What is Set Theory Formula?
The set formula is given in general as n(A∪B) = n(A) + n(B) - n(A⋂B), where A and B are two sets and n(A∪B) shows the number of elements present in either A or B and n(A⋂B) shows the number of elements present in both A and B.
In a set theory, there are three major types of operations performed on sets, such as: Union of sets (∪) Intersection of sets (∩) Difference of sets (–)
Set Operations include Set Union, Set Intersection, Set Difference, Complement of Set, and Cartesian Product of Set
Set Union
The union of sets A and B (denoted by A ∪ B) is the set of elements that are in A, in B, or in both A and B. Hence, A ∪ B = { x | x ∈ A OR x ∈ B }.
n(A∪B) = n(A) + n(B) − n(A∩B)
Set Intersection
The intersection of sets A and B (denoted by A ∩ B) is the set of elements which are in both A and B. Hence, A ∩ B = { x | x ∈ A AND x ∈ B }.
n(A∩B) = n(A)+n(B)−n(A∪B)
Set Difference
The set difference of sets A and B (denoted by A - B) is the set of elements that are only in A but not in B. Hence, A - B = { x | x ∈ A AND x ∉ B }.
Complement of a Set
The complement of a set A (denoted by A’) is the set of elements which are not in set A. Hence, A' = { x | x ∉ A }. More specifically, A'= (U - A) where U is a universal set that contains all objects.
The complement of a universal set is an empty set U′ = ϕ. The complement of an empty set is a universal set ϕ′ = U.
Cartesian Product / Cross Product
The Cartesian product of n number of sets A1, A2, ... An denoted as
A1 × A2 ... × An can be defined as all possible ordered pairs
De-Morgan's Law - The De Morgan's law states that for any two sets A and B, we have (A ∪ B)' = A' ∩ B' and (A ∩ B)' = A' ∪ B'
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Describe the features of the function that can be easily seen when a quadratic function is given
in the form: y= A(x−A )( x− B) and how they can be identified from the equation.
The features of the functions when a quadratic function is given in the form: y = a (x − p) (x − q)
y = value in the y coordinates
a = constant in the equation
p and q = zeros or roots
x = value in the x coordinates
How to identify features in the equationWhen quadratic equation is written of the form y = a (x − p) (x − q), it is called the factored form of quadratic equation
The other form is ax^2 + bx + c and called standard form of quadratic equation
a in both cases are same and it helps to da if the curve opens upward or downward
when a is positive the curve opens upward but when it is negative the curve opens downward
Expanding the factored form of quadratic equation brings the equation to the standard form
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The ratio of boys to girls in a class is 2:3 if there are 48 pupils in the class.How many boy and girls are there?
tysm po
absolute value -2i help me quick please
The absolute value of the expression given as -2i is 2i
How to determine the absolute value?From the question, we have the following parameters that can be used in our computation:
Expression = -2i
The absolute value of an expression is represented as
Absolute value = |Expression|
Substitute the known values in the above equation, so, we have the following representation
Absolute value = |-2i|
Evaluate the expression
Absolute value = 2i
Hence, the result of the expression is 2i
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can someone help with this? there is also a part two. picture is provided :) (not pt 2)
Solution of the given equation x² -6x +10 =0 using quadratic formula or perfect square method is same in complex number and is equal to 3 + i or 3 - i.
As given in the question,
Given equation is:
x² -6x +10 = 0
Complex number i² = -1
Using perfect square method:
x² -6x + 9 +10 -9 =0
⇒x² -6x +9 =-1
⇒ (x - 3)² = (i)²
⇒x-3 = ± i
⇒ x= 3 ± i
Using quadratic formula,
x = [ -(-6) ±√ (-6)² -4(1)(10)] / 2(1)
=( 6 ± √-4)/ 2
= (6± √4i²) /2
= (6 ± 2i) / 2
= 3 ± i
Therefore, solution of the given equation x² -6x +10 =0 using quadratic formula or perfect square method is same in complex number and is equal to 3 + i or 3 - i.
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The polynomial P(x) of degree 4 has
a root of multiplicity 2 at x = 4
• a root of multiplicity 1 at x = 0 and at x = -1
• It goes through the point (5,21)
Find a formula for P(x).
P(x) =
Question Help: Message instructor
Answer:
P(x) = 0.7 [tex]x^{4}[/tex] - 4.9x³ + 5.6x² + 11.2x
Step-by-step explanation:
given a polynomial with roots x = a and x = b , then the factors are
(x - a) and (x - b)
If x = a is of multiplicity 2 then factor is (x - a)²
the polynomial is then the product of the factors
p(x) = a(x - a)(x - b) ← a is a multiplier
give x = 4 is a root with multiplicity 2 then (x - 4)² is the factor
x = 0 has factor (x - 0) , that is x
x = - 1 has factor (x - (- 1)) , that is (x + 1)
the polynomial is then the product of the factors
P(x) = ax(x + 1)(x - 4)² ← expand squared factor using FOIL
= ax(x + 1)(x² - 8x + 16)
= a(x² + x)(x² - 8x + 16) ← distribute
= a([tex]x^{4}[/tex] - 8x³ + 16x² + x³ - 8x² + 16x)
= a([tex]x^{4}[/tex] - 7x³ + 8x² + 16x)
to find a substitute (5, 21 ) into P(x)
21 = a([tex]5^{4}[/tex] - 7(5)³ + 8(5)² + 16(5))
21 = a(625 - 875 + 200 + 80)
21 = 30a ( divide both sides by 30 )
0.7 = a
then
P(x) = 0.7([tex]x^{4}[/tex] - 7x³ + 8x² + 16x) ← distribute parenthesis
P(x) = 0.7[tex]x^{4}[/tex] - 4.9x³ + 5.6x² + 11.2x
If y varies directly as x, find the constant of variation and the direct variation equation for the situation.
y = 0.1 when x = 0.2
[tex]\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{"y" varies with "x"}}{y=kx}\hspace{5em} \textit{we know that} \begin{cases} y=0.1\\ x=0.2 \end{cases} \\\\\\ 0.1=k(0.2)\implies \cfrac{0.1}{0.2}=k\implies 0.5=k\hspace{5em}\boxed{y=0.5x}[/tex]
9x^7/3x^2=3x^9 true or false
Answer:
False
Step-by-step explanation:
using the rule of exponents
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex]
given
[tex]\frac{9x^7}{3x^2}[/tex]
= [tex]\frac{9}{3}[/tex] × [tex]\frac{x^7}{x^2}[/tex]
= 3 × [tex]x^{(7-2)}[/tex]
= 3[tex]x^{5}[/tex]
Problem 3: Suppose you drive a car 168 miles on one tank of gas. The tank holds 12 gallons of gas.
(Assume the car travels the same distance for each one gallon of gas)
The number of miles traveled varies directly with the number of gallons of gas you use.
a.
Write an equation that relates miles traveled to gallons of gas used. (Use any variable you like in
the equation.
b. low far can you drive with 3.7 gallons of gas? (Make sure to show the calculations you did to
determine this answer)
a) An equation relating the miles traveled to gallons of gas used is m = 14g.
b) With 3.7 gallons of gas, one can drive up to 51.8 miles.
What is an equation?An equation is a mathematical statement that makes two mathematical expressions equivalent or equal using the equation symbol (=).
Equations establish the equality of two or more values, variables, or numbers.
The total distance driven on one tank of gas = 168 miles
The quantity of gas used = 12 gallons
The number of miles per gallon of gas = 14 (168/12)
Let m = distance in miles
Let g = gallons of gas used
Equation: m = 14g
Solution:
Gallons of gas used = 3.7
m = 14g
= 14(3.7)
= 51.8 miles
Thus, based on the established equation, with 3.7 gallons of gas used, the driver can cover 51.8 miles.
