X^-2+4x^-1+3=0 solve by making appropriate substitution

Answer:

factored form is: [tex](\frac{x}{2}-\frac{y}{3})(\frac{x^2}{4}+\frac{xy}{6}+\frac{y^2}{9})[/tex]

Step-by-step explanation:

The given expression is:

[tex]\frac{1}{8}x^3 - \frac{1}{27}y^3[/tex]

The expression can be written as:

[tex](\frac{1}{2}x)^3-(\frac{1}{3}y)^3[/tex]

We know, a^3-b^3 = (a-b)(a^2+ab+b^2)

a= x/2 and b = y/3

Putting values in the formula given:

[tex](\frac{x}{2}-\frac{y}{3})((\frac{x}{2})^2+(\frac{x}{2})(\frac{y}{3})+(\frac{y}{3})^2)\\(\frac{x}{2}-\frac{y}{3})(\frac{x^2}{4}+\frac{xy}{6}+\frac{y^2}{9})[/tex]

So, factored form is: [tex](\frac{x}{2}-\frac{y}{3})(\frac{x^2}{4}+\frac{xy}{6}+\frac{y^2}{9})[/tex]

Answer:

x = 16

Step-by-step explanation:

Since the triangles are similar then the ratios of corresponding sides are equal, that is

[tex]\frac{RS}{MN}[/tex] = [tex]\frac{RT}{MO}[/tex], that is

[tex]\frac{8}{x}[/tex] = [tex]\frac{6.5}{13}[/tex] ( cross- multiply )

6.5x = 104 ( divide both sides by 6.5 )

x = 16

Answer:

convert from Celsius to Fahrenheit

Step-by-step explanation:

i work with thermometers i know

For this case we have that by definition, to convert degrees Celsius to Fahrenheit we use the following formula:

[tex]F = \frac {9} {5} C + 32[/tex]

Where:

C: Represents the degrees Celsius

So, we can write a function:

[tex]F (C) = \frac {9} {5} C + 32[/tex]

Answer:

The function allows to convert degrees Celsius to Fahrenheit

Answer:

Hi there!

The answer to this question is: B

Answer choice B is correct because the dash above the two letter represents a line segment or side of a triangle

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

Answer choice A: incorrect

Explanation: The little carrot in front of each letter shows that it is an angle not a side

Answer C: incorrect

Explanation: It tells you points of the triangle

Answer:

Step-by-step explanation:

[tex]A.\ \angle P,\ \angle Q,\ and\ \angle R-\bold{angles}\\\\B.\ \overline{PQ},\ \overline{QR},\ and\ \overline{PR}-\bold{sides}\\\\C.\ P,\ Q,\ and\ R-\bold{vertexs}[/tex]

Answer:

12

Step-by-step explanation:

The general formula for this is

Formula

1/t1 + 1/t2 = 1/t_tot

givens

t1 = 6 hours

t2 = x

t_tot = 4 hours

Solution

1/6 + 1/x = 1/4                 Subtract 1/6 from both sides.

1/6-1/6 + 1/x = 1/4 - 1/6   Change to 12 as your common denominator

1/x = 3/12 - 2/12              subtract

1/x = 1/12                         Cross multiply

x = 12

Tom would need 12 hours to do the job alone.

Answer:

Option D. 12 hours

Step-by-step explanation:

Let the work done by Tom to do the job alone = x hours

So per hour work done by Tom = [tex]\frac{1}{x}[/tex]

Jerry can do the job alone in the time = 6 hours

Per hour work done by Jerry = [tex]\frac{1}{6}[/tex]

Similarly job done by both together in the time = 4 hours

Per hour work done by both together = [tex]\frac{1}{4}[/tex]

Now we know,

Per hour work done by both together = per hour work done by Tom + Per hour work don by Jerry

[tex]\frac{1}{4}=\frac{1}{x}+\frac{1}{6}[/tex]

[tex]\frac{1}{x}=\frac{1}{4}-\frac{1}{6}[/tex]

[tex]\frac{1}{x}=\frac{3-2}{12}[/tex]

[tex]\frac{1}{x}=\frac{1}{12}[/tex]

x = 12 hours

Option D. will be the answer.

Answer:

B.

Step-by-step explanation:

Let's figure out what two consecutive integers is 14 between.

We also need to do this for 3.

14 is between 9 and 16 which means [tex]\sqrt{14}[/tex] is between [tex]\sqrt{9}[/tex] and [tex]\sqrt{16}[/tex].

3 is between 1 and 4 which means [tex]\sqrt{3}[/tex] is between [tex]\sqrt{1}[/tex] and [tex]\sqrt{4}[/tex].

So 14 is closer to 16 which means [tex]\sqrt{14}[/tex] is closer to 4.  Let's say [tex]\sqrt{14}\approx 3.7[/tex]

So 3 is closer to 4 which means [tex]\sqrt{3}[/tex] is closer to 2. Let's say [tex]\sqrt{3}\approx 1.8[/tex].

So now we do 3.7+1.8=5.5.

The answer that is closet to this is 5.47.

Now if we put [tex]\sqrt{14}+\sqrt{3}[/tex] in our calculator we get:

3.74+1.73=5.47

Answer:

[-4, 3]

Step-by-step explanation:

That -h gives you the OPPOSITE terms of what they really are, and k gives you the EXACT terms of what they really are. So, your vertex is [-4, 3].

If you are ever in need of assistance, do not hesitate to let me know by subscribing to my channel [USERNAME: MATHEMATICS WIZARD], and as always, I am joyous to assist anyone at any time.

Using the Pythagorean theorem:

x = √(11.7^2 - 8.6^2)

x = √(136.89 - 73.96)

x = √62.93

x = 7.9

The answer is D.

Answer:

$179.17

Step-by-step explanation:

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Answer: The investment be worth $ 174.05 in 2 years .

Step-by-step explanation:

Given : The principal amount invested  : A= $125

Interest rate : r = 18% =0.18   [ Percent convert into decimal if we divide it by 100]

Time : t = 2 years

The formula to find the accumulated amount if compounded continuously :-

[tex]A=Pe^rt\\\\=(125)(1+0.18)^{2}\\\\= 125 (1.18)^2\\\\ = 125 (1.3924)\\\\=174.05[/tex]

Hence, the investment be worth $ 174.05 in 2 years .

Answer:

The phosphate groups that are the polar of the phospholipid because they are charged - A.

The phosphate groups that are the polar of the phospholipid because they are A. charged

It is group of polar lipids that consist of two fatty acids ,  a glycerol unit and a phosphate group .

A phosphate group has a negatively charged oxygen and a positively charged nitrogen to make this group ionic. A single phospholipid molecule  has a phosphate group on one end and two chains of fatty acids . The phosphate group is negatively charged making the head polar and hydrophilic .

correct answer A) charged

learn more about phospholipid

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The equation of a circle is written as ( x-h)^2 + (y-k)^2 = r^2

h and k is the center point of the circle and r is the radius.

In the given equation (x+3)^2 + (y-1)^2 = 81

h = -3

k = 1

r^2 = 81

Take the square root of both sides:

r = 9

The center is (-3,1) and the radius is 9

Answer:

Step-by-step explanation:

A better way to write the first function would be:

c(n) = 4*c(n-1), meaning that the number of likes is equal to four times the number of likes from the previous day. 

On the first day, c(n)=c(0) = 100

Therefore:

C(n) = 100 * 4^n 

Let's plug in a view values to test our function: 

When n= 0 (first day)

C(0) = 100 * 4 ^0 = 100*1 = 100 likes

C(1) = 100 * 4^1 = 100 * 4 = 400 likes, four times the previous day

C(2) = 100 * 4^2 = 100 * 16 = 1600 likes, four times the previous day

And so on. Our function is an accurate descriptor of the model. 

Answer:

The correct ordered pair is (7,1)

Step-by-step explanation:

The given system has equations:

[tex]2x - 6y = 8....(1)[/tex]

[tex]5x- 4y = 31....(2)[/tex]

We make x the subject in the first equation to get:

[tex]x = 4 + 3y...(3)[/tex]

Put equation 3 into equation 2 to get:

[tex]5(4 + 3y) - 4y = 31[/tex]

Expand:

[tex]20 + 15y - 4y = 31[/tex]

[tex]15y - 4y = 31 - 20[/tex]

[tex]11y = 11[/tex]

[tex]y = 1[/tex]

Put y=1 into equation 3 and solve for x.

[tex]x = 4 + 3( 1) = 7[/tex]

The correct ordered pair is (7,1)

Answer:

The correct answer is A. Each x-value corresponds to exactly one y-value.

Answer:

The constant, k, is 4.32.

Step-by-step explanation:

y varies inversely with x means y=k/x.

y varies directly with x means y=kx.

Anyways we have the first relation: y=k/x where k is a constant.

