The quantified statement ∀x ∃y (xy > x) can be interpreted as "for all x, there exists a y such that xy is greater than x". To determine the truth of this statement in the given domain of positive real numbers, we need to evaluate whether it holds true for every possible value of x in the domain.
Let's take an arbitrary positive real number x and try to find a corresponding y such that xy > x. We can simplify the inequality by dividing both sides by x, which gives us y > 1. Since the domain includes all positive real numbers, we can always find a y that satisfies this inequality, for example by choosing y = x + 1. Therefore, the statement ∀x ∃y (xy > x) is true in the given domain of positive real numbers. This means that for any positive real number x, we can find a corresponding y such that their product is greater than x.
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What is the 4 basic rule in solving equation?
One-step equations can be solved in four different ways: by adding, subtracting, multiplying, and dividing. Both sides of an equation will remain equal if we add the same amount to each side.
What are the four fundamental rules for solving equations?Addition:
In math, addition is the process of adding two or more numbers together. The numbers being added are known as addends, and the outcome of the addition process, or the answer we ultimately get, is known as the sum.Subtraction:
The process of determining a difference between two numbers is called that. The letter "-" (for "minus") is used. In this method, we take a number and divide it by a smaller number.Multiplication:
The result of two numbers being multiplied is known as the product. The multiplier is the quantity that multiplies the number of such equal groups by the multiplicand, the quantity of objects in each group.Division:
In mathematics, division is the process of dividing a number into equal parts and determining how many equal parts can be made. For instance, breaking 15 into 3 equal groups of 5 is equivalent to dividing 15 by 3. The symbol for division, "," or occasionally "/," is used.To know more about the equations, here
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What is the distance between the graph of the equations x =- 4 and x =- 1?
The distance between the graph of the equations x =- 4 and x =- 1 is 3 units.
The equations x =- 4 and x =- 1 can be solved to be -4 and -1 respectively. The difference between these two numbers is 3, so the distance between the graphs of the equations is 3 units.
The distance between the graph of two equations can be found by subtracting the solutions of the two equations. For example, when subtracting the solution of x =- 4 and x =- 1, the difference between -4 and -1 is 3. Therefore, the distance between the graphs of the equations x =- 4 and x =- 1 is 3 units.
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13/6=y/3 I need to know how to solve it
On solving the provided question, we can say that in this equation, we can solve by , 13/6=y/3 = > y = 39/6 = 6.5
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
in this equation,
we can solve by
13/6=y/3
y = 39/6 = 6.5
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what 1\3 of a full rotation
Answer:
120°
Step-by-step explanation:
what 1\3 of a full rotation?
one full rotation = 360°so
360° x 1/3 =
360° : 3 =
120°
What is 7 to the 3rd power and evaluate
Answer: 343
Step-by-step explanation:
7 to the 3rd power
⇒7³
⇒7 × 7 × 7
⇒343 ... answer
hope that helps...
Is 3x² a polynomial?
Answer: Yes and no?
Step-by-step explanation: Yes, because since it is one single number, it would be considered a "linear" polynomial. But no, because since there is only one term, it wouldn't be considered a polynomial.
I only just learned about linear polynomials, so I think the safe answer would just be no, since there is only one term.
Find measurement of V.
The measurement of V can be calculated by adding the two equations: 10x-27 + 2x+29 = V. This simplifies to 12x+2 = V, so V = 12x+2.
Find measurement of V?In order to find the measurement of V, we must first find the value of X.We can do this by solving the equations for Y and W simultaneously.To do this, we must first subtract the equation for W from the equation for Y.This will give us 10x - 2x = 29 - 27, or 8x = 2.We can then divide both sides by 8 to get x = 1/4. Now that we have the value of X, we can substitute it into either of the original equations to find the value of V.If we substitute 1/4 into the equation for Y, we get V = (10 x 1/4) - 27 = 10/4 - 27 = -17/4.Therefore, the measurement of V is -17/4.V is the difference between the two expressions: Y and W. Therefore, V can be found by subtracting W from Y.Y=(10x-27)
W=(2x+29)
V=Y+W
V= 10x-27 + 2x+29
V= 12x+2.
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how to write 9/15 in simplest form
Answer: 3/4 is the simplest form
Step-by-step explanation:
your welcome <3
For your chemitry experiment, you are trying to keep the water temperature at 35 degree Celiu, For the experiment to work properly, the actual temperature can vary by a much a 1%. Write and olve an abolute value inequality to find the acceptable temperature of the water
An absolute value inequality for 35 degrees C with the temperature able to vary as much as 1% is 34.65 ≤ x ≤ 35.35
The term inequality is defined as a relationship between two expressions or values that are not equal to each other
Here we have given that in your chemistry experiment, you are trying to keep the water temperature at 35°C.
And in the experiment to work properly, here the actual temperature can vary as much as 1%.
Here let us consider that x refers the actual temperature
Then it can be written as,
=> 1% of 35
When we simplify this one then we get,
=> 0.01(35) = 0.35
Here let us consider that the value is less that the simplified version, then it can be written as,
=> l x - 35 l ≤ 0.35
Therefore, it can be rewritten as,
=> -0.35 ≤ x - 35 ≤ 0.35
When we simplify this by add the value 35, then we get the resulting inequality as,
=> 34.65 ≤ x ≤ 35.35
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Choose the correct simplification of the expression (3x^3 y^4 z^4) (2x^3 y^4 z^2).
5x^9 y^16 z^8
6x^9 y^16 z^8
5x^6 y^8 z^6
6x^6 y^8 z^6
So, the correct simplification for the expression (3x^3 y^4 z^4) (2x^3 y^4 z^2) is option d: 6x^6 y^8 z^6.
What is simplification?
To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.
The given equation is -
(3x^3 y^4 z^4) (2x^3 y^4 z^2)
On simplification -
=[3·2(x^3+3)(y^4+4)(z^4+2)]
=6x^6y^8z^6
Therefore, the value obtained is 6x^6y^8z^6.
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The simple interest on a sum of money invested at 3% per annum for 2 years was $39.75.
Calculate the sum of money invested
Answer:
$37.50
Step-by-step explanation:
[tex]P+Prt=39.75 \\ \\ P+P(2)(0.03)=39.75 \\ \\ 1.06P=39.75 \\ \\ P=\$37.50[/tex]
A shop offers the following conversions between pounds (£) and US dollars ($) : £1=$1.28 $1= £0.74 if Niamh converts £150 into US dollars and then back into pounds, what percentage of her money will she lose? Give your answer to 1 d.p.
Answer:5.3%
Step-by-step explanation:
we say 150/1 multiplied by 0.74/1=$111
then when we convert it back to pounds, we say 111/1 multiplied by 1.28/1 =142.08
150.00-142.08=7.92
7.92/150.00 multiplied by 100=5.28 to 1 decimal place is 5.3%
hope you understand
Victoria invests money in an account paying a simple interest of 7.2% per year. If she invests $20 and no money will be added or removed from the investment, how much will she have in one year, in dollars and cents?
The amount that Victoria will have in one year if she invests $20 at 7.2% simple interest is $21.44.
What is the simple interest?The simple interest system does not compound the interest.
This statement implies that interest is not computed on the accumulated interest. Periodically, the interest is computed on the principal, using the following simple interest formula:
Simple interest = Principal x Rate x Time
Simple interest rate = 7.2% per year
Investment = $20
Investment period = 1 year
Amount in account after 1 year = P + (P x R x T)
= $20 + ($20 x 7.2% x 1)
= $20 + $1.44
= $21.44
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please help I will give brainlist if you give me the correct answer.
Answer:
A'(2,1) => A(1,-2)
B'(-4,-2) => B(-2,4)
C'(-4,-6) => C(-6,4)
D'(-1,-3) => D(-3,1)
Step-by-step explanation:
:)
1. What guides the end behavior of a function
2. What is the line that a graph approaches
3. What does the variable K represent
Answer:
1The degree and the leading coefficient of a polynomial function determine the end behavior of the graph. The leading coefficient is significant compared to the other coefficients in the function for the very large or very small numbers.
2An asymptote is a line that a graph approaches but never touches. That line can be vertical, horizontal, or even slanted, and graphs can have multiple types of asymptotes.
3constant of variation (k) is a ratio that represents the relationship between the independent variable (x) and the dependent variable (y). It can be found by dividing y by x, if both of those variables have known values.
Lamont earns an annual salary of $58,000. He has to pay a 4.5% income tax on his earnings. How much does Lamont pay in income tax?
Answer:If you make ₱ 58,000 you will be taxed ₱ 4,711. That means that your net pay will be ₱ 53,289 per year, or ₱ 4,441 per month.
what number should be added to 8000 to make it a perfect square
Answer:
100
Step-by-step explanation:
If we add 100 to 8000, get 8100 which is a perfect square: 90^2=8100
4) Write a system of equations to describe the situation below, solve using substitution, and
fill in the blanks.
◄)) Two classmates got together over the weekend to do their assigned History reading.
Olivia can read 3 pages per minute, while Donald can read 4 pages per minute. When they
met, Olivia had already read 22 pages, and Donald had already gotten through 12 pages.
After a while, they had both read the same number of pages. How long did that take? How
many pages had each one read?
◄) After _ minutes, Olivia and Donald had each read _
pages.
It took 19 minutes for each to read 115 pages.
What is Algebraic expression ?
Algebraic expression can be defined as the combination of variables , constants and exponents.
Let x be the number of minutes
And y be the number of pages.
y = 96 + x --equation1 (for danielle )
y=39+4x --equation2 (for lorenzo)
By substituting equation 1 in equation 2.
we get,
96+x = 39 + 4x
96-39+x = 39-39+4x
57+x = 4x
4x-x = 57
3x = 57
x = 57/3
x = 19 .
Substitute x = 19 in equation 1 we get y = 96 + 19 and y=115
in equation 2 we get , y = 39 + 4*19
y = 39+76
y = 115
Hence , it took 19 minutes for each to read 115 pages.
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Is there a triangle whose sides are of length 2cm 3cm and 5cm?
Yes, there is possibility to construct a triangle whose sides are 2 cm, 3 cm and 5 cm.
According to the SSS or side-side-side rule of triangle, the sum of any two sides of triangle should be greater than third side of triangle. Assuming the side a to be 2 cm, side b to be 3 cm and side c to be 5 cm.
Side a + side b > side c
2 + 3 > 5
Performing addition on Left Hand Side of the equation
5 = 5
Side b + side c > side a
3 + 5 > 2
Performing addition on Left Hand Side of the equation
8 > 2
side c + side a > side b
5 + 2 > 3
Performing addition on Left Hand Side of the equation
7 > 3
Thus, we see the sum to be greater in two situations. Hence, the triangle is possible.
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Joe has to take two quizzes tomorrow. He has only enough time to study for
one of them.
• The science quiz has 7 true-or-false questions.
• The English quiz has 4 multiple-choice questions.
Joe calculates the probability that he will get each question correct by
guessing.
Science
English
To get 100%
correct:
Answer 7 of 7
correctly
Answer 4 of 4
correctly
P(guess is
correct)
0.5
0.25
Joe will study for the quiz on which he is likely to do worse by guessing.
Which quiz should he study for?
Answer:
english
Step-by-step explanation:
because by guessing he could only get 1 right on english quiz
Joel should study for science, because the probability of getting all questions correct is 0.004 which is less than 0.016.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given that Joe has to take two quizzes tomorrow.
He has only enough time to study for one of them, such that the science quiz has 7 true-or-false questions and
The English quiz has 4 multiple-choice questions.
We have to find the probability that he will get each question correct by guessing.
P(sciene)=0.5⁸
=0.0039
=0.004
P(English)= 0.25³
=0.0156
=0.016
As we know that 0.0156>0.0039
Hence, Joel should study for science, because the probability of getting all questions correct is 0.004 which is less than 0.016.
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Find the number of sides a regular polygon must have to meet each condition.
Each interior angle measure equals each exterior angle measure.
Each exterior angle measure is one eighth the measure of each interior angle.
Exterior angle of a regular n-sided polygon = 360°/n
Interior angle = 180° - 360°/n
So, with 360/n = (1/8)(180 - 360/n)
360/n = 180/8 - 360/(8n)
(360/n)*(9/8) = 180/8
2*9/n = 1
n = 18
Which of the following is a solution of 3x² 5x 2 0?
The solution of the given equation 3x²+ 5x +2= 0 is given by :
option c. x = -2 / 3 or x = -1.
As given in the question,
Given equation is equal to :
3x²+ 5x +2= 0
Solve the given equation by splitting the middle term of the quadratic equation we have,
3x²+ 5x +2= 0
⇒ 3x²+ 3x + 2x + 2 = 0
⇒ 3x ( x + 1 ) + 2 ( x + 1 ) = 0
⇒ ( 3x + 2 ) ( x + 1 ) = 0
⇒ ( 3x + 2 ) = 0 or ( x + 1 ) = 0
⇒ x = -2 / 3 or x = -1
From the given options :
option c. x = -2 / 3 or x = -1 is the solution.
Therefore, the solution of the given equation 3x²+ 5x +2= 0 is equal to :
option c. x = -2 / 3 or x = -1 .
The above question is incomplete, the complete question is:
Which of the following is a solution of the equation 3x²+ 5x +2= 0?
a. x = 2/3 or x = 1
b. x = -2/3 or x = 1
c. x = -2/3 or x = -1
d. x = 2/3 or x = -1
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You have an isosceles triangle where the two legs form a 90 degree angle. One of these legs is 2cm. What is the hypotenuse of the triangle? Express
your answer using two decimal places only.
Answer:
2.83 cm
Step-by-step explanation:
The other leg is also 2cm
Pythagorean Theorem
hypot ^2 = 2^2 + 2^2
Hypot = sqrt 8 =~ 2.83 cm
Answer:
Step-by-step explanation:
an isosceles triangle where the two legs form a 90-degree angle is an isosceles right triangle. So, the hypotenuse of the triangle is 2√2
A package of 3 pairs of insulated socks costs $21.87. What is the unit price of the pairs of socks ?
