2a^3 + a^2 + a + 4
A Linear
B Cubic
C Quadratic
D: Quartic

Answers

Answer 1

Answer:

C. Quadratic

Step-by-step explanation:

Solve for a:

2 a^3 + a^2 + a + 4 = 0

Hint: | Look for a simple substitution that eliminates the quadratic term of 2 a^3 + a^2 + a + 4.

Eliminate the quadratic term by substituting x = a + 1/6:

23/6 + (x - 1/6)^2 + 2 (x - 1/6)^3 + x = 0

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

Expand out terms of the left hand side:

2 x^3 + (5 x)/6 + 104/27 = 0

Hint: | Write the cubic equation in standard form.

Divide both sides by 2:

x^3 + (5 x)/12 + 52/27 = 0

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

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

52/27 + 5/12 (y + λ/y) + (y + λ/y)^3 = 0

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

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

y^6 + y^4 (3 λ + 5/12) + (52 y^3)/27 + y^2 (3 λ^2 + (5 λ)/12) + λ^3 = 0

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

Substitute λ = -5/36 and then z = y^3, yielding a quadratic equation in the variable z:

z^2 + (52 z)/27 - 125/46656 = 0

Hint: | Solve for z.

Find the positive solution to the quadratic equation:

z = 1/216 (3 sqrt(4821) - 208)

Hint: | Perform back substitution on z = 1/216 (3 sqrt(4821) - 208).

Substitute back for z = y^3:

y^3 = 1/216 (3 sqrt(4821) - 208)

Hint: | Take the cube root of both sides.

Taking cube roots gives 1/6 (3 sqrt(4821) - 208)^(1/3) times the third roots of unity:

y = 1/6 (3 sqrt(4821) - 208)^(1/3) or y = -1/6 (208 - 3 sqrt(4821))^(1/3) or y = 1/6 (-1)^(2/3) (3 sqrt(4821) - 208)^(1/3)

Hint: | Perform back substitution with x = y - 5/(36 y).

Substitute each value of y into x = y - 5/(36 y):

x = 1/6 (3 sqrt(4821) - 208)^(1/3) - 5/(6 (3 sqrt(4821) - 208)^(1/3)) or x = -1/6 (208 - 3 sqrt(4821))^(1/3) - (5 (-1)^(2/3))/(6 (3 sqrt(4821) - 208)^(1/3)) or x = 5/6 ((-1)/(3 sqrt(4821) - 208))^(1/3) + 1/6 (-1)^(2/3) (3 sqrt(4821) - 208)^(1/3)

Hint: | Simplify each solution.

Bring each solution to a common denominator and simplify:

x = ((3 sqrt(4821) - 208)^(2/3) - 5)/(6 (3 sqrt(4821) - 208)^(1/3)) or x = -1/6 (208 - 3 sqrt(4821))^(1/3) - (5 (-1)^(2/3))/(6 (3 sqrt(4821) - 208)^(1/3)) or x = 1/6 (5 ((-1)/(3 sqrt(4821) - 208))^(1/3) + (-1)^(2/3) (3 sqrt(4821) - 208)^(1/3))

Hint: | Perform back substitution on the three roots.

Substitute back for a = x - 1/6:

Answer: a = ((3 sqrt(4821) - 208)^(2/3) - 5)/(6 (3 sqrt(4821) - 208)^(1/3)) - 1/6 or a = -1/6 - 1/6 (208 - 3 sqrt(4821))^(1/3) - (5 (-1)^(2/3))/(6 (3 sqrt(4821) - 208)^(1/3)) or a = 1/6 (5 (-1/(3 sqrt(4821) - 208))^(1/3) + (-1)^(2/3) (3 sqrt(4821) - 208)^(1/3)) - 1/6


Related Questions

Helppppppp!!!!!!!!??????

Answers

Answer:

5/10

Step-by-step explanation:

5(n-3)????????????!!!!!!!!

