The algebraic identities are
(x + y)² = x² + y² + 2xy,
(x – y)² = x² + y² – 2xy,
x² – y² = (x + y) (x – y),
(x + a) (x + b) = x² + (a + b)x + ab,
(x + y)³ = x³ + y³ + 3xy(x + y),
(x – y)³ = x³ – y³ – 3xy(x – y),
(x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx,
x³ + y³ + z³ – 3xyz = (x + y + z) (x² + y² + z² – xy – yz – zx) .
These algebraic identities basically carry variable equations in such a way, that the Left-hand side (L.H.S) of the equation is equal to its Right-hand side(R.H.S).
What is the use of algebraic identities?
Algebraic Identities help in simplification. Algebraic Identities play a major role in solving quadratic equations and higher power equations.
The algebraic identities are also used to calculate products of numbers and other things.
Let us consider x, y and z are variables.
Algebraic Identities for Two Variables x and y :
(x + y)² = x² + y² + 2xy
(x – y)² = x² + y² – 2xy
x² – y² = (x + y) (x – y)
(x + a) (x + b) = x² + (a + b)x + ab ; a and b are two constant values
(x + y)³ = x³ + y³ + 3xy(x + y)
(x – y)³ = x³ – y³ – 3xy(x – y)
Algebraic Identities for Three Variables x, y and z :
(x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx
x³ + y³ + z³ – 3xyz = (x + y + z) (x² + y² + z² – xy – yz – zx)
So, the algebraic identities are
(x + y)² = x² + y² + 2xy,
(x – y)² = x² + y² – 2xy,
x² – y² = (x + y) (x – y),
(x + a) (x + b) = x² + (a + b)x + ab,
(x + y)³ = x³ + y³ + 3xy(x + y),
(x – y)³ = x³ – y³ – 3xy(x – y),
(x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx,
x³ + y³ + z³ – 3xyz = (x + y + z) (x² + y² + z² – xy – yz – zx) .
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How do you identify the horizontal asymptote of a graph?.
The horizontal asymptote of the graph is the horizontal line y = b and the graph approaches a straight line as the input approaches ∞ or −∞.
Horizontal Asymptote: As x moves towards infinity or -infinity, the curve approaches a constant value b, called a horizontal asymptote with equal numerator and denominator. The following are used to determine the horizontal asymptotes:
If the degree of numerator and denominator polynomials are equal, then the horizontal asymptotes is obtained by dividing the highest degree cofficientes.If the numerator degree is less than the denominator degree, the horizontal asymptote is y = 0.If the numerator degree is greater than the denominator degree, there is no horizontal asymptote.For example, function f(x) = 2x / (x - 3) and we have to determine the horizontal asymptotes. As we see the degree of polynomials both in numerator and denominator is equal. So, horizontal asymptotes is equal to number which is obtained by dividing the hightest degree coefficients i.e., 2/1 = 2. Thus, the function has only one horizontal asymptote which is y = 2. Here is the graphical verification.
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help pls i need to pass
The sample space would be ((H, W), (H, M), (T, W), (T, M), (C, W), (C, M)}.
Option (C) is correct.
What is the sample space?
The sample space is the set of all possible outcomes of a random experiment.
In this case, the experiment is ordering a sandwich from the shop, and the possible outcomes are the different combinations of sandwich type and bread type. Choice C represents all the possible outcomes of the experiment and it is the correct answer.
C) ((H, W), (H, M), (T, W), (T, M), (C, W), (C, M)}
Hence, the sample space would be ((H, W), (H, M), (T, W), (T, M), (C, W), (C, M)}.
Option (C) is correct.
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Select all expressions that could be equivalent to x^2+bx-36 where b is negative
The expressions that could be equivalent to x^2+bx-36 where b is negative is option 1: (x + 3)(x - 12) and option 5: (x - 9)(x + 4).