Answer: 7.29
Step-by-step explanation: you divide the total cost which is 21.87 by 3 to get how much one pair of socks would be and that would be the unit price hope this helps
You have 8 marbles: 5 purple, 2 orange and 1 blue. You select a marble without looking at it then put it back. If you do this 48 times, what is the best prediction possible for the number of times you will pick an orange or blue marble?
Write a proportion to solve this problem.
The number of times we will pick an orange or blue marbles = 1/768
What is probability?The term probability refers to the possibility of happening an event. It is the ratio of favorable outcome to the total possible outcome.
What is the probability of picking an orange or blue marble?Available marbles = 8
purple marbles = 5
orange marble = 2
blue marble = 1
probability of picking an orange marble = 2/48 = 1/16
as the marble is put back each time after picking up so
the probability of picking a blue marble = 1/48
Now we multiply the probabilities of each individual events = 1/16 × 1/48
the proportion = 1/768
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7/9 + 5/6=???
I’m rushing to finish this I forgot to do it and I can’t figure it out!
Answer: 29/18 or 1 11/18
Step-by-step explanation: When adding fractions, you need the fractions to have a common denominator. In order to get the common denominator, find the lowest common number between 9 and 6. That number is 18.
7/9 times 18 = 14/18 5/6 times 18 = 15/18 14/18 + 15/18 = 29/18
Improper fraction: 29/18 Mixed number: 1 11/18
The sides of a triangular field are 65m, 156m and 169m. The length of the shortest altitude is
The shortest altitude is 60m when the base of the triangle is 169m.
What is altitude?Altitude, height, or depth are terms used to describe the distance between a point or object and a reference datum. This phrase is also occasionally used to describe depth.
Different reference points and definitions are employed depending on the context (e.g., aviation, geometry, geographical survey, sport, or atmospheric pressure). Altitude can also be used to describe a location's height above sea level, though elevation is more frequently preferred in geography.
Let, a = 65cm , b = 156cm , and c = 169cm
The Area of a triangle = A = √s(s−a)(s−b)(s−c) s ( s − a ) ( s − b ) ( s − c )
s = (65cm + 156cm + 169cm)/2
s = 195cm
A = √195(195−65)(195−156)(195−169)
A = 5070 m²
Now we find the height of each case
[tex]$ \text h = 2\frac{\text A}{\text {base}}[/tex]
Substitute each base a, b and c
[tex]$ \text h = 2\frac{5070}{ 65}[/tex]
h = 156
height of triangle when base is 65m = 156m
[tex]$ \text h = 2\frac{5070}{ 156}[/tex]
h = 65
height of triangle when base is 156m = 65m
[tex]$ \text h = 2\frac{5070}{ 169}[/tex]
h = 60
height of triangle when base is 169m= 60m
Thus, the shortest altitude is 60m when the base of the triangle is 169m.
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A tortilla chip is shaped like an equilateral triangle.
If an exterior angle on this tortilla chip measures(2x-80), which equation can you solve to calculate the value of x?
HINT: The interior angles of an equilateral triangle all measure 60.
Step-by-step explanation:
Two interior opposite angles of a triangle are equal to the exterior angel
[tex]60 + 60 = 2x - 80 \\ 120 = 2x - 80 \\ 2x = 120 + 80 \\ 2x = 200 \\ x = \frac{200}{2} \\ x = 100[/tex]
What is the reason for each step in the solution of the equation?
18−2x=4x
Drag and drop the reasons into the boxes to correctly complete the table.
Answer: 1. Given
2. Combine like terms
3. Division
$9, 100 is invested in an account earning
3% interest (APR), compounded quarterly.
Write a function showing the value of the
account after t years, where the annual
growth rate can be found from a constant
in the function. Round all coefficients in
the function to four decimal places. Also,
determine the percentage of growth per
year (APY), to the nearest hundredth of a
percent.
Answer: A = P(1 + r/n)^(nt)
Where
A is the future value of the account
P is the initial principal amount, which is $9,100
r is the annual interest rate, which is 3%
n is the number of times the interest is compounded per year, which is 4 (quarters)
t is the number of years
So the function for the value of the account after t years is:
A = 9100(1 + 0.03/4)^(4t)
To determine the percentage of growth per year (APY), we can use the formula:
APY = ( (A/P)^(1/t) - 1) * n
In this case,
APY = ( (A/9100)^(1/t) - 1) * 4
APY represents the annual percentage yield, which is the interest rate taking compounding into account.
Please note that in the above expression the coefficient 0.03 is rounded to four decimal places as instructed.
Step-by-step explanation: