F and H are sets of real numbers defined as follows.
F = { v l v < 4}
H = { v l v ≥ 7}
Write F ∩ H and F ∩ H using interval notation. If the set is empty, write ∅.
For the two sets F = {v | v < 4} and H = {v | v ≥ 7}, F∩H = Ф and
F∪H = {v | v ∈ R} - {4, 5, 6}.
What are sets and subsets?A set is a collection of well-defined objects.
A subset contains all the elements or a few elements of the given set.
The improper subset is when it contains all the elements of the given set and the proper subset is when it doesn't contain all the elements of the given set.
Given, Are two sets F = {v | v < 4} and H = {v | v ≥ 7}.
Now, F∩H are those elements of the sets that are common to both here none of the elements are coom so F∩H is Ф.
F∪H are those elements that are either in F or in H or in both.
∴ F∪H = {v | v < 4 or v ≥ 7} Or F∪H = {v | v ∈ R} - {4, 5, 6}
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Please help im desperate and its a 8th grade question only please
Answer:
a. 31/6; 33/6; 35/6
b. + 2/6
c. 37/6; 39/6; 41/6
d. 49/6
Step-by-step explanation:
First we need to find the first three terms.
To do so solve the equations in the boxes.
When dividing by a fraction you multiply by the reciprocal so the equations are now as follows:
2 * 31/12
3 * 11/6
5 * 7/6
Solve these to get
62/12 = 31/6
33/6
35/6
The term to term rule as shown above is adding 2/6 or 1/3.
To find the next three terms in the sequence add 2/6 to the term.
35/6 + 2/6 = 37/6
37/6 + 2/6 = 39/6
39/6 + 2/6 = 41/6.
To find the 10th term you need to write out the arithmetic sequence equation.
an = a1 + (n-1)d
an is the term you want to find and n is the term number in this case that is 10. D is the common difference which in this case is 2/6. Plug these into the equation. A1 is the first term in the equation which in this case is 31/6.
31/6 + (10-1) 2/6
31/6 + (9)2/6
31/6 + 18/6 = 49/6
16.5 + 2.75h = 9h + 7.5 − 4.25h for h. please show how you got
Answer:
h = 4.5
Step-by-step explanation:
16.5 + 2.75h = 9h + 7.5 − 4.25h
Combine like terms on the right side.
16.5 + 2.75h = 4.75h + 7.5
Subtract 4.75 h from both sides.
16.5 - 2h = 7.5
Subtract 16.5 from both sides.
-2h = -9
Divide both sides by -2.
h = 4.5
Answer:
h = 1.2
Step-by-step explanation:
1.) Isolate the variable H. To isolate the variable H, you have to move numbers onto one side and variable onto another. I will show this process in the next steps:
2.) First, move the numbers onto one side. You will subtract 7.5 on both sides, ending up with 16.5 - 7.5 + 2.75h = 9h - 4.25h.
3.) Now, move the variable to one side. You will subtract 2.75h on both sides, and get 16.5 - 7.5 = 9h - 4.25h + 2.75h.
4.) Finally, Simplify. 16.5 - 7.5 = 9. 9h - 4.25h + 2.75h = 7.5h. Therefore, 7.5h = 9.
5.) If we divide both sides by 7.5, we get h = 9/7.5, which is 1.2. By this, h = 1.2
A
B
Solve the following inequality.
-3(x - 3) < -2x - x + 1
All real numbers
No solution
x
No solution is the answer
the larger number is 18 more than twice the smaller . if the sun of the numbers is 93 find both numbers
Answer: The numbers are 25 and 68.
Step-by-step explanation:
Answer:
x = 68
y = 25
Step-by-step explanation:
Let the larger number be x and smaller number be y.
Condition 1:x = 18 + 2y ----------------(1)
Condition 2:x + y = 93 -----------------(2)
Put Eq. (1) in Eq. (2)
18 + 2y + y = 93
18 + 3y = 93
Subtract 18 to both sides
3y = 93 - 18
3y = 75
Divide 3 to both sides
y = 72/3
y = 25Put y = 24 in Eq. (1)
x = 18 + 2(25)
x = 18 + 50
x = 68[tex]\rule[225]{225}{2}[/tex]
which property justifies the step?
2x +3 = -5x -1
7x + 3 = -1
A. distrubutive property
B. addition property of equality
c. commutative property
D. subtraction property of equality
The required property justifies the step is an addition property of equality.
What is mathematical property?
The rules governing how numbers relate to and interact with one another are known as mathematical properties. There are four fundamental properties. i.e. distributive, addition, commutative and subtraction.
