14. A rare bacterial culture is being grown in a lab. As the days progress, the cells multiply and grow.
After 1 day, there is only 1 cell.
After 2 days, there are 9 cells.
After 3 days, there are 20 cells.
After 4 days, there are 34 cells.
Awhich recursive equation represents the pattern? (2 points)
an = an - 1 + 3n
an = an - 1 +n + 2)
an = an - 1 + 3(n + 2)
an = an - 1 + (3n + 2)

Answers

Answer 1

Answer:

  a[n] = a[n-1] +(3n +2)

Step-by-step explanation:

The difference between Day 1 and Day 2 is 9 - 1 = 8 cells. The difference between a2 and a1 in each of the answer choices is a2 -a1 = ...

  3n = 3(2) = 6 ≠ 8

  n+2 = 2+2 = 4 ≠ 8

  3(n+2) = 3(2+2) = 12 ≠ 8

  3n +2 = 3(2) +2 = 8 . . . . . . this is the appropriate choice:

  [tex]\boxed{a_n=a_{n-1}+(3n+2)}[/tex]


Related Questions

Roll a 6-sided die and a 10-sided die. (Both dice are fair and have an ace side.) What is the chance that they will both land on ace? 1/60 (Give exact answer.) What is the chance that neither will land on ace? 3/4 (Give exact answer.) What is the chance that at least one will not land on ace?

Answers

Answer:

a.  [tex]P(Both) = \frac{1}{60}[/tex]

b.   [tex]P(None) = \frac{3}{4}[/tex]

c.  [tex]P(At least 1) = \frac{1}{4}[/tex]

Step-by-step explanation:

Given

A fair 6-sided die

A fair 10-sided die

Both have an ace side

For the 6-sided die;

Probability of landing on Ace: P(A)

[tex]P(A) = \frac{1}{6}[/tex]

Probability of not landing on Ace: P(A')

[tex]P(A') = \frac{5}{6}[/tex]

For the 10-sided die;

Probability of landing on Ace: P(B)

[tex]P(B) = \frac{1}{10}[/tex]

Probability of not landing on Ace: P(B')

[tex]P(B') = \frac{9}{10}[/tex]

Solving (a): Both landing on Ace

This is calculated as thus;

[tex]P(Both) = P(A) * P(B)[/tex]

[tex]P(Both) = \frac{1}{6} * \frac{1}{10}[/tex]

[tex]P(Both) = \frac{1}{60}[/tex]

Solving (b): None landing on Ace

This is calculated as thus;

[tex]P(None) = P(A') * P(B')[/tex]

[tex]P(None) = \frac{5}{6} * \frac{9}{10}[/tex]

[tex]P(None) = \frac{1}{6} * \frac{9}{2}[/tex]

[tex]P(None) = \frac{1}{2} * \frac{3}{2}[/tex]

[tex]P(None) = \frac{3}{4}[/tex]

Solving (c): At least one landing on Ace

This is calculated as thus;

[tex]P(At least 1) = 1 - P(None)[/tex]

[tex]P(At least 1) = 1 - \frac{3}{4}[/tex]

[tex]P(At least 1) = \frac{4 - 3}{4}[/tex]

[tex]P(At least 1) = \frac{1}{4}[/tex]

The required probabilities are,

(a):[tex]P(A)=\frac{1}{60}[/tex]

(b):[tex]P(B)=\frac{3}{4}[/tex]

(c):[tex]P(C)=\frac{59}{60}[/tex]

Given that the die having the 6 sides.

The formula for finding the expected probability is,

[tex]P(A)=\frac{m}{n}[/tex]

Where m= Number of expected observation

n= Number of total observation

Part(a):

P(Both landed on ace) is,

[tex]P(A)=\frac{1}{6} \times\frac{1}{10} \\=\frac{1}{60}[/tex]

Part(b):

P(Neither landed on ace) is,

[tex]P(B)=[1-\frac{1}{6} ][1-\frac{1}{10} ]\\=\frac{3}{4}[/tex]

Part(c):

P(At least one not land on ace) = 1 - P(Both landed on ace)

[tex]1-\frac{1}{60} =\frac{59}{60}[/tex]

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Shauna saw 30 fish. If the number of fish she saw was 6 more than twice the number of clams, which equation could she use to find x, the number of clams?

Answers

Answer:

2x + 6 = 30

hope this helps

The stock of company a gained $0.76 throughout the day and ended at a value of $38.76. By what percentage did the stock rise

Answers

Answer:

Its either 1.98 percentage or 51.

Step-by-step explanation:

Divison?

Answer:2%

Step-by-step explanation: 38.76-0.76=38

38(1+r)=38.76

__________

38

1+r=1.02

R=0.02 (2%)

URGENT HELP PLZ

What is an equation of the line that passes through the points (-3,3) and (-6, 2)?
Put your answer in fully reduced form.

Answers

Answer:

y = 1/3x + 4

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Step 1: Find slope m

m = (2 - 3)/(-6 - -3)

m = -1/(-6 + 3)

m = -1/-3

m = 1/3

y = 1/3x + b

Step 2: Find y-intercept b (plug in coordinates)

3 = 1/3(-3) + b

3 = -1 + b

b = 4

Step 3: Rewrite linear equation

y = 1/3x + 4

units needed 60 unit per case 14

Answers

Answer:

5 cases

Step-by-step explanation:

you'll need at least five cases to fulfill the requirement of 60

Answer:

5 cases are needed

Step-by-step explanation:

For each of the following questions, solve for the unknown quantity by rearranging the given equation.
For numerical answers, make sure to express all answers in scientific notation with the proper number of
significant figures. Be careful to write out all units and convert if necessary.
3.
F=GMm/r^2

a. M =
b. r =
M=kxa^3/p^2

a. P =
b. a =

Answers

Answer:

For F=GMm/r^2

[tex]F = \frac{GMm}{r^{2} }[/tex]

a. [tex]M = \frac{Fr^{2} }{Gm}[/tex]

b. [tex]r = \sqrt{\frac{GMm}{F}}[/tex]

M=kxa^3/p^2

[tex]M = \frac{kxa^{3} }{p^{2} }[/tex]

a. [tex]p = \sqrt{\frac{kxa^{3} }{M}}[/tex]

b. [tex]a = \sqrt[3]{\frac{Mp^{2} }{kx}}[/tex]

Step-by-step explanation:

To solve for the unknown quantity, we will make the unknown quantity the subject of the given equation.

For F=GMm/r^2

a. M =

F=GMm/r^2

[tex]F = \frac{GMm}{r^{2} }[/tex]

The first thing to do is cross multiply, so that the equation gives

[tex]Fr^{2} = GMm[/tex]

Now, divide both sides of the equation by [tex]Gm[/tex], we then get

[tex]\frac{Fr^{2} }{Gm} = \frac{GMm}{Gm}[/tex]

Then, [tex]\frac{Fr^{2} }{Gm} = M[/tex]

Hence,

[tex]M = \frac{Fr^{2} }{Gm}[/tex]

b. r =

F=GMm/r^2

[tex]F = \frac{GMm}{r^{2} }[/tex]

Likewise, we will first cross multiply, we then get

[tex]Fr^{2} = GMm[/tex]

Now, divide both sides by [tex]F[/tex], so that the equation becomes

[tex]\frac{Fr^{2} }{F} = \frac{GMm}{F} \\[/tex]

∴ [tex]r^{2} = \frac{GMm}{F} \\[/tex]

Then,

[tex]r = \sqrt{\frac{GMm}{F}}[/tex]

For M=kxa^3/p^2

a. P =

M=kxa^3/p^2

[tex]M = \frac{kxa^{3} }{p^{2} }[/tex]

The first thing to do is cross multiply, so that the equation becomes

[tex]Mp^{2} = kxa^{3} \\[/tex]

Now, divide both sides by M, we then get

[tex]\frac{Mp^{2} }{M} = \frac{kxa^{3} }{M}[/tex]

∴ [tex]p^{2} = \frac{kxa^{3} }{M}[/tex]

Then,

[tex]p = \sqrt{\frac{kxa^{3} }{M}}[/tex]

b. a =

M=kxa^3/p^2

[tex]M = \frac{kxa^{3} }{p^{2} }[/tex]

Also, we will first cross multiply to get

[tex]Mp^{2} = kxa^{3} \\[/tex]

Then, divide both sides of the equation by [tex]kx[/tex] to get

[tex]\frac{Mp^{2} }{kx}= \frac{kxa^{3} }{kx}\\[/tex]

[tex]\frac{Mp^{2} }{kx}= a^{3}[/tex]

∴ [tex]a^{3} = \frac{Mp^{2} }{kx}[/tex]

Then,

[tex]a = \sqrt[3]{\frac{Mp^{2} }{kx}}[/tex]

2(2x - 3) > 6 solve for x​

Answers

Answer:

x >3

Step-by-step explanation:

2(2x - 3) > 6

Divide each side by 2

2/2(2x - 3) > 6/2

2x-3 > 3

Add 3 to each side

2x-3+3 > 3+3

2x>6

Divide by 2

2x/2 > 6/2

x >3

Answer:

x > 3

Step-by-step explanation:

First, you're going to divide both sides by two

2( 2x - 3) / 2 and 6/2

After that, you will simplify that into....

2x - 3 > 3

Then you want to add three to both sides like so

2x - 3 + 3 > 3 + 3

Once you're done with that, go ahead and simplify the problem

2x > 6

Then, divide by two on each side

2x/2 > 6/2

Lastly, simplify your answer and that's the solution

x > 3

I hope this helped! :)

In which quadrant will each of the following points lie? a. (6, −5) b. (3, 2) c. (−2, −8) d. (6, 4) e. (−1, −12) f. (−3, 4)

Answers

Answer:

Quadrant 1:

(6,4) and (3,2)

Quadrant 2:

(-3,4)

Quadrant 3:

(-2,-8) and (-1,-12)

Quadrant 4:

(6,-5)

HOPE THIS HELPS!!!!!! :)

<3333333333

together Charlotte and vinny have 20 marbles. charlotte has 4 times as many as vinny. how many marbles does Charlotte have, this is an algebra 2 question.

Answers

Answer:

[tex]\Huge \boxed{\mathrm{16 \ marbles}}[/tex]

Step-by-step explanation:

Let the number of marbles that Charlotte has be x.

Let the number of marbles that Vinny has be y.

[tex]x+y=20[/tex]

[tex]x=4y[/tex]

Substitute for x.

[tex]4y+y=20[/tex]

Combine like terms.

[tex]5y=20[/tex]

Divide both sides by 5.

[tex]y=4[/tex]

Vinny has 4 marbles.

Let y = 4.

[tex]x=4(4) \\ \\ \\ x=16[/tex]

Charlotte has 16 marbles.

Answer:

x+y=20

x=4yx=4y

Substitute the given equation for x.

4y+y=20

4y+y=20

Collect all like terms.

5y=20

Divide both sides by 5.

y=4y=4

Vinny has 4 marbles.

Let y = 4.

x=4(4)

x=16

What is the sum of the
interior angles of a polygon
that has 21 sides?

Answers

Answer:

8

Step-by-step explanation:

Answer: 3420 degree

Explanation:

The sum of n sided interior angle of a polygon is: (n - 2) x 180 degree

Since our polygon has 21 sides:

(21 - 2) x 180
= 19 x 180
= 3420 degree

What is 50% MORE than $35?

Answers

Answer:

Step-by-step explanation:

f 35 = 100 % as a whole number then 50% = 17.5

50 % more than 35 must be 35 + 17.5 = 52.5

Answer:

Hey!

Your answer is 52.5

Step-by-step explanation:

50% x 35=

(50/100) x 35=

(50 x 35) / 100=

1750 / 100 = 17.50

NOW...

35+17.5=52.5

ANSWER: 52.5

PLEASE HURRY WILL GIVE EVERYTHIBG find the 13th term of 3x^2, 6x^5, 12x^8.....

Answers

Can you elaborate it more.

Find all angles that are coterminal with the given angle. (Let k be an arbitrary integer.) −225°

Answers

Answer:

Coterminal angles are angles with the same terminal side.

When we have an angle A, the coterminal angles can be written as:

A + k*(360°)

where k can be any integer number. (Notice that when we have k = 0, means that A is coterminal with itself)

Then the set of all the coterminal angles to -225° is:

{-225° + k*360°I k ∈ Z}

where Z is the set of integer numbers.

Please help ASAP!! List the following subsets of the real numbers in order from least inclusive to most inclusive.(1 point) natural numbers, whole numbers, rational numbers, integers natural numbers, whole numbers, integers, rational numbers whole numbers, natural numbers, integers, rational numbers rational numbers, natural numbers, whole numbers, integers

Answers

Answer:

Natural numbers < Whole Numbers < Rational numbers < Integers

Step-by-step explanation:

Natural numbers are the numbers that are called counting numbers.They are numbers you can count. But Zero is not among them. Basically, Natural numbers are numbers you can count with the exception of Zero.

Whole numbers are a bit more than natural numbers. Unlike Natural numbers, whole numbers contain Zero. As a result, we can say they're counting numbers Zero inclusive.

Rational numbers are numbers that are written as ratio. They can be written as a fraction, but then, both the denominator and the numerator would have to be whole numbers.

Integers are whole numbers including negative numbers. Remember, whole numbers are an extension of natural numbers? Well then, Integers are an extension of Whole numbers.

Select the correct inequality to make a true statement

Answers

Step-by-step explanation:

[tex] \frac{1}{4} \boxed{?} \frac{3}{8} \\ \\ \frac{1}{4} = \frac{2}{8} \\ \\ \because \: 2 < 3 \\ \therefore \: \frac{1}{4} \boxed{ < } \frac{3}{8} [/tex]

Choose the BEST answer: Which of the following is true about a balanced budget? It should have a difference within $10 (above or below budget). There is no such thing as a balanced budget. There should be no difference ($0). Your actual expenses should always be more than your actual income.

Answers

Answer:

Option C

Step-by-step explanation:

There should be no difference ($0). This is  true about a balanced budget. Therefore, the correct option is option C among all the given options.

What is balanced budget?

When your expenses are equivalent or lower than to your income, you have a balanced budget. In other words, your ability to live within your means will be shown by a balanced budget.

Any period during that a budget is not in deficit is sometimes referred to as a balanced budget. In other words, your budget is balanced if it is at a profit and has income left over. There should be no difference ($0). This is  true about a balanced budget.

Therefore, the correct option is option C among all the given options.

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a. 5(6 + 7) =
Distributive property

Answers

Answer:

65

Step-by-step explanation:

5(6 + 7)

5 • 6 = 30

5 • 7 = 35

30 + 35 = 65

5 times 6 which equals 30 then 5 times 7 which equals 35 you add that and get 65

HELP ASAP!!! ALGEBRA 2 I NEED HELP!!! WILL MARK BRAINLIEST

Answers

Answer:

Second option.

Step-by-step explanation:

In a mathematical sense, all real values of x are possible, as no real values of x will make it undefined.

However, in a reasonable sense, the length and width of a rectangle should be positive, so 0.5x -2 > 0.

Therefore, in a reasonable sense, x > 4.

Which of the following best decribes a function

Answers

An input that gives exactly one output.

Monique says that the sine of angle A is 5/13. Her teacher marks her wrong, but sometimes Monique’s teacher makes mistakes when grading tests. Is Monique’s answer actually wrong?

Answers

Answer:

yes because

Step-by-step explanation:

this point, we pause to see if it makes sense that we actually have two viable cases to consider. As we have discussed, both candidates for are ‘compatible’ with the given angle-side pair ( ;a) = (30 ;3) in that both choices for can t in a triangle with and both have a sine of 2 3. The only other given piece of information is that c= 4 units.

Round 34,576 to the nearest thousand

Answers

Answer:

35000

Step-by-step explanation:

5. To evaluate a definite integral of tabular function f(x), piecewise quadratic approximation led to ________ a. Trapezoidal Method b. Simpsons Rule

Answers

Answer:

The correct option is;

b. Simpsons Rule

Step-by-step explanation:

The midpoint rule involves the estimation of the area under the curve with the aid of rectangular shaped approximations

The trapezoidal rule, involved the approximation of the curve by linear approximations by using piece by piece linear functions

In the Simpson's rule the curve is approximated using piece by piece quadratic functions. The intervals are partitioned into even numbered smaller intervals having the same width and we approximate the resulting integrals of the intervals.

Find the value of M Angle 3 - M Angle 1.

Answers

Answer:

the value of M angle 3 is 70° and M angle 1 is (90-70)=20° and angle 3 - angle 1 is 70° - 20° is 50°

x² + ___ x + 49 plz answer as soon as possible

Answers

Answer:

14

Step-by-step explanation:

(a + b)² = a² + 2ab + b²

x² + _x + 49

a = x

b = 7

2ab = 2×x×7 = 14x => 2b = 14

Answer:

[tex]\Huge \boxed{\mathrm{14}}[/tex]

[tex]\rule[225]{225}{2}[/tex]

Step-by-step explanation:

Square of a sum formula:

[tex](a + b)^2 = a^2 + 2ab + b^2[/tex]

x² + ___ x + 49

The value of a is x.

The value of b is 7, since 7² = 49.

[tex]x^2 +2(x)(7)+7^2[/tex]

[tex]x^2 +14x+49[/tex]

The missing coefficient is 14.

[tex]\rule[225]{225}{2}[/tex]

find the area of the circle use 3.14

Answers

Step-by-step explanation:

Hey, there!!

It's so simple, you just use the formula as given and put the values in it.

Radius of a circle (r) = 13 cm.

pi= 3.14

Now,

Circumference = 2× pi × r

= (2× 3.14 × 13) cm

= 81.64 cm

Therefore, the answer is 82 cm.

Hope it helps..

Answer:

The answer = 82 cm.

Step-by-step explanation:

By using the formula,

C=2×3.14×13

C= 81.64

then,

The nearest hundredth = 82 cm.

solve with interval notation Solve: 5 | x − 2 | + 4 > 8

Answers

Answer:

x<6/5, x>14/5

Step-by-step explanation:

Steps

$5\left|x-2\right|+4>8$

$\mathrm{Subtract\:}4\mathrm{\:from\:both\:sides}$

$5\left|x-2\right|+4-4>8-4$

$\mathrm{Simplify}$

$5\left|x-2\right|>4$

$\mathrm{Divide\:both\:sides\:by\:}5$

$\frac{5\left|x-2\right|}{5}>\frac{4}{5}$

$\mathrm{Simplify}$

$\left|x-2\right|>\frac{4}{5}$

$\mathrm{Apply\:absolute\:rule}:\quad\mathrm{If}\:|u|\:>\:a,\:a>0\:\mathrm{then}\:u\:<\:-a\:\quad\mathrm{or}\quad\:u\:>\:a$

$x-2<-\frac{4}{5}\quad\mathrm{or}\quad\:x-2>\frac{4}{5}$

Show Steps

$x-2<-\frac{4}{5}\quad:\quad x<\frac{6}{5}$

Show Steps

$x-2>\frac{4}{5}\quad:\quad x>\frac{14}{5}$

$\mathrm{Combine\:the\:intervals}$

$x<\frac{6}{5}\quad\mathrm{or}\quad\:x>\frac{14}{5}$

Does anyone know how to do this? I’m lost

Answers

Answer: B

Step-by-step explanation:

To find the inverse function, you switch x with y and y with x. Then, you solve for y.

[tex]y=(x-1)^{2} -4[/tex]                                  [switch x with y, and y with x]                        

[tex]x=(y-1)^2-4[/tex]                                  [add both sides by 4]

[tex]x+4=(y-1)^2[/tex]                                  [square root both sides]

[tex]\sqrt{x+4} =y-1[/tex]                                    [add both sides by 1]

[tex]\sqrt{x+4} +1=y[/tex]

[tex]f^-^1(x)=1+\sqrt{x+4}[/tex]

Now that we know the inverse function, we can actually tell that the answer is B. We know this because of the restriction that f(x) is x≤1. This makes it positive, and B the answer.

Wayne is planning a Beach vacation he budgets a total of $1,800 for the vacation round trip airfare for the trip will cost $610 all the all-inclusive resort he he plans to stay at will cost $238 per day what is the maximum number of days Wayne can stay at a resort within his budget

Answers

Answer: Maximum of 5 days

Step-by-step explanation: To find that conclusion, you subtract the "610" from "1,800" getting "1,190". But to find the amount of days you would need to divide "1,190" by "238" to get your 5 days.

An equation is formed of two equal expressions. The maximum number of days Wayne can stay at a resort within his budget is 5.

What is an equation?

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given that Wayne's budget for the vacation is $1,800. Therefore, the total amount spent by Wayne during the vacation should be equal to his budget.

Also, it is given that the airfare for the vacation is $610. also, the cost of staying in a hotel for a day is $238. Therefore, the expression for x days staying can be written as,

Total cost = $610 + $238(x days)

Since the total cost or expenses should be equal to the budget, therefore, we can write,

Total cost = budget

610 + 238x = 1800

238x = 1800 - 610

238x = 1190

x = 1190 / 238

x = 5

Hence, the maximum number of days Wayne can stay at a resort within his budget is 5.

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Prove that the
ordered pair (3, 4)
is a solution set to
the equation:
2x + 3y = 18

Answers

Answer:

Hey there!

2x+3y=18

2(3)+3(4)=18

6+12=18

18=18, so this is a valid ordered pair.

Let me know if this helps :)

x+6/x^2+8x+15+3x/x+5-x-3/x+3 Combine as indicated by the signs. Write answer in descending powers of x.

Answers

Answer:

see attachement

Step-by-step explanation:

Solve for x:

8 x + 26 - 3/x + 6/x^2 = 0

Hint: | Write the left hand side as a single fraction.

Bring 8 x + 26 - 3/x + 6/x^2 together using the common denominator x^2:

(8 x^3 + 26 x^2 - 3 x + 6)/x^2 = 0

Hint: | Multiply both sides by a polynomial to clear fractions.

Multiply both sides by x^2:

8 x^3 + 26 x^2 - 3 x + 6 = 0

Hint: | Look for a simple substitution that eliminates the quadratic term of 8 x^3 + 26 x^2 - 3 x + 6.

Eliminate the quadratic term by substituting y = x + 13/12:

6 - 3 (y - 13/12) + 26 (y - 13/12)^2 + 8 (y - 13/12)^3 = 0

Hint: | Write the cubic polynomial on the left hand side in standard form.

Expand out terms of the left hand side:

8 y^3 - (187 y)/6 + 799/27 = 0

Hint: | Write the cubic equation in standard form.

Divide both sides by 8:

y^3 - (187 y)/48 + 799/216 = 0

Hint: | Perform the substitution y = z + λ/z.

Change coordinates by substituting y = z + λ/z, where λ is a constant value that will be determined later:

799/216 - 187/48 (z + λ/z) + (z + λ/z)^3 = 0

Hint: | Transform the rational equation into a polynomial equation.

Multiply both sides by z^3 and collect in terms of z:

z^6 + z^4 (3 λ - 187/48) + (799 z^3)/216 + z^2 (3 λ^2 - (187 λ)/48) + λ^3 = 0

Hint: | Find an appropriate value for λ in order to make the coefficients of z^2 and z^4 both zero.

Substitute λ = 187/144 and then u = z^3, yielding a quadratic equation in the variable u:

u^2 + (799 u)/216 + 6539203/2985984 = 0

Hint: | Solve for u.

Find the positive solution to the quadratic equation:

u = (17 (9 sqrt(157) - 188))/1728

Hint: | Perform back substitution on u = (17 (9 sqrt(157) - 188))/1728.

Substitute back for u = z^3:

z^3 = (17 (9 sqrt(157) - 188))/1728

Hint: | Take the cube root of both sides.

Taking cube roots gives 1/12 17^(1/3) (-(188 - 9 sqrt(157)))^(1/3) times the third roots of unity:

z = 1/12 17^(1/3) (-(188 - 9 sqrt(157)))^(1/3) or z = -1/12 (-1)^(2/3) 17^(1/3) (188 - 9 sqrt(157))^(1/3) or z = -1/12 17^(1/3) (188 - 9 sqrt(157))^(1/3)

Hint: | Perform back substitution with y = z + 187/(144 z).

Substitute each value of z into y = z + 187/(144 z):

y = 1/12 (-17 (188 - 9 sqrt(157)))^(1/3) - (11 (-17)^(2/3))/(12 (188 - 9 sqrt(157))^(1/3)) or y = 11/12 17^(2/3) ((-1)/(188 - 9 sqrt(157)))^(1/3) - 1/12 (-1)^(2/3) (17 (188 - 9 sqrt(157)))^(1/3) or y = -(11 17^(2/3))/(12 (188 - 9 sqrt(157))^(1/3)) - 1/12 (17 (188 - 9 sqrt(157)))^(1/3)

Hint: | Simplify each solution.

Bring each solution to a common denominator and simplify:

y = 1/12 (153 sqrt(157) - 3196)^(1/3) - (11 (-17)^(2/3))/(12 (188 - 9 sqrt(157))^(1/3)) or y = 1/12 17^(1/3) (11 ((-17)/(188 - 9 sqrt(157)))^(1/3) - (-1)^(2/3) (188 - 9 sqrt(157))^(1/3)) or y = -1/12 17^(1/3) (1/(188 - 9 sqrt(157)))^(1/3) ((188 - 9 sqrt(157))^(2/3) + 11 17^(1/3))

Hint: | Perform back substitution on the three roots.

Substitute back for x = y - 13/12:

Answer: x = -13/12 - (11 (-17)^(2/3))/(12 (188 - 9 sqrt(157))^(1/3)) + 1/12 (153 sqrt(157) - 3196)^(1/3) or x = 1/12 17^(1/3) (11 (-17/(188 - 9 sqrt(157)))^(1/3) - (-1)^(2/3) (188 - 9 sqrt(157))^(1/3)) - 13/12 or x = -1/12 (17/(188 - 9 sqrt(157)))^(1/3) (11 17^(1/3) + (188 - 9 sqrt(157))^(2/3)) - 13/12

Answer:

The correct answer is, "8x + 2x^2 + 21 / (x + 5)(x - 3)"

Step-by-step explanation:

This is 100% correct! :)

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