The following is the correct sequence of steps to prove that if n is a perfect square, then n + 2 is not a perfect square:
Step 1: Assume n = m², for some non-negative integer m.
Step 2: If m = 0, then n + 2 = 2, which is not a perfect square. The smallest perfect square greater than n is (m + 1)².
Step 3: Expand (m + 1)² to obtain (m + 1)² = m² + 2m + 1 = n + 2m + 1 > n + 2 + 1 > n + 2.
Step 4: Let's assume m ≥ 1.
Step 5: Hence, n + 2 is not a perfect square.
The first step in the sequence involves making an assumption to start the proof. The second step entails the derivation of the smallest perfect square greater than n. In the third step, we expand the (m + 1)² expression to get n + 2m + 1. The fourth step is an important one, as it shows that m must be greater than or equal to 1.
In the final step, we conclude that n + 2 is not a perfect square.
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Help me with this one pls
1/3y + 28 = -5
Subtract 28 from both sides:
1/3y = -33
Multiply both sides by 3:
y = -99
The answer is E) NOTA
Answer:
look at the picture attached
Which of the following differential equation(s) is/are linear? (Choose all that apply.) 1 2xy" - 5xy' + y = sin(3x) (v)² + xy =In(x) □y' + sin(y)=e3x (x²+1)y"-3y - 2x³y=-x-9 (+1)y'+xy=y"
To determine which differential equation(s) are linear, we need to examine the form of each equation. A linear differential equation is one that can be written in the form a(x)y" + b(x)y' + c(x)y = g(x), where a(x), b(x), c(x), and g(x) are functions of x.
The differential equation 2xy" - 5xy' + y = sin(3x) is linear. It can be written in the form a(x)y" + b(x)y' + c(x)y = g(x), where a(x) = 2x, b(x) = -5x, c(x) = 1, and g(x) = sin(3x).
The differential equation (v)² + xy = In(x) is not linear. It does not follow the form a(x)y" + b(x)y' + c(x)y = g(x) because it contains a term with (v)², where v represents the derivative of y with respect to x. This term does not have a linear coefficient.
The differential equation y' + sin(y) = e^(3x) is linear. It can be written in the form a(x)y' + b(x)y = g(x), where a(x) = 1, b(x) = sin(y), and g(x) = e^(3x).
The differential equation (x²+1)y" - 3y - 2x³y = -x - 9 is not linear. It does not follow the form a(x)y" + b(x)y' + c(x)y = g(x) because it contains a term with (x²+1)y", where the coefficient is a function of x.
The differential equation y' + xy = y" is linear. It can be written in the form a(x)y' + b(x)y = g(x), where a(x) = 1, b(x) = x, and g(x) = y".
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PLZ SOMEONNE HELP! DUE TODAY!!!!!!!!!!!!!
Answer:
2. is the second one, 3. is the 3rd one (i think)
Step-by-step explanation:
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°
Write the equation of a line
Slope m= unidentified
X-intercept = 5
Answer:
x = 5
Step-by-step explanation:
You want the equation of a line with undefined slope and an x-intercept of 5.
Vertical lineSlope is the ratio of "rise" to "run" for a line. If the line is vertical, the "run" is zero, making the denominator of the ratio is zero. Division by zero gives an "undefined" result.
If the slope of a line is "undefined", it is a vertical line. It has the same x-value everywhere. Its equation is ...
x = c . . . . . for some constant
ApplicationHere, the vertical line crosses the x-axis at x=5. That is the equation of the line:
x = 5
solution for y=1/3x+2 and x=9
Hi!
To do this, we plug 9 in for x, and then solve.
y = 1/3(9) + 2
multiply 1/3 and 9
y = 3 + 2
add 3 and 2
y = 5
Hope this helps! :D
HELPP!!!1 Two angles are complementary. One angle is 47 degrees. What is the measure of the other angle?
Answer:
43°
Step-by-step explanation:
Complementary angles add up to 90° in measurement.
One angle is 47 degrees.
\(90-47=\boxed{43}\)
The measurement of the other angle would be 43°.
Hope this helps.
The measure of other angle is 43 degree.
What is complementary angles?Complementary angles are those whose combined angle is 90 degrees or less. To put it another way, two angles are said to be complimentary if they combine to make a right angle. In this case, we say that the two angles work well together.
Given that.
Two angles are complementary.
Now consider one angle = x degree
And other angle = y degree
Then according to question,
Measure of angle x = 47 degree
We know that,
The sum of complementary angles are equal to 90 degree.
Therefore,
x + y = 90
x + 47 = 90
x = 90 - 47
x = 43
Hence, the other angle is = 43 degree.