We divided by x because it said inversely.

We are given (x,y)=(1.2,3.6) is on this curve.

This gives us enough information to find the constant, k.

[tex]y=\frac{k}{x}[/tex] with [tex](x,y)=(1.2,3.6)[/tex].

[tex]3.6=\frac{k}{1.2}[/tex]

Multiply both sides by 1.2:

[tex]3.6(1.2)=k[/tex]

[tex]4.32=k[/tex]

The constant, k, is 4.32.

An inequality is comparing the relation of two equations that are not equal.

Depending on a persons cell phone plan, if they can only talk for so many minutes per month or send so many texts per month, this is an inequality written as number of minutes/ texts per month needs to be less than or equal to the allowable amount.

Typo is probably in "sun" being really "sum".

Just write an equation.

[tex]4(q+p)=4q+4p[/tex]

Hope this helps.

r3t40

Answer:

21

Step-by-step explanation:

you can arrange 7×3 ways

Answer with explanation:

Number of trophies possessed by me= 7

Number of trophies that is to be selected from 7 trophies =3

⇒⇒So, Chosing 3 out of 7 trophies and arranging them on a shelf requires Concept of Permutation, as order of arrangement is also taken into consideration

    [tex]=_{3}^{7}\textrm{P}\\\\=\frac{7!}{(7-3)!}\\\\=\frac{7!}{4!}\\\\=\frac{4!*5*6*7}{4!}\\\\=5*6*7\\\\=210\text{Ways}[/tex]

Or

⇒First place can be filled in 7 ways,second place can be filled in 6 ways and third place can be filled in 5 ways.

So total number of ways of selecting 3 trophies from 7 trophies

                             =7 *6 *5

                             =210 ways

⇒Now, 3 trophies can be arranged in a shelf in 3! =3 *2*1=6 ways.

Answer:

y = 3x - 11

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x - 4 ← is in slope- intercept form

with slope m = 3

• Parallel lines have equal slopes, hence

y = 3x + c ← is the partial equation of the parallel line

To find c substitute (2, - 5) into the partial equation

- 5 = 6 + c ⇒ c = - 5 - 6 = - 11

y = 3x - 11 ← equation of parallel line

the equation of the line that is parallel to y = 3x - 4 and passes through the point (2, -5) is:

To find the equation of a line that is parallel to a given line and passes through a certain point, we need to use the concept that parallel lines have the same slope. The slope-intercept form of a line's equation is y = mx + b, where m is the slope and b is the y-intercept. Given that the line is parallel to y = 3x - 4, it will have the same slope, which is 3. Thus the slope of our new line is also 3.

We want our line to pass through the point (2, -5). Plugging these values into the slope-intercept form, we get:

which simplifies to:

Thus, the y-intercept b of our new line is:

Therefore, the equation of the line that is parallel to y = 3x - 4 and passes through the point (2, -5) is:

Answer:

Lee= 20 L per hour.

Garcia = 40L per hour

Step-by-step explanation:

This formula is:

40x + 20y = 2000L

with if being known that x + y = 60.

In this x is the rate for Garcia and y is the rate for Lee.

You can also say that x = 60 - y, which you can fill in.

40 * (60-y) + 20y = 2000

2400 - 40y + 20y = 2000

-20y = -400

y = 20 L per hour.

So x = 60 - 20 = 40L per hour

Answer:

The age of triplets is 42 years old

Step-by-step explanation:

The question in English is

The sum of the ages of twins and triplets is 150 years if the ages are exchanged the new sum is 120 years. What is the age of triplets?

Let

x -----> twins age

y ----> triplets age

we know that

2x+3y=150 ------> equation A

2y+3x=120 -----> equation B

Solve the system by graphing

The intersection point both graphs is the solution of the system

The solution is the point (12,42)

see the attached figure

therefore

The age of triplets is 42 years old

Answer:

D.

Step-by-step explanation:

First, put your original equation in slope-intercept form to find your slope.

[tex]y=mx+b\\2x+4y=-5\\4y=-2x-5\\y=-\frac{1}{2} x-\frac{5}{4}[/tex]

Now that you have your slope ([tex]-\frac{1}{2}[/tex]) and a point, you can use point-slope form to find your y-intercept.

[tex]y-y1=m(x-x1)\\y-(-8)=-\frac{1}{2} (x-(-4))\\y+8=-\frac{1}{2} (x+4)\\y+8=-\frac{1}{2} x-2\\y=-\frac{1}{2} x-10[/tex]

Your answer choices are all in [tex]Ax+By=C[/tex] form, so lets convert our equation into that form.

[tex]y=-\frac{1}{2} x-10\\1/2x+y=-10\\x+2y=-20[/tex]

If we multiply all of our terms by 2, we can get answer choice D.

Answer:

True

Step-by-step explanation:

We can plug in and see.

If (3,0) is on the graph of P, then P(3) will evaluate to 0.

Let's try it:

P(3)=(3)^3-7(3)^2+15(3)-9

P(3)=27-7(9)+45-9

P(3)=27-63+45-9

P(3)=-36+45-9

P(3)=9-9

P(3)=0

Since P(3)=0, then (3,0) is an ordered pair of P.

Yes it is true that the point (3,0) lies on the graph of

P(x) = [tex]x^{3}-7x^{2} +15x-9[/tex].

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

Given equation

P(x) = [tex]x^{3}-7x^{2} +15x-9[/tex]

If (3,0) is on the graph of P, then P(3) will evaluate to 0.

Substitute x = 3 in the given equation

P(3) = [tex](3)^3-7(3)^2+15(3)-9[/tex]

P(3) = [tex]27-7(9)+45-9[/tex]

P(3) = [tex]27-63+45-9[/tex]

P(3) = 9-9

P(3) = 0

Since P(3)=0, then (3,0) is an ordered pair of P.

Yes it is true that the point (3,0) lies on the graph of

P(x) = [tex]x^{3}-7x^{2} +15x-9[/tex].

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Answer:

15(n-1)-45

Step-by-step explanation:

Increases by 15, so sequence is arithmetic, and goes to positive.

1st term is -45

so 15(n-1) gives us first term.

Reply for any questions I got you

[tex]\bf -45~~,~~\stackrel{-45+15}{-30}~~,~~\stackrel{-30+15}{-15}~~,~~\stackrel{-15+15}{0}~\hspace{7em}\stackrel{\textit{common difference}}{d=15} \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\ \cline{1-1} a_1=-45\\ d=15 \end{cases} \\\\\\ a_n=-45+(n-1)15\implies a_n=-45+15n-15\implies a_n=15n-60[/tex]

Let [tex]W[/tex] be the random variable representing the winnings you get for playing the game. Then

[tex]W=\begin{cases}9&\text{if the sum is odd}\\4&\text{if the sum is 4 or 8}\\49&\text{if the sum is 2 or 12}\\-1&\text{otherwise}\end{cases}[/tex]

First thing to do is determine the probability of each of the above events. You roll two dice, which offers 6 * 6 = 36 possible outcomes. You find the probability of the above events by dividing the number of ways those events can occur by 36.

So the probability mass function for this game is

[tex]P(W=w)=\begin{cases}\frac12&\text{for }w=9\\\frac29&\text{for }w=4\text{ or }w=-1\\\frac1{18}&\text{for }w=49\\0&\text{otherwise}\end{cases}[/tex]

The expected value of playing the game is then

[tex]E[W]=\displaystyle\sum_ww\,P(W=w)=\frac{71}9[/tex]

or about $7.89.

The expected value is positive, so a player can expect to earn money in the long run, and so should play the game.

Let Bikes = B and cars = c

a bike has 2 wheels and a car has 4 wheels.

Equation 1: add bikes and cars to get total students:

b + c = 80

Equation 2: multiply the number of wheels by each type and add to equal the total wheels.

2b +4c = 270

Rewrite the first equation as b = 80- c

Now substitute that for b in the second equation:

2(80-c) + 4c = 270

Simplify:

160 - 2c + 4c = 270

160 +2c = 270

Subtract 160 from both sides:

2c = 110

Divide both sides by 2

c = 110/2

c = 55

Replace c with 55 in the first equation and solve for b:

b + 55 = 80

b = 80-55

b = 25

b = 25, c = 55

Answer:

(x-4)^2 + (y-1)^2 = 6^2

or

(x-4)^2 + (y-1)^2 = 36

Step-by-step explanation:

The equation for a circle is given by

(x-h)^2 + (y-k)^2 = r^2

where (h,k) is the center and r is the radius

(x-4)^2 + (y-1)^2 = 6^2

or

(x-4)^2 + (y-1)^2 = 36

Answer:

(x - 4)^2 + (y - 1)^2 = 6^2

Step-by-step explanation:

Adapt the standard equation of a circle with center at (h, k) and radius r:

(x-h)^2 + (y-k)^2 = r^2

Here we have:

(x - 4)^2 + (y - 1)^2 = 6^2

Answer:

[tex](x-6i)(x+6i)(x-3)(x+3)[/tex]

Step-by-step explanation:

If 6i is a zero then -6i is a zero.

In general, if a+bi is a zero then a-bi is a zero (if the polynomial has real coefficients which this one does: 1,27,-324).

Let's test it to see:

Check [tex]x=6i[/tex]

[tex]P(6i)=(6i)^4+27(6i)^2-324\\

P(6i)=6^4(i^4)+27(6)^2(i^2)-324\\

P(6i)=1296(1)+27(6^2)(-1)-324\\

P(6i)=1296-27(36)-324\\

P(6i)=1296-972-324\\

P(6i)=1296-1296\\

P(6i)=0\\[/tex]

Check [tex]x=-6i[/tex]

[tex]P(-6i)=(-6i)^4+27(-6i)^2-324\\

P(-6i)=(6i)^4+27(6i)^2-324\\

P(-6i)=P(6i)\\

P(-6i)=0\\[/tex]

So yep they both give us 0 when we plug it in.

If x=6i is a zero then x-6i is a factor by factor theorem.

If x=-6i is a zero then x+6i is a factor by factor theorem.

What is (x-6i)(x+6i)?

Let's use the multiply conjugates formula: [tex](u-v)(u+v)=u^2-v^2[/tex].

[tex](x-6i)(x+6i)=x^2-36i^2=x^2-36(-1)=x^2+36[/tex]

Now we know [tex](x^2+36)[/tex] is a factor of [tex]x^4+27x^2-324[/tex].

We can use long division or we could try to find two numbers that multiply to be -324 and add up to be 27 since this is a quadratic in terms of [tex]x^2[/tex] with leading coefficient of 1.

Well we already know we are looking for number times 36 that would give us -324.

So -324=-9(36) and 27=-9+36

So the factored form in terms of real numbers is:

[tex](x^2+36)(x^2-9)[/tex]

We already know the first factor can be factored as (x+6i)(x-6i).

The other can factored as (x-3)(x+3) since (-3)(3)=-9 and -3+3=0.

So the complete factored form is

[tex](x-6i)(x+6i)(x-3)(x+3)[/tex].

To find the remaining zeros of the polynomial, we use synthetic division and find a quadratic factor. The remaining zeros are the solutions to the quadratic equation x^2 + 9 = 0, which are 3i and -3i.

To find the remaining zeros of the polynomial, we can use polynomial long division or synthetic division. Let's use synthetic division:

Since 6i is a zero of P(x), the conjugate -6i is also a zero. We can divide P(x) by (x - 6i)(x + 6i) to find the remaining quadratic factor.

Performing the synthetic division, we get a quadratic factor of x^2 + 9. Therefore, the remaining zeros of the polynomial are the solutions to the equation x^2 + 9 = 0.

Solving the quadratic equation x^2 + 9 = 0, we find that the remaining zeros are x = 3i and x = -3i.

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Answer:

  A.  4·10⁴

Step-by-step explanation:

The problem statement tells you ...

  6×10⁵ miles = 15 × (last year's mileage)

Dividing by 15 gives ...

  (60×10⁴ miles)/15 = (last year's mileage) = 4×10⁴ miles

_____

Further explanation

An exponent is an indication of repeated multiplication.

  10⁵ = 10·10·10·10·10 = 100,000

We can use the associative property of multiplication to rewrite the number of miles:

  6×10⁵ = 6·(10·10·10·10·10) = 600,000 = (6·10)·(10·10·10·10) = 60×10⁴

Answer:

[x + 3][3x - 4]

Step-by-step explanation:

First off, we need to find two numbers that when differed to 5, they also multiply to -36 [3 × -12]. Those numbers are -4 and 9. Next, we find the Greatest Common Factor [GCF], which means the LEAST DEGREE TERM possible:

[3x² - 4x] + [9x - 12]

x[3x - 4] 3[3x - 4]

As you can see, whenever we have a leading coefficient greater than 1, we need to break up our B into our two numbers we found [in BOLD], and have to attach an x to them because it replaced Bx, according to the Quadratic Equation of y = Ax² + Bx + C. So, after we completed our factoring, you see two identical factors, which we use ONCE. The other factor comes from the terms outside the duplicates. So, you get the above answer after you completed the steps: [x + 3][3x - 4].

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