Answer:
f(x) = x³ - 6x² + 10x - 8
Step-by-step explanation:
Complex zeros occur as conjugate pairs, thus
Given x = 1 - i is a zero then x = 1 + i is also a zero
Given the zeros are
x = 4, x = 1 - i, x = 1 + i then the corresponding factors are
(x - 4), (x - (1 - i) ), (x - (1 + i ) ), that is
(x + 4), ( x - 1 + i), (x - 1 - i)
f(x) is then the product of the factors, that is
f(x) = (x - 4)((x - 1) + i)((x - 1) - i ) ← distribute the complex factors
= (x - 4)((x - 1)² - i² ) → i² = - 1
= (x - 4)(x² - 2x + 1 + 1)
= (x - 4)(x² - 2x + 2) ← distribute
= x³ - 2x² + 2x - 4x² + 8x - 8 ← collect like term
f(x) = x³ - 6x² + 10x - 8
The required polynomial is f(x) = x³ - 6x² + 10x - 8 which has a degree is 3 with real coefficients.
What is a polynomial?A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers.
The required polynomial F(x) of degree 3 with real coefficients and the following zeros. 4, 1-i
This means i.e.
x = 4, x = 1 - i, and x = 1 + i
As per the fundamental of algebra, the corresponding factors are (x - 4), (x - (1 - i) ), (x - (1 + i ) ),
The factors are (x + 4), ( x - 1 + i), and (x - 1 - i)
If the above corresponding factors are multiplied then we can find f(x)
f(x) = (x - 4)((x - 1) + i)((x - 1) - i )
f(x) = (x - 4)((x - 1)² - i² ) → i² = - 1
f(x) = (x - 4)(x² - 2x + 1 + 1)
f(x) = (x - 4)(x² - 2x + 2)
f(x) = x³ - 2x² + 2x - 4x² + 8x - 8
f(x) = x³ - 6x² + 10x - 8
Thus, the required polynomial is f(x) = x³ - 6x² + 10x - 8.
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Multiply the polynomials. (x2 – 4) (x2 + 3x – 5)
Answer:
[tex] \boxed{ \bold{ \boxed{ \sf{ {x}^{4} + 3 {x}^{3} - 9 {x}^{2} - 12x + 20}}}}[/tex]
Step-by-step explanation:
[tex] \sf{( {x}^{2} - 4)( {x}^{2} + 3x - 5)}[/tex]
Use distributive property
[tex] \dashrightarrow{ \sf{ {x}^{2} ( {x}^{2} + 3x - 5) - 4( {x}^{2} + 3x - 5)}}[/tex]
[tex] \dashrightarrow{ \sf{ {x}^{4} + 3 {x}^{3} - 5 {x}^{2} - 4 {x}^{2} - 12x + 20}}[/tex]
Collect like terms
[tex] \dashrightarrow{ \sf{ {x}^{4} +3 {x}^{3} - 9 {x}^{2} - 12x + 20}}[/tex]
Hope I helped!
Best regards! :D
The quotient of 24 and x equals 14 minus 2 times x
Answer:
x = 3, x = 4
Step-by-step explanation:
Given
[tex]\frac{24}{x}[/tex] = 14 - 2x ( multiply through by x , x ≠ 0 )
24 = 14x - 2x² ( subtract 14x - 2x² from both sides )
2x² - 14x + 24 = 0 ( divide through by 2 )
x² - 7x + 12 = 0 ← in standard form
(x - 3)(x - 4) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 3 = 0 ⇒ x = 3
x - 4 = 0 ⇒ x = 4
which of the following is the solution to the equation
What is the inverse of y = 2x - 1?
Answer:
Step-by-step explanation:
y = 2x - 1
x = 2y - 1
2y - 1 = x
2y = x + 1
y = x/2 + 1/2
8 times of the eight term of an arithmetic progression is equal to 12 times of the twelfth term. find its first term if the common difference is -2 .
Answer:
38
Step-by-step explanation:
We can express the 8th term as x and the 12th term as y.
This would mean that 8x=12y
Because the common difference between terms is -2 and term 8 and term 12 are 4 terms apart, this means that the 12th term is 8 less than the 8th term, so x-8=y
Now we can use this to substitute y with x in the first equation. This would give us:
8x=12(x-8)
Which we can expand and solve:
8x=12x-96
-4x=-96
Therefore x=24
This means the 8th term is 24 and the 12th term is 16 (24-8).
To test if this is correct we can do:
8x24=12x16
Which indeed are equal, both sides multiply to 192.
Now that we have our 8th term, we can find the 1st term, which is 7 terms away, therefore we just add 14 to the 8th term 24. (7x2=14)
24+14=38.
The first term is 38.
Hope this helped!
Help please don’t get it help!!!!!!!
Answer:
10,542,719
Step-by-step explanation:
The circle chart shows you that an estimated 49% of Australia's population has type O blood. Then the number expected to have type O blood is ...
0.49 × 21,515,754 ≈ 10,542,719
_____
You can choose the correct answer by recognizing that 49% is very slightly less than 1/2, so the number with type O blood will be very slightly less than half of 21 million -- about 10.5 million.
Find the area of a circle that has a radius of 9 mm. Use 3.14 for .
-56.52 mm 2
-28.26 mm 2
-254.34 mm 2
-63.59 mm2
Answer:254.34 mm2
Step-by-step explanation:
Please help me solve this thanks
Answer:
A
Step-by-step explanation:
let r represent rate and d distance.
Given that r varies directly as d² then the equation relating them is
r = kd² ← k is the constant of variation
To find k use the condition r = 4 when d = 15, then
4 = k × 15² = 225k ( divide both sides by 225 )
k = [tex]\frac{4}{225}[/tex]
r = [tex]\frac{4}{225}[/tex] d² ← equation of variation
When r = 9, then
9 = [tex]\frac{4}{225}[/tex]d² ( multiply both sides by 225 )
2025 = 4d² ( divide both sides by 4 )
506.25 = d² ( take the square root of both sides )
d = [tex]\sqrt{506.25}[/tex] = 22.5 = 22 [tex]\frac{1}{2}[/tex] → A
Which function describes this table of values?
Answer:
y = 4/5x
Step-by-step explanation:
We know it's not y = x - 2 because if you plug x into the equation, it works for the first one, but not the second one. Ex: 10 - 2 = 8 but 5 - 2 = 3 not 4.
We also know that it can't be y = -5/4x because if you plug x into that equation, it does not equal y.
y = 4/5x because when you plug x into the equation it works.
TLDR basically you just plug x into the equations.
HELP PLEASE ASYMPTOTES
Answer:
d
Step-by-step explanation:
As x → + ∞, y → + ∞, as x → - ∞, y → - ∞
This means as x increases to the right, y increases upwards (+ ∞ ) and as x increases to the left, y increases downwards (- ∞ )
1 and 2 are examples but I still need help , I don’t understand n this is due today
Answer:
A rational number is a number that can be express as the ratio of two integers. A number that cannot be expressed that way is irrational. ... However, numbers like √2 are irrational because it is impossible to express √2 as a ratio of two integers.
The perfect squares are the squares of the whole numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 … Here are the square roots of all the perfect squares from 1 to 100. 1.
What is the opposite and absolute value of -7?
Answer:
The opposite and absolute of -7 is 7
Step-by-step explanation:
-7 is 7 digits away from 0
What percent is represented by the shaded area?
Answer:
1.91%
Step-by-step explanation:
What value of x would result in the numerical value of zero in the expression 7+x+(−10) ?
Answer:
3
Step-by-step explanation:
7 plus three is 10, adding -10 to that equals zero.
The value of x would result in the numerical value of zero in the expression 7+x+(−10) is 3.
Based on the information given, we simply have to find the value of x. Therefore, the value of x from the equation will be:
7 + x + (-10) = 0
Collect like terms
x = 10 - 7
x = 3
Therefore, the value of x would result in the numerical value of zero in the expression 7+x+(−10) will be 3.
Read related link on:
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-36=9a-63 slove for a
A delivery person uses a service elevator to bring boxes of books up to an office. The delivery person weighs 150lb and each box of books weighs 40lb. The maximum capacity of the elevator is 1140lb. How many boxes of books can the delivery person bring up at one time?
Answer:
24
Step-by-step explanation:
The delivery person can take 24 boxes of books up the elevator at one time. This was my process:
(1140-150) / 40
990 / 40
24.75
But you cannot have three quarters of a box so the final answer would be 24.
Whats 855000 in scientific notation?
Answer:
8.55x10^5 in scientific notation
Answer:
8.55 × 10^5
Step-by-step explanation:
855000 = 855 × 10³
8.55 × 10² × 10³
8.55 × 10²+³
8.55 × 10^5
Find the coordinates for the vertex of the graph of the function y = 3x² – 12x+12.
A (-2, 48)
B. (0, 2)
C. (-2, 0)
D. (2,0)
Point H is on line segment G I ‾ GI . Given G H = 12 GH=12 and G I = 17 , GI=17, determine the length H I ‾ . HI
Answer:
HI = 5 units
Step-by-step explanation:
We are given that:
Line segment GI has a point H on it such that the dimensions are given as:
GH = 12 units
GI = 17 units
To find:
Length of HI = ?
Solution:
As we are given that GI is a line segment that means GI is a straight line.
H is a point that lies on GI.
Kindly refer to the attached image for the given dimensions and given line.
Property of a straight line states that:
If there is a point that lies on the straight line segment that will divide the line in two parts such that the sum of length of two parts will be equal to the length of the line segment.
i.e.
GI = GH + HI
17 = 12 + HI
HI = 17 - 12 = 5 units
A music company sells CDs for a particular artist. The company has advertising cost of $4,000 and recoding costs of $10,000; Their cost for manufacturing, royalties, and distribution are $5.50 per CD. They sell the CDs to Mage-Mart for $7.20 each
Answer:
First, let's write all the costs:
$4,000 in advertising.
$10,000 in the recording.
$5,50 per cd.
