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
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?
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
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.
What does it mean by "interpret its meaning"? I underlined it for you guys.
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
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
Write the number 3 2/5 in a/b form
Answer:
Step-by-step explanation:
16/5
5*3=15+1=16
16/5
what is 63 times 4? pls help
Answer:
252
Step-by-step explanation:
Hope this helps
Answer:
252
Step-by-step explanation:
.a. Find the LCM of the 45 and 70
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 .
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Answer:
this sentence is grammatically incorrect
lol
Answer:
Thanks for the points luv
Step-by-step explanation:
Have a good day/night :)
Brainliest pls?
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
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;)
if 2x – 1 is a factor of 16x4
24x3 + 2x + f, find f.
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
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
Look at image. Please help quick.
Answer:
its most likely B
Step-by-step explanation:
Write three factors of 24 which have a sum of more than 37 and less than 40
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
what is the rate of change for the graph?
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
Helppppppp!!!!!!!!??????
Answer:
5/10
Step-by-step explanation:
2. What is the y-intercept of each equation?
a, y=6r+2
b. 10r + 5y = 30
c.y- 6 = 2(3x – 4)
Answer: 2 5 12
Step-by-step explanation:
Solve for x: 3x + 2 = 11
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
What is the slope of the perpendicular lines?
y = - 5/2x - 8
A) y = - 5x
B) y = 5x
C) y = x - 5
Answer: x=16/5
Step-by-step explanation:
Answer:
16/5
Step-by-step explanation:
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
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
Does anyone know what the answer is ???? PLEASE HELP
Answer:
they should meet at point (1, 1)
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?
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.
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.
Answer:
the answer is 6.6 or at estimation 7Answer:7
Step-by-step explanation:
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.
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.
round 0.532 to the nearest hundredth
The answer is 0.53
This is because the second digit (in the decimal range) is in the hundredths.
help please im begging
Answer:
D and E :)
Step-by-step explanation:
42.564in expanded form
Find the value of X: 3x (-35) = 2x
5(n-3)????????????!!!!!!!!
Answer:
5n-15Step-by-step explanation:
[tex]5(n-3)[/tex]
Expand
[tex]5\times n = 5n\\\\5\times -3 =-15\\\\5n -15[/tex]
You start at (4,4). You move up 1 unit and left 7 units. Where do you end?
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.
8.h=7
108 18 what is h
Answer:
its 8.7× 108 18
Step-by-step explanation:
ye thats basically it solve it now