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This equation is really confusing can someone help me plz
Answer:
X=10
Step-by-step explanation:
Lol I hate algebra but 725-475=250 Then 250/25=10
But can you show what the select answers are?
Evaluate ÷x+2 for x=49
12
2
9
15
Answer:12
Step-by-step explanation:but you cant divide by nothing
The angle measurements in the diagram are represented by the following expressions. A=5x-5 B=3x+13
Answer:
Step-by-step explanation: 5x-5=3x+13---> 5x-3x=13+5---> 2x=13+5---- 2x=18----> x=9 hope it helps
Answer:
Step-by-step explanation: 40
HELP MATH ASAP!! MARKING BRAINLIST-!
Answer:
-55
Step-by-step explanation:
Answer:
It's -55, you just plug in the coordinates and the slope and solve till you get the y intercept on one side.
*BRAINIEST & 25 POINTS*
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Answer:
thank u so much dost pls give me extra free point Pls mark as a brilliant pls dost
The identity a squared minus B squared equals parentheses a plus B parentheses parentheses a minus B parentheses is true for all values of ANB. Compute the whole number value of 2021 squared -2022The identity a squared minus B squared equals parentheses a plus B parentheses parentheses a minus B parentheses is true for all values of A and B. Compute the whole number value of 2021 squared -2020 squared
Question:
The identity \(A^2 - B^2 = (A + B) (A - B)\) is true for all values of A and B. Compute the whole number value of \(2021^2 -2022^2\)
Answer:
\(2021^2 - 2022^2 = -4043\)
Step-by-step explanation:
Given
\(A^2 - B^2 = (A + B) (A - B)\)
Required
Solve: \(2021^2 -2022^2\)
In: \(2021^2 -2022^2\)
\(A = 2021; B = 2022\)
\(A^2 - B^2 = (A + B) (A - B)\) becomes
\(2021^2 - 2022^2 = (2021 + 2022)(2021 - 2022)\)
\(2021^2 - 2022^2 = (4043)(-1)\)
\(2021^2 - 2022^2 = -4043\)
If a person bikes 3.2 miles in 10 minutes how far can he bike in 2.5
Answer: 0.8 miles
Step-by-step explanation:
Let the distance in miles for 2.5 minutes be A
10 minutes -> 3.2 miles
2.5 minutes -> A miles
Using proportion,
2.5 / 10 = A / 3.2
1 / 4 = A / 3.2
Hence,
A = 3.2 / 4 = 0.8
Below is a table of hourly wages for receptionists working for various companies. What is the average wage for receptionists in this group? $9.67 $11.15 $11.60 $12.15 $14.50
The average wage for receptionists in this group is $11.60
How to calculate the average wageIt's important to note that "average wage" can be calculated in a few different ways, such as mean, median, and mode. Mean is the sum of all wages divided by the number of individuals, while median is the middle value in a range of wages. Depending on which method is used, the average wage figure can vary.
The table of hourly wages for receptionists working for various companies, the average wage for receptionists in this group will be:
= $58 / 5
= $11.60
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Mrs. Crosland asked students to factor the expression 28x - 8. The students offered the answers shown
Carlos: 2(14x - 4)
Danny: 7(4x - 1)
Irene: 4(7x - 2)
Which student(s) offered answer(s) equivalent to the original expression?
Equivalent expression for the given expression is
4(7x-2)
Irene offered answer equivalent to the original expression
Given :
Mrs. Crosland asked students to factor the expression 28x - 8
The student are given some expression . To find correct expression , we need to factor the given expression
\(28x-8\)
Both 28 and 8 are divisible by 4
Lets factor out 4 from the given expression.
When we factor out 4, then we divide each term by 4
\(28x-8\\4(\frac{28}{4} -\frac{8}{4} )\\4(7x-2)\)
The students offered the answers shown
Carlos: 2(14x - 4)
Danny: 7(4x - 1)
Irene: 4(7x - 2)
so , from the answer we can say that Irene offered answer equivalent to the original expression
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what the metric system of measurement is based on the number?
The metric system of measurement is based on the number 10.
This system is also known as the International System of Units (SI) and is used in most countries around the world. In the metric system, various units of measurement are defined as multiples or fractions of a base unit, which is defined for each quantity being measured. For example, the base unit for length is the meter, and the base unit for mass is the kilogram. Prefixes such as kilo-, centi-, and milli- are used to indicate multiples or fractions of the base unit, based on factors of 10. For example, a kilometer is 1000 meters, a centimeter is 1/100 of a meter, and a milligram is 1/1000 of a gram. This makes the metric system easy to use and convert between units, as well as consistent and universally recognized.