Then we have that the cost will be:
C(x) = $4,000 + $10,000 + $5.50*x
where x is the number of CDs distributed.
C(x) = $5.50*x + $14,000.
Now, they win $7.20 per cd, so the tota wins are:
W(x) = $7.20*x
The profit will be the difference between the total win and the cost:
p(x) = $7,20*x - $5.50*x - $14,000 = $1.7*x - $14,000
Now with this function, we can calculate the number of CDs that the company needs to sell in order to break even, that is when the profit is exactly zero.
P(x) = $0 = $1.7*x - $14,000
$1.7*x = $14,000
x = $14,000/$1.7 = 8,235.3 CDs, that we should round up to 8,236.
This means that the company must sell more than 8,236 if they want to have a positive profit.
The set of all points in a plane that are equidistant from two points is a(n): A. point B. line c. ray O D. angle
Answer:
Line
Step-by-step explanation:
Answer:line
Step-by-step explanation:
1. Benito embroiders and sells T-shirts. The graph
shows his profit as a function of the number
of shirts sold. After selling a certain number of
shirts, Benito uses some earnings to buy more
materials and then increases the price of the
shirts. Which of the following is true?
A )Benito increases the price after selling 50 shirts.
B)The y-intercept represents the cost of one
T-shirt.
C)The x-intercept represents the shirts he has to sell before making a profit.
D)The domain of the function is {x|x is a real number greater than or equal to 0).
Answer:
D
Step-by-step explanation:
Answer:
c.
Step-by-step explanation:
3(x+6)+2x-5=-2(x+1)+10
Step-by-step explanation:
3x+18+2x-5= -2x+-2+10
combining like terms
3x+2x+2x=5-2+10-18
7x=-5
x=-5/7
Riley is playing a game that requires rolling a number cube 1-6 ans spinning a spinner with 3 consonants and 1 vowel. The sections of the spinner are all the same size. What is the probability that Riley rolls a number less than 3 and lands on a consonants. 1. 1/12 2. 3/8 3. 1/8 4. 1/8 Answer now to get 10 points!!!
Work Shown:
The outcomes of the cube are {1,2,3,4,5,6}. The outcomes less than 3 are {1,2}. We have 2 outcomes we want out of 6 total, so the probability of getting an outcome less than 3 is 2/6 = 1/3.
The probability of landing on a consonant is 3/4 because there are 3 consonants and 3+1 = 4 letters total
Multiply the two probabilities: (1/3)*(3/4) = (1*3)/(3*4) = 1/4
The probability of getting a dice roll less than 3, and getting a consonant on the spinner, is 1/4.
Using it's concept, it is found that the probability that Riley rolls a number less than 3 and lands on a consonants is given by: [tex]\frac{1}{4}[/tex].
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem:
For the number cube, 2 out of the 6 numbers are less than 3, hence P(A) = 2/6 = 1/3.For the spinner, 3 out of the 4 sections are consonants, hence P(B) = 3/4.The events are independent, hence the probability of both is given by:
P(A and B) = P(A) x P(B) = 1/3 x 3/4 = 1/4.
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Which set of ordered pairs represents y as a function of X?
A {(1,5), (3, 1), (2,7), (1,8)}
B {(8,2), (4,3), (7,2), (8, 6)}
C {(6,3), (3, 5), (2,5), (9,6)}
D {(4,7), (4, 6), (4,4), (4,1)}
Answer:
C
because any of the x-coordinates are repeated than its not a function..
Danny wants to sell his house. He would like to receive $136,000 after deducting the 6% commission due to the real estate agent. What should the selling price for the house be to the nearest dollar?
Answer:
The selling price of the house is $144,681
Step-by-step explanation:
The computation of the selling price of the house is shown below:
Let us assume the selling price be x
So, the commission would be 0.06x
Now the danny would received
= x - 0.06x
= 0.94x
And, the amount received is $136,000
So equate this value
Like this
0.94x = $136,000
x = [tex]\frac{\$134,000}{0.94}[/tex]
= $144,681
Hence, the selling price of the house is $144,681
Which of the following transformations will not produce a congruent image?
A.
rotation
B.
translation
C.
dilation
D.
reflection
Answer:
Translation, rotation and reflection
Step-by-step explanation:
please brainliest <3
Ron is playing a board game. His game piece is currently on space number 11 on the board. When Ron takes his turn he draws a care that instructs him to move backward 7 spaces. On his following turn he draws a card that instructs him to move forward 7 spaces. Where is Ron’a piece on the board after his turn?
WILL GIVE BRANLIEST ANSWER ASAP
Find the intersection of the two sets.
{2,3,4,5,7} n{2,4, 6, 8, 10}
{2,4, 10)
{2,4}
{2,3,4,5,6,7,8, 10)
Answer:
{2, 4}
Step-by-step explanation:
Intersection of given sets would be {2,4}.
Answer:
C) {2,4}
Step-by-step explanation:
C) {2,4}
The union would be all of them. The intersection are the ones they have in common.
help please thank you
Answer:
a) n/4 - 8
Step-by-step explanation:
A quotient is an answer to a division equation, in this case, is n/4