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7th grade math: can you help? i only need help on 1, 2, 3, & 4
By using percentage, it can be calculated that
1) Percentage increase in area = 25 %
2) Percentage increase in area = 60 %
3) Percentage decrease in area = 25 %
4) Percentage decrease in area = 40 %
What is percentage?
Sometimes there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage.
For example 2% means [tex]\frac{2}{100}[/tex]. Here 2 is expressed as a fraction of 100
1) Original area = 12 sq. yard
New area = 15 sq. yard
Increase in area = 15 - 12 = 3 sq. yard
Percentage increase = [tex]\frac{3}{12}\times 100 \\[/tex]
= 25 %
1) Original area = 15 sq. yard
New area = 24 sq. yard
Increase in area = 24 - 15 = 9 sq. yard
Percentage increase = [tex]\frac{9}{15}\times 100 \\[/tex]
= 60 %
1) Original area = 12 sq. yard
New area = 9 sq. yard
Increase in area = 12 - 9 = 3 sq. yard
Percentage decrease = [tex]\frac{3}{12}\times 100 \\[/tex]
= 25 %
1) Original area = 10 sq. yard
New area = 6 sq. yard
Increase in area = 10 - 6 = 4 sq. yard
Percentage increase = [tex]\frac{4}{10}\times 100 \\[/tex]
= 40 %
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If the quotient is 0 , what is the dividend?
Answer: 0
Step-by-step explanation:
If the dividend and the divisor are the same, the quotient is always 1. If the dividend is the, then the quotient would always be 0. A division equation with 0 dividend and 0 divisor is not valid.
Answer: All real numbers
Step-by-step explanation: Anything that's being divided by 0, is always going to be 0. For example, 0/7 is always 0.
Solve for d. 3 + d < 3 −d
d < −6
d < 6
d < 0
d < −3
Answer:
d is great than -3
Step-by-step explanation:
because negative numbers are less than whole numbers
My friend is hoping to move to your town but is concerned because she doesn’t have a car. Do you think this will present a big problem for her? Use the distance formula in some way to justify your response.
There are many things obstructing the route so yes. I cannot give a detailed answer as I have not been given the "distance formula" sorry
This is just a question but. if I had a power of ten that was let's say.... 10 3 would i write it like 10000 or 1000?
Answer:
10^3 = 1000
Step-by-step explanation:
10 * 10 * 10 = 1000
Answer:
1000
Step-by-step explanation:
it is ten to the third power so 10*10*10 and then you get the answer of:
1000
I hope this helped!
The time is takes an object to move a certain distance is inversely propotional to the speed that it's travelling at.
it takes a car 12 minutes to travel the length of a road if it goes at an average speed of 60mph
a) How long would it take the car to travel down the same road if it travelled at an average speed of 30mph
Answer:
Hope the picture will help you
What is the solution to -4(8-3x) ≥ 6x - 8?
O
4
x²--1/32
O x≤
xs--1/72
Ox≥4
Ox≤4
Answer:
x ≥ 4
Step-by-step explanation:
-4 ( 8 - 3x ) ≥ 6x - 8
First, solve the brackets.
- 32 + 12x ≥ 6x - 8
Subtract 6x from both sides.
- 32 + 12x - 6x ≥ - 8
- 32 + 6x ≥ - 8
Add 32 to both sides.
6x ≥ - 8 + 32
6x ≥ 24
Divide 6 by both sides.
x ≥ 4
1.You need to earn at least $90. You earn $7 for each hour you work.
Which inequality represents the number of hours h that you need to
work?
(Look at the picture for options for the answer)
2. Write a graph that represents the solution
Answer:
Inequality:
Graph choice:
Step-by-step explanation:
Inequality
It says at least 90, which means we have to use the greater than or equal to sign
Our inequality so far: 90≥______
Now it says you earn 7 dollars per hour, which means 7 times the number of hours you work or 7h. Our inequality now looks like this:
90≥7h
The answer choice that matches is A (90≥7h = 7h≤90)
For the second question on the bottom, I added an image.
