Answer:
Step-by-step explanation:
Solve for x:
3 x^4 - 16 x^3 + 4 x + 363 = 0
Eliminate the cubic term by substituting y = x - 4/3:
363 + 4 (y + 4/3) - 16 (y + 4/3)^3 + 3 (y + 4/3)^4 = 0
Expand out terms of the left-hand side:
3 y^4 - 32 y^2 - (476 y)/9 + 3059/9 = 0
Divide both sides by 3:
y^4 - (32 y^2)/3 - (476 y)/27 + 3059/27 = 0
Add 2/3 sqrt(3059/3) y^2 + (32 y^2)/3 + (476 y)/27 to both sides:
y^4 + 2/3 sqrt(3059/3) y^2 + 3059/27 = 2/3 sqrt(3059/3) y^2 + (32 y^2)/3 + (476 y)/27
y^4 + 2/3 sqrt(3059/3) y^2 + 3059/27 = (y^2 + sqrt(3059/3)/3)^2:
(y^2 + sqrt(3059/3)/3)^2 = 2/3 sqrt(3059/3) y^2 + (32 y^2)/3 + (476 y)/27
Add 2 (y^2 + sqrt(3059/3)/3) λ + λ^2 to both sides:
(y^2 + sqrt(3059/3)/3)^2 + 2 λ (y^2 + sqrt(3059/3)/3) + λ^2 = (476 y)/27 + 2/3 sqrt(3059/3) y^2 + (32 y^2)/3 + 2 λ (y^2 + sqrt(3059/3)/3) + λ^2
(y^2 + sqrt(3059/3)/3)^2 + 2 λ (y^2 + sqrt(3059/3)/3) + λ^2 = (y^2 + sqrt(3059/3)/3 + λ)^2:
(y^2 + sqrt(3059/3)/3 + λ)^2 = (476 y)/27 + 2/3 sqrt(3059/3) y^2 + (32 y^2)/3 + 2 λ (y^2 + sqrt(3059/3)/3) + λ^2
(476 y)/27 + 2/3 sqrt(3059/3) y^2 + (32 y^2)/3 + 2 λ (y^2 + sqrt(3059/3)/3) + λ^2 = (2 λ + 32/3 + (2 sqrt(3059/3))/3) y^2 + (476 y)/27 + 2/3 sqrt(3059/3) λ + λ^2:
(y^2 + sqrt(3059/3)/3 + λ)^2 = y^2 (2 λ + 32/3 + (2 sqrt(3059/3))/3) + (476 y)/27 + 2/3 sqrt(3059/3) λ + λ^2
Complete the square on the right-hand side:
(y^2 + sqrt(3059/3)/3 + λ)^2 = (y sqrt(2 λ + 32/3 + (2 sqrt(3059/3))/3) + 238/(27 sqrt(2 λ + 32/3 + (2 sqrt(3059/3))/3)))^2 + (4 (2 λ + 32/3 + (2 sqrt(3059/3))/3) (λ^2 + 2/3 sqrt(3059/3) λ) - 226576/729)/(4 (2 λ + 32/3 + (2 sqrt(3059/3))/3))
To express the right-hand side as a square, find a value of λ such that the last term is 0.
This means 4 (2 λ + 32/3 + (2 sqrt(3059/3))/3) (λ^2 + 2/3 sqrt(3059/3) λ) - 226576/729 = 8/729 (729 λ^3 + 243 sqrt(9177) λ^2 + 3888 λ^2 + 864 sqrt(9177) λ + 165186 λ - 28322) = 0.
Thus the root λ = 1/9 (-sqrt(9177) - 16) + (85 13^(2/3) (i sqrt(3) + 1))/(6 (3 (i sqrt(7766346) - 4023))^(1/3)) + ((-i sqrt(3) + 1) (13 (i sqrt(7766346) - 4023))^(1/3))/(6 3^(2/3)) allows the right-hand side to be expressed as a square.