Given, 2x +3 = -5x -1
Applying addition property of equality,
Adding 5x to both sides, we get
7x + 3 = -1
Hence, the required property justifies the step is an addition property of equality.
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SOLVE FOR P!
2p − 10 = –2
P=
8x - 3y = 12
-8x+3y=5.
Answer:
No solution-------------------------
Given system:
8x - 3y = 12,- 8x + 3y = 5.We see constants are same with opposite sign.
To make them same multiply both sides of the second equation by -1:
( -1 )( -8x + 3y) = ( - 1)*5 ⇒ 8x - 3y = - 5Now we have two equations with same left sides but different right sides:
12 = - 5This is false and hence the system has no solution.
y = 5x + 4
y = 5x - 2
One solution
No solution
Infinite solution
Answer: No solution
Step-by-step explanation:
Since both equations are equal to y you can set them equal to each other
5x+4=5x-2
0=-6
zero does not equal -6 which is that there is no solution.
Answer:
Step-by-step explanation:
the answer is 2 1/2 miles
Find the missing angle
RPQ= __________
The value of angle RPQ in the circle is 115 degrees.
How to find the angle in the circle?Using angles of intersecting chord theorem, If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.
Therefore,
∠RPQ = 1 / 2 (arc angle RQ + arc angle SA)
arc angle RQ = 175 degrees
arc angle SA = 55 degrees
Hence,
∠RPQ = 1 / 2 (175 + 55)
∠RPQ = 1 / 2 (230)
∠RPQ = 115 degrees.
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Answer: 115 degrees
Step-by-step explanation:∠
RPQ = 1 / 2 (175 + 55)
∠RPQ = 1 / 2 (230)
∠RPQ = 115 degrees.
Car makers (Toyota, Ford, Honda, Hyundai, etc.) often provide low-interest financing to attract people to buy: 3%, 2%, 1%, and even 0%. A 1% loan for 4 years ends up costing about 2% of the original loan. How much total interest is paid for a $20,000 loan?
Using the formula of simple interest, the total interest paid on a $20000 loan at rate of 2% over 4 years is $1600
Simple InterestSimple interest is calculated with the following formula: S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r% and is to be written as r/100.
Principal: The principal is the amount that initially borrowed from the bank or invested. The principal is denoted by P.Rate: Rate is the rate of interest at which the principal amount is given to someone for a certain time, the rate of interest can be 5%, 10%, or 13%, etc. The rate of interest is denoted by R.Time: Time is the duration for which the principal amount is given to someone. Time is denoted by T.Amount: When a person takes a loan from a bank, he/she has to return the principal borrowed plus the interest amount, and this total returned is called Amount.The formula is given S.I = P(1 + RT)
Data;
P = 20000r = 2%t = 4 yearsS.I = 20000(1 + 0.02 * 4)
S.I = 21600
The total interest paid is 21600 - 20000 = 1600
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SOLVE F FOR FFF
1 + 8f = -6+ 7f
F =
Answer:
f = -7
Step-by-step explanation:
1 + 8f = -6 + 7f
Add 6 on both sides
7 + 8f = 7f
Subtract 8f on both sides
7 = -1f
Divide by -1 to make f positive
f = -7
at the zoo 1/3 of the animals are mammals. 1/4 of the mammals are elephants. what fractuon of the animals at the zoo are elephants
Hence, the fractuon of the animals at the zoo are elephants is [tex]\frac{7}{12}[/tex].
What is the fraction?
A fraction defined as the part of the whole thing.
Fractions help to distribute and judge the numbers easily and make the calculation faster.
Here given that,
At the zoo [tex]\frac{1}{3}[/tex] of the animals are mammals [tex]\frac{1}4}[/tex] of the mammals are elephants.
So, the fraction of the animals at the zoo are elephants is
[tex]\frac{1}3}+\frac{1}{4}=\frac{4+3}{12}\\\\=\frac{7}{12}[/tex]
Hence, the fractuon of the animals at the zoo are elephants is [tex]\frac{7}{12}[/tex].
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Which graph represents the function f(x)=4x?
Responses
Answer:
slope = 4
points on graph = (0,0), (1,4)
Step-by-step explanation:
line going through quadrants 1 and 3. Straight line.
Consider the following data of mathematics students.
60 study French, 30 study French and German
55 study German, 25 study French and Russian
75 study Russian, 35 study German and Russian
12 students study all the three languages.
