2a^3 + a^2 + a + 4
A Linear
B Cubic
C Quadratic
D: Quartic
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
Write a story that can be represented by the following equation: x + 16 = 42
Answer:
Amanda bought 42 apples and gave 16 away how many are left.
Step-by-step explanation:
X=26
Answer:
Renee runs a dogwalking business. She walked 42 dogs over the weekend. On Saturday she walked 16 dogs but Renee can't remember how many she walked on Sunday. Write and equation to find how many dogs Renee walked on Sunday where x is the number of dogs she walked on Sunday.
can you help me please
Answer: i think it would be 5
[tex]\sqrt{x} \left \{ {{y=2} \atop {x=2}} \right. \lim_{n \to \infty} a_n \int\limits^a_b {x} \, dx \\[/tex]
The mode of the following data is 5 ?
0, 2, 2, 5, 2, 5, 0
Answer:
The answer is 2.
Step-by-step explanation:
2 appears three times while the others appear only twice
-3(4x + 9) = 15
Please help
Answer:
x=-7/2
Good luck!
on of Tho Mcd
8. Write the standard form of the equation y + 4 = - 12 (x – 1).
Answer:
12x + y = 16
Step-by-step explanation:
Standard Form: Ax + By = C
Step 1: Write point-slope form
y + 4 = -12(x - 1)
Step 2: Find slope-intercept form
y + 4 = -12x + 12
y = -12x + 16
Step 3: Find standard form
12x + y = 16
segment addition postulate
Step-by-step explanation:
for 1:
we know that bc+cd=bd
plug in what we wre given
23+22= bd
add.
for 2:
we know that ef+fg=eg
plug in what we know
4x+3 + 6x+9 = 72
combine like factors
10x+12=72
solve
(subtract 12 on both sides) 10x=60
(divide by 10 on both sides) x=6
2.) During typhoon ambo PAGASA tracks the amount of the accumulating rain fall. For the first three hour's of typhoon that rain fell at a constant rate of 25 mm per hour. The typhoon slows down for an hour ad started again at a constant rate of 20 mm per hour for the next 2 hour's . Write a piecewise function that models the amount of rain fall as function of time.
(this is for a friend)
Answer:
Step-by-step explanation:
Given that :
First 3 hours, rain fell at a constant rate of 25mmper hour
Next one hour, tmrain slowed down
Next 2 hours, rate of 20mm per hour
Piecewise function which models the situation :
________{25t ; t in range {0, 3)
f(x)______{75 ; t in range {3,4}
________{75 + 20(t-4) ; t in range {4,6}
Hence, the function.
HELP PLEASE
BRAINLIEST IF CORRECT
Answer:
1. 7 and 8
2. Pi so the second one
3. between the square root of 6 and the square root of 25
4. the only one left, which is the top one. I am in honors algebra. TRUST ME BROS
Step-by-step explanation:
Which of the following does not represent a function? (1 point)
Answer this as quick as possible
Answer:
The oval
Step-by-step explanation: A function must pass the vertical line test.
Answer:
The third one (oval)
Step-by-step explanation:
To see if something is a function or not, you do the vertical line test. So just draw lines vertically over the x-values. If an x-value has more than one y-value then it is not a function. It is a relation.
3.5+y=-1 solve for y
Answer:
C is your best bet i got it good on ed
Answer:
-4.5
Step-by-step explanation:
How much time will Alex need to walk to his school, which is 2 1/4 miles away from his house, if he would walk with the speed of
4 1/2 mph
Which of the following expression are equivalent to -11/4?
Answer:
B
Step-by-step explanation:
The equivalent expression to - 11/4 is, - (-11/-4).
Option B is true.
What is mean by Fraction?A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.
Given that;
The fraction is,
⇒ - 11/4
Now, By option B;
The number is,
⇒ - (- 11/ - 4)
Multiply by - 1 in denominator and numerator,
⇒ - (- 1 × - 11 / - 1 × - 4)
⇒ - (11/4)
⇒ - 11/4
Thus, The equivalent expression is, - (-11/-4).
Learn more about the fraction visit:
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The complete question is this,
Which of the following expression are equivalent to -11/4?
A) - (11/ - 4)
B) - (-11/-4)
C) None of these
PLSSS!!!!! HELP ME!!!! I WILL MARK U!!! MATH!!!!!!!!!!!!
Answer:
48
Step-by-step explanation:
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition SubtractionStep 1: Define
bc² - b
b = 2
c = -5
Step 2: Substitute and Evaluate
Substitute: 2(-5)² - 2Exponents: 2(25) - 2Multiply: 50 - 2Subtract: 48Answer:
48
Step-by-step explanation:
Hello,
[tex]bc^2-b=b(c^2-1)\\ \\\text{So for b = 2 and c = -5} \\\\2\times ((-5)^2-1)=2\times (25-1)=2\times 24 = 48[/tex]
Thanks
A whale is 215 feet below sea level and descends 23 feet then ascends 119 feet. What is the location of the whale?
Answer:
354 feet below sea level
Step-by-step explanation:
Subtract 23 from 215, then add 119
What is one goal you would like to accomplish over the next twenty months? In other words, what is one goal you would like to accomplish by the end of middle school? Explain. (2+ sentences)
Answer:
One goal that I would like to accomplish over the next twenty months is to become a better person. Academically and personally. As cliché as it sounds, I would love to get better grades. Personally, I would like to get better at my emotional regulation when working on school. I would love to discover better study habits.
When x = -3, then y = ?
Step-by-step explanation:
the answer is y=-6 when x=-3
4
13) While shopping for a gift, you find the perfect wallet on sale
for 89% off its original $5.62 price. How much will you pay for
the wallet?
I
14) A wallet is marked with a sale sticker saying it is 76% off
The original price is $57.41. What is the sale price?
15) Originally priced at $48.69, a wallet was found on a 10% off
rack. What is the sale price of the wallet?
Answer:
13) 0.61 cent
14) 13.78 $
15) 3.82 $
Step-by-step explanation:
Hope this helps
The required solutions are given as,
13) Discounted price of the walled 0.61 cents,
14) the sale price is given as $ 13.78,
15) sale price of the wallet is $ 3.82,
The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
(1)
The perfect wallet is on sale for 89% off its original $5.62 price,
Discounted price, = 5.62 - 89% of 5.62
= 5.62 - 0.89 × 5.62
= 5.62(1 - 0.89)
= 5.62(0.11)
= 0.61 cents
Similarly,
14) the sale price is given as $ 13.78,
15) sale price of the wallet is $ 3.82,
Learn more about percentages here:
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Please help me with me.
Answer:
9; the initial fee.
Step-by-step explanation:
pls pls pls pls help im helpless idk what to doo or how pls helppp ill mark brainliest
1. Simplify−3+(5+3)
2. Evaluate3|2+5|+2|3−2|+ 43; = −1
3. You are renting a beach house for the summer. The cost of renting the beach house plus the one-time security deposit is represented by the equation = 151 + 575, where x represents the number of days that the beach house is rented and y is the total cost of the rental. What is the cost of the security deposit?
4. Write an expression that represents the perimeter of the rectangle.
one side is 32 and the bottom is 4 − 7
Solve each equation for the indicated variable.
5. 3−4=12 for y
6. =2+1 h for h
Match the property of real numbers illustrated by the equation.
7. 4.5(1.2 ∙ 6.7) = (4.5 ∙ 1.2) ∙ 6.7
8. 9+√2=√2+9 9. ∙1=
10.3 ∙ 4 = 1 43
11.2( + ) = 2 + 2
A. Inverse Prop. Of Multiplication
B. Distributive Prop.
C. Associative Prop. Of Multiplication
D. Identity Prop. Of Addition
E. Commutative Prop. Of Addition
Write an algebraic expression to model each situation.
12. the product of 8 and the sum of a number x and 3
13. The piggy bank contained $35 and you added $2.75 each day
14. You spent $45 on pencils, calculators, and rulers. Pencils (p) cost $2, calculators (c) cost $25, and rulers (r) cost $4, each.
Solve each inequality and graph the solution.
15. 2−5≥−23
16. −30 4−1 Or 3 > −4 + 15
Solve the absolute value equations and check for extraneous solutions.
18. |5−2|=9 Case 1: (Positive) (5 − 2) = 9 Case 2: (Negative) −(5 − 2) = 9
19.|2 − 8| = −4 − 2 Case 1: (Positive) Case 2: (Negative)
Solve the absolute value inequality and graph the solution.
20.6| − 4| ≤ 48 Case 1: (Positive) 6( − 4) ≤ 48 Case 2: (Negative) 6(−( − 4)) ≤ 48
Answer:b
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
solve for x. 4=6x/a +5
una madre tiene 35 años mas que su hija y dentro de 5 años tendra el doble
¿que edad tiene cada uno?
if you are asked to solve a system of equations in which there is no linear equation to start with, you can sometimes begin by isolating and substituting a variable that is squared in both equations.
Answer:
A. True
Step-by-step explanation:
A. P. E. X. Just took the quiz.
Answer:
Step-by-step explanation:
it is true
Isabel wants to start saving more money so that she can purchase new clothes for college. She has $200 and will add $5 to her savings every day. Which equation models Isabel’s savings, where n represents each day ?
Answer:
Step-by-step explanation:
n-5=200
Answer: an= 5n +
Step-by-step explanation:
I don’t really know but she has $200 and she wants to add $5 to her savings everyday so it can’t be an= 5an-1 because we’re adding but n means everyday so 5n would represent that so yeeahhhh hope that helped
I need the answer ASP ILL GIVE EXTRA POINTS
The table shows the results of a survey to choose a new
school mascot.
Vx
Four hundred students participated in the survey.
Which expression would you use to find how many
students voted for the cougar?
What should be the new school mascot?
Cougar
10%
400 - 2
0400 +4
Eagle
15%
0400 - 5
Falcon
0400 + 10
50%
Panther
25%
Intro
Done
Answer:
400 divided by 10 Got it right in the assignment
Answer:400 divided by 10
Step-by-step explanation:
<3
True or False?
-6 is a solution for -4x > 16
Answer:
True
Step-by-step explanation:
-4x > 16
Divide each side by -4, remembering to flip the inequality since we are dividing by a negative
-4x/-4 < 16/-4
x < -4
-6 is less than -4 so -6 is a solution to the inequality
Answer: True
Step-by-step explanation:
It equals 24>16
Can you please help this is due in a few hours
Answer:
Rounded to the hundreds is 500, and rounded to the tens place is 480.
Step-by-step explanation:
You figure out if 476 is closer to 480 or 470 and in this case it is closer to 480, thus that is the answer. Same thing goes for the hundredes place just focusing your attention in the tens or hundreds place. - Hope this helps :)
A birthday cake was cut into equal pieces, and two pieces were eaten. The
fraction below shows how many pieces were left. According to the fraction,
how many pieces were not eaten?
9
11
A. 13
B. 9
C. 2.
O
D. 11
O
Answer:
I think c is the answers but I could be wrong
pls help! will give brainliest