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Using the table below, determine the unit rate in beats per minute.
minutes
beats
3
171
4
228
5
285
Answer: Where is the table?
Step-by-step explanation: i wish i could help but im afraid there isnt a table
Is 2 − –46 positive or negative?
Answer:
Negative
Step-by-step explanation:
Positive + Positive= Positive
Negative +Negative= Positive
Positive +Negative Or Negative + Positive= Negative
Guppies are small fish that live in South American rivers. They can have different- sized spots on their bodies.
The river bottoms are covered in rocks. Guppies with spots that are the same size as the rocks on the bottom are harder for bigger fish to see and catch.
The diagram below shows a population of guppies that live in a river. At time 1, the population had the same number of guppies with small and large spots. At time 2, after many generations, there were many more guppies with small spots and fewer guppies with large spots in the population.
How did the environment change between time 1 and time 2? How did the population change?
a. You cannot tell how the environment changed. With each generation, more guppies passed on the gene for small spots to their offspring.
b. The rocks became smaller. With each generation, more guppies with small spots survived long enough to pass on the gene for small spots to their offspring.
c. The rocks became smaller. Guppies with small spots are more likely to survive, so the guppie
The rocks became smaller. Guppies with small spots are more likely to survive, so both kinds of guppies passed on the gene for small spots to their offspring.
The environment changed in such a way that, "guppies with small spots had a better chance of survival and reproduction, leading to an increase in their population and a decrease in the population of guppies with large spots".
Over many generations, guppies with small spots had a survival advantage in the river because the rocks on the river bottom became smaller. This made guppies with small spots harder for larger fish to see and catch, increasing their chances of survival and reproduction.
As a result, more guppies with the small spot gene passed it on to their offspring, leading to an increase in the population of guppies with small spots. At the same time, the population of guppies with large spots decreased as they were more visible to predators and had a lower chance of survival. This process of natural selection led to a change in the frequency of different traits within the population of guppies.
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Are the following linear equations? If they are, put them in the form Lu linear operator L, and classify them as homogeneous or inhomogeneous:
(A) Ut = (xux)2 + (yuy)y + xy (B) uux + Uxxx = Ut (C) Utt = Uxxxx + Uyyyy
A homogeneous equation.
Yes, the following are linear equations:
(A) Ut = (xux)2 + (yuy)y + xy
This equation can be put in the form Lu linear operator L as follows: LAUt = 0, which is a homogeneous equation.
(B) uux + Uxxx = Ut
This equation can be put in the form Lu linear operator L as follows: LBu = Ut, which is an inhomogeneous equation.
(C) Utt = Uxxxx + Uyyyy
This equation can be put in the form Lu linear operator L as follows: LCT = 0, which is a homogeneous equation.
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whoever answers first will get brainliest
Answer:
y = 2x + 0
Step-by-step explanation:
Answer:
Step-by-step explanation:
2x50=100
2x30=60
100x2=200
Match the plot with a possible description of the sample.
60 70 80 90 100
Choose the correct answer below
A. Wait time (in minutes) for a sample of doctors offices
B.Ages (in years) of a sample of residents of a retirement home.
C. Highest yearly temperatures (F) for a sample of deserts.
D. Time (in hours_ spent watching TV in a day for a sample of teenagers.
Ages (in years) of a sample of retirement home inhabitants is option B. For the lowest wait time, the maximum frequency is anticipated to be right-skewed. A desert cannot have a maximum annual temperature of 60°F, and it is not conceivable to watch 60+ hours of TV in a single day.
Residents of senior living facilities are typically 84 years old. While there are many couples in these communities, the majority of people who live in independent living are women. Some people move in at or near the minimum age (often around 65), but most people do so between the ages of 75 and 84. Residents come from all different backgrounds.
Many people are choosing senior living in a community environment, including teachers, nurses, small business owners, big business CEOs, university professors, housewives, lawyers, engineers, musicians, and more. Current residents will attest that the rich diversity of origins fosters amazing interactions and relationships. And contrary to popular belief, the majority of residents of independent living are quite active.
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Correct Question:
Match the plot with a possible description of the sample.
60 70 80 90 100
Choose the correct answer below
A. Wait time (in minutes) for a sample of doctors offices
B. Ages (in years) of a sample of residents of a retirement home.
C. Highest yearly temperatures (F) for a sample of deserts.
D. Time (in hours_ spent watching TV in a day for a sample of teenagers.
let y be defined implicitly by x2 y5 ey = 0. compute dy dx in terms of x and y.
The derivative dy/dx is equal to -2 / (5x) in terms of x and y.
We are asked to find the derivative dy/dx of the implicitly defined function x² × \(y^5\) × \(e^y\) = 0. To find this, we'll use implicit differentiation.
Implicit differentiation means we differentiate both sides of the equation with respect to x, treating y as a function of x, and then solve for dy/dx. So, let's differentiate both sides:
d/dx (x² × \(y^5\) × \(e^y\)) = d/dx (0)
First, we'll differentiate the left side using the product rule and chain rule:
(2x × y^5 × e^y) + (x² × 5y^4 × e^y × dy/dx) = 0
Now, we'll isolate dy/dx by subtracting the first term from both sides and then dividing by the second term:
dy/dx = - (2x × \(y^5\) × \(e^y\)) / (x² × \(5y^4\) ×\(e^y\))
We can simplify this expression by canceling out some common factors:
dy/dx = - (2x) / (5x²)
Further simplification gives:
dy/dx = -2 / (5x)
Thus, the derivative dy/dx is equal to -2 / (5x) in terms of x and y.
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How many years would 18 months be?
1.5 years
1.8 months
about 2 years
Answer:
18 months=1.5 years
Step-by-step explanation:
I hope this helps
Answer:
1.5 years
Step-by-step explanation:
1 year = 12 months
18/12 = 1\(\frac{6}{12}\) = 1.5 years
5/6 x 21 in simplest form
Step-by-step explanation:
\( \frac{5}{6} \times 21\)
\( \frac{5}{2} \times 7\)
\( \frac{35}{2} \)
17.5 (Ans)
Graph the solution set of the inequality and write the solution using interval notation. Please give me a step by step explanation.
We have the inequality:
-4 < (3x - 2)/5 ≤ 6
We multiply all the sides by 5:
-4*5 < 5*(3x - 2)/5 ≤ 6*5
-20 < 3x - 2 ≤ 30
Now, we add 2 to all the sides of the inequality:
-20 + 2 < 3x - 2 + 2 ≤ 30 + 2
-18 < 3x ≤ 32
Finally, we divide by 3:
-18/3 < 3x/3 ≤ 32/3
-6 < x < 32/3
Now, using interval notation:
x = (-6, 32/3]
This means that x takes all the values greater than -6 and less or equal to 32/3. Graphically, this is:
Use the work shown below to write the equation for a line that has a slope of Negative two-fifths and passes through (15, –2).
y = mx + b
1. Substitute the known values: negative 2 = negative two-fifths (15) + b. 2. Solve for b: negative 2 = negative 6 + b. b = 4.
What is the equation of the line in slope-intercept form?
Negative 2 = negative two-fifths x + 4
y = negative two-fifths (15) + 4
y = negative two-fifths x minus 4
y = negative two-fifths x + 4
Answer:
y=negative two fifths x plus 4
Step-by-step explanation:
DNA tbh ishrb jd ge kem is j.g cr. ks i.v rgjs gusnrie84b isbsuosb sojdl
Answer:
its A
Step-by-step explanation:
mark me brainliest
pls and ty
<3 anmol
In your answers below, for the variable > type the word lambda; for the derivativeX(x) type X'; for the double derivative ² X(x) type X"; etc. Separate variables in the following partial differential equation for u(x, t): t²uU xx xuat tu tru=0 = A • DE for X(x): = 0 • DE for T(t): 0 (Simplify your answers so that the highest derivative in each equation is positive.)
It can be partial differential equations, one for the function of x (X(x)) and another for the function of t (T(t)). suggests that the product of the second derivative of X(x) with respect to x and function T(t) is equal to a constant multiplied by the function U(x, t).
The given partial differential equation is t^2 * uU_xx + x * u * at * tu = 0, where u represents the function u(x, t), and subscripts denote partial derivatives with respect to the respective variables. To solve this equation, we can separate the variables by assuming u(x, t) = X(x) * T(t), where X(x) represents the function solely dependent on x, and T(t) represents the function solely dependent on t.Substituting this assumption into the original equation, we obtain t^2 * (X''(x) * T(t)) + x * (X(x) * T'(t) + X'(x) * T(t)) = 0. Now, we can divide the equation by t^2 * X(x) * T(t), resulting in (X''(x) / X(x)) + (x * T'(t) + X'(x) * T(t)) / (t * T(t)) = 0.
Since the left-hand side depends only on x, and the right-hand side depends only on t, they must be equal to a constant, denoted by A. Therefore, we have X''(x) / X(x) = -A and (x * T'(t) + X'(x) * T(t)) / (t * T(t)) = A.These equations can be further simplified and solved independently to find the functions X(x) and T(t), thus determining the solution u(x, t) = X(x) * T(t) of the given partial differential equation.
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2/3a-1/6=1/3 help please
Answer:
1/3a might be the correct answer...