The solution set of the inequality is the set of all real numbers larger than 5, written in interval form as (5, ∞)
How to solve the inequality for x?Here we have a simple inequality:
x - 2 > 3
To solve this we need to isolate x in one side of the inequality.
Now, remember that we can do the same operation in both sides of the inequality. So, if we add in both sides the same number, then the truth value of the inequality does not change.
Then if we add 2 in both sides of the inequality we get:
x - 2 + 2 > 3 + 2
x > 5
Then the solution set of the inequality is the set of all real numbers larger than 5, written in interval form as (5, ∞).
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Find a general solution. show the steps of derivation. check your answer by substitution.y'=e^(2x-1)y^2
The general solution of the given equation is y² = 8x²Inx + cx².
Linear first order differential equation:A first-order linear differential equation is one that has the formula:
[tex]\frac{d y}{d x}+p(x) y=q(x)[/tex]
where p(x) and q(x) are continuous functions of x.
We begin by determining the integrating factor for the first-order linear differential equation.
I.F. = [tex]e^{\int p(x) d x}[/tex]
The solution to the first order linear differential equation is:
[tex]y \cdot e^{\int p(x) d x}=\int q(x) \cdot e^{\int p(x) d x} d x+c .[/tex]
Where c is the constant of integration.The solution to the first order linear differential equation is:
[tex]\int \frac{1}{x} d x=\ln x+c[/tex]
Where c is the constant of integration.So, given: [tex]y^{\prime}=\frac{\left(4 x^2+y^2\right)}{(x y)}[/tex]
The above differential equation can be written as:
[tex]\begin{aligned}&\frac{d y}{d x}=4 \frac{x}{y}+\frac{y}{x} \\&\frac{d y}{d x}-\frac{y}{x}=\frac{4 x}{y} \\&y \frac{d y}{d x}-\frac{y^2}{x}=4 x\end{aligned}[/tex]
Substitute, [tex]y^2=t, 2 y \frac{d y}{d x}=\frac{d t}{d x}[/tex].
[tex]\begin{aligned}&\frac{1}{2} \frac{d t}{d x}-\frac{t}{x}=4 x \\&\frac{d t}{d x}-\frac{2 t}{x}=8 x\end{aligned}[/tex]
Because this is a first-order linear differential equation, we must first determine the integrating factor:
[tex]\text { I. F. }=e^{-2 \int \frac{1}{x} d x}=e^{-2 \ln x}\\\text { I.F. } F=\frac{1}{x^2}[/tex]
As a result, the following is the general solution to the given IVP:
[tex]$$t \cdot(I . F .)=\int(I . F .) \cdot 8 x d x+c$$$t \cdot\left(\frac{1}{x^2}\right)=\int\left(\frac{1}{x^2}\right) \cdot 8 x d x+c$$t \cdot\left(\frac{1}{x^2}\right)=8 \int \frac{1}{x} d x+c$$t \cdot\left(\frac{1}{x^2}\right)=8 \ln x+c$$t=8 x^2 \ln x+c x^2$[/tex]
By reversing the value of t:
[tex]y^2=8 x^2 \ln x+c x^2[/tex]
We now test the solution by substituting [tex]y^2=8 x^2 \ln x+c x^2[/tex] it in the original differential equation.
[tex]\begin{aligned}&\frac{d}{d x}\left(y^2\right)=\frac{d}{d x}\left(8 x^2 \ln x+c x^2\right) \\&2 y \frac{d y}{d x}=16 x \ln x+8 x+2 c x \\&\frac{d y}{d x}=\frac{16 x \ln x+8 x+2 c x}{2 y} \\&\frac{d y}{d x}=\frac{8 x \ln x+4 x+c x}{y}\end{aligned}[/tex]
We calculated the value of [tex]y^2[/tex] and [tex]\frac{d y}{d x}[/tex] from the original differential equation:
[tex]\begin{aligned}&\frac{8 x \ln x+4 x+c x}{y}=\frac{4 x^2+8 x^2 \ln x+c x^2}{x y} \\&8 x \ln x+4 x+c x=8 x \ln x+4 x+c x .\end{aligned}[/tex]
Therefore, the general solution of the given equation is y² = 8x²Inx + cx².
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The complete question is given below:
For the following ODE, find a general solution, show the steps of derivation and check your answer by substitution.
[tex]y^{\prime}=\frac{\left(4 x^2+y^2\right)}{(x y)}[/tex]
Different plans are available from two cellphone carriers. AT&K charges a monthly flat rate of $100 plus $10 for each gigabyte of data used,verikon communications does not have a flat rate, but instead charges $40 for each gigabyte of data used let c represent your total cost and d represent the data used. What is the equation system that represents these two plans
The equation system to represent these two plans is:
c=100+10d, c=40d where c is the total cost and d represents the data used.
We have to understand the plans provided by AT&K and Verikon separately to find the equation system. We know that the total cost incurred is c and the amount of data used is d. It is given that AT&K charges a monthly flat rate of $100 and additional $10 for every gigabyte of data used. We can say that for a month the total cost incurred from AT&K is $100 plus $10xd, the amount of data used.
c=100+10d
For verikon it is given that it does not have any flat monthly rate and it charges $40 for each gigabyte of data used.We can easily say that the total cost in this case is $40 multiplied to amount of data used.
c=40d
Thus the system of equation for the two different plans is
c=100+10d and c=40d
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How to right 730,812 in word form
Step-by-step explanation:
seven-hundred thirty thousand eight-hundred twelve
Substitute the expressions for length and width into the formula 2l 2w. distribute 2 to each term in the parentheses. combine like terms. inches
The perimeter of the rectangle with length 8x - 1 and width 10x + 3 is 20x + 6
What is perimeter of the rectangle?
The formula P=2l+2w, where l is the rectangle's length and w is its width, determines the perimeter P of a rectangle. The equation A=lw, where l is the length and w is the width, determines the area A of a rectangle.The perimeter of the rectangle with length 8x - 1 and width 10x + 3 is 20x+ 6
The formula for calculating the perimeter of a rectangle is expressed as:
P = 2( l + w)
Given the following parameters
length l = 8x - 1
width w = 2x + 4
Substitute the expressions for the length and width into the formula;
P = 2(8x - 1 + 2x + 4)
P = 2(10x + 3)
Distribute 2 over each term in the parenthesis
P = 2(10x) + 2(3)
P = 20x + 6
Hence the perimeter of the rectangle with length 8x - 1 and width 10x + 3 is 20x + 6.
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The complete question is -
The perimeter formula for a rectangle is 2l + 2w, where l is the length and w is the width. Complete the steps to find an expression that represents the perimeter of the rectangle. Substitute the expressions for length and width into the formula 2l + 2w. Distribute 2 to each term in the parentheses. Combine like terms. inches
Go to school kid and pay attention
An inductive proof that p(n) is true for all n always starts with the base case. what is the base case?
The base case for which the inductive proof for p(n) is defined, is the smallest value of n for which p(n) is defined.
What is Mathematical Induction?Mathematical induction refers to a strategy for demonstrating a theorem's correctness by first demonstrating that, if it holds true in one particular situation, it will also hold true in all subsequent cases in the series.
Now,
The proof of mathematical induction is based upon showing the given expression true for one value, assuming that it will be true for some other value and finally proving that it will be true for all the values.The base case is the proof for which the expression is showed to be true in the beginning.In general cases, this initial value is 1 when the expression is defined for the values of variables belonging to Natural Numbers, i.e., the proof starts by showing that the given expression is true for the value of variable = 1.Hence, the base case for which the inductive proof for p(n) is defined, is the smallest value of n for which p(n) is defined.
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HELP PLEASE! Use the diagram below to analyze another student's work.
S
80°
45°
Nathan stated that angle q is 20 degrees because 80 degrees + 20 degrees = 100
degrees. Straight lines are measured as 100 degrees.
Did Nathan correctly calculate the measurement for angle q? Justify your answer
1pt for identifying if Nothan was
correct or not
2pts for justification
Answer: No, Nathan didn't measure angle correctly
Step-by-step explanation:
The sum of angles that are formed on a straight line is equal to 180°
So the value angle q is 80° because the sum of angle q and 100° is 180°
∠q+100°=180°∠q= 180°-100°
∠q= 80°
No, Nathan didn't measure angle correctly.
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1/3 x =5 solved, please help me if anyone can! :)
11. The following describes the United States nuclear stockpile from
1944 to 1974. From 1944 to 1958, there was a gradual increase in the
number of warheads from 0 to about 5000. From 1958 to 1966, there
was a rapid increase in the number of warheads to a maximum of
about 32,000. From 1966 to 1970, there was a decrease in the number
of warheads to about 26,000. Finally, from 1970 to 1974, there was
a small increase to about 28,000 warheads. Sketch a graph of the
function.
10.
nxhudkdodisuhaiioavsbos
Does the figure below appear to have line symmetry if so how many lines of symmetry
What is the domain and range of the function below?
solve the literal equation for y
4x+1=9+4y show steps please i am confused
The solution to the literal equation is y = x - 2.
What is the solution to inequality?To solve inequality in y, we need a number such that the assertion holds if we replace y with that number. Isolating the variable on one side of the inequality and leaving the other terms constant is the first step in resolving the inequality.
From the given information:
4x + 1 = 9 + 4y
To solve for y, we have to switch the sides:
9 + 4y = 4x + 1
Subtract 9 from both sides
9 - 9 + 4y = 4x + 1 - 9
4y = 4x - 8
Divide both sides by 4
[tex]\dfrac{4y}{4}= \dfrac{4x}{4}-\dfrac{8}{4}[/tex]
y = x - 2
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3. the difference of two-thirds of a number x and
6 is at least -24. which inequality represents all
possible values for x?
The inequality which represents all the possible values for x is (2x/3) - 6 ≥ 24.
It is given in the question that the difference of two-thirds of a number x and 6 is at least -24.
We have to find the inequality which represents all the possible values for x.
In mathematics, Inequality is a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
Hence, according to the data given in the question, we can write,
(2x/3) - 6 ≥ 24
Here, we can also find the possible values of x.
(2x/3) - 6 ≥ 24
2x/3 ≥ 24 + 6
2x/3 ≥ 30
x ≥ 30*3/2
x ≥ 45
Hence, every number greater than or equal to 45 will be a possible value of x.
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Small, random genetic changes that occur over generations is known as _________.
Small, random genetic changes that occur over generations is known as genetic drift.
What is genetic drift?Genetic drift is an evolutionary process in which the frequency of a given gene allele varies randomly across a population. The impacts of genetic drift can be severe, often causing traits to become excessively common or to vanish from a community, even though it predominantly affects small, isolated populations.
Some people might merely by coincidence leave behind a few more offspring (and genes, of course!) than others in each generation. The next generation's DNA and other genetic components will come from the "fortunate" people, not necessarily the healthier or "better" people.
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3/4x+8<41 graph it as well
Answer:
x<44
Step-by-step explanation:
The domain and the range of the reciprocal function are the set of all real numbers. True or false?.
False. All real numbers, with the exception of 0 because f (0) = 1 0, fall inside the reciprocal function's domain and range. Y cannot be 0 if x cannot, either.
What are real numbers?In mathematics, a real number is a quantity that may be represented by an endless number of decimal expansions. In contrast to the natural numbers 1, 2, 3,... that result from counting, real numbers are used in measurements of continuously varying quantities such as size and time. They are distinguished from imaginary numbers, which use the symbol I or the square root of 1, by the word "real." A complex number has a real (1) and an imaginary I component, like 1 + i. The positive and negative integers, as well as the fractions created from them (also known as rational numbers), as well as the irrational numbers, are all real numbers.
Contrary to rational numbers, whose decimal expansions always contain a digit or group of digits that repeats itself, such as 1/6 = 0.16666... or 2/7 = 0.285714285714, irrational numbers have decimal expansions that do not repeat themselves. Since there is no regularly repeating group in the decimal produced as 0.42442444244442, it is irrational.
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Triangle T R S has centroid Z. Lines are drawn from each point to the midpoint of the opposite side to form line segments T W, R V, and S U.
In triangle TRS, VZ = 6 inches. What is RZ?
In triangle TRS, VZ = 6 inches. Then the length of the line segment RZ will be 12 inches.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
The centroid Z of the triangle TRS. Line sections TW, RV, and SU are created by drawing lines from every point to the center of the opposing side.
