Answer:
k = -55 x - 2 x^3
Step-by-step explanation:
Solve for k:
2 x^3 + 55 x + k = 0
Hint: | Solve for k.
Subtract 2 x^3 + 55 x from both sides:
Answer: k = -55 x - 2 x^3
3/2 is not a Root of this equation - see below, those are the Roots/Zeros.
Solve for x:
2 x^3 + 55 x + k = 0
Divide both sides by 2:
x^3 + (55 x)/2 + k/2 = 0
Change coordinates by substituting x = y + λ/y, where λ is a constant value that will be determined later:
k/2 + 55/2 (y + λ/y) + (y + λ/y)^3 = 0
Multiply both sides by y^3 and collect in terms of y:
y^6 + y^4 (3 λ + 55/2) + (k y^3)/2 + y^2 (3 λ^2 + (55 λ)/2) + λ^3 = 0
Substitute λ = -55/6 and then z = y^3, yielding a quadratic equation in the variable z:
z^2 + (k z)/2 - 166375/216 = 0
Find the positive solution to the quadratic equation:
z = 1/36 (sqrt(3) sqrt(27 k^2 + 332750) - 9 k)
Substitute back for z = y^3:
y^3 = 1/36 (sqrt(3) sqrt(27 k^2 + 332750) - 9 k)
Taking cube roots gives (sqrt(3) sqrt(27 k^2 + 332750) - 9 k)^(1/3)/6^(2/3) times the third roots of unity:
y = (sqrt(3) sqrt(27 k^2 + 332750) - 9 k)^(1/3)/6^(2/3) or y = -((-1)^(1/3) (sqrt(3) sqrt(27 k^2 + 332750) - 9 k)^(1/3))/6^(2/3) or y = ((-1)^(2/3) (sqrt(3) sqrt(27 k^2 + 332750) - 9 k)^(1/3))/6^(2/3)
Substitute each value of y into x = y - 55/(6 y):
x = (sqrt(3) sqrt(27 k^2 + 332750) - 9 k)^(1/3)/6^(2/3) - 55/(6^(1/3) (sqrt(3) sqrt(27 k^2 + 332750) - 9 k)^(1/3)) or x = -(55 (-1)^(2/3))/(6^(1/3) (sqrt(3) sqrt(27 k^2 + 332750) - 9 k)^(1/3)) - ((-1)^(1/3) (sqrt(3) sqrt(27 k^2 + 332750) - 9 k)^(1/3))/6^(2/3) or x = (55 ((-1)/6)^(1/3))/(sqrt(3) sqrt(27 k^2 + 332750) - 9 k)^(1/3) + ((-1)^(2/3) (sqrt(3) sqrt(27 k^2 + 332750) - 9 k)^(1/3))/6^(2/3)
Bring each solution to a common denominator and simplify:
Answer: x = (6^(1/3) (sqrt(81 k^2 + 998250) - 9 k)^(2/3) - 55 6^(2/3))/(6 (sqrt(81 k^2 + 998250) - 9 k)^(1/3)) or x = -((-1)^(1/3) ((sqrt(81 k^2 + 998250) - 9 k)^(2/3) + 55 (-6)^(1/3)))/(6^(2/3) (sqrt(81 k^2 + 998250) - 9 k)^(1/3)) or x = ((-1)^(1/3) ((-1)^(1/3) (sqrt(81 k^2 + 998250) - 9 k)^(2/3) + 55 6^(1/3)))/(6^(2/3) (sqrt(81 k^2 + 998250) - 9 k)^(1/3))
Combine like terms.
5x – (-10x) - 4 – (-7x) – 8
Answer:
22x - 12
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Combining Like TermsStep-by-step explanation:
Step 1: Define expression
5x - (-10x) - 4 - (-7x) - 8
Step 2: Simplify
Distribute negative: 5x + 10x - 4 + 7x - 8Combine like terms (x): 22x - 4 - 8Combine like terms (Z): 22x - 12Answer: 22x - 12
Step-by-step explanation:
5x - (-10x) -4 - (-7x) -8
The x’s are 5x + 10x + 7x = 22x
The numbers are -4 - 8 = -12
Combining these we get 22x - 12
There are 1,000 grams in 1 kilogram. Nate is mailing a package that has a mass of 8,000 grams.
He wants to know the mass of the package in kilograms.
1.000
8,000
12,000
grams
kilograms
0
1
12
Multiply or divide?
What is the unit rate. ?
I give brainless!!!!!!!!
Nate's package is 8 kilograms. This is because, if there are 1,000 grams in 1 kilogram, 8,000/ 1,000= 8 Therefore, the mass of his package is 8 kilograms.
Have a Merry Christmas!
Please help guys!!!!!!
Answer:I think its 68
Step-by-step explanation:
Answer:
The measure of angle N is 68 degrees.
Step-by-step explanation:
Since this shape is a parallelogram, opposite angles will be equivalent. So to start, set (6x - 2) equal to (4x + 36).
— 6x - 2 = 4x + 36
Next, subtarct the 4x from both sides of the equation as well as add 2 to both sides of the equation an simplify.
— 6x - 4x - 2 + 2 = 4x - 4x + 36 + 2
— 2x = 38
Now, divide both sides of the equation by 2 to find the value of x.
— 2x/2 = 38/2
— x = 19
Finally, substitute 19 for every x in the original equation. Simplify.
— 6(19) - 2 = 4(19) + 36
— 114 - 2 = 76 + 36
— 112 = 112
We now know that these two angles are 112 degrees. If a parallelogram's angles must add up to 360 degrees, then subtract 112 twice from 360 to find the combined total angle measure of N and Q. Then divide that number by 2 to find the measure of N.
— 360 - 112 - 112 = 136
— 136/2 = 68
The measure of angle N is 68 degrees.
what is the equation of the line through (2,-1) and (0,5)
A. y= -3x + 5
B. y= 3x - 5
C. y= -3x - 5
D. y= 3x + 5
A curve is defined by parametric functions x (t) and y(t), where dx/dt= 3t^2 and dy/dx= t^7– 2t^4. For what positive value of t is d^2y/dx^2 =1
A
1.079
B
1.149
С
1.202
D
1.525
Answer:
i do not know
Step-by-step explanation:
Car x travels 162 miles in 3 hours: write an equation of the line that describes the relationship between distance and time. Use x for the time in hours and y for the distance in miles
Answer:
A:The equation y=54x describes the relationship
B: y as 216 and x being 4
If a car travels for 0 hours, it will travel 0 mile(s). This means it will pass through the point (0,0)
.Use the slope to move 3 units to the right of the origin and
162 unit(s) up to find the point
(3,162) that can be used to graph the relationship. Step-by-step explanation:
please please help me!
Answer:
Option 4
Step-by-step explanation:
It has a negative slope of -[tex]\frac{1}{5}[/tex] (move down one and to the right 5)
HELP PLS
A) 16
B) -4
C) -16
Answer:
B) -4 is the crct answer may be
10 ( y - 2)
what is the answer
Answer:
10y-20
Step-by-step explanation:
sorry if I am incorrect
A company produces fruity drinks that contain a percentage of real fruit juice. Drink A contains 20% real fruit juice and Drink B contains 10% real fruit juice. How many liters of real fruit juice would be needed to produce 250 liters of Drink A and 150 liters of Drink B? How many liters of real fruit juice would be needed to produce aa liters of Drink A and bb liters of Drink B?
Answer:
y = 290 liters Drink B
Step-by-step explanation:
Drink A contains 20% real fruit juice. x liters
and Drink B contains 5% real fruit juice. y liters
y=x+80
20%x +5%y =56.5
20x+5y==5650
-x + y = 80.00
20x + 5 y = 5650.00 .............2
Eliminate y
multiply (1)by -5
Multiply (2) by 1
5.00 x -5.00 y = -400.00
20.00 x 5.00 y = 5650.00
Add the two equations
25.00 x = 5250.00
/ 25.00
x = 210.00
plug value of x in (1)
-1.00 x + 1.00 y = 80.00
-210.00 + 1.00 y = 80.00
1.00 y = 290.00
y = 290.00
Ans x = 210 liters Drink A
y = 290 liters Drink B
Which of the following scenarios is not proportional.
a. Getting paid hourly for babysitting.
b. selling lemonade for $1 per cup.
c. Paying $5 per ticket to a baseball game, plus a $7.50 online service fee.
d. Jogging at a rate of 10 minutes per mile.
Help with this question please ASAP!! :)
Answer:
options 1, 3, and 6.
Step-by-step explanation:
on the diagram, ∠2 is in the area of line EA and EG. If you are reading it by letters, ∠GEA is equal to ∠2 because they are in the same area. The last option (6) being ∠AEG, the middle angle is E which is the same as ∠GEA and ∠2.
hope this helps!! :))
A scientist teacher murdered $3980 worth of microscopes and dissension kits for the new science lab a total of 38 microscopes and 47 dissension kids were ordered a microscope cost four times as much as a Ascension kit write a system of linear equations that represents the situation what is the cost of each item
Answer:
dang
Step-by-step explanation:
._.
I know the answer is 36 but I need to know the working out and I am unsure how to work the question out.