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
The given expression is - x² + bx - 36
The first expression is - (x + 3)(x - 12)
Solve using the multiplication property -
= (x + 3)(x – 12)
= x(x - 12) + 3(x - 12)
= x² - 12x + 3x - 36
= x² - 9x - 36
The second expression is - (x - 2)(x + 18)
Solve using the multiplication property -
= (x - 2)(x + 18)
= x(x + 18) - 2(x + 18)
= x² + 18x - 2x - 36
= x² + 16x - 36
The third expression is - (x - 13)(x - 3)
Solve using the multiplication property -
= (x - 13)(x - 3)
= x(x - 3) - 13(x - 3)
= x² - 3x - 13x + 39
= x² - 16x + 39
The fourth expression is - (x + 4)(x + 9)
Solve using the multiplication property -
= (x + 4)(x + 9)
= x(x + 9) + 4(x + 9)
= x² + 9x + 4x + 36
= x² + 13x + 36
The fifth expression is - (x - 9)(x + 4)
Solve using the multiplication property -
= (x - 9)(x + 4)
= x(x + 4) - 9(x + 4)
= x² + 4x - 9x - 36
= x² - 5x - 36
Therefore, the choices for b being negative is x² - 5x - 36, and x² - 9x - 36.
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Select all expressions that could be equivalent to x^2+bx-36 where b is negative.
(x + 3)(x - 12)
(x - 2)(x + 18)
(x - 13)(x - 3)
(x + 4)(x + 9)
(x - 9)(x + 4)
Why earthquakes with the greatest magnitude do not always cause the highest number of deaths?.
The earthquakes with the greatest magnitude do not always cause the highest number of death because other factors like area ( ground, water , sand etc.), soil structure, buliding constutor material etc. also affect the earthquake intensity.
The biggest earthquakes are not necessarily the most devastating ones. But other factors are also involved here. In areas of water-saturated sand, shaking loosens the sand particles from each other, causing them to "float" on the water and turn into quicksand. Sand at rest is still and hard, but when shaken it forms liquid mud. Buildings and other structures built on such sand simply sink and collapse. Other types of soil structures and terrain can amplify and resonate seismic waves, potentially causing more damage. Of course, if an earthquake occurs at sea, it can create a devastating tsunami. Also, certain structures and buildings are less susceptible to vibration than others due to how they are constructed and the materials used. For example, a large magnitude 9.0 earthquake might cause minor damage due to its remote location. But if 6.0 occurs in an underdeveloped and densely populated area, it could kill thousands.
The more people there are, the more people die. For example, the 2001 earthquake in India occurred in a densely populated area.
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What is the complete factor of 3x² 6x?.
The complete factor 3x² 6x or 3x² - 6x are 3x and (x-2) and the factor form can be written as 3x( x - 2).
Polynomial factorization represents a polynomial with coefficients in a given field, or an integer as a product of irreducible factors with coefficients in the same domain. Full factoring is a three step process :
Factor a Greatest Common Factor (GCF) from the expression, if possible. Example: 3x² + 9x³ + 12x⁴, factored into 3x²(1 + 3x + 4x²).2. Factor a Trinomial, if possible.
Example: x² – 2x – 3 factored into
(x + 1)(x – 3).
3. Factor a difference between two
Squares as many times as possible.
Example: y²– 9 factored into
(y + 3)(y – 3).
We have, a polynomial (binomial) say, p(x) = 3x² - 6x , and we have to complete factorize it. Follows the steps,
=> 3x( x - 2 ) , (irreducible factors). Therefore, the 3x is a common factor that we can be factored out and keeping the x minus sign 2 .
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Kate buy 10 ticket to a how. She alo pay a $5 parking fee. She pent $35 to ee the how
The equation in the said case is 10x + 5 = 35
Tickets bought = 10
Parking fee paid = $5
Money spent on seeing the show = $35
Determining the equation in the given case -
10x + 5 = 35
Where x is the cost of each ticket, and 10x represents the total cost of the tickets.
The equation states that the total cost of the tickets which is 10x plus the cost of the parking fee which is $5 is equal to the total amount spent by Kate which will be 35$.
This equation can be further used to find the cost of each ticket by isolating x:
10x + 5 = 35
10x = 30
x = 3
Therefore, each ticket cost $3.
Complete Question:
kate buys 10 tickets to the show. She also pays a 5$ parking fee. she spent $35 to see the show. What equation is this
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HELP!! pls this is the last chance
Step-by-step explanation:
the arc angle KLI = 142°.
that means that the arc angle KJI = 360 - 142 = 218°.
this is twice the inscribed opposite angle on the arc (L).
so,
(a)
angle KLI = 218/2 = 109°
(b)
for the same reason
angle LKJ is half of the arc angle LIJ.
arc angle LIJ = 2× angle LKJ = 2×66 = 132°
that means
arc angle LKJ = 360 - 132 = 228°
angle LIJ = half of arc angle LKH = 228/2 = 114°
FYI for such an inscribed quadrilateral there is Akari the rule that the sum of opposite angles have to be 180°.
so, angle LIJ is opposite of angle LKJ.
angle LIJ = 180 - angle LKJ = 180 - 66 = 114°
How do you find the lower limit of a modal class 10?.
The lower limit of a modal can be calculated by determining the lowest frequency interval having a smallest value.
In mathematics, limits are the points at which a function approaches the output for the specified input values. Calculus and mathematical analysis depend heavily on limits, which are required to determine integrals, derivatives, and continuity. It is applied during the analysis process and always focuses on the function's behavior at a certain time.
Let the least term 'h' of a sequence be a term which is smaller than all but a finite number of the terms which are equal to 'h'. Then 'h' is called the lower limit of the sequence.
A lower limit of a series,
lower[tex]\lim_{n \to \infty} S_n = \lim_{n \to \infty} S_n = h[/tex]
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Sue and Jaya were selling magazines. They collected $10.25 the first day, $14.35 the second day, $15.45 the third day, and $9.60 the fourth day. If Sue and Jaya had set a goal of $60.00, how much more money do they need to earn from the sales of magazines?
Answer:
10.35
Step-by-step explanation:
Add 10.25+14.35+15.45+9.60= 49.60
60-49.65=10.35
How to multiply 2 digit numbers by 2 digit numbers without regrouping?.
Multiply the number in the one's place. Multiply the number in the ten's place. And then add them up.
Multiply 2-Digit Numbers Without Regrouping:
Follow along with example 43 × 32:
Place one number above the other so that the ones' place digits and tens' place digits are lined up. Draw a line beneath the bottom number.
4 3
×3 2
_______
Multiply the ones' place digits (2 × 3 = 6) and one's place of the second number by the ten's place of the first number (2 × 4 = 8). Place the 6 below the line in the ones' place column and 8 below the line in the tens' place column.
4 3
×3 2
_________
8 6
Multiply the digit in the tens' place column (3) by the digit in the ones' place of the first number (3). The result is 3 × 3 = 9 and Multiply the digit in the tens' place column (3) by the digit in the tens' place of the first number (4). The outcome is 3 × 4 = 12. Now add the numbers and place the answer below the line.
4 3
×3 2
__________
8 6
12 9×
__________
13 76
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3. Jen answered 80% of the 150 test
questions correctly. How many
questions did she not answer
correctly?
What do you call to a function of the form f/x )= Logbx where B 0 and B ≠1?.
An
What is the degree of the polynomial function f x 2x3 7x5 − 4x − 12?.
The highest power of this function is 5 , so the degree of this polynomial is 5 .
The degree of polynomial is highest power of variable in a polynomial expression. The polynomial’s degree is the greatest power of a variable in a polynomial equation. The degree of polynomial indicates the highest exponential power in polynomial (the coefficients are ignored).
the polynomial function is ⇒ f(x) = 2x³ + 7x⁵ + 4x + 12 ;
we see that the second term "7x⁵" has the greatest power ,
So , we can conclude that the degree of the polynomial function is 5 .
The given question is incomplete , the complete question is
What is the degree of the polynomial function f(x) = 2x³ + 7x⁵ + 4x + 12 ?
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find slope and y intercept for brainliest
Answer: Slope = - 1/3, the y-intercept = -4
Step-by-step explanation:
Pick two coordinates: (-1, -1), (2, -2)
Find the slope: y2 -y1 / x2 - x1
-2 - (-1) / 2 - (-1) = - 1/3
Slope intercept form: y = mx + b
Substitute in what you know to find b:
-1 = -1/3 (-1) + b substitution property
-1 = 1/3 + b distributive property
-3 = 1 + b multiplication property
-4 = b subtraction property
arturo walks from school to the city library. He walks 4 miles per hour. When Arturo is 0.2 mile from school, Carson leaves school. Carson jogs 6 miles per hour. The system of equations can be used to find when Carson catches up with Arturo.
4t + 0.2 = 6(t+x) this system of equations can be used to find when Carson catches up with Arturo.
What is a system of equations?
A solution to a system of equations is a set of values for the variable that satisfy all the equations simultaneously. In order to solve a system of equations, one must find all the sets of values of the variables that constitute solutions of the system.
The system of equations that can be used to find when Carson catches up with Arturo is:
distance = speed x time
For Arturo:
distance = 4t + 0.2
For Carson:
distance = 6(t+x)
where t is the time in hours that Arturo has been walking, x is the time in hours that Carson has been jogging, and distance is measured in miles.
Equating the two equations to find when they meet:
4t + 0.2 = 6(t+x)
And solving for x, the time in hours that Carson has been jogging.
x = (4t + 0.2 - 4t)/6 = 0.2/6 = 1/30
This is the time in hours that Carson has been jogging when he catches up with Arturo.
Hence, 4t + 0.2 = 6(t+x) this system of equations can be used to find when Carson catches up with Arturo.
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What is equivalence class class 12?.
The equivalence class of a is [a] = {x ∈ A: (a, x) ∈ R}. This includes all elements of A that are related to 'a'.
An equivalence class is the name we give to the subset S that includes all elements that are equivalent to each other. If there is an equivalence relation between any two elements, they are called equivalent.
Equivalence class properties : The relation ~ is an equivalence relation if and only if:
It is reflexive: any a∈ X , a ~ aIt is symmetric: Let a, b ∈ X . if a ~b ⇔ b ~ a.It is transitive: Let a, b, c ∈ X ; if a ~ b and b ~ c, it follows that a ~ c.When our relation ~ satisfies the above three properties, we can write the definition of an element equivalence class as follows [a] = { x ∈ X | and ~ x}. Consider an example, If X were the set of all polygons and the equivalence relation ~ was defined as "having the same number of sides", the set of all triangles, the set of all quadrilaterals, the set of all pentagons, etc., are represents the equivalence classes.
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Complete question:
What is equivalence class ?
please help answer this
Answer: 24.2
Step-by-step explanation: Use the Pythagorean Theorem:
10^2 + 22^2 = x^2
100 + 484 = x^2
x^2 = 584
x = 24.16609..
which is close to 24.2
Answer: 24.2
Step-by-step explanation:
Use the Pythagorean Theorem.
[tex]a^2 + b^2 = c^2[/tex]
We already know a and b.
We can plug it in into the theorem.
[tex]10^2 + 22^2 = c^2[/tex]
[tex]584 = c^2[/tex]
Then, take the square root of 584.
[tex]\sqrt{584}[/tex] ≈ 24.2 (24.16 rounded up is 24.2)
An antique store increases all of its prices by 40$ and then announces a 25 off-everything sale. What percent of the original prices (before the increase) is the new prices?
Answer: 62.5%.
hope this helped
What is the sum of 11 of the interior angles of a regular dodecagon?
Regular dodecagons have internal angles that are the same size and have equal length sides and the interior angles of the dodecagon total 1800 degrees.
What is a dodecagon?A regular dodecagon is a shape with equal-length sides and equal-sized internal angles.
It features rotational symmetry of order 12 and twelve reflected symmetry lines.
The Schläfli symbol for a regular dodecagon is 12, and it can be formed from a truncated hexagon (t6) or twice-truncated triangle (tt3).
In a regular dodecagon, the internal angle at each vertex is 150°.
The dodecagon's internal angles add up to 1800 degrees.
A 12-sided polygon is called a dodecagon.
The illustrations above show several unique varieties of dodecagons.
A regular polygon known as a regular dodecagon is a dodecagon with vertices evenly placed around a circle and all sides having the same length.
Therefore, the interior angles of the dodecagon total 1800 degrees.
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You took a taxi to your house from the airport. The taxi company charges an initial fee of $5 and then $4 per mile. When the ride is over, you end up paying a total fare of $49. How many miles away is your house from the airport?
Answer:11 miles
Step-by-step explanation:
so, no matter what you pay $5, and each mile is $4, so you pay $49 dollars. First do 49 - 5, which equals 44, and 44 ÷ 4 = 11, so the answer is 11 miles
Let us assume that you started a job on 08/21/2019. You graduated on 05/20/2022. How many days have you been working at the job as a student?
Group of answer choices
1215
1287
905
1003
I have been working 1004 days at the job as a student
What are algebraic operations?They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
To solve this problem we must perform the following algebraic operations with the given information
Information about the problem:
Start = 08/21/2019Graduated = 05/20/2022Days = ?Calculating the days from 08/21/2019 to 08/21/2022, we get:
Days 1 = (08/21/2022 - 08/21/2019) * (365 days/1 year)
Days 1 = 3 years * (365 days/1 year)
Days 1 = 1095 days
Calculating the days from 05/21/2019 to 08/21/2019, we get:
Days 2 = (08/21/2019 - 05/21/2019) * (30 days / 1 month)
Days 2 = 3 month * (30 days / 1 month)
Days 2 = 90 days
Calculating the days from 05/20/2019 to 05/21/2019, we get:
Days 3 = 05/21/2019 - 05/20/2019
Days 3 = 1 day
Calculating the total days from 08/21/2019 to 05/20/2022, we get:
Total days = Days 1 - days 2 - days 3
Total days = 1095 days - 90 days - 1 day
Total days = 1004 days
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What is an example of a linear inequality?.
An example of a linear inequality: 5m > 7 + 3p
We know that the linear inequality in two variables represents the inequalities between two algebraic expressions with two variables .
It is an unequal relation between two algebraic expressions.
The symbols used between the expression: less than ‘<’,
greater than ‘>’,
less than or equal to ‘≤’
greater than equal to ‘≥’,
consider an example of a linear inequality:
3x < 2y + 5
5m > 7 + 3p
We can say that a linear inequality is like a linear equation (ax + by = c) but it has an inequality (like <, >, ≤, or ≥) instead of an =
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Help me again I really need help
The simplified expression of the given expression is 6x + (-21).
What is simplified expression?
Simplified expression is that expression which does not contains any like terms. When in an expression, all the like terms are combined and all of the specified brackets are solved, then only unlike terms are left in the simplified expression which cannot be further reduced.
We are given expression as 6 + 2(x-8) + 3x -11 + x
Now, on simplifying the expression, we get
⇒ 6 + 2x - 16 + 3x - 11 + x
⇒ 6x - 21
⇒ 6x + (-21)
Hence, the simplified expression of the given expression is 6x + (-21).
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Since, there are multiple questions so the question I answered is attached below.
Aiko works in the fish department of a pet store. She must drain, clean, and refill two reef tanks. the first tank hold 175 gallons of water and drains at a rate of 25 gallons per hour. The second tank holds 200 gallons of water and drains at a rate of 30 gallons per hour.
1. Write an equation for each tank representing the total amount of water in gallons in the tank, y, in terms of the number of hours, x, that the tank drains
2. what is the solution to this system of equations.
3. suppose Aiko starts draining the tanks at the same time. When will both tanks have the same amount of water? How much water is in each tank at that time
The answers to each part is mentioned above.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that Aiko works in the fish department of a pet store. She must drain, clean, and refill two reef tanks. The first tank hold 175 gallons of water and drains at a rate of 25 gallons per hour. The second tank holds 200 gallons of water and drains at a rate of 30 gallons per hour.
( 1 ) -Equation for tank {1} -
y = 175 - 25x
Equation for tank {2} -
y = 200 - 30x
( 2 ) -For the solution we can write -
175 - 25x = 200 - 30x
- 25x + 30x = 200 - 175
5x = 25
x = 5
and
y = 200 - 150
y = 50
( 3 ) -For the same amount of water we can write -
175 - 25x = 200 - 30x
- 25x + 30x = 200 - 175
5x = 25
x = 5 hours
In tank (1), there is : 175 - 25 x 5 = 50 gallons
In tank (2), there is : 200 - 30 x 5 = 50 gallons
Therefore, the answers to each part is mentioned above.
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A hark i born meauring 20 inche in length. After 6 month, the hark i now 46 inche long. If x i the age of the hark in month, then y i the length of the hark in inche. At what rate i the hark growing? State your anwer a a reduced fraction. Inche per month Find an equation of a line in the form y = mx b that decribe the hark' length
A line is a one-dimensional shape that is straight. The equation of the line that describes the shark's length is [tex]y = \frac{13}{3}x + 20\\[/tex].
What is the equation of a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by:
[tex]y = mx + c[/tex]
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is constant.
Given when the shark was born the length of the shark was 20 inches, therefore, the coordinates can be written as (0,20).
Similarly, the length of the shark is 46 inches, while the age of the shark is 6 months. Therefore, the coordinates can be written as (6,46).
Now, the slope of the line can be written as,
m = (46-20)/(6-0) = 13/3
Now, the equation of the line can be written as [tex]y = \frac{13}{3}x + c[/tex], further, substitute the value of any point in the equation of the line, therefore,
20=13/3(0)+c
c=20
Hence, the equation of the line that describes the shark's length is :
[tex]y = \frac{13}{3}x + 20\\[/tex].
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Question 7 of 25
f(x)=√x-4. Find the inverse of f(x) and its domain.
OA. f-¹(x) = x² + 4; x≥0
OB. f-¹(x) = (x+4)²; x ≥ -4
OC. f-¹(x) = x² + 4; x ≥-4
OD. f-¹(x) = (x+4)²; x≥0
The inverse of the function f(x) and its domain include the following: D. f⁻¹(x) = (x + 4)²; x ≥ 0.
How to find an inverse function?In order to determine an inverse function or the inverse of any function, you should swap both the input value (x-value) and output value (y-value) as follows;
f(x) = √x - 4
y = √x - 4
x = √y - 4
√y = x + 4
Taking the square of both sides of this inverse function, we have:
f⁻¹(x) = (x + 4)²
For the domain of this function, we have the following:
f(x) = √x - 4
When x= 0, we have:
f(0) = √0 - 4
f(0) = 0.
In conclusion, the domain of this function cannot be equal to -4 because it is impossible to find the square root of a negative number.
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what is the value of 1/2 divided by 1/3
Answer:
1 1/2
Step-by-step explanation:
The cost of 2 footballs and 3 tennis balls is £21.73. The cost of 5 footballs and 7 tennis balls is £53.20. Work out the cost of a) a football. b) a tennis ball.
Answer:
cost of football = 7.49
cost of tennis = 2.25
Step-by-step explanation:
One meter equals 3.281 feet, so 4 meters=
Do not round your asnwer.
feet
Answer:
13.124 ft
Step-by-step explanation:
1 m = 3.281 ft
4 m = 4 × 3.281 ft = 13.124 ft
How do you find the range of a negative function?.
The range of a negative function are those which lies in the intervals where the function is below the x-axis.
The range function can be positive or negative because the range formula substracts the lowest number from the highest number. A negative function has all negative values. The negative function has values that are all negative. The domain of the function can be positive. Every output must be less than zero. A negative function has values that are negative for all arguments of its domain. The function values can be positive or negative. They can increase or decrease as the input increases.
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