What are the possible rational roots of the polynomial equation?

0=2x7+3x5−9x2+6

Answers

Answer 1

Answer: [tex]\pm\frac{1}{1}, \pm\frac{1}{2},\pm\frac{2}{1},\pm\frac{3}{1}, \pm\frac{3}{2}[/tex]

Step-by-step explanation:

We can use the Rational Root Test.

Given a polynomial in the form:

[tex]a_nx^n +a_{n- 1}x^{n - 1} + … + a_1x^1 + a_0 = 0[/tex]

Where:

- The coefficients are integers.

- [tex]a_n[/tex] is the leading coeffcient ([tex]a_n\neq 0[/tex])

- [tex]a_0[/tex] is the constant term [tex]a_0\neq 0[/tex]

Every rational root of the polynomial is in the form:

[tex]\frac{p}{q}=\frac{\pm(factors\ of\ a_0)}{\pm(factors\ of\ a_n)}[/tex]

For the case of the given polynomial:

[tex]2x^7+3x^5-9x^2+6=0[/tex]

We can observe that:

- Its constant term is 6, with factors 1, 2 and 3.

- Its leading coefficient is 2, with factors 1 and 2.

 Then, by Rational Roots Test we get the possible rational roots of this polynomial:

[tex]\frac{p}{q}=\frac{\pm(1,2,3,6)}{\pm(1,2)}=\pm\frac{1}{1}, \pm\frac{1}{2},\pm\frac{2}{1},\pm\frac{3}{1}, \pm\frac{3}{2}[/tex]

Answer 2

The possible rational roots of the polynomial equation [tex]0 = 2x^7 + 3x^5 - 9x^2 + 6.[/tex] are ±1, ±2, ±3, ±6, ±1/2, ±1, ±3/2, and ±3.

Given equation [tex]0 = 2x^7 + 3x^5 - 9x^2 + 6[/tex].

The Rational Root Theorem states that if there are any rational roots (fractions in the form p/q) for the polynomial equation, then p must be a factor of the constant term (in this case, 6), and q must be a factor of the leading coefficient (in this case, 2).

So, the possible rational roots (fractions p/q) for this polynomial are all the combinations of p and q, where:

p is a factor of 6, and

q is a factor of 2.

The factors of 6 are ±1, ±2, ±3, and ±6.

The factors of 2 are ±1 and ±2.

So, the possible rational roots are all the combinations of these factors:

±1/1, ±2/1, ±3/1, ±6/1, ±1/2, ±2/2, ±3/2, and ±6/2.

Simplify these fractions:

±1, ±2, ±3, ±6, ±1/2, ±1, ±3/2, and ±3.

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Related Questions

21. (4pts) Please answer in a complete sentence in Spanish.
¿Te gusta jugar videojuegos?


22. (4pts) Please write your answer in a complete sentence in Spanish using the vocabulary from your course. List at least 2 activities from our course to answer the question.
¿Qué te gusta hacer?


23. (4pts) Answer the following question in a complete sentence in Spanish. List at least 2 activities from our course to answer the question.
¿Qué no te gusta hacer?


24. (4pts) Using your course vocabulary what are two ways to agree with someone in Spanish? Hint: These are the ways to say “Me too” and “Me either” in Spanish.



25. (4pts) Answer the following question in a complete sentence in Spanish.
¿Qué te gusta más, esquiar o nadar?

Answers

Final answer:

This answer provides complete sentences in Spanish to answer the questions, along with examples of activities and ways to agree in Spanish.

Explanation:

21. Sí, me gusta jugar videojuegos. (Yes, I like playing video games.)

22. Me gusta leer y practicar deportes. (I like reading and practicing sports.)

23. No me gusta hacer ejercicio y estudiar matemáticas. (I don't like exercising and studying math.)

24. Dos formas de estar de acuerdo en español son: 1) A mí también, 2) Yo tampoco. (Two ways to agree in Spanish are: 1) Me too, 2) Me either.)

