The 12 identities in mathematics are Commutative property of addition, Commutative property of multiplication, Associative property of addition, Associative property of multiplication, Distributive property, Identity property of addition, Identity property of multiplication, Additive inverse property, Multiplicative inverse property, Transitive property, Substitution property, Reflexive property.
In mathematics, an identity is a statement or equation that is true for all values of the variables involved. For example, the Pythagorean theorem, which states that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse, is an identity.
In summary, identities in mathematics are statement that are true for all values of variables, they are used to simplify expressions, solve equations and prove theorems, and they play an important role in the study of mathematical structures.
The 12 algebraic identities in mathematics are:
Commutative property of addition: a + b = b + a
Commutative property of multiplication: a x b = b x a
Associative property of addition: (a + b) + c = a + (b + c)
Associative property of multiplication: (a x b) x c = a x (b x c)
Distributive property: a x (b + c) = (a x b) + (a x c)
Identity property of addition: a + 0 = a
Identity property of multiplication: a x 1 = a
Additive inverse property: a + (-a) = 0
Multiplicative inverse property: a x (1/a) = 1
Transitive property: a = b and b = c then a = c
Substitution property: a + b = b + a
Reflexive property: a = a
It's worth noting that these are some of the algebraic identities which are frequently used in algebra and other related mathematical branches.
The 12 identities in mathematics are Commutative property of addition, Commutative property of multiplication, Associative property of addition, Associative property of multiplication, Distributive property, Identity property of addition, Identity property of multiplication, Additive inverse property, Multiplicative inverse property, Transitive property, Substitution property, Reflexive property.
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The ale price of a pring break vacation package i $209. 99 the travel agent aid by booking early, you aved $35. Find the percent decreae in price
The percent decrease in price for booking early for a spring break vacation package is 16.5%.
This was calculated by taking the amount of money saved ($35) and dividing it by the original price of the package ($209.99). Then, the resulting decimal was multiplied by 100 to convert it into a percentage.
Mathematically, the calculation looks like this:
(35/209.99) ×100 = 16.5%.
The 16.5% decrease in price is a substantial savings and could be used to purchase additional items or activities during the vacation. Booking early is often a great way to save money on vacation packages, since travel agents and companies often lower the prices to incentivize travelers to book in advance.
It is important to remember, however, that the savings may not always be 16.5%. Depending on the travel agent or company, the percentage of savings may vary. Additionally, some packages may not offer any savings at all. Therefore, it is important to do research and compare different packages before booking.
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65. Find the slope and y-int
a. 4x + 5y = 7
Answer:
slope = -4/5x
y - int = 7/5
Step-by-step explanation:
4x + 5y = 7
-4x on each side
5y = -4x + 7
divide by 5 on each side
y = -4/5 x + 7/5
How do you write 9 more than a number?.
In mathematical notation, you can use the following format to write "9 more than a number":
total + 9
This indicates that you are adding 9 to the original number.
For instance, you can write "9 more than 5" as 5 + 9 = 14 if the integer is 5.
Another option is to use the format: 9 + number.
The outcome is the same as this.
If a variable, such as x, is used to denote the number, you can express "9 more than x" as x + 9 or 9 + x.
This way, you can use the same expression for any number.
In general, when you want to find out a value which is 'x' more than a number 'a', you can use the following mathematical notation:
a + x
This is read as "a plus x".
So ,this indicates that you are adding 9 to the original number.
Therefore, the adding 9 to original number is the answer of this question.
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if a figure is dilated by a factor of 6, the area of the figure will change by a factor of _____.
ANSWER THE QUESTIONS WITH STEPS FOR BRAINLESS
the last answer choice on number 7 is (c) I don’t know
You can find the inverse of any function y=f(x) by reflecting it across the line y=x.
Hence, Option A is correct.