Plz explain
Thanks in advance!! :)
Answer:
36
Step-by-step explanation:
Since the 3 numbers have a ratio of 2:3:7, that means it simplifies to that. So, there must be a common factor, let’s say x, for each of the numbers. Thus, the numbers are 2x, 3x, and 7x. To find the mean, we add up all of the numbers and divide by the number of numbers: (2x + 3x + 7x)/3 = 12x/3 = 4x = 48. Dividing by 4 on both sides gets x = 12. The median of the numbers is the number in the middle which is 3x. Substituting x = 12, we get: 3(12) = 36.
I hope this helps!!! :)
student 1 y=-3x+x student 2 y=7x/10 student 3 y=4(2-x) Which students write an equation of a nonlinear function?
Answer:
its 547632
Step-by-step explanation:
cuz yeeeeeeeeee
Find an equation of the parabola with vertex (2, -1) and directrix y=-7.
Answer:
the answer to this is y=7x-15
sharice is putting jars of jam into boxes. she puts 8 jars into each box, and she has a total of 144 jars. sharice wants to know how many boxes she needs.
she needs 18 boxes.
What is factoring?A polynomial with coefficients in a certain field or in integers is expressed as the product of irreducible factors with coefficients in the same domain in mathematics and computer algebra, which is known as polynomial factorization.
Given
Based on the given conditions, formulate: 8 x = 144
Divide both sides of the equation by the coefficient of variable: x = 144/8 out the common factor: x = 18
To know more about factoring refer to :
https://brainly.com/question/25829061
#SPJ2
You eat 80% of your daily calories at breakfast. Does this statement make sense?
Answer:
you so dumb
Step-by-step explanation:
Answer:
this statement does make sense
100 points. Consider functions f and g
Answer:
D I think
Hope you have an amazing christmas!
Solve the equation - [tex]\frac{w}{5}[/tex] +9=13. What is w?
Answer:
w = -20
Step-by-step explanation:
-[tex]\frac{w}{5}[/tex] + 9 = 13
Shift the (+9) to the other side of the equation. (+9) will turn into (-9).
-[tex]\frac{w}{5}[/tex] = 13 - 9
= 4
Shift the (÷5) to the other side of the equation. (÷5) will turn into (×5).
-w = 4 × 5
= 20
Multiply both sides of the equation by (-1) so that -w will turn into w.
w = (-1) × 20
w = -20
Given the function f(x) = x2-2, find the average rate of change over the interval -2 sxs 4
Answer:
The correct answer for that is (98)
The sum of 2 times p and 2 is 48. What is p?
Answer:
p = 23
Step-by-step explanation:
2p + 2 = 48
-2 -2
2p = 46
/2 /2
p = 23
Hope this helps and I hope u have an Amazing day!!
Write an recursive rule for the sequence 7,14,21,28
Which ratio is equivalent to 1:3 and 12:36? (A) 2:18 (B) 4:9 (C) 4:12 (D) 6:6
Answer:
I think the right answer is c 4:12
Answer:
(C) - C for Correct!
Step-by-step explanation:
We can look at ratios as a fraction, so 1:3 = 1/3 and 12:36 = 12/36. We can simplify the second fraction into 12/36 = 1/3 by canceling 12 from the numerator and denomerator. We can do this with all of the answer choices:
(A) Wrong - 2/18 = 1/9
(B) Wrong - 4/9
(C) Correct - 4/12 = 1/3
(D) Wrong - 6/6 = 1
I hope this helps!!! :)
Given that f(x) = x2 + 4x – 21 and g(x) = x - 3, find f(x) · g(x) and
express the result in standard form.
9514 1404 393
Answer:
(f·g)(x) = x^3 +x^2 -33x +63
Step-by-step explanation:
The product of the two functions can be found using the distributive property.
[tex]f(x)\cdot g(x)=(x^2+4x-21)\cdot(x-3)\\\\=(x^2+4x-21)(x)+(x^2+4x-21)(-3)\\\\=x^3+4x^2-21x-3x^2-12x+63\\\\\boxed{(f\cdot g)(x)=x^3 +x^2-33x+63}[/tex]
how long will it take for 95% of a sample to decay
I searched up the entire problem. I solved it and got 129.7 seconds but I'm not sure it's right.
3) 15x + 4 = 106
Can someone show me the steps ? Pls :)
1) Subtract 4 from both sides to get 15x = 102
2) Divide by 15 on both sides to get x = 6.8
Answer:
x=6.8
Step-by-step explanation:
15x + 4 = 106
subtract 4 from both sides
15x=102
divide both sides by 15
x=6.8
PLEASE HELP 6TH GRADE
What is 3 3/8 divided by 9
Answer:
0.375
Step-by-step explanation:
Answer:
3/8
Reason:
I just did a question exactly like this, and this was the answer.
11) (-x - 3) + (3x + 8)
i don’t understand these
Answer:
-8x-25
Step-by-step explanation: