The relation that represents a one-to-one function is
A. x with entries 5, 14, 7, 13, 12.
f(x) with entries 26, 197, 50, 170, 197.
Option A is the correct answer.
We have,
A one-to-one function is a function that has one output for one input.
Now,
A.
x with entries 5, 14, 7, 13, 12.
f x) with entries 26, 197, 50, 170, 197.
This is a one-to-one function.
B.
x with entries -2, -1, 0, 1, 2.
f(x) with entries 5, 2, 1, 2, 5.
This is not a one-to-one function.
The x values -1 and 1 have the same f(x) value 2.
C.
x with entries 7.25, 7.5, 7.75, 8, 8.5.
f(x) with entries 11, 13, 15, 13, 11.
This is not a one-to-one function.
The x values 7.25 and 8.5 have the same f(x) value 11.
Thus,
The relation that represents a one-to-one function is
A. x with entries 5, 14, 7, 13, 12.
f(x) with entries 26, 197, 50, 170, 197.
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Provided below is a line graph containing the combined annual attendance of the Walt Disney World theme parks in Orlando (Magic Kingdom, Epcot, Animal Kingdom, and Hollywood Studios). Use the data provided below and your research skills to write a brief report for someone at Disney addressing the following questions.
a. (QS 2) Determine the average rate of change in attendance from 2011-2021 and use that to predict the annual attendance for 2022.
b. (QS 2) Consider any years that showed somewhat unusual growth rates and provide examples that might have contributed to the anomalous growth.
c. (QS 1) Develop a linear model for the expected attendance t years after 2011.
d. (QS 3) Use the model from c) to project the expected attendance for 2025 and 2030.
e. (QS 3) What are some important factors that could help/hinder future attendance? Explain how these might impact your projections above including whether your model should be more accurate for 2025 vs 2050.
The average rate of change in attendance from 2011-2021 is 1.132 per year
Average rate of change in attendance from 2011-2021From the graph, we have:
Population in 2011 = 47.45Population in 2021 = 58.77The average rate of change is then calculated as:
Rate = (58.77 - 47.45)/(2021 - 2011)
Evaluate
Rate = 1.132
2022 is 11 years from 2011.
So, the predicted annual attendance for 2022 is;
Attendance = 47.45 + 1.132 * 11
Attendance = 59.90
Year with unusual growthThe years with unusual growth are 2020 and 2021.
This is so because they have the same attendance.
The factor that might have contributed to the anomalous growth include
Government policiesNatural occurrenceThe linear model for the attendanceIn (a), we have:
Attendance = 47.45 + 1.132 * 11
Express as a function
y(t) = 47.45 + 1.132(t)
Expected attendance for 2025 and 20302025 is 14 years from 2011.
So, we have:
y(14) = 47.45 + 1.132(14)
y(14) = 63.298
2030 is 19 years from 2011.
So, we have:
y(19) = 47.45 + 1.132(19)
y(19) = 68.958
Factors that could help/hinder future attendanceThe factors include:
Government policiesNatural occurrenceTicket priceBasic amenitiesRead more about linear functions at:
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Classify the triangle as acute, right, or obtuse and classify it as equilateral, isosceles, or scalene.
The triangle is Obtuse and scalene , Option C is the correct answer.
What is a Triangle ?A triangle is a polygon with three sides , three angles and three vertices.
A triangle can be classified as Acute , Right or Obtuse on the basis of the angle in a Triangle .
and it is classified as scalene , equilateral and isosceles on the basis of the length of the sides of a triangle.
The triangle given in the question has all the sides different , so it is a scalene triangle.
One of the angle is obtuse angle and so it can be classified as a Obtuse Angle Triangle.
Therefore , Option C is the correct answer.
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Answer:
right angle
Step-by-step explanation:
On Monday, Chris and Rachel went to the gym. Chris plans to return every second day. Rachel plans to return every fourth day. If they follow their plans, what is the next day of the week they will both be at the gym on the same day?
A. Wenesday B. thursday C. friday D. saturday
Volume and surface area
Answer: 290.6
Step-by-step explanation:
The volume of the cone is [tex]\frac{1}{3}(\pi)(5.6^{2})(13.8-7)=\frac{26656}{375}\pi[/tex].
The volume of the cylinder is [tex](\pi)(5.6^2)(7)=219.52\pi[/tex].
Adding these together gives the exact volume to be [tex]\frac{108976}{375}\pi[/tex], which is 290.6 to the nearest tenth.
write the zeros of this function: f(x) = 25 - 75x - 100x^2
Please help. I just need to know what the missing side is.
Answer:
14 inches
Step-by-step explanation:
If you think about it, if you were to shift the side DC to the left until it aligns with FE, you would get a straight line. This line would be parallel, and equal to AB, which can be determined by using the right angles, which are given. So AB = FE + DC, and the value of AB is given as well as the value of DC. So plugging in the known values you get 20 = FE + 6. Now subtract 6 from both sides and you get 14 = FE. So FE is 14 inches
Answer:
14 inStep-by-step explanation:
Please help. I just need to know what the missing side is.
from the question you are looking for EF
EF + CD = 20 in (from AB misure)
so
20 - 6 = 14 = EF
6) The circumference of a circle is
approximately 37.68 centimeters. What is the radius of the circle to the nearest centimeter?
A. 6 cm
C. 12 cm
B. 8 cm
D. 16 cm
Answer: A, 6 cm
Step-by-step explanation:
Circumference is 2(radius) * pi.
A. 12pi C. 24pi B. 16pi D. 32pi
Assuming pi is roughly 3,
A = 36
C = 72
B = 48
D = 96
A is the closest and if you actually used pi, it would be about 3.14159265 which would make the circumference slightly over 36, which 37.68 is.
Hope this helped.
Angles AandB are complimentary. Angle A measures x. Angle B measures (2 x +9) what is the value of x
Answer:
x = 27°
Step-by-step explanation:
Hello!
Complementary angles add up to 90°.
Since angles A and B are complementary, we can sum up the equations to 90° and solve for x.
Solve for x[tex]A + B = 90\°[/tex][tex]x + 2x + 9\° = 90\°[/tex][tex]3x + 9\° = 90\°[/tex][tex]3x = 81\°[/tex][tex]x = 27\°[/tex]The value of x is 27°.
Can some explain how to do this.
We can simplify the expression by using exponent properties, and we will see that the correct option is the fourth option.
How to simplify the expression?Remember the exponent property:
[tex]\frac{a^n}{a^m} = a^{n - m}[/tex]
Here we have the expression:
[tex]\frac{83.9*10^{12}*2.87*10^{-3}}{3.76*10^2}[/tex]
We can reorder this to get:
[tex]\frac{83.9*10^{12}*2.87*10^{-3}}{3.76*10^2} = \frac{83.9*2.87}{3.76}*\frac{10^{12}*10^{-3}}{10^2}[/tex]
The right side can be simplified to:
[tex]\frac{83.9*2.87}{3.76}*\frac{10^{12}*10^{-3}}{10^2} = 64.04*10{12 - 3 - 2} = 64.04*10^{7}[/tex]
Now, we can move the decimal point one time to the left and increase the exponent by one, so we get:
[tex]6.404*10^8[/tex]
Then we conclude that the correct option is the last one (where I rounded the expression to only 3 values after the decimal point).
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Find the volume of a cone with a diameter of 12 m and a height of 7m.
A. 84 m^3
B. 84π m^3
C. 336 π m^3
D. 252 π m^3
Answer Fast!
I am giving 100 points and brainliest!
Answer:
84π m^3
Step-by-step explanation:
1. The formula of a cone is: (1/3) · π · r^2 · h
2. The radius is 6m. (Diameter / 2)
3. (1/3) * π * (6^2) * 7
4. Multiply all numbers besides pi to get the answer in terms of pi
5. (36 / 3 ) = 12 * 7 = 84
6. 84π
[tex] \Large \purple \maltese \Huge\: \underline {\rm {{{\color{cyan}{Given...}}}}} \: [/tex]
Diameter = 12 Radius = 12/2 = 6mHeight = 7m[tex] \Large \purple \maltese \Huge\: \underline {\rm {{{\color{cyan}{To \: Find ...}}}}} \: [/tex]
Volume of cone[tex] \Large \purple \maltese \Huge\: \underline {\rm {{{\color{cyan}{Formula \: Using ...}}}}} \: [/tex]
[tex]\Large❏ \: \Large\begin{gathered} {\underline{\boxed{ \sf {{\large {\tt {{{\color{blue}{Volume_{ \red{( cone)}}}}}}}\large\orange\implies \tt \large \: \frac{1}{3}\pi {r}^{2} h}}}}}\end{gathered}[/tex]
Where,
r is radiush is height[tex] \Large \purple \maltese \Huge\: \underline {\rm {{{\color{cyan}{Solution ...}}}}} \: [/tex]
Substituting the given values in formula.
[tex]\large {\tt {{{\color{blue}{Volume_{ \red{( cone)}}}}}}}\large\orange\implies \tt \large \: \frac{1}{3}\pi {r}^{2} h[/tex]
[tex]\large {\tt {{{\color{blue}{Volume_{ \red{( cone)}}}}}}}\large\orange\implies \tt \large \: \frac{1}{3}\pi {(6)}^{2} \: \times \: 7[/tex]
[tex] \large {\tt {{{\color{blue}{Volume_{ \red{( cone)}}}}}}}\large\orange\implies \tt \large \: \frac{1}{ \cancel3}\pi \: \times \: \cancel{ 36} \: \: ^{ \pink{12}} \: \times \: 7 \\ [/tex]
[tex]\large {\tt {{{\color{blue}{Volume_{ \red{( cone)}}}}}}}\large\orange\implies \tt \large \:\pi \: \times \: 12 \: \times \: 7 \\ [/tex]
[tex]\large {\tt {{{\color{blue}{Volume_{ \red{( cone)}}}}}}}\large\orange\implies \tt \large \: 84 \pi \: {m}^{3} [/tex]
Hence , option b is the correct answer
Keep the Old Car or Buy a Used Car
Manny is an online student who currently owns an older car that is fully paid for. He drives, on average, 140 miles per week to commute to work. With gas prices currently at $2.87 per gallon, he is considering buying a used, fuel-efficient car, and wants to know if it would be a good financial decision.
The old car Manny owns currently gets 20 miles per gallon for average fuel efficiency. It has been a great vehicle, but with its age, it needs repairs and maintenance that average $740 per year (as long as nothing serious goes wrong).
He is considering buying a newer used car that will cost a total of $5,500 over a three-year loan process. The used car gets 33 miles per gallon and would only require an average of $10 per month for general maintenance. To help make a decision Manny wants to calculate the total costs for each scenario over three years. He decides to use the Quantitative Reasoning Process to do this.
Find the total costs for the newer used car (gas, maintenance/repairs, purchase price) for each scenario over the three years.
Round your answers to the nearest dollar.
Answer:
buy a new car because cars depreciates
This table shows equivalent ratios.
A 2-column table has 4 rows. Column 1 is labeled A with entries 12, 24, 32, 48. Column 2 is labeled B with entries 2, 4, 6, 8.
Which ratio is not equivalent to the other ratios shown in this table?
12 to 2
24 to 4
32 to 6
48 to 8
Using proportions, the ratio that is not equivalent to the ones shown in the table is given by:
32 to 6.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In the table, the ratios is given as follows:
r1 = 12/2 = 24/6 = 48/8 = 6.r2 = 32/6 = 5.3.Hence the different ratio is:
32 to 6.
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Kristina invests a total of $28,500 in two accounts. The first account earned a rate of return of 10% (after a year). However, the second account suffered a 4% loss in the same time period. At the end of one year, the total amount of money gained was $1,310.00. How much was invested into each account?
$_______was invested in the account that gained 10% and
$_______ was invested in the account that lost 4%.
Answer:
$17,500 was invested in the account that gained 10% and
$11,000 was invested in the account that lost 4%
Step-by-step explanation:
Define the variables:
Let x be the money invested in the account that gained 10%.Let y be the money invested in the account that lost 4%.Given information:
$28,500 = total amount invested between the two accounts$1,310.00 = total amount gainedPercentages in decimal form:
10% = 0.14% = 0.04Create a system of equations using the given information and defined variables:
[tex]\begin{cases}x + y = 28500\\0.1x - 0.04y = 1310 \end{cases}[/tex]
Rewrite Equation 1 to make y the subject:
[tex]\implies y=28500-x[/tex]
Substitute into Equation 2 and solve for x:
[tex]\implies 0.1x-0.04(28500-x)=1310[/tex]
[tex]\implies 0.1x-1140+0.04x=1310[/tex]
[tex]\implies 0.14x=2450[/tex]
[tex]\implies x=17500[/tex]
Substitute the found value of x into Equation 1 and solve for y:
[tex]\implies 17500+y=28500[/tex]
[tex]\implies y=11000[/tex]
Conclusion
$17,500 was invested in the account that gained 10% and
$11,000 was invested in the account that lost 4%
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solve for x
[tex]\bold{4x - 64 = 0}[/tex]
ty! ~
Answer:
[tex]\tt x = 16[/tex]
Step-by-step explanation:
[tex]\tt 4x-64=0[/tex]
Add 64 to both sides.
[tex]\tt 4x - 64 + 64 = 0+ 64[/tex]
Simplify.
[tex]\tt 4x = 64[/tex]
Divide both sides by 4.
[tex] \tt \cfrac{4x}{4} = \cfrac{64}{4} [/tex]
Simplify.
[tex]\tt x = 16[/tex]
Done!!!
[tex]\Large\maltese\star\underline{\textbf{What is Asked}}\star\maltese[/tex]
Solve for x. [tex]\bf{4x-64=0}[/tex].[tex]\Large\maltese\star\underline{\textbf{The required answer is below -:}}\star\maltese[/tex]
First we need to add 64 to both sides. That way, we will be one step closer to solving this in terms of x.
[tex]\bf{4x-64+64=0+64}[/tex] | on the left side the 64's sum to zero
[tex]\bf{4x=0+64}[/tex] | the right side is now 64
[tex]\bf{4x=64}[/tex] | divide the equation by 4
[tex]\bf{x=16}[/tex]
[tex]\cline{1-2}[/tex]
[tex]\gray\star\bf{Result / Required\;Answer:}[/tex]
[tex]\star\blacksquare\Large\boxed{\boxed{\bf{X=16.}}}\blacksquare\star[/tex]
Key to solving this problem -:When you're solving an equation in terms of x, or any other variable, use inverse operations to solve it. For instance, if something is added to x, use subtraction. If something is subtracted to x, use addition.
If x is multiplied by something, use division. If x is divided by something, use multiplication.
[tex]\infty\LARGE\boxed{\bf{\brace aesthetic\not1\theta\ell}}\infty[/tex]
3,900,000,000,000,000,000,000,000,000,000,000 X 245,000
Answer:
955,500,000,000,000,000,000,000,000,000,000,000,000
or 9.555 x 10^38
Step-by-step explanation:
multiply 245 x 39 first and then add all the zeros from both numbers after
Identify a transformation of the function f(x) = x by observing the equation of the function g(x) = x − 16.
A vertical shift 16 units upward.
A vertical shift 16 units downward.
A horizontal shift 16 units to the left.
A horizontal shift 16 units to the right
The transformations are
(b) A vertical shift 16 units downward.(d) A horizontal shift 16 units to the rightHow to determine the transformation?The functions are given as:
f(x) = x
g(x)= x - 16
When a function is shifted right, the transformation rule is:
(x, y) = (x - h, y)
This means that the transformation is (d) A horizontal shift 16 units to the right
Since the parent function is a base linear function.
The transformation can also be represented as:
(x, y) = (x, k - h)
This gives
g(x)= x - 16
This means that the transformation is (b) A vertical shift 16 units downward.
Hence, the transformations are (b) and (d)
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4.22 next decimal in number
Answer:
4.23
Step-by-step explanation:
add 0.01
regular number after 167, 118, 82, 57, 41, ?
Answer...
32!!
Step-by-step explanation:
Subtract the numbers to see a pattern of decreasing odd numbers
167-118 = 49
118-82 = 36
82-57 = 25
57-41 = 16
The difference between is 13 then 11 then 9 so the next number should be x-7
what is the next # in this sequence 3, 5, 12, 55, 648
Answer:
35 585
Step-by-step explanation:
Each term is the product of the previous two terms minus the term that is two before
3*5 - 3 = 12
5 x12 - 5 = 55
12 x 55 - 12 = 648
55 * 648 - 55 = 35 585
or each term is term that is two before x (term before -1)
3 (5-1) = 12
5 x (12-1) = 55
12 * (55-1) = 648
55 * ( 648-1) = 35 585
The required next term in the sequence is 35,185.
What is inductive reasoning?Inductive reasoning is defined as, tempting judgments by moving from the details to the fact. It's usually determined with inferential reasoning, where you move from known information to precise conclusions.
here,
Given sequence 3, 5, 12, 55, 648
The given sequence has the following pattern,
3 × 5 - 3 = 12
5 × 12 - 5 = 55
12 × 55 - 12 = 648
55 × 648 - 55 = 35,185
Thus, the required next term in the sequence is 35,185.
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14 MINS LEFT HELP ME PLS Lakesha gave three tenths of her cookies to Bailey and five tenths of her cookies to Helen. What fraction of her cookies did Lakesha give away?
eight tenths of her cookies,
five tenths of her cookies,
three tenths of her cookies,
or two tenths of her cookies.
Lakesha gave away 8/10 of her cookies.
What fraction of her cookies did Lakesha give away?
We know that she gave away 3/10 of her cookies to Bailey and 5/10 of her cookies to Helen.
Then the fraction that she gave away is:
3/10 + 5/10
Notice that both fractions have the same denominator, then we can directly add the numerators:
3/10 + 5/10 = 8/10
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Translate the shape A by the vector ( 1 4 ) .
Translating shape A by the vector [tex](^1_4)[/tex] means translating 1 unit right and 4 unit up to get A'(4, 7), B'(7, 7), C'(7, 5) and D'(4, 5)
What is a transformation?Transformation is the movement of a point from its initial point to a new location. Types of transformation are reflection, rotation, translation and dilation.
Let us assume that the vertices of shape A is at A(3, 3), B(6, 3), C(6, 1) and D(3, 1)
Translating shape A by the vector [tex](^1_4)[/tex] means translating 1 unit right and 4 unit up to get A'(4, 7), B'(7, 7), C'(7, 5) and D'(4, 5)
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Jorge earns $8.50 per hour at his job. Last month, Jorge earned $544. Which equation can be used to find the number of hours, h, Jorge worked last month?
Answer:544/8.50=h
Step-by-step explanation:
544 divided by 8.50 = the number of hours
I need help with this question please!! :)
Problem 34
Answer: [tex]\boldsymbol{n(B) = 3}[/tex]
Reason:
We count the number of items inside set B. In this case there are 3 values, so that is why n(B) = 3
===========================================================
Problem 36
Answer: [tex]\boldsymbol{n(A \cap C) = 1}[/tex]
Reason:
To be able to count the number of items inside set [tex]A \cap C[/tex], we first need to determine what this set looks like. In other words, we need to know the number(s) inside this set.
The upside down U symbol is the intersection symbol. It indicates we want to find what the sets A and C have in common. In this case, it's the value "4" and nothing else. This number is in both set A and set C at the same time. It might help to draw a venn diagram as you see below. I'm ignoring set B entirely since your teacher is not asking about the set in this problem.
We can then say [tex]A \cap C = \{4\}[/tex]
There's only one item inside this set, which is why [tex]n(A \cap C) = 1[/tex]
Jenny is preparing a roast chicken dinner in honour of her daughter coming back for the holidays after studying abroad. Her daughter will be on Flight BM1264. Jenny will arrive at the airport ten minutes before the flight arrives and will leave with her daughter fifteen minutes after it lands. Her journey to the airport takes 25 minutes. Jenny wants to do all the preparation for the meal before leaving for the airport. It takes 30 minutes to prepare. She will leave for the airport straight after finishing the preparation. Jenny has bought a 2.4kg chicken. It takes 35-45 minutes per kg plus an additional 30 minutes to cook the chicken. Jenny will start cooking five minutes after getting back from the airport. QUESTION IS: HOW LATE CAN THEY EAT DINNER, ALSO PLANE ARRIVES AT 4PM
The addition is one of the four fundamental mathematical operations. Jenny can have dinner at 7 pm and 7.5 mins.
What is Addition?The addition is one of the four fundamental mathematical operations, the others being subtraction, multiplication, and division. When two whole numbers are added together, the total quantity or sum of those values is obtained.
The time can be calculated as,
Time taken for preparation = 30 minTime is taken to travel to airport = 25 minsShe will wait for 10 mins before the flight arrive = 10 minFlight lands at 4 pm
She will leave 15 mins after the flight lands = 15 minsIt takes 25 mins to travel back home ⇒ 15 + 25 minsShe will start cooking after 5 mins ⇒ 15+25+5 minJenny has bought a 2.4kg chicken. It takes 35-45 minutes per kg plus an additional 30 minutes to cook the chicken. Time needed for cooking the chicken = (2.5×45 + 30) = 142.5 min
⇒ 15+25+5+142.5 min
Thus, the total time it takes for Jenny to cook the food starting when the flight lands are ⇒ 187.5 mins = 3 hours 7.5 mins
Since the flight lands at 4 pm
⇒ 4 pm + 3 hours 7.5 mins
⇒ 7 pm and 7.5 mins
Hence, Jenny can have dinner at 7 pm and 7.5 mins.
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i need to get this done, please help
The expression that is a sum of cubes is given as follows:
[tex]-27a^3b^6 + 8a^9b^12[/tex]
What is a sum of cubes?An expression that is a sum of cubes is given as follows:
a³ + b³.
For the sum, all numeric factors have to be powers of 3, while all exponents have to be multiples of 3. Hence the expression that is a sum of cubes is given as follows:
[tex]-27a^3b^6 + 8a^9b^12[/tex]
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Which graph represents y > 2x^2 – 8x + 4?
Answer:
C ON EDGE
Step-by-step explanation:
Match the systems of equations with their solution sets. y + 12 = x2 + x x + y = 3 y − 15 = x2 + 4x x − y = 1 y + 5 = x2 − 3x 2x + y = 1 y − 6 = x2 − 3x x + 2y = 2 y − 17 = x2 − 9x -x + y = 1 y − 15 = -x2 + 4x x + y = 1 Solution Set Linear-Quadratic System of Equations {(-2, 3), (7, -6)} arrowRight {(-5, 8), (3, 0)} arrowRight {(-2, 5), (3, -5)} arrowRight {(2, 3), (8, 9)} arrowRight
The System of Equations 1, 2, 3, and 4 have solutions corresponding to the option B, A, C, and D.
What is a System of Equations?A system of equations is a set of equations that have a common solution.
The first system of equations is
y+12 = x² +x
x+y = 3
To determine the solution, the equations are plotted on the graph and the intersection of the equations gives the solution.
The solution is (-5,8) (3,0)
The second system of equation is
y-15 = -x² +4x
x+y = 1
The solution to the system is (7,-6) (-2,3)
The third system of equation is
y+5 = x²-3x
2x+y = 1
The solution to the system is (3,-5) (-2,5)
The fourth system of equation is
y-17 = x²-9x
-x+y =1
The solution to the system is (2,3) , (8,9)
Therefore, the System of Equations 1, 2, 3, and 4 have solutions corresponding to the option B, A, C, and D.
The graphs are attached with the answer.
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factorize it
evaluate it
factorise it
evaluate
factorize
Answer:
[tex](x^2+y^2+xy)(x^2+y^2-xy)[/tex]
Step-by-step explanation:
Rewrite the middle term.
[tex]x^4+2x^2y^2-x^2y^2+y^4[/tex]
Rerrange terms.
[tex]x^4+2x^2y^2+y^4-x^2y^2[/tex]
Factor first three terms by perfect square rule.
[tex](x^2+y^2)^2-x^2y^2[/tex]
Rewrite [tex]x^2y^2[/tex] as [tex](xy)^2[/tex].
[tex](x^2+y^2)^2-(xy)^2[/tex]
Since both terms are perfect squares, factor using the difference of squares formula, [tex]a^2-b^2=(a+b)(a-b)[/tex] where [tex]a=x^2+y^2[/tex] and [tex]b=xy[/tex].
[tex](x^2+y^2+xy)(x^2+y^2-(xy))[/tex]
Remove parentheses.
[tex](x^2+y^2+xy)(x^2+y^2-xy)[/tex]
If a container is ¾ full of water which is equivalent to 30litres. What will be the full capacity of the container?
HELP PLS BRAINLIEST IF POSSIBBLE
factor each polynomial completely a^2-ab-8a+8a brainly
Answer:
a(a - b)
Step-by-step explanation:
given polynomial: a²- ab - 8a + 8a
We can first simplify this answer by removing like terms,
- 8a + 8a = 0
so we have a²- ab in. the simplest form
we can take this one step further and factor out the a (not simplest form)
a time a = a²
a times b = ab
hence, a(a - b)
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