You need to find a number that, when multiplied by a given number modulo a certain value, produces a remainder of 1. This can be done using the extended Euclidean algorithm, and the resulting inverse is the residue of the coefficient modulo the modulus.
Finding the inverse of a modulo involves finding a number that, when multiplied by a given number modulo a certain value, produces a remainder of 1. This process is important in modular arithmetic, where calculations are performed with remainders of a fixed integer modulus.
To find the inverse of a modulo, you can use the extended Euclidean algorithm, which is a method for finding the greatest common divisor of two integers.
The steps for finding the inverse of a modulo are as follows:
1. Identify the number you want to find the inverse of (let's call it "a") and the modulus (let's call it "m").
2. Use the extended Euclidean algorithm to find the greatest common divisor of "a" and "m", and the coefficients x and y such that ax + my = gcd(a,m).
3. If gcd(a,m) = 1, then "a" has an inverse modulo "m" and the inverse is given by x mod m.
4. If gcd(a,m) is not equal to 1, then "a" does not have an inverse modulo "m".
In step 3, x mod m represents the residue of x modulo m, which is the unique non-negative integer less than m that is congruent to x modulo m. In other words, it is the remainder when x is divided by m.
For example, to find the inverse of 5 modulo 7, we can use the extended Euclidean algorithm to find that 2(5) + (-1)(7) = 1. Therefore, the inverse of 5 modulo 7 is 2.
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I need help please and thank you
Solve for X
Answer:
12
Step-by-step explanation:
The large triangle is 4 times the size of the smallest one.
17*4=68, 8*4=32, and 15*4=60.
We know what the side length is now, so we set up an equation.
60=4x+12
Subtract 12 from both sides.
60-12=4x+(12-12)
48=4x
Divide
48/4=4x/4
12=x
Collin did the work to see if 10 is a solution to the equation StartFraction r Over 4 EndFraction = 2.5.
StartFraction r Over 4 EndFraction = 2.5. StartFraction 10 Over 4 EndFraction = 2.5. 2.5 = 2.5.
Is 10 a solution to the equation?
Yes, because 10 and 4 are both even.
Yes, because if you substitute 10 for r in the equation and simplify, you find that the equation is true.
No, because 10 is not divisable by 4.
No, because if you substitute 10 for r in the equation and simplify, you find that the equation is not true.
Answer:
Yes, because if you substitute 10 for are in the equation and simplify, you find that the equation is true.
Step-by-step explanation:
Yes, because if you substitute 10 for are in the equation and simplify, you find that the equation is true.
what does 40 oz mean in ml
Answer: 40 fluid ounces is approximately equal to 1182.94 milliliters.
Step-by-step explanation:
A fluid ounce (oz) is a unit of volume used in the United States and some other countries, while milliliters (ml) are used in the metric system. To convert ounces to milliliters, we can use the conversion factor of 29.5735 ml per fluid ounce.
So, 40 fluid ounces is equal to:
40 oz * 29.5735 ml/oz = 1182.94 ml
Therefore, 40 fluid ounces is approximately equal to 1182.94 milliliters.
The value of a certain investment over time is given in the table below. Answer the questions below to determine what kind of function would best fit the data, linear or exponential.
linear function would best fit the data because as x increases, the y values change values by 4518. The slope of this function is approximately 4518
What is a linear equation?
A linear equation is an equation in which each term has at max one degree. Linear equations in variables x and y can be written in the form
y = mx + c
Linear equation with two variables, when graphed on the cartesian plane with axes of those variables, give a straight line.
linear function would best fit the data because as x increases, the y values change values by 4518.
The slope of this function is approximately 4518
Slope = change in y values / change in x values
=( 27520.99-23002.99)/(2-1)
= 4518/1
= 4518
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I've been having trouble figuring out trigonometry and I really could use somebody who knows this kind of stuff to help me out. Can anyone answer this by showing me how to do it and what the answer would be?
Answer: The positive acute angle between the x-axis and the angle's terminal side, or the angle's terminal side wherever it is, measured so that the reference angle is positive and less than 90° (or 2) is known as the reference angle for a given angle in trigonometry.
This is all I know I don't have a class like this sorry hope this helps you!