(Answer is B)
SOMEONE HELP GEOMETRY THXX
The lines p and q are parallel.
What are alternate exterior angles?Alternate Exterior Angles are a pair of angles on the outer side of each of those two lines, but on opposite sides of the transversal.
Given a figure,
Since, ∠ 1 ≅ ∠ 5 and they are alternate exterior angles, then we can conclude that p║q by alternate exterior angles theorem.
Hence, The lines p and q are parallel.
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3. Simplify the expression.
(3-i)-(2+6i)
01-7i
0-1+7i
0-6i
05+ Si
Answer:(3-i) - (2 +6i)
Combine like terms:
3-2 = 1
-i - 6i = -7i
Combine to get 1 -7i
Step-by-step explanation:
1: A middle School had a school spirit day
In one class the ratio of students who wore
School colors to the number of students who
Didnt was 8 to 5 Ten students didn't wear school
Colors, Determine the number of students who wore School
Colors.
Answer:
The number of students who wore School colors are 8/13. If, Ratio of students who wore School colors to the number of students who didn't are given.
Define ratio.A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, and the divisor or number that is dividing is referred to as the consequent. A ratio compares two numbers by division. A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.
Given,
Ratio of students who wore School colors to the number of students who didn't
8:5
Total number of student = 13
Number of students who wore school colors = 8/13
The number of students who wore School colors are 8/13. If, Ratio of students who wore School colors to the number of students who didn't are given.
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What is wrong with having the hypotenuse of a right angled triangle, whose shorter sides are each of one unit, not corresponding to a number?
By using Pythagoras Theorem, it can be verified that
The hypotenuse of a triangle with shorter sides 1 unit each is not an integer
What is Pythagoras Theorem?
Pythagoras Theorem states that in a right angled triangle, the square of the hypotenuse is equal to the square of the sum of Perpendicular and base
According to the question given,
Shorter sides are 1 unit each
Let the length of the hypotenuse be h units
By Pythagoras Theorem,
[tex]h^2 = 1^2 + 1^2\\h^2 = 2\\h = \sqrt{2} \ units[/tex]
[tex]\sqrt{2}[/tex] is not an integer
So the hypotenuse here is not an integer.
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wats the slope?ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ
Anyone please help me
Part 1
[tex]\frac{x}{3.2}=\frac{4}{2} \implies x=6.4 \\ \\ \frac{y}{2.4}=\frac{2}{4} \implies y=1.2[/tex]
Part 2
[tex]\frac{x}{3.6}=\frac{10.8}{5.4} \implies x=7.2 \\ \\ \frac{y}{5.4}=\frac{15.2}{10.8} \implies y=7.6[/tex]
The meteorologist at Channel 8 News predicted that a snowstorm would drop 7 inches of
snow. After the storm, she reported that the actual snowfall was 4 inches. What is the
percent error for the meteorologist's prediction?
If necessary, round your answer to the nearest tenth of a percent.
%
THE percent error is, 5
what is percent error?Percent error calculates the difference between an estimate and a right value and expresses it as a percentage. Analysts can use this statistic to determine how big the error is in relation to the actual number. It is also referred to as % error and percentage error.The estimate and accurate values in this situation might be any of the following:a measurement, an approximation, a value obtained experimentally, or a guess.Correct Value: A number that has been established or is widely regarded as accurate. It might serve as a standard measurement for something tested as a measurement system. Or a value that is theoretically valid and is known, like a circle's circumference.hence,THE percent error is, 5
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1/3[6y+3]-24=3[1/3y-6]
y-3=y-7
x+2x=1/3x-8
y-9=y-2
x-5=6x-5
step by step explanation please
Answer:
Step 1: Simplify both sides of the equation.
1/3(6y+3)−24 = 3(1/3y−6)
1/3(6y) + 1/3(3) -24 = 3(1/3y) + 3(-6)
2y +1 −24 = y−18
2y −23 = y −18
Subtract y from both sides.
2y−23−y=y−18−y
y−23=−18
Step 3: Add 23 to both sides.
y−23+23 = −18+23
y = 5
Step-by-step explanation:
how are the zeros of a polynomial function related to the equation and graph of a function
The way that zeros of a polynomial function is related to the equation and graph of a function because they act as solutions to the equation and also x-intercepts of a graph.
What graphing relationship does a zero have?When the quadratic equation's graph crosses the x-axis, those points are known as the zeros of the equation.
The graph's x-intercepts and a function's zeros are the same thing. If the zero of f has an odd multiplicity, the graph of f will cross the x-axis at that x value. The x-axis will be touched by the graph of f if it has an even multiplicity zero.
Hence, A polynomial's zeros are the answers to any equation such as p(x) = 0, where p(x) stands for the polynomial. Since the values of x where y = 0 if we graph this polynomial as y = p(x). In other words, these are the graph's x-intercepts.
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Adam has 6 cookies less than
Tony, there are a total of 15 cookies between both of them.
How many cookies does Tony
have?
Tony has 10.5 cookies.
What is linear equation?A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order term, where m is the slope and b is the y-intercept.
Given that, Adam has 6 cookies less than Tony, there are a total of 15 cookies between both of them.
Let the number of cookies Tony has be x,
x+x-6 = 15
2x - 6 = 15
2x = 21
x = 21/2 = 10.5
Hence, Tony has 10.5 cookies.
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please help me i never learned divison im sorry87,628÷931=
Answer:
94.1224489796
this is the answer
Select the correct answer.
Consider the function given below.
f(x) = lx-5l +2
Which of the following statements about the y-values of the graph of the function is true?
A. The y-values are all greater than or equal to 5.
B. The y-values are all greater than or equal to 2.
C. The y-values are all less than or equal to 2.
D. The y-values are all less than or equal to 5.
The statement which is true about the y-values of the graph of the function as required is; Choice B; The y-values are all greater than or equal to 2.
Which statement is true regarding the y-values?It follows from the task content that the statement which is true regarding the y-values of the graph defined by; f(x) = lx-5l +2 is to be determined.
Therefore, we must recall that expressions enclosed in the absolute value sign upon evaluation are always greater than or equal to zero.
Hence, it can be concluded that we the y-values of the resulting graph to be greater than or equal to 2 (on the occasion that; lx-5l = 0).
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Work out the values of a, b, c and d.
Justify each of your answers.
In the given circle, the values of required angles are as follow:
a = 51°, b = 28° , c = 31°, and d = 70°.
As given in the question,
In the given circle,
As we know by theorem , angles formed in the same arc are congruent.
Angle a° and angle 51° is formed in the same arc XY .
⇒ Value of a = 51°
Angle b° and angle 28° is formed in the same arc ZY .
⇒ Value of b = 28°
Angle c° and angle 31° is formed in the same arc WX .
⇒ Value of c = 31°
Angle d° and angle 70° is formed in the same arc WZ .
⇒ Value of d = 70°
Therefore, in the given circle the values of required angles are as follow: a = 51°, b = 28° , c = 31°, and d = 70°.
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write the equation of the line that is perpendicular to the line y=-2 and passes through (4,-2)
the equation of the perpendicular line is x = 4, as the line vertical and the slope is undefined
What is the equation of the line that passes through the given point and is perpendicular to the given line?The point-slope formula is expressed as
y - y₁ = m( x - x₁ )
The slope intercept formula is expressed as;
y = mx + b
Where m is the slope and b is y-intercept.
Given the data in the question;
Equation: y = -2Point (x,y) : (4,-2)First, we determine the slope of the initial line by comparing to the slope intercept form y = mx + b
y = -2
Hence
Slope of initial line m = 0
Slope of the perpendicular line will be negative reciprocal of the initial line
m = -1/0
Slope m is undefined
Therefore, the perpendicular line is vertical and the slope is undefined
Hence.
x = 4.
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