0.95)^41 x 0.05 = 0.2564.P(X = 42) = (0.95)^42 = 0.1160.Hence:
P(X > 40) = 0.2564 + 0.1160 = 0.3724.
Hence the probability of a vacant seat is of:
1 - 0.3724 = 0.6276 = 62.76%.
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Find limit for given function.
The value of limit for given function is,
⇒ lim x→4⁺ f (x) = 31
We have to given that;
Function is defined as;
⇒ f (x) = { - 2x + 3 , x ≤ 4
= { - x² + 6x - 9 , x > 4
Now, We can formulate;
⇒ lim x→4⁺ f (x)
⇒ lim x→4⁺ (- x² + 6x - 9)
⇒ lim x→4⁺ (- 4² + 6×4 - 9)
⇒ lim x→4⁺ (16 + 24 - 9)
⇒ 31
Thus, The value of limit for given function is,
⇒ lim x→4⁺ f (x) = 31
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Consider the quadratic function f(x) = −2x² + 8x + 24 . Which question is different?
What is the maximum value of the function?
What is the greatest number in the range of the function?
What is the y-coordinate of the vertex of the graph of the function?
What is the axis of symmetry of the graph of the function?
The answer to the question that is different is ___
The answer to the questions that are the same is ___
The number 32 represents the answer to the questions that are the same, which are:
The maximum value of the function.The greatest number in the range of the function.The y-coordinate of the vertex.The axis of symmetry of the figure is of 2, which is the answer to the question that is different.
How to obtain the vertex of a quadratic function?The standard definition of a quadratic function is given as follows:
y = ax² + bx + c.
The vertex is classified as a maximum or minimum depending on the term a, which multiplies x², as follows:
If a > 0, the vertex is a minimum.If a < 0, the vertex is a maximum.The function for this problem is given as follows:
y = -2x² + 8x + 24.
The coefficients are given as follows:
a = -2, b = 8 and c = 24.
The x-coordinate of the vertex, representing the axis of symmetry, is given as follows:
x = -b/2a
x = -8/-4
x = 2.
The y-coordinate of the vertex is given as follows:
y = -2(2)² + 8(2) + 24
y = 32.
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help plsssss
........................
Answer:
rectangle D is the answer
Hello! I really need help with this question!!!
Answer:
Some rational numbers that you can use are numbers like 25 and 12.5
An irrational number that you can use is π = 3.14159265...
Step-by-step explanation:
Pls give me brainliest thx
If it's wrong then don't bother
Kanene wants to know how much wrapping paper she needs to cover this cube. how much wrapping paper does she need?
surface area =6(s^2)
Answer:
ARE YOU TRYING TO CHEAT IN EDIO FROM MARK ARTLEYS CLASS, HUH?????
Caught you in 4k
Step-by-step explanation:
I simply caught you in 4k and snapped it (virtually)
Very simple stuff
Which system is represent in the graph?
y
y> 3x+4
y> x^2 + 4x-2
y< 3x+4
y ≤ x^2+4x-2
y ≥ 3x+4
y>x^2+4x-2
y> 3x+4
The system represented in the graph is: y > x² + 4x - 2 and y > 3x + 4.
What is inequality?In mathematics, an inequality is a mathematical expression that compares two values, indicating whether one value is greater than, less than, or equal to the other value. Inequalities use mathematical symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to) to indicate the relationship between the values. Inequalities can involve a variety of mathematical operations, including addition, subtraction, multiplication, division, exponents, and roots. They are commonly used to represent a range of possible values for a variable or to describe conditions that must be satisfied. Solving an inequality involves finding the values of the variable that make the inequality true. The solutions to an inequality may be a range of values, rather than a single value as in an equation.
Here,
The shaded region above both of the lines represents the solutions to this system of inequalities.
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Assume the following information for the month of August. June sales= $40,000; July sales=$65,000; August sales= $52,850. All sales are on account and are collected as follows: 20% in thecurrent month. 50% in the month following, 25% in the second month following, and 5%uncollectible. The beginning cash balance is $14,670, with cash payment of $ 24,653. If theminimum cash balance is $50,000, what is the amount needed by the bank, or how much isavailable to pay towards the bank loan? Show the amount needed as positive number, and theamount to repay a loan as a negative number
The net cash balance for the month of August is $148,767.00 after taking into account the sales for the month of June, July and August, and the payments made during the month.
The minimum cash balance required is $50,000 and the amount needed by the bank for this month is $98,767.00, while the available amount to pay towards the loan is -$98,767.00.
Amount is a numerical quantity or value representing a monetary sum. It is typically used to refer to the total amount of money paid or received, such as in a business transaction or a financial transaction. It can also refer to a quantity of something other than money, such as units of time or volume. Amount is also used to refer to the amount of a particular resource or commodity, such as the amount of water in a lake or the amount of oil in a barrel.
Beginning Cash Balance: $14,670
June Sales: $40,000
July Sales: $65,000
August Sales: $52,850
Current Month Collection:
June Sales * 20% = $8,000
July Sales * 20% = $13,000
August Sales * 20% = $10,570
Total Current Month Collection = $31,570
Next Month Collection:
June Sales * 50% = $20,000
July Sales * 50% = $32,500
August Sales * 50% = $26,425
Total Next Month Collection= $78,925
Second Month Collection:
June Sales * 25% = $10,000
July Sales * 25% = $16,250
August Sales * 25% = $13,212.50
Total Second Month Collection= $39,462.50
Uncollectible Collection:
June Sales * 5% = $2,000
July Sales * 5% = $3,250
August Sales * 5% = $2,642.50
Total Uncollectible Collection= $7,892.50
Total Cash Receipts = $31,570 + $78, 925 + $39,462.50 + $7,892.50 = $157,750.00
Payments: $24,653
Net Cash Balance: $14,670 + $157,750.00 - $24,653 = $148,767.00
Bank Loan Needed: $50,000 - $148,767.00 = -$98,767.00
The amount needed by the bank is $98,767.00 and the available amount to pay towards the loan is -$98,767.00.
Conclusion:
The net cash balance for the month of August is $148,767.00 after taking into account the sales for the month of June, July and August, and the payments made during the month. The minimum cash balance required is $50,000 and the amount needed by the bank for this month is $98,767.00, while the available amount to pay towards the loan is -$98,767.00.
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HELP PLS NEED ASAP PLS HELP
The number is greater than 30.
What are numbers?
Numbers are mathematical symbols used to represent quantities or values.
These are essential in various fields such as science, economics,finance,engineering .
Numbers can be classified into different categories including natural numbers, whole numbers, integers, rational numbers, irrational numbers and real numbers.
We know Natural numbers are positive integers starting from 1 .
Again whole numbers include 0 and all natural numbers. Integers include both positive and negative whole numbers.
Rational numbers are numbers that can be expressed as fractions while irrational numbers cannot be expressed as fractions and have non-repeating, non-terminating decimals.
Let's the number be "x".
According to the problem when the number is increased by one-half of itself, we get:
x + 0.5x = 1.5x
We know that 1.5x is greater than 45.
So, 1.5x > 45
Dividing both sides by 1.5, we get:
x > 30
So the answer is (B) greater than 30.
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A gardener is building a flower garden with a border of mulch around it. A model of the design is shown. A large rectangle with dimensions of 10.5 feet by 16 feet. A smaller rectangle with dimensions of 5.5 feet by 8 feet inside of the larger one. Part A: Find the area of the mulch border that surrounds the 5.5 ft by 8 ft flower garden. Show all work. (6 points) Part B: If the mulch cost $3.64 per sq ft, how much will the mulch for this project cost? Show all work. (6 points)
The mulch for this project cost is $451.36.
Part A: To find the area of the mulch border surrounding the flower garden, we need to first find the area of the larger rectangle and the area of the smaller rectangle. Then we can subtract the area of the smaller rectangle from the area of the larger rectangle to find the area of the garden, and finally subtract the area of the garden from the area of the larger rectangle to find the area of the mulch border.
Area of the larger rectangle = length × width=
10.5 ft 16 ft = 168 sq ft Area of the smaller rectangle = length × width= 5.5 ft × 8 ft = 44 sq ft
Area of the garden = 44 sq ft
Area of the mulch border area of the larger rectangle - area of the garden = 168 sq ft - 44 sq ft = 124 sq ft
Part B: The cost of the mulch for the project can be found by multiplying the area of the mulch border by the cost per square foot.
Cost of mulch = area of the mulch border * cost per sq ft
Cost of mulch = 124 sq ft × $3.64/sq = ft $451.36
Therefore, the mulch for this project cost is $451.36.
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Work out height of tree
Answer:
13.8m
Step-by-step explanation:
angle ATB = 32° - 19° = 13°
In angle OBT:
sin 32° = opposite/hypotenuse = h/BT
h = BT * sin 32
h = 18 * sin 19* sin 32 / sin 13= 13.8 m
So, The height of tree ≈ 13.8 m.
Can anyone help me
for each answer type
1
2
3
4
Answer:
Step-by-step explanation:
this may help i don't know the answer but it can help you i think
Videos
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¿Que es mayor?60% de 800 o 80% de 600
Slicing a solid horizontally or vertically creates a cross section that looks like the
________or one of the ___________of the solid.
Slicing a solid horizontally or vertically creates a cross section that looks like the Rectangle or one of the Square of the solid.
Cross Sections:A cross section is the intersection of a figure in three-dimensional space with a plane. It is the face you obtain by making a "slice" through a solid object. A cross section is two-dimensional. The figure (face) obtained from a cross section depends upon the orientation (angle) of the plane doing the cutting.
Slicing a solid horizontally or vertically creates a cross section that looks like the Rectangle or one of the Square of the solid.
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A city has a population of 270,000 people. Suppose that each year the population grows by 3.5 . What will the population be after 13 years? Use the calculator provided and round your answer to the nearest whole number.
The population of the city after 13 years with growth rate of 3.5% per year is equal to 422268 people.
Population of the people in the city = 270,000
Population grow by 3.5% per year
Time = 13 years
We can use the formula for exponential growth,
P = P₀(1 + r)ⁿ
where P₀ is the initial population,
r is the annual growth rate as a decimal,
n is the number of years,
and P is the final population.
Using the values given in the problem, we have,
P₀ = 270,000
since the annual growth rate is 3.5%
r = 0.035
Since we want to know the population after 13 years.
n = 13
Plugging these values into the formula, we get,
P = 270,000(1 + 0.035)¹³
= 270,000 (1.56395 )
≈ 422268.1
Rounding to the nearest whole number, the population after 13 years will be approximately 422268 people.
Therefore, the population of the city after 13 years is equal to 422268 people.
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Mr. Wells, a science teacher, recorded his students' scores on their last 20-point quiz. HH 10 12 Quiz scores 14 What was the range of scores? 16 18 20 Vide
The range of the scores is 10
How to find the range of the scores?The range of scores is the difference between the lowest and the highest score.
Given that the scores are: 12, 10, 14, 16, 20, and 18
The lowest score is 10, and the highest score is 20
[tex]\text{Range} = 20 - 10[/tex]
[tex]\boxed{\bold{= 10}}[/tex]
Therefore the range of the scores is 10
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A Van de Graaff generator is a machine that produces very high voltages by using small, safe levels of electric current. One machine has a current that can be modeled by I(t) = t+ 2, where t > 0 represents time in seconds. The power of the system can be modeled by P (t) = 0.5t3 + 6t2 + 10t. Write an equation expression that represents the voltage of the system.
The voltage V is related to current I and power P by the equation V = P
T
The equation that represents the voltage of the system is V (t) = t² + 10t.
What is the equation that represents the voltage of the system?The equation that represents the voltage of the system is calculated by applying Ohms law as follows;
P = IV
where;
P is the power of the syetemI is the current flowing in the systemV is the voltage of the systemThe voltage is calculated as;
V = P/I
P = 0.5t³ + 6t² + 10t
I = t + 2
divide P through by 0.5 and then factorize;
P = t³ + 12t² + 20t
P = t(t + 10)(t + 2)
V = P/I
V = (t(t + 10)(t + 2)) / (t+2)
V = t(t + 10)
V (t) = t² + 10t
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What are the solutions to the system of equations graphed below? O A. (-2, 0) and (2, 0) • B. (-2, 0) and (6, 0) O c. (-3, 3) and (6, 0) O D. (-3, -3) and (0, 6)
The solution of the system of equations graphed are (4,8) and (0, -8)
A system of equations is a set or collection of two or more equations with the same variables.
The common solutions are the intersecting points of the equations.
Given that is a graph of system of equations, we need to find the solution,
We know that the common solutions are the intersecting points of the equations.
So, here the curve and the line are intersecting at (4,8) and (0, -8)
Hence, the solution of the system of equations graphed are (4,8) and (0, -8)
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Exercises 1-4, find the surface area of the regular pyramid. (See Example
15.4 mm
7.2 mm
The surface area of the square pyramid is 3920 square feet.
How to calculate the surface areaWe can use the Pythagorean theorem to find the slant height:
h² = (1/2 * edge length)^2 + height^2
h² = (1/2 * 40)^2 + 21^2
h² = 400 + 441
h² = 841
h = 29
Area of each face = 1/2 * base * height
Area of each face = 1/2 * 40 * 29
Area of each face = 580 square feet
Finally, we can find the surface area of the pyramid by adding up the area of the base and the four triangular faces:
Surface area = Area of base + 4 * Area of each face
Surface area = 1600 + 4 * 580
Surface area = 1600 + 2320
Surface area = 3920 square feet
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write each of the following expressions without using absolute value:
|y-x| if y>x
Answer:
y - x
Step-by-step explanation:
You want the simplified form of |y -x| if y > x.
Absolute valueThe absolute value function is defined as ...
|a| = a . . . . for a ≥ 0
|a| = -a . . . . for a < 0
ApplicationWe have the expression |y -x|. Using the above function rule, it is ...
|y -x| = y -x . . . . for y -x ≥ 0 ⇒ y ≥ x
|y -x| = -(y -x) = x -y . . . . for y -x < 0 ⇒ y < x
The problem statement tells us we're interested in the case y > x, so the first version applies:
|y -x| = y -x . . . . if y > x