The inverse function is denoted by f-1 or F-1 if the function is denoted by f or F.In mathematics, an inverse function is a function that reverses the action of a function. The inverse of f is denoted if it exists and only if f is a bijective function.The function that "undoes" what f did can be defined as the inverse of f since it "acts on" numbers and transforms them. Alternatively put,A function that can change into another function is referred to as being inverse or anti.To know more about inverse of function here
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What is the solution of the equation 2x y 5 and 3x 2y 4?.
Solving the 2 equations will give us the value of x to be -14 and that of y to be 33.
Here we have two equations
2x + y = 5 and 3x - 2y = 4
Now we will use the substitution method to solve the equations
The first equation is
2x + y = 5
or, y = 5 - 2x [1]
Let 3x - 2y = 4 be equation 2
Substituting the value obtained in equation [1] in [2] we get
3x - 2(5 - 2x) = 4
or, 3x - 10 + 4x = 4
or, x = -14 [3]
Substituting the value of x obtained in equation [3] to equation [1] we get
y = 5 - 2(-14)
or, y = 5 + 28
or, y = 33
Hence, x = -14 and y = 33
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Complete Question
What is the solution of the equations 2x + y = 5 and 3x - 2y = 4?
How do you find the domain of a function?.
Domain of any function is all the input value of the function for which condition of the function exist.
Domain is set of the input values for which output exist.Let us consider y = f(x) be the function.'y' is the dependent variable and 'x' is the independent variable.All the input values of x for which successful output value exist for the function.y = 2x , x > 4 , x ∈ N.Here. domain is equal to 5, 6, 7, ....∞ implies y = 10, 12, 14, ......Therefore, the domain of the function is its input value for which there exist a successful output value.
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What is an equation with 3 variables called?.
Answer:
Linear equations
Step-by-step explanation:
hope this helps
Can someone help me with this please?
The longest and the shortest distances are 1 mile and 5 miles
The greatest number of miles left is 4.5 miles
How to determine the longest and the shortest distancesFrom the question, we have the following distances that can be used in our computation:
Luke = 3 miles
Logan = 2 miles
This means that
Shortest = 3 - 2 = 1 mile
Longest = 3 + 2 = 5 miles
The compound inequalityRepresent the distance with x
So, we have
3 - 2 < x < 3 + 2
Evaluate
1 < x < 5
The number line is | 1 | 2 | 3 | 4 | 5 |
The greatest number of miles leftIn (a), we have
Longest = 5 miles
So, we have
Greatest = 5 - 0.5
Greatest = 4,5 miles
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A small town had a population of 12,000 people in 2001. The population has been decreasing at a rate of 3.5% each year. How many people lived in the town in 2016?
Answer:7032
Step-by-step explanation:
The population of the town in 2016 will be 7032
What is percent of decrease?Percentage decrease is the difference between starting and ending values. It shows a loss of value from the original expressed as a percentage regardless of units. The amount of decrease is the original amount minus the final amount.
Given that, A small town had a population of 12,000 people in 2001. The population has been decreasing at a rate of 3.5% each year.
We know that, Decrease rate =
A = P(1-r)ⁿ
A = final amount
P = initial amount
r = rate
n = years or time
Therefore,
A = 12000(1-0.035)¹⁵
A = 12000(0.965)¹⁵
A = 7032.19
A ≈ 7032
Hence, the population of the town in 2016 will be 7032
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Is 16 < b + 8, if b = 22 true or false
Answer:
true
because 22+8=30,
and 30 is greater than 16.
I drove 10 mile north 14 mile eat 16 mile north 2 mile eat 4 mile north how far am I
The total distance traveled is 46 miles.
Distance Traveled:
Distance traveled is the path covered by a body to get from a starting point to an endpoint in a certain period of time, at a certain velocity. Time and velocity play a major role in measuring the distance traveled. The distance travel formula is: d = v x t
To determine the total distance you have traveled, you will need to add up all the distances you have driven in each direction.
You drove 10 miles north, 14 miles east, 16 miles north, and 2 miles east, 4 miles north.
10 miles north + 14 miles east + 16 miles north + 2 miles east + 4 miles north = 46 miles
So, you have traveled 46 miles.
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list the sides of triangle MNP from least to greatest if m =64 degrees and n = 48 degrees
pls help
Answer:
Click or copy the link and that is the answer
https://www.leonschools.net/cms/lib/FL01903265/Centricity/Domain/3141/ch%205%20review%20answers.pdf
Step-by-step explanation:
hope it helps :)
mark me as brainliest!
if not try this (copy or paste)
mehttps://www.leonschools.net/cms/lib/FL01903265/Centricity/Domain/3141/ch%205%20review%20answers.pdf
Answer:MP, NP, MN
Step-by-step explanation:
The monthly cot of driving a car depend on the number of mile driven. Lynn found that in May it cot her $428 to drive 460 mi and in June it cot her $494 to drive 680 mi. (a) Expre the monthly cot C a a function of the ditance driven, d, auming that a linear relationhip give a uitable model
Rate does Lynn's cost increase for every additional mile she drives will be $0.25
The following is the linear relationship between the two variables:
Eq. 1: C f(d) = m*d + k
where m and k are evaluation-needed constants
Find m: We'll determine the angle of the line connecting the points (480, $380) and (800, $460).
Line slope (m) equals $0.25 per mile
Consider one of the two positions and enter (480,$380) in Eq 1 to find k.
k = 380 - 0.25(480) = $260
The line's equation is C f(d) = 0.25*d + 260.
This equation may be used to plot the graph for section a.
The rate of cost per mile is determined by the graph's slope when the units are scrutinized; as a result, $0.25
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find the value of x
Answer:
x = 73⁰
Step-by-step explanation:
all values show are measures of exterior angles
the sum of all exterior angles for any polgon is 360 degrees
to find 'x':
50 + 48 + 59 + x + x + 58 + 39 = 360
combine like terms:
2x + 214 = 360
2x = 146
x = 73
LInda, Laura, Loraine, and Lila run on a relay team. Each run 0. 5 kilometer. How far doe the team run altogether?
Answer: Linda, Laura, Loraine, and Lila run 2 kilometers altogether.
Step-by-step explanation:
0.5 + 0.5 + 0.5 + 0.5 = 2 km
I hope this helps!
What is the solution of the system of equations y 4x 4 y 3x 3?.
After solving, the solution of the pair of equation is (-1, 0).
In the given question, we have to find the solution of the system of equations y = 4x + 4 and y = -3x - 3.
The given equations are:
y = 4x + 4.....................(1)
y = -3x - 3.....................(2)
Now putting the value of y from equation 1 to the equation 2
4x + 4 = -3x - 3
Subtract 4 on both side, we get
4x = -3x - 7
Add 3x on both side, we get
7x = -7
Divide by 7 on both side, we get
x = -1
Now putting the value of x in equation 1
y = 4(-1) + 4
y = -4 + 4
y = 0
Hence, the solution of the pair of equation is (-1, 0).
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The complete question is:
What is the solution of the system of equations y = 4x + 4 and y = -3x - 3?
How do you find the sides of a 30 60 90 triangle?.
A 30-60-90 triangle is a special type of right triangle that has angles of 30 degrees, 60 degrees, and 90 degrees. It has the following properties:
The side opposite the 30-degree angle is half the length of the hypotenuse (the side opposite the 90-degree angle).
The side opposite the 60-degree angle is √3 times the length of the side opposite the 30-degree angle.
To find the sides of a 30-60-90 triangle, you can use these properties.
If you know the length of the hypotenuse (the side opposite the 90-degree angle), you can find the length of the other two sides using the following formulas:
The side opposite the 30-degree angle: hypotenuse / 2
The side opposite the 60-degree angle: (√3) * (hypotenuse / 2)
If you know the length of one of the other two sides, you can use the above formulas to find the length of the hypotenuse and the other side.
For example, if you know the length of the side opposite the 30-degree angle, you can find the length of the hypotenuse by multiplying it by 2 and the length of the side opposite the 60-degree angle by multiplying it by √3
In summary:
The hypotenuse is always twice the length of the shorter leg.
The longer leg is √3 times the length of the shorter leg.
The hypotenuse is always the longest side in a 30-60-90 triangle.
Write an equation of the line that passes through (−1,3)
and is parallel to the line y=2x+2
.
The linear equation parallel to the line y=2x+2 is:
y = 2x + 5
How to write the equation of the line?A general linear equation is:
y = a*x + b
Where a is the slope and b is the y-intercept.
Two lines are parallel if the lines have the same slope, then for example for:
y = 2x + 2
A parallel line will be:
y = 2x + b
And the line must pas through (-1, 3), then:
3 = 2*-1 + b
3 = -2 + b
3 + 2= b
5 = b
Then the linear equation is:
y = 2x + 5
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To make 4 cups of rice, Iain needs 5 cups of water. To make 16 cups of rice, he needs 20 cups of water. Write this as a proportion.
4/?=?/?
The proportion when to make 4 cups of rice, Iain needs 5 cups of water and make 16 cups of rice, he needs 20 cups of water is 4/5 = 16/20.
How to calculate the proportion?Proportion in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).
In this case, to make 4 cups of rice, Iain needs 5 cups of water and make 16 cups of rice, he needs 20 cups of water. The proportion will be:
4/5 = 16/20
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Jacob walks 2/5 kilometres in 1/4 hour. what is jacobs speed in kilometres per hour?
Jacob's speed in kilometers per hour is equal to 8/5 kilometers per hour.
What is speed?In Science, speed can be defined as the distance covered by a physical object or body per unit of time. This ultimately implies that, speed is a scalar quantity because it has magnitude but no direction.
Mathematically, the speed of a physical object or body can be calculated by using this formula;
Speed = distance/time
Substituting the given points into the speed formula, we have the following;
Speed = 2/5/(1/4)
Speed = 2/5 × 4/1
Speed = 8/5 kilometers per hour.
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What was the intensity of the earthquake on the Richter scale?.
The intensity of the earthquake on the Richter scale of magnitude 5.3 can be calculated for moderate earthquakes, and a strong earthquake can be estimated at magnitude 6.3.
The idea of a logarithmic earthquake magnitude scale was first developed by Charles Richter in the 1930s to measure the magnitude of earthquakes occurring in Southern California using relatively high frequency data from a nearby seismometer station. Developed. The magnitude of an earthquake is expressed on a scale called the Richter scale. The Richter scale is a base 10 logarithmic scale, meaning that each magnitude is ten times stronger than the last. So 2 is 10 times stronger than 1 and 3 is 100 times stronger. On the Richter scale, the increment is the amplitude of the wave. In the Richter scale, magnitude is represented by whole numbers and decimals. More destructive earthquakes are usually between magnitude 5.5 and 8.9. A truly destructive earthquake is an earthquake that exceeds magnitude 7 on the Richter scale.
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tyler works in a shoe store. the store bought a pair of shoes for 50$, and sold it for 80$. what percentage was the markup?
Answer:160%
Step-by-step explanation:
100%...........50 80:0.5=160
1%..............0.5 50:100=0.5
?.............80
160%...............80
What is the distance between the points 2 0 and (- 2 0?.
The required distance between given pair of points ( 2, 0 ) and ( -2,0 ) is equal to 4 units.
As given in the question,
Given pair of points in the coordinate plane is represented by the coordinates
( x₁ , y₁ ) = ( 2, 0 )
( x₂ , y₂ ) = ( -2,0 )
Apply the standard formula to calculate the distance between two pair of points in the coordinate plane is :
= √(x₂ - x₁ )² + ( y₂ - y₁ )²
Substitute the values in the formula and calculate the distance between two pair of points :
= √ ( -2 - 2 )² + ( 0 - 0 )²
= √(-4)² + 0²
= √16
= 4
Therefore, the required distance between the given pair of points ( 2, 0 ) and ( -2,0 ) is equal to 4 units.
The above question is incomplete , the complete question is:
What is the distance between the pair of points (2, 0) and (-2, 0) ?
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Answer: The answer is 2
Step-by-step explanation:
What is the circumference of a circle with a diameter of 62 centimeters?
Answer:194.78 cm
Step-by-step explanation:
Muic player A: y= 191x-32
Muic player B: y=-x^2200x20
A. On what day did the company ell the ame number of each player?
B. How many player were old on that day?
a. On the 13th day the company sold the same number of each player.
b. 2,451 players were sold on that day.
a. The day on which the company sold the same number of players can be calculated by equating the values of y that we have ;
y = 191x-32 and y = -x² + 200x + 20
Equating both, we have;
191x-32 = -x² + 200x + 20
⇒x² -200x + 191x-20-32 = 0
⇒x²-9x-52 = 0
⇒x²-13x + 4x -52 = 0
⇒x(x-13)+4(x-13) = 0
⇒(x-13)(x+4) = 0
⇒x = 13 or -4
as days cannot be negative, so we choose only x = 13
This means that the company sold equal numbers of players on the 13th day.
b. To get the number of players sold on that day, we select any of the y equations and substitute x = 13
Thus, y = 191x -32; 191(13) - 32 = 2,451 players
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The complete question is:
The equation below models the numbers of two portable music players (y) and days after both players were introduced (x).
Music player A: y=191x-32 and music player B: y=-x^2+200x+20
1. on what day(s) did the company sell the same number of each player?
2. how many players were sold on THAT day (use your answer from #1
60% of tudent like wimming, 40% like dancing, 20% of tudent that like wimming like dancing , how many tudent don't like wimming
So, 40% of students don't like swimming.
We know that 60% of students like swimming, and 40% of students like dancing. We also know that 20% of students that like swimming also like dancing.
First, we can find the number of students that like swimming and dancing by multiplying the percentage of students that like swimming by the percentage of students that like dancing and also like swimming:
20% * 60% = 12%
This means that 12% of students like both swimming and dancing.
To find the percentage of students who don't like swimming, we can subtract the percentage of students who like swimming from 100%.
100-60 = 40%
So, 40% of students don't like swimming.
It's important to note that if the problem had provided a total number of students this information would have been useful to calculate the exact number of students who don't like swimming.
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hep me with the question please!
Answer:
i can not see the question
Step-by-step explanation:
please upload a New photo
How do you calculate equivalent form?.
To calculate equivalent form of an algebraic expression we can use the following :
1) distributing property
2) factoring.
Two mathematical expressions are said to be equivalent if they yield the same result upon solving them. To represent equivalent form an equality (=) sign is used. 3(x + 2) and 3x + 6 are equivalent expressions because the value of both the expressions remains the same for any value of x. To calculate equivalent form by using Distributive Property :
Start with an algebraic expression. Let's take an example 2x(3y + 2).Distribute the multiple 2x throughout the rest of the equation. That is multiplying 2x by 3y and by 2, we get 6xy + 4x.This is our equivalent expression. It can be represent as equality : 2x(3y + 2) = 6xy + 4x.To calculate equivalent form Using Factoring :
Identify the common factors in the expression. If possible divide the equation to find an equivalent expression.Let the expression 5xy + 4x, in this case, both numbers 4 and 5 are co-prime. As we see that there is common factor, x. Take the other common factors: x(5y + 4).This gives you an equivalent form . Again, the equality form, 5xy + 4x = x(5y + 4). Thus, the required equivalent form is determined.
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An investor invested a total of $3,200 in two mutual funds. One fund earned a 6% profit while the other earned a 4% profit. If the investor's total profit was $152, how much was invested in each mutual fund?
$1200 was invested at a mutual fund of 6% profit while $2000 was invested at a mutual fund of 4% profit
What is an equation?An equation is an expression showing the relationship between numbers and variables.
Let x represented the money at 6% profit and y represent the money at 4% interest. A total of $3200 was invested, hence:
x + y = 3200 (1)
If the investor's total profit was $152, therefore:
0.06x + 0.04y = 152 (2)
From both equations:
x = 1200, y = 2000
$1200 was invested at 6% while $2000 was invested at 4%
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