We know that the centroid divides the median of the triangle in a ratio of 2: 1.
In triangle TRS, VZ = 6 inches. Then the length of the line segment RZ will be
RZ / ZV = 2 / 1
RZ / 6 = 2
RZ = 6 x 2
RZ = 12 inches
In triangle TRS, VZ = 6 inches. Then the length of the line segment RZ will be 12 inches.
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Will mark brainly-est. Please Help me with this Geometry question.
Juliana wrote -16+x=8 on the board
Answer: x = 24
Step-by-step explanation:
-16 + 24 = 8
Select the two categories that would yield quantitative data.
a.) gender of pet
b.) weight of pet
c.) color of pet
d.) type of pet
e.) age of pet
Weight of pet & age of pet are the two categories that would yield quantitative data.
What foundation does qualitative data have?
Information that cannot be quantified, counted, or simply stated using numbers is referred to as qualitative data. Data visualization technologies like word clouds, idea maps, graph databases, timelines, and infographics are used to communicate the information that is gathered from text, audio, and visual sources.Which two sorts of quantitative data are there?
There are two forms of quantitative data: discrete data and continuous data. Interval and ratio data are subsets of continuous data. Quantitative data consists of numerical values and their associated numerical attributes.Weight of pet & age of pet are the two categories that would yield quantitative data because both quantity can measured or counted.
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A water well drilling rig has dug to a height of -30 feet after one full day (24 hours),of continuous use. assuming the rig drilled at a constant rate, what was the height of the drill after 15 hours (5/8 days)?
The Height of the drill after 15 hours was 18.75 feet deep or (-18.75) feet.
Given that in 24 hours
the water well drilling rig dig -30 feet .
we know that ,
24 hours = 1 day
So,
1 hour =1/24 day
15 hours = [tex]\frac{15}{24} =\frac{5}{8} day[/tex]
Now according to the question ,
in 1 day the drilling rig dug -30 feet
So in [tex]\frac{5}{8} day[/tex] the drilling rig will dig =[tex]\frac{5}{8} *(-30)=-18.75feet[/tex]
in 15 hours (5/8 days ) drilling rig dig -18.75 feet.
Therefore , The Height of the drill after 15 hours (5/8 days) was 18.75 feet deep or (-18.75) feet.
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Laila needs 6 1/4 feet of chain to complete a project an outdoor project. She has two small pieces measuring 1 1/4 feet and 2 1/2 feet. How many feet of chain does laila need to purchase?
First you want to make the fractions have equal denominators. So you want to convert 1/2 to 2/4. Now you can add 1 1/4 to 2 2/4. After adding that subtract it from 6 1/4. Whatever your answer is will be how much more she needs.
(6/7x-2/3)+3/5(5/8x-6/7)
Answer:
Step-by-step explanation:
1035x-992/840
help me out!(with explanation)
Answer:
a) 512cm³ b) 2 × 2 ×2
Step-by-step explanation:
A CUBE'S LENGTH WIDTH AND HEIGHT ARE EQUAL
a) Volume of a cube = length × width × height
as the length width and height are equal so it will be
8 × 8 × 8 = 512
b) Volume of a cube = length × width × height
as length, width and height are equal lets suppose the value of each of them will be = x
volume = x × x × x
vol = x³
8 = x³
∛8 = x
x = 2
(7x-11) (6x-1) find the value of x
Answer:
Hey!
Since we know that both expressions lay on a straight line, we know that when both lines add up it should be 180°
We can write the expression as (7x - 1) + (6x - 1) = 180
Simplify
→ (7x + −1) + (6x + −1) = 180
Combine Like Terms
→ (7x + 6x) + (-1 + -1) = 180 → 13 + -2 = 180
Add 2 To Both Sides
→ 13x - 2 + 2 = 180 + 2 → 13x = 182
Divide 13 To Both Sides
13x/13 = 182/13 → x = 14
Hence, the value of x is 14!
-------------------------------------------------
Hope This Helped! Good Luck!
the lcm of (1/√2) + (1/√2)
Answer: LCM would be [tex]\sqrt{2}[/tex]
Step-by-step explanation:
First we need to find number of which we need to find lcm
here we dont have any two number but operator (+) is present
so
first we need to solve this operation
=1/[tex]\sqrt{2}[/tex] + 1/[tex]\sqrt{2}[/tex]
=[tex]\sqrt{2}[/tex]
so lcm of [tex]\sqrt{2}[/tex] would be [tex]\sqrt{2}[/tex].
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find the equations for the lines through the point (a, c) that are parallel to and perpendicular to the line y
Lines can be perpendicular or parallel to one another.
The parallel line's equation is y = mx - am + c.The perpendicular line's equation is y = -(x/m) + a/m + c.What do we mean by linear equation?
A linear equation is an algebraic equation with only a constant and a first-order (linear) term of the form y=mx+b, where m is the slope and b is the y-intercept. The above is sometimes referred to as a "linear equation of two variables," where y and x are the variables.So,
A linear equation is written as: y = mx + b
Where, m = slope.
(A) Parallel equation:
The slope of a line parallel to y = mx + b is the same as the slope of y = mx + b, that is the slope is the equation in m.
The equation is then solved as follows:
y = m(x - x₁) + y₁Where:
(x₁,y₁) = (a,c)Now, put (x₁,y₁) = (a,c) in y = m(x - x₁) + y₁ as follows:
y = m (x - a) + c
y = mx - am + c
So, the equation of a line is y = mx - am + c.
(B) Parallel equation:
The slope (m2) of a perpendicular line to y = mx + b is:
m₂ = -(1/m)The equation is then solved as follows:
y = m₂(x - x₁) + y₁Where:
(x₁,y₁) = (a,c)m₂ = -(1/m)Now, put (x₁,y₁) = (a,c) in y = m(x - x₁) + y₁
y = -(1/m)(x - a) + cy = -(x/m) + a/m + cThe perpendicular line's equation is y = -(x/m) + a/m + c.
Therefore, lines can be perpendicular or parallel to one another.
The parallel line's equation is y = mx - am + c.The perpendicular line's equation is y = -(x/m) + a/m + c.Know more about the linear equation here:
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The correct question is given below:
Find the equations for the lines through the point (a,
c.that are parallel to and perpendicular to the line y = mx + b where m ≠ 0. use y for the dependent variable and all letters in lower case.
What lines would you use to solve –3x – 2 = 2x + 8? Graph the line for the left side of the equation. Graph the line for the right side of the equation.
Answer:
See attached graph for lines
Left side line is y = -3x-2
Right side line is y = 2x + 8
Point of intersection is at (-2,4)
Step-by-step explanation:
The line graphs are attached
The solution for (x, y) is the point of intersection of the two lines
This is at point (2,4)
We can also solve this algebraically by solving first for x and then y
–3x – 2 = 2x + 8
The two line equations are
y = -3x - 2 and y = 2x+8
3x – 2 = 2x + 8
==> 3x -2x - 2 = 2x-2x + 8 (subtract 2x on both sides)
==> -5x -2 = 8
==> -5x -2 + 2 = 8 + 2 (add 2 on both sides to isolate the x term)
==> -5x = 10==> -5x/5 = 10/5 (divide by 5 both sides)
==> x = -2
Plug this value of x into the RHS giving
y = 2(-2) + 8 ==> y = -4 + 8 ==> y = 4
So (-2,4) is the point of intersection of the two lines and is consistent with the point of intersection on the graph
50 pts to whoever solves this for me
Rubén put an empty cup underneath a leaking faucet after 1 1/2 hours Ruben had collected 1/4 cup of water. What is the rate in cups per hour at which the water is leaking from the faucet
The rate of water leaking from the faucet is 0.167 cups per hour.
What is defined as the flow rate?The volume of fluid which flows through with a given cross-sectional unit of time is defined as flow rate.The volume per time unit offered to the flow of gases or even other fluid substances that emerge from an orifice, pump, turbine, or pass through a conduit or channel is referred to as flow rate.For, the given question;
Divide the amount of water accumulated by the number of hours to find the rate that the water is leaking out from faucet.
Let 'r' be the flow rate.
The formula for flow rate is;
Flow rate = volume / time
r = 0.25 cup / 1.5 hours
r = 0.167 cup/hour
As a result, the rate of water leaking from faucet is roughly equivalent to 0.167 cup/h.
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