Answers

Answer:

5n-15

Step-by-step explanation:

[tex]5(n-3)[/tex]

Expand

[tex]5\times n = 5n\\\\5\times -3 =-15\\\\5n -15[/tex]

what is 63 times 4? pls help

Answers

Answer:

252

Step-by-step explanation:

Hope this helps

Answer:

252

Step-by-step explanation:

if 2x – 1 is a factor of 16x4
24x3 + 2x + f, find f.

Answers

Answer:

f = -5

Step-by-step explanation:

If 2x – 1 is a factor of 16x4 + 24x3 + 2x + f, find f.

If 2x - 1 = 16x⁴ + 24x³ + 2x + f, find f.

2x - 1 = 0

2x = 1

x = 1/2

Hence

f(1/2) = 16(1/2)⁴ + 24(1/2)³ + 2(1/2) + f

= 16(1/16) + 24(1/8) + 1 + f

= 1 + 3 + 1 + f

= 5+ f

f = -5

What is the slope of the perpendicular lines?

y = - 5/2x - 8

A) y = - 5x
B) y = 5x
C) y = x - 5

Answers

Answer: x=16/5

Step-by-step explanation:

Answer:

16/5

Step-by-step explanation:

Which postulate or theorem proves that these two triangles are congruent?
A. ASA Congruence Postulate
B. AAS Congruence Theorem
C. HL Congruence Theorem
D. SAS Congruence Postulate

Answers

Answer:

Option (B)

Step-by-step explanation:

From the given picture,

Given:

Two lines PM and QR are intersecting each other at a point N.

∠NMR ≅ ∠NPQ

NR ≅ QN

To prove:

ΔMNR ≅ ΔPNQ

              Statements                               Reasons

1). NR ≅ QN                                 1). Given

2). ∠NMR ≅ ∠NPQ                     2). Given

3). ∠MNR ≅ ∠PNQ                     3). Definition of vertical angles

4). ΔMNR ≅ ΔPNQ                     4). AAS theorem of congruence

Therefore, Option (B) will be the correct option.

Answer:

B: AAS Congruence Theorem

8.h=7
108 18 what is h

Answers

Answer:

its 8.7× 108 18

Step-by-step explanation:

ye thats basically it solve it now

Sheila makes $12.50 per hour. Calculate her earnings for a 40-hour week.
Gross Earnings
Taxes Withheld
Gross Pay
Social Security Tax
$31.00
Medicare Tax
$7.25
Total Amount of Withholdings/
Federal Tax
$44.05
Deductions:
State Tax
$15.85
Deductions
Net Pay:
Net Earnings
$
Accompanies: Employee Compensation Components

Answers

Shelia's gross pay is $500. Shelia's total amount of withholding / deductions is $98.15. Shelia's net pay is $401.85.

What is the gross pay, net pay and the total witholding?

Gross pay is the total amount earned before any deductions.

Gross pay 12.50 x 40 = $500

Shelia's total amount of withholding is the sum of all the taxes paid.

Shelia's total amount of withholding = 31 +  7.25 + 44.05 +  15.85 = $98.15

Net pay is the gross pay less the total withholding.

$500 - $98.15 = $401.85.

To learn more about taxes, please check: https://brainly.com/question/25311567

help please im begging

Answers

Answer:

D and E :)

Step-by-step explanation:

Charlotte is working two summer jobs, making $18 per hour lifeguarding and making $6 per hour walking dogs. In a given week, she can work at most 15 total hours and must earn a minimum of $150. If Charlotte worked 5 hours walking dogs, determine the minimum number of whole hours lifeguarding that she must work to meet her requirements. If there are no possible solutions, submit an empty answer.

Answers

Answer:

the answer is 6.6 or at estimation 7

Answer:7

Step-by-step explanation:

Write the number 3 2/5 in a/b form

Answers

Answer:

Step-by-step explanation:

16/5

5*3=15+1=16

16/5

The Sugar Sweet Company will choose from two companies to transport its sugar to market. The first company charges $3995 to rent trucks plus an additional fee of $225.75 for each ton of sugar. The second company charges $5500 to rent trucks plus an additional fee of $150.50 for each ton of sugar.

Answers

Given :

The Sugar Sweet Company will choose from two companies to transport its sugar to market.

The first company charges $3995 to rent trucks plus an additional fee of $225.75 for each ton of sugar.

The second company charges $5500 to rent trucks plus an additional fee of $150.50 for each ton of sugar.

To Find :

How, many tons of sugar will cost same in both companies.

Solution :

For company 1 :

P1 = (225.75)x + 3995

For company 2 :

P2 = (150.50)x + 5500

For same cost :

P1 = P2

(225.75)x + 3995 = (150.50)x + 5500

x( 225.75 - 150.50 ) = ( 5500- 3995)

x( 75.25 ) = 1505

x = 20

Therefore, 20 tons of sugar will cost same.

Hence, this is the required solution.

.a. Find the LCM of the 45 and 70​

Answers

Answer:

630.

Find the Prime factorization of 45, 3 x 3 x 5

Find the prime factorization of 70, 2 x 5 x7

Multiply each factor the greater number of times it occurs.

You get 630.

LCM of 45 and 70 :

= 45 ÷ 5 , 70 ÷ 5 ( Both the numbers are being divided by 5 ; which is their smallest common factor )

= 14 , 9

= 14 ÷ 14 , 9 ( We are dividing 14 by 14 as both 9 and 14 dont have have a common factor )

= 1 , 9

= 1 , 9 ÷ 3 ( 9 is being divided by 3 )

= 1 , 3

= 1 , 3 ÷ 3 ( 3 is being divided by 3 )

= 1 , 1

LCM of 45 and 70 = 5 × 14 × 3 × 3

LCM of 45 and 70 = 630

Therefore , the LCM of the 45 and 70 = 630 .

Write three factors of 24 which have a sum of more than 37 and less than 40

Answers

Answer:

24, 12, 2

Step-by-step explanation:

24, 12, and 2 are all factors of 24.

24+12+2=38

37<38<40

the three factors of 24 that have a sum between 37 and 40 are 2, 12, and 24, with a sum of 38. Another combination is 4, 8, and 24, also with a sum of 38.

To find three factors of 24 with a sum between 37 and 40, we can start by listing the factors of 24:

1, 2, 3, 4, 6, 8, 12, 24

Next, we'll try different combinations of these factors to see if any three of them add up to a sum between 37 and 40:

1 + 2 + 24 = 27 (not within the desired range)

1 + 3 + 24 = 28 (not within the desired range)

1 + 4 + 24 = 29 (not within the desired range)

1 + 6 + 24 = 31 (not within the desired range)

1 + 8 + 24 = 33 (not within the desired range)

1 + 12 + 24 = 37 (not within the desired range)

2 + 3 + 24 = 29 (not within the desired range)

2 + 4 + 24 = 30 (not within the desired range)

2 + 6 + 24 = 32 (not within the desired range)

2 + 8 + 24 = 34 (not within the desired range)

2 + 12 + 24 = 38 (within the desired range)

3 + 4 + 24 = 31 (not within the desired range)

3 + 6 + 24 = 33 (not within the desired range)

3 + 8 + 24 = 35 (not within the desired range)

3 + 12 + 24 = 39 (within the desired range)

4 + 6 + 24 = 34 (not within the desired range)

4 + 8 + 24 = 36 (within the desired range)

4 + 12 + 24 = 40 (not within the desired range)

6 + 8 + 24 = 38 (within the desired range)

6 + 12 + 24 = 42 (not within the desired range)

8 + 12 + 24 = 44 (not within the desired range)

Therefore, the three factors of 24 that have a sum between 37 and 40 are 2, 12, and 24, with a sum of 38. Another combination is 4, 8, and 24, also with a sum of 38.

Learn more about factors here

https://brainly.com/question/11907868

#SPJ2

Does anyone know what the answer is ???? PLEASE HELP

Answers

Answer:

they should meet at point (1, 1)

(1,1) is the answer for your question it’s correct

Please answer this as SOON as posible!!
In a recent year, 23% of all college students were enrolled part-time. If 6.2 million college students were enrolled part-time that year, what was the total number of college students?

Answers

Answer:

17,222,222

Step by Step Solution:

If 26% equals 6,200,000, then

1% equals 6,200,000/23, and

100% equals (6,200,000/23)*100 = 17,222,222.222222222222222222222222

Hence, there were about 17,000,000 (seventeen million) students.

To be a bit closer to the number, there where about 17,222,222 students.

A truck can be rented from Company A for ​$120 a day plus ​$0.20 per mile. Company B charges ​$50 a day plus ​$0.60 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for Company A and Company B are the same.

Answers

The answer would be 175miles

round 0.532 to the nearest hundredth​

Answers

The answer is 0.53

This is because the second digit (in the decimal range) is in the hundredths.

Look at image. Please help quick.

Answers

Answer:

its most likely B

Step-by-step explanation:

please please help!!!
Number of Chores, x
Days, y
The table shows the number of days required to
perform a given number of chores. The number of days
varies directly with the number of chores. What is the
constant of variation that completes the equation?
6
18
y =
9
27
12
36

Answers

Answer:

the answer is 3

Step-by-step explanation:

The table shows the number of days required to perform a given number of chores. The number of days varies directly with the number of chores. What is the constant of variation that completes the equation?

y =   3x

Answer:

3

Step-by-step explanation:

edge 2021;)

Hrhdldkxbdmskshd dahtjfvcjcjc

Answers

Answer:

this sentence is grammatically incorrect

lol

Answer:

Thanks for the points luv

Step-by-step explanation:

Have a good day/night :)

Brainliest pls?

One store was selling a box of baseball cards for $20. You have to pay 9% sales tax on the item.

1. How much would the tax be?

2. What would be the total cost of the baseball cards?

Answers

Answer: 1. $1.80

2. $21.80

Step-by-step explanation:

You apply sales tax to 20 which is 9% or 0.09 so you p multiply 20 by 0.09 which is 1.8. That’s the tax then add that to 20 and get 21.80

Mark the brainliest it would be aprreciated

2. What is the y-intercept of each equation?
a, y=6r+2
b. 10r + 5y = 30
c.y- 6 = 2(3x – 4)

Answers

Answer: 2 5 12

Step-by-step explanation:

y = 6r + 2 would be 2

10r + 5y = 30
5y = -10r + 30
y = -2r + 6 this one is 6

y - 6 = 2(3x - 4)
y - 6 = 6x - 8
y = 6x -2 this one is 2

Solve for x: 3x + 2 = 11

Answers

Answer:

x = 3

Step-by-step explanation:

3 x 3 + 2 = 11  Because 3x3 = 9 and 9 + 2 = 11

I hope this helps!

Answer:

x=3

Step-by-step explanation:

3x+2=11

(subtract 2 on both sides)

3x=9

(divide by 3 on both sides)

x=3

You start at (4,4). You move up 1 unit and left 7 units. Where do you end?

Answers

Answer: i believe it would be (-3 , 5)

Step-by-step explanation:

Correct me if im wrong

Answer:

(-3, 5)

Step-by-step explanation:

I could be mistaken, but I'm pretty sure it's that. You may want to graph the point yourself and double-check just to make sure.

What does it mean by "interpret its meaning"? I underlined it for you guys.

Answers

it’s asking what is the graph showing basically what is it telling or showing you. so for number 17 it would be that every two hours, the miles traveled decreases by 100 miles. i hope i explained this well enough for you, good luck :)

Find the value of X: 3x (-35) = 2x

Answers

X=0
Pls mark brainliest

what is the rate of change for the graph?

Answers

Answer:

Step-by-step explanation:

1,2

2,7

7-2 is 5 and 2-1 is 1

5/1 is the slope

7=2*5+b

7=10+b

-3=b

y=5x-3

Please help me! Is the ordered pair, in the form (x, y) x , y , a solution of the equation below?
Ordered Pair: (−1, −12)
Linear Equation: 4x − y = 8
options:
True
False

Answers

The answer is true because 4 times -1 equals-4. Then -4 minus -12 you would flip the sign to a plus sign and -12 to a positive and -4+12 equals 8.

42.564in expanded form

Answers

40 + 2 + 0.5 + 0.06 + 0.004
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