Your job in a company is to fill quart-size bottles of oil from a full
150-gallon oil tank. Then you are to pack
24 quarts of oil in a case to ship to a store. How many full cases of oil can you get from a full
150-gallon oil tank?
you can get 25 full cases of oil from a full 150-gallon oil tank.
What are quarts?Quarts (abbreviated as "qt") is a unit of measurement commonly used for volume in both the US customary and British imperial measurement systems. One quart is equal to 32 fluid ounces, 2 pints, or 0.25 gallons.
given by the question: -
There are 4 quarts in a gallon, so a 150-gallon oil tank contains:
150 gallons * 4 quarts/gallon = 600 quarts of oil
To pack a full case of oil, we need 24 quarts of oil. So, the number of full cases of oil that can be obtained from a 150-gallon oil tank is:
600 quarts of oil / 24 quarts per case = 25 cases of oil
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Need help, please! *With step-by-step answer, thanks!
$3,600
Step-by-step explanation:Simple interest is the amount of money earned based on the initial amount invested.
Simple Interest Formula
The formula for simple interest is A = P(1 + rt). Let's define each of these variables.
A is the total amount of money in the accountP is the principal or the initial amount depositedr is the interest rate expressed as a decimalt is time in yearsTo solve for simple interest, we need to plug in the information we are given.
Solving Simple Interest
In the question, we're told that $3000 is the initial amount deposited, so P = 3000. The rate is 2%, which means that r = 0.02. Also, this interest is earned over 10 years, thus t = 10. Now, plug this into the formula above.
A = 3000(1 + 0.02*10)Then, just simplify the right side of the equation.
A = 3000(1 + 0.2)A = 3000 * 1.2A = 3600This means that after 10 years, there will be a total of $3600 in the account.
I know that the first term of the sequence is -2, and the fifth term is -1/8. What do you know?Type of sequence : Common ratio or difference : Explicit equation : Recursive equation :
Answer:
Type of sequence: Geometric
Common ratio: [tex]\mbox{\large \dfrac{1}{2}}[/tex]
Explicit equation:
[tex]a_n = a_1 \cdot \left(\dfrac{1}{2}\right)^{n-1 }[/tex]
Recursive Equation:
[tex]\mbox{\large a_n = \dfrac{1}{2} \cdot a_{n-1}}[/tex]
Step-by-step explanation:
Looking at the first and fifth terms it appears to be a geometric sequence where each successive term is r x previous term
r is referred to as the common ratio = aₙ/aₙ₋₁ where aₙ is the nth term and aₙ₋₁ the previous term
The nth term can be found by using the formula
aₙ = a₁ x rⁿ⁻¹
where a₁ is the first term
We have a₁ = -2
a₅ = - 1/8
Plugging these into the general equation for a geometric sequence we get
[tex]-\dfrac{1}{8} = -2 \cdot r^{5-1}\\\\\\-\dfrac{1}{8} = -2 \cdot r^{4}\\\\r^4 = -\dfrac{1}{8} \div -2\\\\\\r^4 = \dfrac{1}{16}\\\\\\r = \sqrt[4]{\dfrac{1}{16}} \\\\r = \dfrac{1}{2} \;\;\;\;\textrm(since \; 2^4 = 16)[/tex]
Recursive equation relates the nth term to the (n-1)th term and is
[tex]a_n = \dfrac{1}{2} \cdot a_{n-1}[/tex]
If we start at the first term
a₁ = -2
a₂ = 1/2 x (-2) = - 1
a₃ = 1/2 x (-1) = - 1/2
a₄ = 1/2 x (-1/2) = -1/4
a₅ = 1/2 x (-1/4) = - 1/8
So everything pans out fine
Suppose that f is continuous, 5∫-2 f(x)dx=11 and 5∫-2 f(x)dx=14 Find the value of the integral 2∫5 f(x)dx
Answer:
C. 3
Step-by-step explanation:
One of the (many) properties of definite integrals is
[tex]\mbox{\large \int\limits _{a}^{b}f(x)\,dx + \int\limits _{b}^{c}f(x)\,dx = \int\limits }_{a}^{c}f(x)\,dx[/tex]
Therefore
[tex]\mbox{\large \int\limits _{-2}^{5}f(x)\,dx + \int\limits _{5}^{2}f(x)\,dx = \int\limits }_{-2}^{2}f(x)\,dx[/tex]
Given
[tex]\mbox{\large \int\limits _{-2}^{5}f(x)\,dx = 11}}}\para[/tex]
and
[tex]\mbox{\large \int\limits _{-2}^{2}f(x)\,dx = 14}}[/tex]
We get
[tex]\mbox{\large 11+ \int\limits _{5}^{2}f(x)\,dx} = 14[/tex]
Subtracting 11 from both sides we get
[tex]\mbox{\large \int\limits _{5}^{2}f(x)\,dx} = 14 - 11 = 3\\[/tex]
Answer: Choice C which is 3
Factor the polynomial: 10w^2-31w+15
Answer:
(5w - 3)(2w - 5)
Step-by-step explanation:
As this polynomial is of the form ax² + bx + c, where a = 10, b = -31, and c = 15 (and x = w), in this case, as a is a number other than 1, the first step is to multiply a and c, replacing c with that product and removing the coefficient from the w² term, giving us:
w² - 31w + 150 (as 10 × 50 is 150)
Now, we are looking for two numbers that when they're multiplied together you get c, which is 150, and those same two numbers when added together gives us b, -31.
After looking through all of the possible factors of 150, we see that -25 and -6 fulfill both of these requirements (as -25 × -6 = 150 and -25 + -6 = -31)
Now, as we have our two numbers we can set up our factors:
(w - 6)(w - 25)
However, as we had to get rid of the 10 in front of the w², we now have to bring it back in front of both w's, giving us:
(10w - 6)(10w - 25)
Now we look and see if we can simplify.
We can see that 10 and -6 can both be simplified by 2, giving us:
(5w - 3)(10w - 25)
We can also see that 10 and -25 can be simplified by 5, giving us:
(5w - 3)(2w - 5)
name the point of concurrency of the angle bisectors
The point of concurrency of the angle bisectors is called the incenter. The incenter is the center of the incircle of a triangle, which is the largest circle that can be inscribed within the triangle.
The center present in the largest circle that can be inscribed in the triangle is defined as incircle. It is in the equal distance from all the sides present in the triangle , which makes it unique comparing to others.
The line that bisects the angle which is also called as angle bisector is one of the method to find the incenter. It divide the entire triangle into three triangles of same area and length. The triangle includes three bisectors to each angle.
These bisectors are intersected at the same point in the triangle , which is also termed as incenter of the triangle. This is because the incenter is in equal distance from each of the every side of the triangle, and this makes the angle bisectors to divide the triangle into parts which makes the incenter equidistant from all three sides of the triangle.
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Solve the system of equations using elimination: -2x+3y=-10 and -7x+3y+25
The solution to the system of equations is x = 35/9 and y = -20/27.
What is an expression?Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.
I assume the second equation is supposed to be equal to zero, so the system of equations is:
-2x + 3y = -10
-7x + 3y = -25
To solve this system of equations using elimination, we can add the two equations together. This will eliminate the y variable and give us an equation in terms of x:
-2x + 3y + (-7x + 3y) = -10 - 25
-9x = -35
x = 35/9
Now that we know x, we can substitute it into either equation to solve for y. Let's use the first equation:
-2x + 3y = -10
-2(35/9) + 3y = -10
-70/9 + 3y = -90/9
3y = -20/9
y = -20/27
Therefore, the solution to the system of equations is x = 35/9 and y = -20/27.
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find the size of the angle xyz
give you answer to 1 decimal point
hypotenuse is 15cm and the adjacent is 6
Answer:
Step-by-step explanation:
no
What does mu X mean statistics?
Mu X is a statistical concept used to measure the difference between two means.
It is calculated by subtracting the mean of one group from the mean of another group. Mu X is often used to compare the means of two or more groups, or to compare the means of two subgroups within a group. It can also be used to measure the relative size of a group's mean compared to the grand mean or the size of a group's mean compared to the mean of another group. Mu X is a useful tool for distinguishing between true and false differences between two means. It is also useful for understanding the relative importance of different factors in a study. Mu X is sometimes referred to as the difference in means or the mean difference, and it is an important concept in inferential statistics.
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use the box method to distribute and simplify (5x+4)(x-2)
after you put it in the box you have to simplify plsss
The simplified expression by using box method to distribute is [tex]5x^2 - 6x - 8.[/tex]
What is expression ?In mathematics, an expression is a combination of symbols, numbers, and operators (such as +, -, x, ÷, etc.) that represents a quantity or a relationship between quantities. Expressions can be simple, such as a single number or variable, or complex, such as an algebraic expression with multiple terms and variables. Expressions can be evaluated, simplified, and manipulated using various algebraic techniques.
According to given information :To use the box method, we draw a box and divide it into four parts, with each part representing a multiplication of one term from the first expression with one term from the second expression:
We then add up the terms in each box to simplify:
(5x + 4)(x - 2) = [tex]5x^2 - 10x + 4x - 8[/tex]
= [tex]5x^2 - 6x - 8[/tex]
Hence, the simplified expression is [tex]5x^2 - 6x - 8.[/tex]
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1. Interpret the domain restrictions on the demand and the supply functions. What do they represent in context of the scenario?
2. Suppose that in her first month Yaseen is able to create 15 kits. How much should she charge for each of these kits based on her supply function? How much should she charge for each of these kits based on her demand function? Show your work.
3. In her first month of business, Yaseen sells out of her kits in 3 days. In her second month of business, she decides to supply 60 kits. How much should she charge for each of these kits based on her supply function? How much should she charge for each of these kits based on her demand function? Show your work.
4. If Yaseen creates 60 kits in her second month of business and offers them for sale at $66 each, do you think she will sell all of them? Why or why not?
5. What family of functions do f(x) and g(x) belong to? How do you know?
6. If you were to graph two quadratic functions on the same xy-plane, how many intersection points could there be? Use examples to explain your thinking.
7. Use algebraic methods to find where Yaseen’s demand and supply functions intersect. What does this point(s) represent in context of this problem? Show all your work.
8. Confirm your answer from question 7 by using Desmos to create a single graph that shows both () and () with their domain restrictions. Provide a screenshot of your graph with the intersection point(s) marked.
According to Yaseen's demand function, if she can produce 60 kits, the function cost per kit should be set at:
[tex]p = 30 - 0.5q\s60 = q = > p = 30 - 0.5(60) (60) > p = $15[/tex]
What is function?Probability theory is an area of mathematics that deals with calculating the likelihood that an event will occur or a proposition will be true. A risk is a number between 0 and 1, where 0 represents the possibility of an event occurring and 1 represents certainty.
Probability is a mathematical expression of the possibility that an event will occur. The proportion of equally plausible options that actually occur relative to all potential outcomes when an event happens is known as the probability, and it may also be written as an integer between 0 and 1.
According to Yaseen's supply function, if she can produce 15 kits, the cost per kit she should charge is:
[tex]p = 10 + 0.5q[/tex]
[tex]p = 10 + 0.5(15) (15)[/tex]
[tex]p = $17.50[/tex]
According to Yaseen's demand function, if she can produce 15 kits, the cost per kit she should charge is:
[tex]p = 30 - 0.5q\sp = 30 - 0.5(15) (15)[/tex]
[tex]p = $22.50[/tex]
According to Yaseen's supply function, if she can provide 60 kits, the cost per kit should be as follows: [tex]p = 10 + 0.5q 60 = q p = 10 + 0.5 (60)[/tex]
[tex]p = $40[/tex]
According to Yaseen's demand function, if she can produce 60 kits, the cost per kit should be set at:
[tex]p = 30 - 0.5q\s 60 = q[/tex]
[tex]p = 30 - 0.5(60) (60)[/tex]
[tex]p = $15[/tex]
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Answer:
Step-by-step explanation:
1. Demand- 0<=x<=85 / Supply- 0<=x<=100
The company is estimating that no more then 85 kits will be demanded each month. The company can supply no more then 100 kits per month.
2. x=15
S(15)=0.01(15)^2+0.5(15)=9.75
D(15)=0.02(15-100)^2=144.5
3. x=60
S(60)=0.01(60)^2+0.5(60)=66
D(60)=0.02(60-100)^2=32
4. The supply in question 3 is larger then the demand. Supply>Demand- No, because the demanding price is much lower.
5. X^2- Quadratics because in math the quadratic equation of degree 2 is the highest exponent of the equation with the standard as y=ax^2+bx+c
6. See attachment
7. f(x)=0.02(x-100)^2 g(x)=0.01x^2+0.5x
They intersect on the graph at (50, 50) so the products is 50.
8. See Attachment
f(x)=0.02(x-100)^2
g(x)=0.01x^2+0.5x
Solve for a.
Set up your equation using the
Pythagorean Theorem.
a² + b² = c²
a² + [?]²=
12
Hint: Plug in the given leg
length for b.
12
a
9
Enter help
Answer: a²+ 9² = 12² (look at the image for the solution)
Step-by-step explanation:
find the surface area of a Sphere of diameter
36 cm. tak x=22 7
Answer: The surface area of a sphere can be calculated using the formula:
A = 4 * π * r^2
Where r is the radius of the sphere.
The diameter of the sphere is 36 cm, so the radius can be found by dividing the diameter by 2:
r = 36 cm / 2 = 18 cm
Now that we have the radius, we can plug it into the formula:
A = 4 * π * r^2 = 4 * π * (18 cm)^2 = 4 * π * 324 cm^2 = 1296 * π cm^2
Since π is approximately equal to 3.14, we can get an approximate answer:
A ≈ 1296 * 3.14 = 4071.84 cm^2
So the surface area of the sphere with a diameter of 36 cm is approximately 4071.84 square centimeters.
Step-by-step explanation:
Which function represents g(c) a reflection of f(c)=6(1/3)^x across the y axis?
The function represents g(c) a reflection of ff(c) = 6 (1/3)ˣ across the y axis is g(c) = -6(1/3)⁻ˣ and option B is the correct answer.
What is reflection of a function?A function can be transformed by flipping its graph around an axis, which is known as a reflection function. Reflecting or reflection in mathematics, and more precisely in geometry, refers to flipping. Hence, a function's reflection is essentially the mirror image of the supplied function or graph. As a result, reflecting functions are a common name for them.
The given function is: f(c) = 6 (1/3)ˣ.
When a function is reflected along the y-axis the coordinates of the graph change as follows:
(x, y) → (-x, y)
The function f(c) = 6 (1/3)ˣ when reflected will have the function g(c) as:
g(c) = -6(1/3)⁻ˣ
Hence, the function represents g(c) a reflection of ff(c) = 6 (1/3)ˣ across the y axis is g(c) = -6(1/3)⁻ˣ and option B is the correct answer.
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Less variables: What is the value of the expression 5a - 7b + c when a =5 , b =3, and c = 1?
3
24
5
39
Answer:
5
Step-by-step explanation:
5(5) - 7(3) + 1 = 5
⚠️PLEASE HELP⚠️ URGENT (all separate questions) (middle school math) not advanced I will give everyone who answers this everything good that you can possibly give⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️
. You get scores of 85 and 91 on two history tests. Write and solve an
inequality to find the scores you can get on your next history test to have
an average of at least 90.
. You and a group of friends wait hour to ride an amusement park ride. You
go on the ride a second time and wait hour. You want to go on a third
time. Write and solve an inequality to find how many minutes you can wait
for your average waiting time to be at most hour. (Hint: Convert the
waiting times to minutes.)
Write and solve an inequality to find the possible
values of x so that the rectangle has an area of more
than 130 square units.
The rectangle is 5 on the left side and
3x + 2 on the bottom
Answer:
8>x
Step-by-step explanation:
A>L×B
where A=area of rectangle,L=length,B=breath
A=>130,L=51,B=3x+2
130>(5)(3x+2)
130>15x+10
130-10>15x
120>15x
8>x
L=3(8)+2=24+2=26
HELPPP PLEASE WILL GIVE BRAINLIEST
Answer: look at the images for the answers and solutions
Step-by-step explanation:
Iker runs laps on the track each week and increases what he runs by the same amount each Saturday. He began by running 24 laps and on the next Saturday he ran 35. A) How many laps did he start running?
b) How many more laps did he run each week?
c) Write the equation for this situation that models this type of growth:
A) Iker started running 24 laps on the track each week. This is mentioned in the question.
B) Iker ran 11 more laps each week.
C) The equation for this situation would be: y = 11x + 24
Determine the number of lapsTo find out how many more laps he ran each week, we can subtract the number of laps he ran on the first week from the number of laps he ran on the second week: 35 - 24 = 11 So, Iker ran 11 more laps each week.
To write an equation that models this type of growth, we can use the following formula: y = mx + b
Where y is the number of laps he runs, m is the number of additional laps he runs each week, x is the number of weeks, and b is the number of laps he started running.
In this case, m = 11 (the number of additional laps he runs each week) and b = 24 (the number of laps he started running).
So the equation for this situation would be: y = 11x + 24 This equation shows that the number of laps Iker runs each week (y) is equal to 11 times the number of weeks (x) plus the number of laps he started running (24).
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Please someone help me
Answer:
[tex]\frac{3}{2}[/tex]
Step-by-step explanation:
[tex]\frac{5-2(4+3(-1))}{2} \\ \\ =\frac{5-2(4-3)}{2} \\ \\ =\frac{5-2(1)}{2} \\ \\ =\frac{3}{2}[/tex]
what is 1 usd to thai baht?
Answer: 1 usd to thai baht is 33.44 thai baht or 33 thai baht
Step-by-step explanation:
There's no need for an explanation for this as you can just search this on the internet.
[tex] \frac{y }{8} + \frac{y}{4} [/tex]
Simplify.
I don't know how to do this, could someone please explain this for me.
y/8 + y/4
Algebraic Fractions
The expression of fractions y/8 + y/4 can be simplify as 3y/8.
How can the expression be simplified?Given that the expression is y/8 + y/4
Then we can find the number number that both 8, and 4 can go in, which is 8. and this will serves as the LCM. then we will start from the first value, 8 will divide 8 in just one times, then times y( numerator) which equals to y. for the right hand side values, 4 will divide 8 in two times which is 2, then times y equalos 2y.
y +2y/8
=(y+2y)/8
= 3y/8
Hence the simplification is 3y/8
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Given AXYZ, find the length of XZ.
Y
8
X
6
N
Answer:
WJENW
Step-by-step explanation:
Function (f) is defined by the equation f(x)=3x-7. Find the value of c so that f(c) =20 is true.
The required value of c is 9 so that [tex]f(c) =20[/tex] is true, where the function is defined by the equation f(x)=3x-7.
What is the solution to the equation?A solution to an equation is a number that can be substituted for the variable to provide a true number statement.
To determine the value of c such that [tex]f(c) = 20[/tex], we can simply substitute in the given equation and solve for c.
So, we have:
[tex]f(c) = 3c - 7[/tex]
And, we know that [tex]f(c) = 20[/tex], so we can substitute to get:
20 = 3c - 7
Adding 7 to both sides, we get:
27 = 3c
Dividing both sides by 3, we get:
c = 9
Therefore, the value of c that satisfies the equation [tex]f(c) = 20[/tex] is 9.
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85 can be written as the sum of two square numbers in two different ways. Show how this can be done.
An answer pls
The number 85, written as the sum of two square numbers in two different ways is 2² + 9² and 6² + 7²
Writing a number as the sum of two squaresFrom the question, we are to write the given number as the sum of two square numbers in two different ways.
From the given information, the given number is 85
First, we will evaluate the squares of numbers from 1 to 9
1² = 1
2² = 4
3² = 9
4² = 16
5² = 25
6² = 36
7² = 49
8² = 64
9² = 81
From above,
4 + 81 = 85
Thus,
2² + 9² = 85
and
36 + 49 = 85
Thus,
6² + 7² = 85
Hence, the sum of the squares are 2² + 9² and 6² + 7²
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Lou went shopping for a piano at our ST store a piano originally priced at $860 had a price reduction of 65% what was the reduced price
The reduced price of the piano is $301 if Lou went shopping for a piano at our ST store a piano originally priced at $860 had a price reduction of 65%
What is percentage ?
Percentage can be defined as the product of ratio of given value, total value and hundred.
To find the reduced price of the piano, we need to multiply the original price by the discount percentage (65%) and then subtract the result from the original price.
The amount of the discount is:
65% of $860 = 0.65 x $860 = $559
So, the reduced price of the piano after the discount is:
Reduced price = Original price - Discount
Reduced price = $860 - $559
Reduced price = $301
Therefore, the reduced price of the piano is $301.
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