True/False: Negative Numbers Closed Under Subtraction.Provide An Example If False. (2024)

-2-6= -8

you can try to do it like me on the number line will be easier for you

y = \frac{-x}{2 } + \frac{1}{4} + ce^-{2x} is the general solution to the differential equation put the problem in standard form.

What is meant by integrating factor?

A function called an integrating factor is used to solve differential equations in mathematics. It is a function that can be made integrable by multiplying it by an ordinary differential equation. Ordinary differential equations are typically solved using this method. This factor is also applicable to multivariable calculus.

x² + 2xy + x . dy/dx = 0

x dy/dx + 2xy = [tex]- x^{v}[/tex]

[tex]\frac{dy}{dx} =+ 2y = -x[/tex]

[tex]left u(x) = e^{\int\limits^_ {} } 2dx = e^{2x}[/tex]

integration factor p(x) = u(x) = [tex]e^{2x}[/tex]

Now ,multiply [tex]e^{2x}[/tex] both sides

[tex]e^{2x} ( \frac{dy}{dx} + 2y ) = -x . e^{2x}[/tex]

[tex]e^{2x} \frac{dy}{dx} + 2e^{2x} . y = -x e^{2x}[/tex]

[tex]\frac{d}{dx} (e^{2x} .y) = -x e^{2x}[/tex]

integrate both sides

∫ [tex]d .( e^{2x} .y )[/tex] = ∫[tex]-xe^{2x} .dx[/tex]

[tex]e^{2x} .y = -\frac{e^{2x}}{2} . x + \frac{e^{2x}}{4} + c[/tex]

[tex]y = \frac{-x}{2 } + \frac{1}{4} + ce^-{2x}[/tex]

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The complete question is -

Find the general solution to the differential equation 2 dy X+ + 2xy + x dx = 0 Put the problem in standard form. Find the integrating factor, p(x) = 2x - Find y(x) Use C as the unknown constant.

Answer:

493%

Step-by-step explanation:

To convert a decimal to percentage, muiltiply the decimal by 100.

Answer:

80

Step-by-step explanation:

[tex]\frac{24.5}{100} *x = 19.6\\x = 19.6 *\frac{100}{24.5} \\x = 80[/tex]

19.6 is 24.5% of 80

Answer:

24.5% of 80= 19.6

Step-by-step explanation:

24.5% of what number is equal to 19.6

24.5

____ x = 19.6

100 100

x = 19.6 x ____

24.5

= x =80

HOPE IT HELPS

There is no real solution of given equation.

There is a special case that will tell us if a quadratic has no real solution: if b = 0 when a and c share the same sign (both positive or both negative), then there will be no real solution. The quadratic formula becomes much simpler when b = 0.

given equation [tex]x^{2} =-16[/tex]

[tex]x=\sqrt{-16},\:x=-\sqrt{-16}[/tex]

[tex]x=4i, x=-4i[/tex]

we get imaginary solutions of given equation

so, there is no real solution equation is exist.

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The price of a clematis vine, rose bush, and peony plant is given by a set of three linear equations with three variables: 29, 14, 13.

What do mathematical linear equations mean?

A linear equation is one that has a degree of 1 as its maximum value .In a linear equation, no variable has an exponent bigger than 1, thus.. A linear equation's graph will always be a straight line.

An algebraic equation known as a linear equation has an exponent of 1 for each term, and when it is graphed, it always yields a straight line.

According to given data;

let c is price of clematis vine

let r is price of rose

P is price of peony plants.

bush

c=2p+3

r=c+5+

=3c + 4r+ 2p = 233

b) putting(1) in 2

a 2p+ 3 + 5 2 p +8 -9 putting(1) and (4)in 3

3(2p+3)+4(2p+8) + 2 p² 233

2

6p+9+8p+16+2p = 233

16p=25=233

16 p= 233-25

16p = 208

p=208÷13

p= 13

putting value of p in (1)and(4)

c= 2 p +3

=2X13+3

C = 29

r= 2p+8

=2×13+8

=34

price of clematis vines =29

rose bush = 34.

peony plants = 13.

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Answer:

y = 4x + 5

Step-by-step explanation:

y = 4x + 5 is the only one that graphs a straight line

Those methods involving the collection, presentation, and characterization of a set of data in order to properly describe the various features of that set of data are called descriptive statistics.

Descriptive statistics:- Descriptive statistics helps to describe, summarize and organize the set of data efficiently and in an informative way, so that it'll be easier to make conclusion about the data in order to make rational decisions. This method describes the characteristics of a dataset.

Example:- The average test score for the students of a particular class, gives descriptive sense of the typical scores.

There are three types of descriptive statistics-

Univariate statistics:- It summarizes only one variable at a time.Bivariate statistics:- It compares between two variables.Multivariate statistics:- It compares between more than two variables.

Thus we can conclude that, those methods involving the collection, presentation, and characterization of a set of data in order to properly describe the various features of that set of data are called descriptive statistics.

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Using Dot product

Two vectors x and y are said to be orthogonal if their dot product is zero

⇒ x.y = 0

This is because orthogonal vectors are make an angle of 90° with each other and therefore θ becomes 90°

Dot product is given by :

x.y = x*y*cosθ = xycos90°

∵cos90° is zero , x.y=0 for orthogonal vectors.

Let u,v,y be vectors in R

y is orthogonal to u and v

⇒ y.u = 0 and y.v=0

Now, we have to prove that y is orthogonal to (u+v)

The dot product of these vectors is given by:

y.(u+v) = y.u + y.v (Dot product is distributive) = 0 + 0 = 0

∵The dot product is zero , vector y and (u+v) are orthogonal

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Answer:

y-intercept : 3

x-intercepts are 1 and 2

Vertex is at (2,-1)

Axis of symmetry is at x = 2

Step-by-step explanation:

See attached graph.

The equation y = x² – 4x + 3 represents a parabola

y-intercept at is at B(0,3); y-intercept is 3

x-intercept points at C(1,0) and D(3,0) so x-intercepts are 1 and 3

The vertex is the lowest point on this parabola (2-1)

Axis of symmetry is a line passing through the vertex and dividing the parabola into two equal halves. This is the vertical line x = 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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Answer:

[tex] \sf \large \: x≥ \frac{7}{2}orx≤ \frac{3}{2}[/tex]

Step-by-step explanation:

Let's solve your inequality step-by-step.

5−3(|2x−5|)≤−1

−3(|2x−5|)+5≤−1

Step 1: Add -5 to both sides.

−3(|2x−5|)+5+−5≤−1+−5

−3(|2x−5|)≤−6

Step 2: Divide both sides by -3.

−3(|2x−5|)/−3 ≤ −6/−3

|2x−5|≥2

Step 3: Solve Absolute Value.

|2x−5|≥2

We know either2x−5≥2or2x−5≤−2

2x−5≥2(Possibility 1)

2x−5+5≥2+5(Add 5 to both sides)

2x≥7

2x/2 ≥ 7/2

(Divide both sides by 2)

x≥7/2

2x−5≤−2(Possibility 2)

2x−5+5≤−2+5(Add 5 to both sides)

2x≤3

2x/2 ≤ 3/2

(Divide both sides by 2)

x≤ 3/2

Answer:

type 1 in a1 type 2 in a2, (or whatever ur preferred no.s are),then heighlight both cells, then go to the bottom right corner of a2 and drag down or double click

Step-by-step explanation:

Drag down or double-click the bottom right corner of a2 to begin with a 1 in a1 and a 2 in a2 and complete the sequence.

What is excel?

Excel is a software in which we can process large amount of data and data handling easily and effectively, Excel can be used in Data analysis.

in a1 type 1 Type 2 in cell a2 (or whatever your chosen numbers are), highlight both cells, and then drag down or double-click the bottom right corner of a2.

Thus, drag down or double-click the bottom right corner of a2 to begin with a 1 in a1 and a 2 in a2 and complete the sequence.

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Answer: Choice D

======================================================

Explanation:

To find the inverse, we swap x and y, then solve for y.

y = 2x-3

x = 2y-3

x+3 = 2y

2y = x+3

y = (x+3)/2

y = x/2 + 3/2

y = (1/2)x + 3/2

This shows the original function y = 2x-3 leads to the inverse y = (1/2)x+3/2, and vice versa.

--------------

Another approach:

Since we're given a list of multiple choice answers, we can rule out the non-answers.

Plug x = 0 into the first equation of choice A. It leads to y = 2

That output 2 is then plugged into the second equation for choice A. It leads to y = 13/2. We do not get the original input 0, which shows that the equations in choice A do not undo one another. They aren't inverses of each other.

This allows us to rule out choice A. Choices B and C are similar stories.

Notice that plugging x = 0 into the first equation of choice D leads to the output y = -3. Then plug this as the input into y = (1/2)x+3/2 and you should get y = 0 to get us back where we started. This partially helps confirm we have a pair of functions that are inverses of each other. I'll let you try other values.

Answer:

Step-by-step explanation:

Algorithm for deriving the formula of the inverse function

Step 1. In the formula for the original function, replace the notation of the argument and the value:

Step 2. From the resulting formula, express y(x).

Step 3. Take into account the constraints on the area of definition and the area of values of the original and/or inverse functions.

[tex]\displaystyle\\ y=\frac{1}{2}x+2\\\\ 1.\ x=\frac{1}{2}y+2\\ \Rightarrow\ x-2=\frac{1}{2}y \\2.\ Multiply\ both\ parts\ of\ the\ equation\ by\ 2:\\\\2(x-2)=y\\\\2x-4=y\\Thus,\\y=2x-4\neq 3x+\frac{1}{2} \\Answer:\ no\\\\2.\ y=5(x-2)\\\\1.\ x=5(y-2)\\\\2.\ Divide\ both\ parts\ of\ the\ equation \ by\ 5:\\\\\frac{x}{5} =y-2\\\\\Rightarrow\ \frac{x}{5}+2=y \\Thus,\\\\y=\frac{x}{5}+2 \neq \frac{1}{5}(x+2)\\ Answer:\ no[/tex]

[tex]y=2x-3\\1.\ x=2y-3\\\\2,\ x+3=2x\\\\Divide\ both\ parts\ of\ the \ equation\ by \ 2:\\\\\frac{1}{2}(x+3)=y\\\\ Thus,\\\\y=\frac{1}{2}x+\frac{3}{2} \equiv\frac{1}{2}x+\frac{3}{2} \\\\Answer:\ yes[/tex]

Answer is {(1, 1), (1, 2), (1, 3), (1,4)}
The third choice

Step by step

{(1, 1), (1, 2), (1, 3), (1,4)} does not satisfy the requirements of a function because it has multiple x values of 1.
A function must have unique x values to pass the vertical line test. See attached picture showing the vertical line test.

These satisfy the requirements of a function.

O {(1, 1), (2, 2), (3, 3), (4,4)}

O {(1,4), (2,4), (3, 4), (4,4)}

O {(1, 2), (2, 3), (3, 4), (4,1)}

A relation will be only a function if and if only for every single value of x there must be only one output thus {(1,1),(1,2), (1,3), (1,4)} will not be a function, therefore, option (C) will be correct.

What is a function?

A certain kind of relationship called a function binds inputs to essentially one output.

A function can be regarded as a computer, which is helpful.

Given the coordinates,

In option (B) {(1,4),(2,4),(3,4),(4,4)} in this for y = 4 → x = 1,2,3,4 so it will be a function becuase for every single x value there is a single y value but for a single y value, there could be two x.

In option (D) {(1,1),(1,2), (1,3), (1,4)} for x = 1 → y = 1,2,3,4 so it will not a function.

Hence "{(1,1),(1,2), (1,3), (1,4)} will not be a function".

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The number of marbles left in the pocket after losing is 29 { after narrating the story in numerical sentences}

Given that Tran bought 25 marbles and put them in his pocket with 10 other marbles. He had a hole in his pocket and lost 6 marbles. and asked to narrate the story in numerical form

Total number of marbles Tran bought=25 marbles

Total number of marble Tran has before buying new marbles=10 marbles

Total number of marbles after buying new marbles=35 marbles

Given that he lost 6 marbles because of the hole in his pocket

Therefore, the Total number of marbles left=35-6

The total number of marbles left=29 marbles.

Therefore, The number of marbles left in the pocket after losing is 29 { after narrating the story in numerical sentences}

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Ella's bait and tackle shop sells 230,385 in April and May.

Based on the given conditions, formulate:

Bait and tackle sold in 128,278 live worms in April

Bait and tackle sold in 102,278 live worms in May

So the total number of Bait and tackles sold in April and May =

=128,107+102,278

= 230,385

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Answer:

x = -23

Step-by-step explanation:

3.5(x+20) = 6 + .75(x + 1) Multiply the terms inside the parentheses on the left by 3.5 and the parentheses on the left by .75

(3.5)x +(3.5)(20) = 6 + (.75)x +(.75)(1)

3.5x + 70 = 6 + .75x + .75 Combine the 6 and .75 on the right side

3.5x + 70 = 6.75 + .75x Subtract .75x from both sides of the equation

2.75x + 70 = 6.75 Subtract 70 from both sides of the equation

2.75x = -63.25 Divide both sides by 2.75

x = -23

Check

3.5(-23+20) = 6 + .75(-23 + 1)

3.5(-3) = 6 +.75(-22)

-10.5 = 6 +(-16.5)

-10.5 = -10.5

Answer:

x = -23

Step-by-step explanation:

3.5(x+20)=6+.75(x+1)

3.5x + 70 = 6 + .75x + .75

3.5x+70=.75x+6.75

2.75x+70=6.75

2.75=−63.25

divide^

x = -23

Answer:

184300

Step-by-step explanation:

When rounding to the nearest anything, you look at the place 1 unit smaller. Here, we'd look at the tens place.

184329

Anything 5 or greater increases the value of the place 1 unit bigger. Here, we have a 2 in the tens place. That doesn't increase the 3 in the hundreds place, so we round down to 184300.

The value of both the interior angles of the triangle is calculated as 70° and 35°.

What is the exterior angle property?

If a triangle side is formed, the exterior angle made is equal to the sum of a 2 interior opposite angles.

When an equivalent angle is chosen to take at each vertex of the triangle, this same exterior angles always add up to 360°.Each exterior angle equals 180° minus the interior angle. If the relating interior angle is given, this formula can be used. Exterior angle = Sum of opposite angles on the inside. When the exterior angle's distant interior opposite angles are given, this formula can be used to find it.

Now, as per the given question;

The exterior angle of a triangle is 105°.

Let one of the interior angle is 'x'.

Then, the other interior angle is 35 degree less; x - 35°.

By the exterior angle property.

Sum of interior angles = exterior angle

x + x - 35° = 105°

2x = 105° + 35°

2x = 140°

x = 70°

The other interior angle is; x - 35°

= 70° - 35°

= 35°

Therefore, the two interior angles of the triangles are estimated as 70° and 35°.

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Answer: The slope of f(x) is less than the slope of g(x) because the slope of f(x) is -3

Step-by-step explanation:

Define slope?

The slope of a line is the ratio of the amount that y increases as x increases some amount. Slope tells you how steep a line is, or how much y increases as x increases. The slope is constant (the same) anywhere on the line.

We can write:

m=(y2-y1) / (x2-x1)

If,

g(x) = 2x - 6

The slope of g(x), m = 2

Let, x1=0

y1=2

x2=-1

Y2=1

So, we take (x1, y1) and (x2, y2) Then consider (0, 2) and (-1, 1)

Solve it:

Replace with x1, y1 and x2, y2

m = [1-(-2)/(-1)]

m=[(1+2) /(-1) ]

m=3/(-1)

m=-3

Thus, the slope of f(x) is less than the slope of g(x) because the slope of f(x) is -3.

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Answer:

D

Step-by-step explanation:

the simplification of 12.9 - 2.8 - 7.2 + 9.1 is 12

Answer:

f(x)=

1. 48x when x < or = 3,

2. 45x when 4 < or = x < or = 8

3. 42x when 9 < or = x < or = 19

4. 38x when x > 19

Step-by-step explanation:

3 boxes or less = Cost of tiles = $48

4 - 8 boxes ; cost = $45

9 - 19 boxes ; cost = $42

> 19 boxes ; cost = $38

Answer:

I think y is 29

Step-by-step explanation:

It's what the results gave me

Answer:

y =x + 3

Step-by-step explanation:

i gotchu

Answer:

T9=60

Step-by-step explanation:

step 1: solve for x

it is an arithmetic pattern,so the 1st difference is the common difference (d)

therefore...9x+199x+11-(4x+44x+4)=14x+18-(9x+199x+11)

128x+11-48x-4=14x+18-128x-11

80x+7=-144x+7

80x+144x=7-7

224x=0

224x/224=0/224

X=0

step 2: substitute for x

4(0)+44(0)+4=4[1st term]

9(0)+119(0)+11=11(2nd term)

14(0)+18=18(3rd term)

step 3:find the common difference

d=3rd term- 2nd term, 2nd term-1st term

3rd term-2nd term

18-11=7

2nd term-1st term

11-4=7

therefore...d=7

step 4:find the general formula

we use the formula Tn=a+(n-1)d to find the general formula/ nth term

where: Tn is the nth term

a is the first term

n is the number of term

d is the common difference

Tn=a+(n-1)d

=4+(n-1)7

=4+7n-7

=7n-3

step 5:find the 9th term

Tn=a+(n-1)d

=7n-3

=7(9)-3

=60

The constant term in the expression is 3.

The expression is 4x ₋ 2y ₊ 3.

Here in this equation we have variables and constants.

variables = x and y whose coefficients are 4 and ₋2 respectively.

A variable is anything whose value can change and is not fixed. Typically, the letters x, y, z, etc. are used to indicate variables.

The above equation is in the form ax ₊ by ₊ c

An object with a fixed value in a circ*mstance is said to be a constant. We are aware that the constant is fixed, even though we do not know its exact value. In general, constants are represented by the letters a, b, c, p, q, etc. if their values are unknown or not given, and by particular numerical values) if their values are known.

Hence we get the constant term as 3.

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Answer: x= -3

Step-by-step explanation:

Answer:

x=-3

Step-by-step explanation:

First you must start by multiplying the parentheses by -5. Once you do that, your equation comes out to -35x+45-6=144. Then you must combine like terms which comes out to -35x+39=144. After that you must get x by itself, so to do that subtract 39 from 144 which comes out to 105. Then you must do the opposite of multiplication and divide 105 by -35 which comes out to x=-3. Hope this helps

Answer:

this is a finance and it is an