25. Me gusta más nadar que esquiar. (I like swimming more than skiing.)

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What is the distance between the points (2,7) and (-2,7)

Answers

0 is the correct answer i dont know anything

Susan is planning a vacation. The travel agent says the average high temperature at the resort is 10 degrees Celsius. What is the equivalent Fahrenheit temperature

Answers

Answer:

50° F

Step-by-step explanation:

To convert C° to F°, Multiply the celcius temperature by 9/5, then add 32 to it.

10 x 9/5 = 18

18 + 32 = 50

Seventeen less than eight times a number is equal to 11 more than six times the number.
What is the number? ​

Answers

Answer:

the answer is 14

Step-by-step-explanation

the first equation is 8x-17

the second one is 6x+11

do some simple calculations to find x on both and compare.

Answer:

its 14

Step-by-step explanation:

the first equation is 8x-17

the second one is 6x+11

do some simple calculations to find x on both and compare.

just did it on a Quiz i hop this helped :D

#43. find (e). also please explain it.

Answers

Square root of SZ. Because you multiply by z on each side. Giving you sz=e^2. Then you take the square root giving you sqrt(sz)=e

what is the answer to this product 7 6/7 plus 14/21

Answers

Answer:

Exact Form: 179/21

Decimal Form: 8.523809

Mixed Number Form: 8 11/21

Step-by-step explanation:

Convert the mixed numbers to improper fractions, then find the LCD and combine.

The Cooking Club made some pies to sell
at a basketball game to raise money for the
new math books. The cafeteria
contributed three pies to the sale. Each
pie was then cut into five pieces and sold.
There were a total of 40 pieces to sell.
How many pies did the club make?

Answers

The club made 5 pies. If each pie is cut into 5 slices, and there are now 40 slices after the cafeteria donated, divide 40 by 5, which is 8. Subtract the 3 that the cafeteria donated.

Division the action of separating something into the parts. It is a basic mathematics operation. The number of pies made by the cooking club to sell  at a basketball game to raise money for the  new math books is 2.

Given-

The cafeteria  contributed three pies to the sale.

Each  pie was then cut into five pieces and sold.

There were a total of 40 pieces to sell.

What is division?

Division the action of separating something into the parts. It is a basic mathematics operation.

Total 40 pieces are there to sell. Each  pie was cut into five pieces. Hence the total pie in 40 pieces were,

[tex]=\dfrac{40}{8}[/tex]

[tex]=5[/tex]

Thus total 5 pies was made.

Now as the cafeteria contributed three pies to the sale but we have total 5 pieces was made. For find out the number of pies made by the cooking club we have to subtract the total pies made to the pies contributed by the cafeteria.Thus the number of pies made by the cooking club,

[tex]=5-3[/tex]

[tex]=2[/tex]

Hence the number of pies made by the cooking club  to sell  at a basketball game to raise money for the  new math books is 2.

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After a snow storm, michael measured 6 7/8 inches of snow. What is this amount as a decimal????? URGENTTTTT!!

Answers

Answer:

The answer is 6.875 inches.

Step-by-step explanation:

After a snow storm, Michael measured [tex]6\frac{7}{8}[/tex] inches of snow.

We will convert this to improper fraction and then solve.

[tex]6\frac{7}{8}=\frac{55}{8}[/tex]

Now we can divide 55 by 8 to get decimal value.

This becomes 6.875 inches.

Intr-o clasa sunt 27 de elevi. Daca din clasa ar pleca 3 fete si 4 baieti atunci numarul fetelor ar fii egal cu triplul nr. baietiilor. Cati baieti sunt in casa

Answers

The number of boys in class is 9.

How to determine the number of boys in class

Let the number of boy = b and girls = g

We can create the following equations from the parameters

b + g = 27 ____(1)

g - 3 = 3(b - 4) ___ (2)

From (1)

g = 27 - b ___(3)

Substitute (3) into (2)

27 - b - 3 = 3(b - 4)

24 - b = 3b - 12

collect like terms

-b - 3b = -12 - 24

-4b = -36

b = 9

Hence, the number of boys is 9

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What’s 8/15 divided by 4/5

Answers

Answer: 2/3

Step-by-step explanation: In this problem, we have 8/15 ÷ 4/5. Dividing by a fraction is the same as multiplying by its reciprocal. In other words, we can change the division sign to multiplication and flip the second fraction.

8/15 ÷ 4/5 can be rewritten as 8/15 × 5/4

Now, we are simply multiplying fractions so we multiply across the numerators and multiply across the denominators.

8/15 × 5/4 = 40/60 = 2/3

Two planes , which are 2445 miles apart fly toward each other. Their speed differ by 65mph. If they pass each other in 3 hours , what is the speed of each?

Answers

The speed of each planes are 375 mph and 415 mph.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now,

Let x be the speed of the slower plane, in mph.

Then, the speed of the other plane is x +40 mph.

Hence, The distance between two planes decreases at the rate;

⇒ x + (x+40)

⇒ 2x + 40 mph.

So, we can write equation as;

⇒ 3950 / (2x+40) =  5

⇒ 3950 = 10x + 200

⇒ 10x = 3750

⇒ x = 375

Thus, The speed of the slower plane = x

                                                         = 375  mph.

And, The speed of the other plane = x +40

                                                      = 375 + 40

                                                      = 415 mph.

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Final answer:

To solve the problem, we use the concept of relative speed and set up an equation with the combined distance traveled by both planes. Solving the equation reveals that the speed of the slower plane is 375 mph and the faster plane is 440 mph.

Explanation:

The problem of two planes flying toward each other with a speed difference and meeting after a certain amount of time is a typical algebra question in relative speed and motion. We can let the slower plane's speed be x mph and the faster plane's speed be x + 65 mph. Since they meet after 3 hours and are 2445 miles apart, the sum of their distances traveled will equal 2445 miles.

Using the equation d = rt, where d denotes distance, r the rate, and t the time, we set up two expressions for the distances each plane travels:

Distance by slower plane: 3xDistance by faster plane: 3(x + 65)

We then add these expressions and set the sum equal to the total distance:

3x + 3(x + 65) = 2445

Solving for x, we get:

6x + 195 = 2445

6x = 2445 - 195

6x = 2250

x = 375

Therefore, the speed of the slower plane is 375 mph and the speed of the faster plane is 375 + 65 = 440 mph.

math help owo pls will reword #_# pleath

Answers

Question 13: The answer is D

Question 7: The answer is C

Question 14: The answer is B

And the question for the last Pic, the correct graph is B.

Answer:

d

c

b

b

Step-by-step explanation:

7(5t - 4) – (2 +15t) < 60

Answers

Answer:

Step-by-step explanation:

Find the area of the figure. (Sides meet at right angles.)

Answers

Answer:

The area of the figure is 48 cm^2

Step-by-step explanation:

Break it into 3 different quadrilaterals and find the area of each one.

Which ordered pair is part of the solution set of the inequality 12 + y ≤ –3x? Question 11 options: a) (3, –16) b) (4, –1) c) (–16, 3) d) (1, 4)

Answers

Answer:

C (-16, 3)

Step-by-step explanation:

[tex] 12 + 3 \leqslant - 3 \times - 16 \\ 15 \leqslant 48[/tex]

replace x and y

Answer:

c) (-16,3)

Step-by-step explanation:

Given: inequality [tex]12+\text{y}\leq -3\text{x}[/tex]

To Find: Which ordered pair is part of the solution set of the inequality

Solution:

Simplifying inequality,

[tex]12+\text{y}\leq -3\text{x}[/tex]

[tex]12}\leq -3\text{x}-\text{y[/tex]

now,

putting ordered pairs from options

a) [tex](3,-16)[/tex]

[tex]-3\times3-(-16)[/tex][tex]16-9=7[/tex]

as [tex]7<12[/tex], it does not satisfy inequality

b)  [tex](4,-1)[/tex]

[tex]-3\times4-(-1)[/tex][tex]1-12=-11[/tex]

as [tex]-11<12[/tex], it does not satisfy inequality

c)  [tex](-16,3)[/tex]

[tex]-3\times(-16)-(3)[/tex][tex]48-3=45[/tex]

as [tex]45>12[/tex], it satisfy inequality

d)  [tex](1,4)[/tex]

[tex]-3\times1-(4)[/tex][tex]-3-4=-7[/tex]

as [tex]-7<12[/tex], it does not satisfy inequality

So, from above only option c is part of the solution set of inequality.

What is the sum of 12 and 34

Answers

12+34 = 46

Please mark Brainliest if this helps!

Sum: the total of 2 or more numbers added together

12 + 34 = 46

Find the volume of the earth if the diameter is 7917.5 miles.

Answers

Final answer:

The volume of the earth is approximately 1.0839 x 10¹⁵ cubic miles.

Explanation:

To find the volume of the earth, we can use the formula for the volume of a sphere: V = (4/3)πr³. Since we are given the diameter of the earth, we can calculate the radius by dividing the diameter by 2. In this case, the diameter is 7917.5 miles, so the radius is 3958.75 miles. Now, we can substitute the radius into the formula to find the volume:

V = (4/3)π(3958.75 miles)³

V ≈ 1.0839 x 10¹⁵ cubic miles.

Pls help :) it would mean a lot

Answers

Answer:

17=3x+2            x=5  

Step-by-step explanation:

3x+2=17

3x=17-2

x=15/3

x=5

MARK AS BRAINLIEST

1. Laura gave the clerk $20 for purchases of a
$4.25 notebook and a $3.59 set of markers.
How much change did she receive?
A $12.16
B $12.26
© $13.16
D $13.26​

Answers

Answer:

A

Step-by-step explanation:

1. 3.59 + 4.25 =7.84

2. 20.00 - 7.84 =12.16

at 2 P.M the level of the water in the pool was 10 feet. At 6 P.M the level of water was 2 feet. Find the constant rate of change of the water.

Answers

decreases by 2ft every hour

8.
f(x) = -0.75x
find the inverse function f-1(x) for the given functions f(x)

Answers

The inverse function of f(x) = -0.75x is [tex]\(f^{-1}(x) = -\frac{4}{3}x\)[/tex].

What is the inverse of the function?

To find the inverse function [tex]\( f^{-1}(x) \)[/tex]for the given function f(x) = -0.75x , you can follow these steps:

1. Start with the original function:

   f(x) = -0.75x

2. Replace f(x)  with y:

   y = -0.75x

3. Swap x and y to solve for x:

x = -0.75y

4. Solve for y:

  Divide both sides by -0.75:

[tex]\( y = \frac{x}{-0.75} )\\ \( y = -\frac{4}{3}x \)[/tex]

5. Replace y with [tex]\( f^{-1}(x) \)[/tex]:

[tex]\( f^{-1}(x) = -\frac{4}{3}x \)[/tex]

So, the inverse function for f(x) = -0.75x  is [tex]\( f^{-1}(x) = -\frac{4}{3}x \)[/tex].

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Final answer:

The response provides the inverse function of f(x) = -0.75x step-by-step.

Explanation:

Given: f(x) = -0.75x

To find the inverse function f-1(x):

Replace f(x) with y: y = -0.75x

Swap x and y: x = -0.75y

Solve for y: y = x/-0.75 = -4/3x

Therefore, f-1(x) = -4/3x

What is the product? -4 x [8 -1 -5 9]

Answers

To obtain the product, each element in the expression [tex]\([8, -1, -5, 9]\)[/tex] is multiplied by -4, resulting in [tex]\([-32, 4, 20, -36]\).[/tex]

To find the product of -4 and the expression [tex]\([8, -1, -5, 9]\),[/tex] we multiply each element in the expression by -4.

This involves multiplying -4 by 8, -1, -5, and 9 individually.

The result of these multiplications is [tex]\([-32, 4, 20, -36]\).[/tex]

In other words, each element in the original expression is multiplied by -4 to obtain the corresponding element in the product.

This operation is a scalar multiplication, where a single number (in this case, -4) is multiplied by each element of a vector or array.

Scalar multiplication is a fundamental operation in linear algebra and is used to scale vectors or matrices by a constant factor.

In this context, multiplying the expression by -4 changes the magnitude of each element by a factor of 4 while preserving their relative positions within the array.

48 less than 4 times a number is equal to the number

Answers

Answer:

Step-by-step explanation:

4x - 48 = x there is the equation

Answer:

x = 48/5

Step-by-step explanation:

Let x = number, then:

[tex]48 - 4x = x[/tex]

By adding 4x on each side:

[tex] 48 - 4x + 4x = x + 4x[/tex], which is [tex] 48 = 5x [/tex]

Then, divide by 5 on both sides:

[tex]\frac{48}{5} = \frac{5x}{5}[/tex]

Simplifying x = 48 / 5


Fill in the blanks to make the statement true
2t - t +4= 0
Solving this equation will result in a [quadratic/linear]
equation that
[Can/cannot]
be solved by factoring.​

Answers

Answer:

[tex]2t-t+4=0[/tex] gives me [tex]t=-4[/tex]

This is a linear equation.

Did you really mean [tex]2t-t+4=0[/tex]? I just want to make sure since you said something about a quadratic in your question.

Step-by-step explanation:

[tex]2t-t+4=0[/tex] can be simplified to [tex]t+4=0[/tex].

This is a linear equation since the exponent on all the variables we have is 1.

To solve [tex]t+4=0[/tex] for t we are going to subtract 4 on both sides:

[tex]t+4-4=0-4[/tex]

[tex]t=-4[/tex]

Please help. Answer with method please, thanks a lot ​

Answers

Answer:

62.83 m²

Step-by-step explanation:

The area of the path is calculated as

area of outside circle - area of reservoir

= πr₁² - πr₂²

where r₁ is the radius of the outer circle and r₂ the radius of the reservoir

diameter of reservoir = 8 m, hence radius = 4 m

radius of outer circle = radius of reservoir + width of path = 4 + 2 = 6 m, thus

area of path = π × 6² - π × 4² = 36π - 16π = 20π ≈ 62.83 m²

The sum of 8 times a number and 6 is equal to 7 times the number

Answers

Answer:

8x + 6 = 7x

x = -6

Step-by-step explanation:

this is the solution

solve for c: E=mc^2

Answers

E=mc²
E/m = c²
c = sqrtE/m

Answer: E=mc^2

E/m=c^2

Square root of e/m = c

C = square root symbol e/m

Yw :)

What is the y-intercept of y=5?

Answers

The y-intercept of the line y = 5 is given as: 5

How to find the y-intercept?

The general form of the equation of the line in slope intercept form is expressed as:

y = mx + c

where:

m is slope

c is y-intercept

Now, we are told that the equation is y = 5

This tells us that the y-intercept is 5

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Evaluate 4(3 - 1)2
ОА. 32
Ов. 64
Ос. 16
Op. 128

Answers

In order to get this answer you will have to use PEMDAS and solve the expression step by step.

[tex]4(3-1)2[/tex]

Using PEMDAS:

[tex]3-1=2[/tex]

[tex]4\times2\times2[/tex]

[tex]2\times4=8[/tex]

[tex]8\times2[/tex]

[tex]8\times2=16[/tex]

[tex]=16[/tex]

Therefore your answer is option C "16."

Hope this helps.

Answer:

C. 16

Step-by-step explanation:

basically the order of operations states you deal with parentheses first then indices then either division/multiplication and then addition/subtraction

So when you deal with 3- 1=2

the only operation left is multiplication(something in parenthesis stuck on another mathematical term without any other operation attached to it signals multiplication and it is commutative so it can be done in any pair. so u have 4×2×2=16

Identify the x-intercept.

1) y= 1/5x + 3

2) y= 6x - 7

3) y= -8/3x + 9

Answers

1) 1/5x + 3=0

1/5x=-3

x=(-3)(5)=-15

2)6x-7=0

6x=7

x=7/6=1.17

3) -8/3x+9=0

-8/3x=-9

-8x=-27

x=27/8=3.375
1) x=5y-15
2)x=1/6y+7/6
3) x=3/8y-27/8
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Aaron relies on Zlateh for milk, and Zlateh eats the hay. 2 of 20 Which intermolecular force or bond is primarily responsible for the solubility of CH3OH in water? lonic bonding Hydrogen bonding Covalent bonding Dipole-dipole force lon-dipole force Navigator F10 F11 F12 PSC A teacher divides the students into three groups for project each group has the same number of students in the total of number students prime or composite Please help!!1.Which settlement was part of New Spain?A.Massachusetts BayB.St. AugustineC.BrazilD.Cbola2.What did the Spanish government expect colonists who received land and labor under the encomienda system to do?A.pay Native Americans for their laborB.provide health care and food for Native Americans on the landC.convert Native Americans to ChristianityD.remove the Native Americans from the land3.Which colony was established primarily for financial gain?A.New HavenB.ConnecticutC.MarylandD.Rhode Island4.Which of the following was a principle from the Magna Carta that impacted colonists' beliefs about government?A.the belief in freedom of religionB.the belief in the monarchy's right to taxC.the belief in the king's divine right to ruleD.the belief that the people could force the king to obey the laws5.Which of the following was a draw for indentured servants coming to the Americas?A.food, clothing, and shelterB.a large salary upon arrivalC.a land grant upon arrivalD.a skilled office job6.What resulted from the English expansion some 100 miles into the interior of Virginia?A.a treaty between the English and PowhatanB.a forced English retreat to coastal landsC.the killing of hundreds of English by the PowhatanD.the movement of the Powhatan to new lands in Massachusetts7.Which of the following was an effect of the increase in slavery in the Americas during the late 1600s and early 1700s?A.African kingdoms began to resist European slave traders.B.Slavery became an integral part of American cultural life.C.Enslaved Africans could demand wages for their work.D.Many colonists who opposed slavery left the Americas and returned to Europe. 8.What resulted from the English expansion some 100 miles into the interior of Virginia?A.a treaty between the English and PowhatanB.a forced English retreat to coastal landsC.the killing of hundreds of English by the PowhatanD.the movement of the Powhatan to new lands in Massachusetts9.Which of the following was an effect of the increase in slavery in the Americas during the late 1600s and early 1700s?A.African kingdoms began to resist European slave traders.B.Slavery became an integral part of American cultural life.C.Enslaved Africans could demand wages for their work.D.Many colonists who opposed slavery left the Americas and returned to Europe. 10.Which of the following was the biggest cause of Native American deaths during the colonial period? A.warfare with EuropeansB.warfare with rival Native American groupsC.drought and starvationD.European diseases11.What was a primary goal of King Philip of Spain in the New World?A.to stop the spread of ProtestantismB.to build more churches like those in EuropeC.to create an alliance with HollandD.to share colonial management with Catholic France12.How did the Great Awakening affect the colonists' relationship with Great Britain?A.It strengthened ties between the colonies and Great Britain.B.It weakened ties between the colonies and Great Britain.C.It made the colonies more dependent on trade with each other.D.It made the colonies less dependent on trade with each other.13.Which of the following was an Enlightenment thinker whose ideas influenced American political thought?A.George WhitefieldB.Jonathan EdwardsC.King George IID.John Locke14.What created a greater sense of colonial ties to Britain?A.French victory over the British in CanadaB.British victory in the French and Indian WarC.the loss of British territory in the CaribbeanD.a fear of the Spanish expansion in Florida15.In a paragraph, explain the events of the Glorious Revolution and how they later impacted American colonists. The following are features of civilization except The vapor pressure of substance X is 100. mm Hg at 1080.C. The vapor pressure of substance X increases to 600. mm Hg at 1220.C. Determine the molar heat of vaporization of substance X using the derived form of the Clausius-Clapeyron equation given below. (Include the sign of the value in your answer.) ____ kJ/mol Enter the expression 2cos2()1 , where is the lowercase Greek letter theta. 2cos2()1 2 c o s 2 ( ) 1 = nothing What is a proportion? Give an example with your description Calculate capacitance of two parallel flat circular conducting plates with a space d between them and radius R>>d. How good an approximation is your result? A newspaper article informs you that most businesses reduced production in the last quarter but also sold from their inventories during the last quarter. Based on this information GDP likely a. increased. b. decreased. c. stayed the same. d. may have increased, decreased, or stayed the same The basic structural unit of the body is the:heartbraintissueCell Linda has a cup of coffee sitting in the cup holder in her car. She has to suddenly slam on her brakes and stop. The cup remained in the cup holder, but the coffee splashed and spilled everywhere. Newton's _____ law can best describe why this happened. A. first B. second C. third