(This value will be substituted later):
(y^2 + sqrt(3059/3)/3 + λ)^2 = (y sqrt(2 λ + 32/3 + (2 sqrt(3059/3))/3) + 238/(27 sqrt(2 λ + 32/3 + (2 sqrt(3059/3))/3)))^2
Take the square root of both sides:
y^2 + sqrt(3059/3)/3 + λ = y sqrt(2 λ + 32/3 + (2 sqrt(3059/3))/3) + 238/(27 sqrt(2 λ + 32/3 + (2 sqrt(3059/3))/3)) or y^2 + sqrt(3059/3)/3 + λ = -y sqrt(2 λ + 32/3 + (2 sqrt(3059/3))/3) - 238/(27 sqrt(2 λ + 32/3 + (2 sqrt(3059/3))/3))
Solve using the quadratic formula:
y = 1/6 (sqrt(2) sqrt(9 λ + 48 + sqrt(9177)) + sqrt(2) sqrt(48 - sqrt(9177) - 9 λ + 238 sqrt(2) 1/sqrt(9 λ + 48 + sqrt(9177)))) or y = 1/6 (sqrt(2) sqrt(9 λ + 48 + sqrt(9177)) - sqrt(2) sqrt(48 - sqrt(9177) - 9 λ + 238 sqrt(2) 1/sqrt(9 λ + 48 + sqrt(9177)))) or y = 1/6 (sqrt(2) sqrt(48 - sqrt(9177) - 9 λ - 238 sqrt(2) 1/sqrt(9 λ + 48 + sqrt(9177))) - sqrt(2) sqrt(9 λ + 48 + sqrt(9177))) or y = 1/6 (-sqrt(2) sqrt(9 λ + 48 + sqrt(9177)) - sqrt(2) sqrt(48 - sqrt(9177) - 9 λ - 238 sqrt(2) 1/sqrt(9 λ + 48 + sqrt(9177)))) where λ = 1/9 (-sqrt(9177) - 16) + (85 13^(2/3) (i sqrt(3) + 1))/(6 (3 (i sqrt(7766346) - 4023))^(1/3)) + ((-i sqrt(3) + 1) (13 (i sqrt(7766346) - 4023))^(1/3))/(6 3^(2/3))
Substitute λ = 1/9 (-sqrt(9177) - 16) + (85 13^(2/3) (i sqrt(3) + 1))/(6 (3 (i sqrt(7766346) - 4023))^(1/3)) + ((-i sqrt(3) + 1) (13 (i sqrt(7766346) - 4023))^(1/3))/(6 3^(2/3)) and approximate:
y = -2.83639 - 2.06535 i or y = -2.83639 + 2.06535 i or y = 2.83639 - 1.07606 i or y = 2.83639 + 1.07606 i
Substitute back for y = x - 4/3:
x - 4/3 = -2.83639 - 2.06535 i or y = -2.83639 + 2.06535 i or y = 2.83639 - 1.07606 i or y = 2.83639 + 1.07606 i
Add 4/3 to both sides:
x = -1.50306 - 2.06535 i or y = -2.83639 + 2.06535 i or y = 2.83639 - 1.07606 i or y = 2.83639 + 1.07606 i
Substitute back for y = x - 4/3:
x = -1.50306 - 2.06535 i or x - 4/3 = -2.83639 + 2.06535 i or y = 2.83639 - 1.07606 i or y = 2.83639 + 1.07606 i
Add 4/3 to both sides:
x = -1.50306 - 2.06535 i or x = -1.50306 + 2.06535 i or y = 2.83639 - 1.07606 i or y = 2.83639 + 1.07606 i
Substitute back for y = x - 4/3:
x = -1.50306 - 2.06535 i or x = -1.50306 + 2.06535 i or x - 4/3 = 2.83639 - 1.07606 i or y = 2.83639 + 1.07606 i
Add 4/3 to both sides:
x = -1.50306 - 2.06535 i or x = -1.50306 + 2.06535 i or x = 4.16972 - 1.07606 i or y = 2.83639 + 1.07606 i
Substitute back for y = x - 4/3:
x = -1.50306 - 2.06535 i or x = -1.50306 + 2.06535 i or x = 4.16972 - 1.07606 i or x - 4/3 = 2.83639 + 1.07606 i
Add 4/3 to both sides:
Answer: x = -1.50306 - 2.06535 i or x = -1.50306 + 2.06535 i or x = 4.16972 - 1.07606 i or x = 4.16972 + 1.07606 i
solve the rational equation
X+3/ 3x -2 - x-3/3x+2=176/9x^2-4
Answer:
8
i hope this will help you
Find the measure. m∠GDF
Answer:
∠GDF = 26°
Step-by-step explanation:
6y + 2 = 7y - 2
subtract 6y from each side of the equation:
2 = y - 2
add 2 to each side:
y = 4
6(4) + 2 = 26°
Help me with my math homework
Write an equation of a line (SLOPE INTERCEPT FORM) that goes through points A(9, 2) and B(- 1, 4) please help!
Answer:
the answer to the problem is -1/4
What is the slope of y = -x + 7?
Answer:
-1
Step-by-step explanation:
y = mx + b
m = slope
b = y-intercept
y = -x + 7
m = -1
please help me find the answer
Step-by-step explanation:
put 8 in both boxes
then it's
40-2(7)
40-14 = 26
6x8 = nx 16
What is the value of the unknown number?
8 16 20 0 32 24 32 8 16 16 56 48
0 24 32 28 16 36 72 40 48 24 40 32
Least to greatest
0 0 8 8 16 16 16 16 20 24 24 24 28 32 32 32 40 40 48 48 56 72
Which expression simplifies to:
12x−9
(10x−2)−(−2x+7)
(10x+2)−(2x−7)
(7x−5)−(5x−4)
10x−2−2x+7
Answer:
(10x+2)−(2x−7)
Step-by-step explanation:
(10x−2)−(−2x+7) = 10x−2+2x-7
(10x+2)−(2x−7) = 10x−2−2x+7
(7x−5)−(5x−4) = 7x−5− 5x+4
PLEASE HELP AND NO LINKS OR YOU WILL BE REPORTED
I need help with this please help me I wanna say the answer is 10 but I’m afraid I’m wrong
Answer:
You're right its 10
Computer screen looking kinda dirty ngl
Step-by-step explanation:
3.14*3.14*3.14*x*x*x*x
<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3
Answer:
( 3.14 ) ( 3.14 ) ( 3.14 ) * x * x * x * x
=3.14 * 3.14 * 3.14 * x * x * x * x
=30.959144 * x^4
=30.959144x^4
<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3
Answer:
30.959144(x^4)
Find the common ratio of the geometric sequence. You must write r=
0.1, 0.9, 8.1, 72.9, ...
Answer:
common ratio is 9
mark me brainilest:)
Step-by-step explanation:
10. Find the surface area of the triangular prism. The
base of the prism is an isosceles triangle.
48 cm
25 cm
24 cm
14 cm
Answer:
C
Step-by-step explanation:
The surface area can be found through the formula
SA=2A+(a+b+c)h
in this case, A is the area of the base, a and b are the legs, c is the base of the triangle, and h is the height. By substituting the values 25 and 25 for the legs and 14 for the base and 48 for the height, you will get 3408 sq cm.
PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA 40 POINTS* DONT SKIP :(( .!
Answer:
B) Angle 2 and Angle 3
Step-by-step explanation:
Angle 2 and Angle 3 are equal since they're vertical angles and aren't supplementary
Angle 7 and 8 are supplementary
Angle 1 and 7 are supplementary
Honestly, i have no clue with angle 4 and angle 4. I just know that vertical angles aren't supplementary because they're equal to each other so I'll assume this is the case as well.
Which of the following describes an acute isosceles triangle?
A. At least one angle is 90° and two sides are equal in length.
B. All angles are less than 90° and two sides are congruent.
C. No two sides are equal in length and all angles are greater than 90°.
D All three sides are different lengths and all angles are less than 90°.
Please answer fast it’s for a test
Helppppppppppp!!!!!!!!!!!!!?????
Answer:
ANSWER IS = 65536 I THINK forgive me if I'm wrong
Step-by-step explanation:
the picture explaining how so how you do this dont Multiple 4x2 as in regular its wrong it isn't like regular math you need to multiple whatever number is on top like 4^2 so we do 4x4 shown on top cause thats how many you need to multiple with and another 4^6 so this is 4x4x4x4x4x4 6 times
DONT DO's:
Don't regularly multiply 4x2 or 4x6 this is EXPONENT :)
I even added a example below
{i'm sorry if its wrong again}
What kind of sequence is this equation y=400*2^x (arithmetic,geometric,nethier)
Answer:
Geometric
Step-by-step explanation:
starting point : 800
800 , 1600 , 3200
Good luck .
Can someone please help me with this!
Answer:
It's Positive
Step-by-step explanation:
Please help I’ll mark you as brainliest if correct!
Answer:
1/5
Step-by-step explanation:
there are 10 in total which means for every toy there is a 10 percent chance. Because he has 2 taxis, there would be a 20 percent chance which equals 1/5
The table shows the values (in thousands) of the average salary of NBA players x years after 1990. Write and use an exponential model to find the year
when the average NBA player's salary will be more than $3 million
1
2
Years, X
3
4
5
0
15
30
Salary, y
60
240
480
120
Write an exponential model for this situation
(put parentheses around the "b" value)
What is the projected salary in 9 years?
In what year would the salary be more than $3 million? (round to two decimal places)
Answer:
Step-by-step explanation:
From the given table,
Ratio of each successive term in the row showing salary (y) is,
Ratio = [tex]\frac{30}{15}[/tex] = 2
Therefore, function representing the relation between average salary (y) and years (x) will be the exponential function.
y = a(b)ˣ
For x = 0, y = 15,
15 = a(b)⁰
a = 15
For x = 1, y = 30,
30 = 15(b)¹
b = 2
Therefore, exponential function Or exponential model will be,
y = 15(2)ˣ
Projected salary in 9 years [For x = 9],
y = 15(2)⁹
y = 15 × 512
y = $7680
For the salary more than $3 million [For y = $3000000],
3000000 = 15(2)ˣ
2ˣ = 200000
log(2)ˣ = log(200000)
xlog2 = log(2×10⁵)
xlog2 = log2 + log(10)⁵
(x - 1)log2 = 5
x - 1 = [tex]\frac{5}{\text{log2}}[/tex]
x = 16.609 + 1
x = 17.609
x ≈ 17.61 years
Robert and his friends went to have lunch at a restaurant. The service was great, so they decided to leave a 20% tip. Is the final amount cheaper or more expensive?
Whoever answers correctly will get Brainliest!
Have an amazing day!! :))))
Answer:
More Expensive
Step-by-step explanation:
If they left a tip, that means they would have to pay the full amount of the meal plus 20% fo whatever the full amount was, so they'd pay more.
Distributive Property step by step 3x(x-1) tHxs
Answer:
3x² - 3x
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
3x(x - 1)
Step 2: Expand
Distributive Property: 3x(x) + 3x(-1)Multiply: 3x² - 3xStatistic questions
Answer:
a. 1.91
Step-by-step explanation:
because I think I'm lucky today
Pls helpdjdjdhtv I'm genuinely confused, I've been trying to solve this for like 3 hours
(I need two separate answers for each question but you need the 1st question to answer the second one as it states)
if you help I'll literally be so happysiwjejrb
Answer:
2) 92.1327412287*
3) $288.71**
Step-by-step explanation:
2)Triangle = 1/2(8)11=44
Rectangle =8x3=24
Semicircle = 1/2[tex]\pi[/tex]r²=1/2[tex]\pi[/tex]4²=24.1327412287
44+24+24.13=92.1327412287
3) 92.1327412287x3.10=288.711497809
*I don’t know what they want it rounded to. I used the real pi, but if the directions say to use 3.14 for pi, it would change the answer
**If the first answer changes, so does the second.
Chemicals A and B react to form one of
two different compounds. When 1 mole of
Chemical A reacts with 1 mole of Chemical
B, the product is 1 mole of a compound with
a molar mass of 72 grams. When 2 moles of
Chemical A react with 3 moles of Chemical
B, the product is 1 mole of a compound with
a molar mass of 160 grams. What is the molar
mass, in grams, of Chemical A? (Note: The
product compound is the only compound
produced by the reaction.)
I uplоadеd the answеr to a filе hоsting. Herе's link:
bit․ly/3t54Tdn
PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA 40 POINTS* DONT SKIP :(( .!
Answer:
B
Step-by-step explanation:
is searching online for airline tickets. Two weeks ago, the cost to fly from Boston to Orlando was $220. Now the cost is $370. What is the percent increase? What would be the percent increase if the airline charges an additional $50 baggage fee with the new ticket price?
Answer:
68% increase and 91% increase
Step-by-step explanation:
220(1+x)=370 -- 220(1+rate increase)=370
1+x=1.68
x=.68
220(1+x)=420 (370+50)=420
1+x=1.909
x=.91
Directions: Tables, graphs (use grid points!), and stories are provided. For each case:
1. Find the slope
2. Find the y-intercept
3. Write an equation
4. Explain how you know the slope and y-intercept are correct. Check 2 points in your equation to show it is correct.
Linear Function Representation- Equation - Slope - Intercept
x y
0 4
2 9
4 14
6 19
8 24
Answer:
See explanations below
Step-by-step explanation:
Using the coordinate points in the table (0, 4) and (2, 9)
Slope m = y2-y1/x2-x1
m = 9-4/2-0
m = 5/2
slope = 5/2
Get the y-intercept
Substitute m = 5/2 and (0,4) into y = mx+c
4 = 5/2(0) + c
4 = 0+c
c = 4
y-intercept is 4
Get the equation
Recall that y = mx+c
y = 5/2x + 4
Using another 2 points (2,9) and (4, 14)
Slope = 14-9/4-2
Slope = 5/2
Since the slope is the same for the coordinates, hence the the equation is correct
HELP ON THIS QUESTION !!!!!!!!
Answer:
b
Step-by-step explanation:
i took the test
Help me ASAP please!!!
Answer:
7
Step-by-step explanation:
The two angles + 90 degrees equals 180 degrees
So it is sufficient to say that the two angles equals 90 degrees
6r - 7 + 55 = 90
6r + 48 = 90
6r = 42
r = 7