solve for x
2/x -2 = 3/2x +3​

Answer:

20

Step-by-step explanation:

A common denominator is a number that is a multiple of both denominators.

To find it just write the multiplication table of the numbers and find a number that appears in both of them.

In this case, we have 4 and 5:

4, 8, 12, 16, 20, 24, 28, 32, 36, 40

5, 10, 15, 20, 25, 30, 35, 40, 45, 50

Since it only asks for a common denominator, it can be 20, 40, 60, 80... Although it's usually smarter to pick the lower number.

[tex]1\dfrac 34 =1+ \dfrac 34 =\dfrac 74 = \dfrac{35}{20}\\\\\\1\dfrac 45 = 1+ \dfrac 45 = \dfrac 95 =\dfrac{36}{20}\\\\\text{The answer is 20}[/tex]

Answer:8x-40

Step-by-step explanation:

Because when we simply 4(x-5)/2

We multiply both sides by 2 because the inverse operations of division is multiplication. 2*4(x-5)*2/2 we cancel two by two then it leave us 4*2(x-5).

Next four times two is eight. So 8(x-5) we distribe eight that means eight times x and 5, 8x-40thos is the answer. Hope this help

1. The given equation is probably supposed to read

y'' - 2y' - 3y = 64x exp(-x)

First consider the homogeneous equation,

y'' - 2y' - 3y = 0

which has characteristic equation

r² - 2r - 3 = (r - 3) (r + 1) = 0

with roots r = 3 and r = -1. Then the characteristic solution is

[tex]y = C_1 e^{3x} + C_2 e^{-x}[/tex]

and we let y₁ = exp(3x) and y₂ = exp(-x), our fundamental solutions.

Now we use variation of parameters, which gives a particular solution of the form

[tex]y_p = u_1y_1 + u_2y_2[/tex]

where

[tex]\displaystyle u_1 = -\int \frac{64xe^{-x}y_2}{W(y_1,y_2)} \, dx[/tex]

[tex]\displaystyle u_2 = \int \frac{64xe^{-x}y_1}{W(y_1,y_2)} \, dx[/tex]

and W(y₁, y₂) is the Wronskian determinant of the two fundamental solutions. This is

[tex]W(y_1,y_2) = \begin{vmatrix}e^{3x} & e^{-x} \\ (e^{3x})' & (e^{-x})'\end{vmatrix} = \begin{vmatrix}e^{3x} & e^{-x} \\ 3e^{3x} & -e^{-x}\end{vmatrix} = -e^{2x} - 3e^{2x} = -4e^{2x}[/tex]

Then we find

[tex]\displaystyle u_1 = -\int \frac{64xe^{-x} \cdot e^{-x}}{-4e^{2x}} \, dx = 16 \int xe^{-4x} \, dx = -(4x + 1) e^{-4x}[/tex]

[tex]\displaystyle u_2 = \int \frac{64xe^{-x} \cdot e^{3x}}{-4e^{2x}} \, dx = -16 \int x \, dx = -8x^2[/tex]

so it follows that the particular solution is

[tex]y_p = -(4x+1)e^{-4x} \cdot e^{3x} - 8x^2\cdot e^{-x} = -(8x^2+4x+1)e^{-x}[/tex]

and so the general solution is

[tex]\boxed{y(x) = C_1 e^{3x} + C_2e^{-x} - (8x^2+4x+1) e^{-x}}[/tex]

2. I'll again assume there's typo in the equation, and that it should read

y''' - 6y'' + 11y' - 6y = 2x exp(-x)

Again, we consider the homogeneous equation,

y''' - 6y'' + 11y' - 6y = 0

and observe that the characteristic polynomial,

r³ - 6r² + 11r - 6

has coefficients that sum to 1 - 6 + 11 - 6 = 0, which immediately tells us that r = 1 is a root. Polynomial division and subsequent factoring yields

r³ - 6r² + 11r - 6 = (r - 1) (r² - 5r + 6) = (r - 1) (r - 2) (r - 3)

and from this we see the characteristic solution is

[tex]y_c = C_1 e^x + C_2 e^{2x} + C_3 e^{3x}[/tex]

For the particular solution, I'll use undetermined coefficients. We look for a solution of the form

[tex]y_p = (ax+b)e^{-x}[/tex]

whose first three derivatives are

[tex]{y_p}' = ae^{-x} - (ax+b)e^{-x} = (-ax+a-b)e^{-x}[/tex]

[tex]{y_p}'' = -ae^{-x} - (-ax+a-b)e^{-x} = (ax-2a+b)e^{-x}[/tex]

[tex]{y_p}''' = ae^{-x} - (ax-2a+b)e^{-x} = (-ax+3a-b)e^{-x}[/tex]

Substituting these into the equation gives

[tex](-ax+3a-b)e^{-x} - 6(ax-2a+b)e^{-x} + 11(-ax+a-b)e^{-x} - 6(ax+b)e^{-x} = 2xe^{-x}[/tex]

[tex](-ax+3a-b) - 6(ax-2a+b) + 11(-ax+a-b) - 6(ax+b) = 2x[/tex]

[tex]-24ax+26a-24b = 2x[/tex]

It follows that -24a = 2 and 26a - 24b = 0, so that a = -1/12 = -12/144 and b = -13/144, so the particular solution is

[tex]y_p = -\dfrac{12x+13}{144}e^{-x}[/tex]

and the general solution is

[tex]\boxed{y = C_1 e^x + C_2 e^{2x} + C_3 e^{3x} - \dfrac{12x+13}{144} e^{-x}}[/tex]

Answer:

Step-by-step explanation:

0 = 5x + 7

-7 = 5x

x = - 7/5 = -1.4

Answer:

-1.4

Step-by-step explanation:

h(x)=0=5x+7

or, 5x= -7

x= -7/5= -1.4

Answer:

2:1  or  2

Step-by-step explanation:

*** (Ratios can be written as " a : b", or can be written as a fraction " a / b".

 >> therefore 10/5 can be simplified to 2/1 )***

    For every 10 notebooks, there are 5 ballpens.

    Therefore, for every 2 notebooks there is 1 ballpen (The simplification).

EXTRA:  

**Also remember that the ratio of notebooks to ballpens cannot be reversed into ballpen to notebook ratio, because this would change the meaning.

  2/1 is not the same as 1/2 **

Answer:

Just go to the 6 on the bottom line, and add a point

Answer:

see below

Step-by-step explanation:

(6,0)

 The first coordinate is the x coordinate.  Since it is positive we go to the right 6 units.  The second coordinate is the y coordinate.  We go up zero units

Answer: 1.075s

Step-by-step explanation:

s*175/100=1.075s

Answer:

Yes, because (-1,2) is a solution to both inequalities

Step-by-step explanation:

2>-1 so the first inequality is correct

-1+2>0 so the second inequality is correct

Answer:

The angle value 433.54 π rad (pi radian) in words is "four hundred and thirty-three point five four π rad (pi radian)".

Step-by-step explanation:

got the information from the internet

Answer:

They are both the same.

Step-by-step explanation:

-2.875

7/8 = 0.875 thus -2 7/8 is equal to -2.875

Step-by-step explanation:

The first step is to Know the condition for two lines be parallel is that have the same slope, and this form the slope given is 2, therefore the new function has its slope too

2)  with the slope and the two points givens, you can find the equation

Y-Y1 = m( X-X1) ,   Y-6 = 2[(X-(-3)]  ⇒Y-6 = 2X+6 ⇒Y = 2X+12, AND THIS IS THE EQUATION PARALLEL TO THE LINE Y = 2X-7

Answer:

1/98

Step-by-step explanation:

Step 1: Translate statement into equation.

Step 2: Multiply both sides by 7x.

Step 3: Divide both sides by 98.

Step 4: Check if solution is correct.

Therefore, the answer is 1/98.

Answer:

.25

Step-by-step explanation:

Answer:

15:8=15/8

Step-by-step explanation:

45:24=45/24

15/8=15:8

there you go the answer is in the picture

Answer:

Step-by-step explanation:

if 50 AED= 12 Euro

for 1 AED ? Euro

50AED/1AED= 12Euro/x

cross multiplication:

50*x=12*1

50*x=12

x=12/50

x=0.24 Euro

so for 1AED you will get 0.26 Euro

Answer:

250

Step-by-step explanation:

You can take the explicit formula and simply substitute the n value with 64:

-2 + 4 * (64 - 1)

-2 + 4 * (63)

-2 + 252

250

Answer:

slope = - [tex]\frac{6}{5}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (2, 7 ) and (x₂, y₂ ) = (7, 1 )

m = [tex]\frac{1-7}{7-2}[/tex] = [tex]\frac{-6}{5}[/tex] = - [tex]\frac{6}{5}[/tex]

Hello there! :)

To find the slope of the line when we are given 2 points, we use the following formula:

m=[tex]\frac{y2-y1}{x2-x1}[/tex]

m=[tex]\frac{1-7}{7-2} \\\frac{-6}{5}[/tex]

So the slope is -6/5. Hope this helps!

~Just a cheerful gal

#CarryOnLearning

[tex]MysteriousNature :)[/tex]

9514 1404 393

Answer:

  10.49

Step-by-step explanation:

Since we know 110 = 10² +10, we can make a first approximation to the root as ...

  √10 ≈ 10 +10/21 . . . . . where 21 = 1 + 2×integer portion of root

This is a little outside the desired approximation accuracy, so we need to refine the estimate. There are a couple of simple ways to do this.

One of the best is to use the Babylonian method: average this value with the value obtained by dividing 110 by it.

  ((220/21) + (110/(220/21)))/2 = 110/21 +21/4 = 881/84 ≈ 10.49

An approximation of √110 accurate to hundredths is 10.49.

__

The other simple way to refine the root estimate is to carry the continued fraction approximation to one more level.

For n = s² +r, the first approximation is ...

  √n = s +r/(2s+1)

An iterated approximation is ...

  s + r/(s +(s +r/(2s+1)))

The adds 's' to the approximate root to make the new fraction denominator.

For this root, the refined approximation is ...

  √110 ≈ 10 + 10/(10 +(10 +10/21)) = 10 +10/(430/21) = 10 +21/43 ≈ 10.49

_____

Additional comment

Any square root can be represented as a repeating continued fraction.

  [tex]\displaystyle\sqrt{n}=\sqrt{s^2+r}\approx s+\cfrac{r}{2s+\cfrac{r}{2s+\dots}}[/tex]

If "f" represents the fractional part of the root, it can be refined by the iteration ...

  [tex]f'=\dfrac{r}{2s+f}[/tex]

__

The above continued fraction iteration adds 1+ good decimal places to the root with each iteration. The Babylonian method described above doubles the number of good decimal places with each iteration. It very quickly converges to a root limited only by the precision available in your calculator.

Answer:

[tex]-6\leq x\leq 6[/tex]

Step-by-step explanation:

This is answer for the last question.

Answer:

42.20

Step-by-step explanation:

132 ×0.32

=42.24

rounded off it give 42.20

Answer:

5

Step-by-step explanation:

First subtract 6 from 16 to find how many cucumbers she has,

16 - 6 = 10

Now we know she has 10 cucumbers.

Subtract 5 from the 10 cucumbers to find out how many she has after giving away 5.

10 - 5 = 5

After subtracting the 5 cucumbers she gave away, we are left with 5

This means Maya has 5 cucumbers now

Answer:

Uuuuh thats kind of suspicious, maybe you could post your question without  a link? But links are usually scams, so dont do that :)

To answer this question, you would need to divide the total amount of cereal in the box by the serving size.

This would be 12 2/3 divided by 1 1/3.

We can write each mixed number as an improper fraction first before we divide:12 2/3 = 38/3 and 1 1/3 = 4/3

Now divide 38/3 by 4/3. Recall that dividing by a fraction is accomplished by multiplying by the reciprocal of the divisor: 38/3 * 3/4 = 114/12 = 38/4 OR 19/2

Also, 19/2 is equivalent to 9 and 1/2. There would be 9 and 1/2 servings in the box of cereal.

Hope this helps

Answer:

with what

Step-by-step explanation:

Answer:

help with? there's nothing there

Answer:

i need the question

Step-by-step explanation:

Answer:

-6.4 is GREATER.

The number closest to 0 is greater.

9514 1404 393

Answer:

  D. choosing first second-, and third-place winners in a cooking contest​

Step-by-step explanation:

Permutations are involved when order matters. The order of people surveyed, sundae flavors, and flowers are irrelevant. The order of first-second-third is entirely relevant.

Cooking contest winners involve permutations.

Answer:

at most 17 pitches per inning

Step-by-step explanation:

It is given that a baseball pitcher makes 53 pitches in the first 4 innings of a game and plans to pitch in the next 3 innings.

We need to write and solve an inequality to find the possible average pitches per inning the pitcher made in the next 3 innings if the pitcher is assigned a maximum of 105 pitches.

From part (a) we know  3 p + 53 3p+53 represents the total number of pitches made if the pitcher makes an average of  p pitches per inning in the next 3 innings.

If the pitcher can make at most 105 pitches, then:

3 p + 53 ≤ 105 3p+53≤105 ​  

To solve the inequality, first subtract 53 on both sides of the inequality to isolate the variable term:

3 p + 53 − 53 ≤ 105 − 53 3 p ≤ 53      

3p+53≤105 [tex]p\leq 17\frac{1}{3}[/tex]

at most 17 pitches per inning

​

(Hope this helps can I pls have brainlist (crown)☺️)