Let F, G, R denote the set of students studying French, German and Russian respectively. Then find the number of students studying at least one of the three languages i.e, n(FUGUR)
The value of n (FUGUR) will be;
⇒ n (FUGUR) = 112
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The data of mathematics students is,
60 study French, 30 study French and German
55 study German, 25 study French and Russian
75 study Russian, 35 study German and Russian
12 students study all the three languages.
Now,
Let F, G, R denote the set of students studying French, German and Russian respectively.
And, The data of mathematics students is,
n (F) = 60, n (F ∩ G) = 30
n (G) = 55, n (F ∩ R) = 25
n (R) = 75 , n (G ∩ R) = 35
n (F ∩ G ∩ R) = 12
Since, We know that;
⇒ n (FUGUR) = n (F) + n (G) + n (R) - n (F ∩ G) - n (F ∩ R) - n (G ∩ R)
+ n (F ∩ G ∩ R)
Substitute all the values, we get;
⇒ n (FUGUR) = n (F) + n (G) + n (R) - n (F ∩ G) - n (F ∩ R) - n (G ∩ R)
+ n (F ∩ G ∩ R)
⇒ n (FUGUR) = 60 + 55 + 75 - 30 - 25 - 35 + 12
⇒ n (FUGUR) = 112
Thus, The value of n (FUGUR) will be;
⇒ n (FUGUR) = 112
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given h(x)=-x+1, find h(2)h(2).
Answer:
h(2)=-1
h(2)=-1
Step-by-step explanation:
Use the given functions to set up and simplify
h
(
2
)
You have $20 to spend and apples cost $1 per apple. The independent variable is apples. What is the Range and Domain?
The Range and Domain for the apples as per the given information is (1, 20) and (1, 20).
What is meant by range?The difference between the greatest and lowest values of a set of integers is defined as its range. To find it, subtract the distribution's lowest number from its highest.
Because the term "range" can have multiple meanings, it is recommended that it be defined the first time it is used in a textbook or article. When older books use the term "range," they usually indicate what is currently known as the codomain. More recent works, if they use the phrase "range," usually use it to refer to what is now known as the picture. A number of current books avoid using the word "range" entirely to avoid confusion.
Given,
We need to spend $20 for each apple
And also given that,
The cost of each apple is $1
Here the independent variables are apples
Range=(1, 20)
Domain=(1, 20)
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Let a,b,c be positive real numbers. Prove the inequality
[tex]\dfrac{(a+b)^2}{c} +\dfrac{c^2}{a} \geq 4b.[/tex]
If a,b,c are positive real numbers, the inequality [tex]\frac{(a+b)^{2} }{c} +\frac{c^{2} }a[/tex] [tex]\geq 4b[/tex] is not correct because it gives the value a³+2a²b+ab²≥4abc
How to find the solution set of an inequality?
Inequality is a mathematical statement showing that two quantities are not equal.
The given inequality is [tex]\frac{(a+b)^{2} }{c}[/tex] +[tex]\frac{c^{2} }{a}[/tex][tex]\geq[/tex]4abc
Simplifying the inequality we have [tex]\frac{(a+b)(a+b)}{c}[/tex] +[tex]\frac{c^{2} }{a }[/tex] [tex]\geq[/tex]4b
This implies that: [tex]\frac{a^{2}+ab+ab+b^{2} }{c}[/tex] +[tex]\frac{c^{2} }{a}[/tex] [tex]\geq[/tex] 4b
Taking the LCM,
[tex]\frac{a^{2}+2ab+b^{2} }{c}[/tex] +[tex]\frac{c^{2} }{a}[/tex] [tex]\geq[/tex]4b
Simplifying further
[tex]\frac{a^{3}+2a^{2}b+ab^{2}+c^{3} }{ac}[/tex] [tex]\geq[/tex]4b
The expression gives that: a³+2a²b+ab²≥4abc
Comparing the values of a,b,c on both sides of the inequality, the inequality is wrong.
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The exponential model A = 796.2e0.006t describes the population, A, of a country in millions, t years after
2003. Use the model to determine the population of the country in 2003.
Answer:
796.2 million
(796,200,000)
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function with base $e$}\\\\$y=ae^{kx}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $e$ is Euler's number. \\ \phantom{ww}$\bullet$ $k$ is some constant.\\\end{minipage}}[/tex]
Given exponential function:
[tex]A=796.2e^{0.006t}[/tex]
where:
A is the population of the country in millions.t is the number of years after 2003.The initial value is 796.2, which means the population of the country in 2003 was 796.2 million.
If Alex earns $380/week. How much would he make per year, and per month? Explain
Answer:
$19,760 per year
$1,520 per month
Step-by-step explanation:
There are 4 weeks in 1 month, so multiply $380 by 4:
380 x 4 = $1,520 per month.
1 year = 52 weeks:
380 x 52 = $19,760 per year.
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 10 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
Evaluate the expression: −(8 − 12) + 60 + (−4)2.
Answer: 80
Step-by-step explanation:
⇒ −(8 − 12) + 60 + (−4)²
⇒ -(-4) + 60 + 16
⇒ 4 + 60 + 16
⇒ 80
2x - 7 + 3x + 10 > x - 6 + 8x - 11
The answer would be (5,0)
Find an equation of the line that goes through the points (7,20) and (2,10). Write your answer in the slope-intercept form, y = mx + b.
Answer: y =
The linear equation of the line that goes through points (7,20) and (2,10) is y = 2x + 6.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
A linear equation or function is given as ;
y = mx + b
Now,
At x = 0 ⇒ y = b so it will be a y-intercept.
The slope associated with two points (x₁, y₁) and (x₂, y₂) is given by
Slope = (y₂ - y₁)/(x₂ - x₁)
Slope = (10 - 20)/(2 - 7) = 2
Substitute,(2,10) and m = 2
10 = 2(2) + b
b = 6
Thus, the equation will be y = 2x + 6
Hence "The linear equation of the line that goes through points (7,20) and (2,10) is y = 2x + 6".
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Geometry help please! 50 points
it is Abe and afe
hope this helps
Write an equation of the line in slope-intercept form. Use x and y for variable.
Which ordered pair could represent another vertex of the image? (0, –1) (2, 6) (4, 0) (6, 1)
Answer:
Step-by-step explanation:
t says that's 4 units distant from the another vertex. So, if a square is formed by 4 equal sides and 4 right angles, then you just have to add 4 units on x or y.
-> (2, 1) -> + 4 units on X
-> = (6, 1)
or
-> (2, 1) -> +4 units on Y
-> = (2, 5)
(2, 5) isn't an answer so the unique possible answer is (6, 1)
Answer: (6, 1)
Given (x – 7)2 = 36, select the values of x.
For the given equation, [tex](x-7)2=36[/tex] the value for [tex]x=25[/tex].
Calculating the value of the unknown variable while keeping the equation balanced on both sides is the process of solving equations.
A condition on a variable is an equation when it ensures that two expressions in the variable have the same value. The equation's solution is the amount of the variable for which the condition is met.
Initially, the equation [tex](x-7)2=36[/tex] must be made simplified to find [tex]x[/tex].
[tex](x-7)2=36[/tex]
By using distributive law,
⇒ [tex](x-7)2=36[/tex]
⇒ [tex]2x-14=36[/tex]
Now add 14 on both sides,
⇒ [tex]2x-14+14 =36+14[/tex]
⇒ [tex]2x =36+14[/tex]
⇒ [tex]2x =50[/tex]
As the next step, divide both sides by 2,
⇒ [tex]\frac{2x }{2} =\frac{50}{2}[/tex]
⇒ [tex]x=25[/tex]
Therefore, after solving the equation step-by-step, [tex]x=25[/tex].
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The cleaning service charges $15 per hour. Mr. Henrickson is hiring the cleaning service but does not want to spend more that $75. What is the maximum number of hours that he can hire the cleaning service? Write an inequality and solve.
The maximum number of hours that he can hire the cleaning service is 5.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let us consider the number of hours for which the total cost would be the same be x
The first equation would be
$15x > $75
Now equate these equations
$15x - $75 = 0
15x = 75
x = 5
Hence, the maximum number of hours that he can hire the cleaning service is 5.
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A video store is having a sale where you can buy 2 new-release DVDs for $22 or you can buy 4 new-release DVDs for $40. Are these rates equivalent? Explain your reasoning.
Answer: These rates are not equivalent.
Step-by-step explanation:
2/22 = 1/11
4/40 = 1/10
Hence, 1/11 and 1/10 are not equivalent because they do not have the same denominator.
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identifying values in the domain f(x)=x-3/x+2
The rational function f(x) = (x - 3) / (x + 2) have a domain corresponding to any real number except x = - 2.
What is the domain of a rational equation?
In this problem we find a defined rational functions whose numerator and denominator are both linear equation. The domain of a function is the set of all values of x such that f(x) exists.
By function theory, the domain of all linear equations is the set of all real numbers and the domain of rational equations is the domain of the numerator except the values of x such that the denominator becomes zero.
Then, we need to determine the values of x such that:
x + 2 = 0
x = - 2
The domain of the rational function f(x) = (x - 3) / (x + 2) is all the real numbers except x = - 2.
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