Find a degree 3 polynomial with real coefficients having zeros 3 and 1 − 4i and a lead coefficient of 1. Write P in expanded form.
Answers
[tex]\text{Let,}\\\\~~~~~~~x=1-4i,\\\\\implies x-1 = -4i\\ \\\implies (x-1)^2 =(-4i)^2\\\\\implies x^2 -2x +1 = -16\\\\\implies x^2 -2x +1 +16 = 0\\\\\implies x^2 -2x +17=0\\\\\text{So,}~ x^2 -2x +17 ~\text{is a factor of the 3 degree polynomial.}\\ \\\text{The polynomial is,}\\\\P(x) = (x-3)(x^2 -2x +17)\\\\~~~~~~~=x^3-2x^2+17x -3x^2 +6x -51\\\\~~~~~~~=x^3 -5x^2 +23x -51[/tex]
Related Questions
Which real-world scenario involves a right triangle?
Answers
Answer:
There are a few different scenarios
Step-by-step explanation:
Bathroom Tiles,Kitchen flooringTriangle Backsplash ( tile behind your sink in kitchenDrywall work if you need right edges, you will need a right triangleFinally any sort of contracting and Deck workFROM- THE GENIUS ANSWERER
Which graph of f(x) satisfies the conditions Limit of f (x) as x approaches 2 minus = –4 and Limit of f (x) as x approaches 2 plus = 0? HURRY WILL GIVE BRAINLIEST FOR CORRECT ANSWER!!
Answers
The graph of f(x) that satisfies the condition of f(x)'s left sided limit at 2 being -4 and right sided limit at x = 2 being 0 is given by the first graph.
What is one-sided limit for function of single variable?In rough terminologies, the limit from one side is when we only use one side of the function with respect to the considered point of interest (in input) to predict the value of the function at that point.
For this case, we need to find the graph of the function f(x) from the considered 4 graphs for which:
[tex]\lim_{x\rightarrow 2^{-}}f(x) = -4\\\\\lim_{x\rightarrow 2^{+}}f(x) = 0\\[/tex]
For the first graph, for the point x=2, on left from the point x = 2 lies a ray. If thats the function, we can hope that the function will continue having the same line to the right too, so the prediction for value of function on x = 2 is the value that line gives for y.
That is -4.
Thus, prediction of function from left of x = 2 is -4, or
[tex]\lim_{x\rightarrow 2^{-}}f(x) = -4[/tex]
Similar to that, from the right of the point 2, there is some yellow curve. That predicts that the function's value at point x = 2 should be 0 (the yellow curve seems like touching the x-axis where y = 0 at the point x=2.
Thus, we have:
[tex]\lim_{x\rightarrow 2^{+}}f(x) = 0\\[/tex]
So graph first is correctly pertaining such function f(x).
Second graph when refered, we see that if we predict value at x =2 from left, the yellow curve in the left will make us predict that the function would be 0, so: [tex]\lim_{x\rightarrow 2^{-}}f(x) = 0[/tex]
Thus, its wrong graph.
Third graph when refered, we see that if we predict value at x =2 from left, the green line in the left will make us predict that the function would be -2 at x = 2 (see the green point in the third graph), so: [tex]\lim_{x\rightarrow 2^{-}}f(x) = -2[/tex]
Thus, its wrong graph.
Similarly, for the fourth graph, we see that if we predict value at x =2 from left, the yellow curve in the left will make us predict that the function would be 0, so: [tex]\lim_{x\rightarrow 2^{-}}f(x) = 0[/tex]
Thus, its wrong graph.
Thus, the graph of f(x) that satisfies the condition of f(x)'s left sided limit at 2 being -4 and right sided limit at x = 2 being 0 is given by the first graph.
Learn more about one-sided limits here:
https://brainly.com/question/23625942
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Answer:answer a
Step-by-step explanation: got right on edge 2023
please show your work, tysm :D
~giving brainliest!~
Answers
Answer:
1/16th
Step-by-step explanation:
You can write this problem as a function of time.
Let x be the amount of acetaminophen that you start off with.
Let n be the amount of 2.5 hour intervals that have passed
x*0.5^n
The reason this function works is because with each 2.5 hour interval, you multiply the total product by another 1/2.
Plugging in 4(because 4 2.5 hour intervals in 10 hours), you get:
x*0.5^4,
which is x/16.
This shows that 1/16th of the acetaminophen is left in the body after 10 hours.
Find the value of X.
Answers
Answer: 23
Step-by-step explanation:
3. The math exam scores for a class are shown below.
a
Make a data display. What percent of the scores are 90
and greater?
24, 68, 83, 75, 81, 99, 98, 80, 85, 70, 89, 92, 77, 96,
180, 64, 88, 96, 76, 88
Answers
Answer:
30 percent of the scores are 90 and greater
Which statement is true?
∞Σn=1 0.2(-3)^n-1 converges because r< 1.
∞Σn=1 0.2(-3)^n-1 diverges because |r| <1.
∞Σn=1 0.2(-3)^n-1 diverges because |r| > 1.
∞Σn=1 0.2(-3)^n-1 converges because r> 1.
Answers
The mode of the ratio of the sequence should be greater than one for the divergence. Then the correct option is C.
What are sequence and series?A series is a sum of sequence terms. That is, it is a list of numbers with adding operations between them.
We know that the condition of the converges of the series will be given as
[tex]\rm \Sigma ^{\infty}_{n=1} \ 0.2(-3)^{n-1}\ \ diverges \ because \ |r| > 1.[/tex]
The mode of the ratio of the sequence should be greater than one for the divergence.
More about the series link is given below.
https://brainly.com/question/10813422
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Answer: It’s C
Step-by-step explanation:
Find the greatest common factor of 8 and 24.
Answers
Answer:
8
Step-by-step explanation:
Factors of 8: 1, 2, 4, 8
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
They do share a few factors but the greatest one shared between the two is 8
Leila had 160 dollars to begin with. She just spent k dollars. Using k, write an expression for the number of dollars she has left.
Answers
Answer:
160 - k dollars
Step-by-step explanation:
Hello!
If Leila has 160 dollars and spends the amount k, then you are therefore subtracting k from 160. This is because you are using the value of k from 160.
So the expression would be 160 - k dollars
what is this number? 1,010,020,030,040,050,060,070,080,090,010,020,030,040,050,060,070,080,090,010,020,030,040,050,060,070,080,090,010,020,030,040,050 WILL MARK BRAINLIEST
Answers
Answer:
that isn't a number
Step-by-step explanation:
How to graph the equation y=-x^2+6x-5 on the accompanying set of axes?
Answers
Answer: See attached
Step-by-step explanation:
Given:
y = -x² + 6x - 5
Since this is a quadratic function, we will have a parabola.
Because our x² value is negative, this parabola will be a "frowny face" instead of a "smiley face" like the parent function.
The - 5 means we shift the function 5 units to the right from the parent function.
See attached for our graph.
What parent function am I mentioning?
The parent function of y = -x² + 6x - 5 is y = x²
which is more likely to have a mass close to 3 kilograms small feather a five year old cat or a grown elephant or a peach. dont delete this question dbs at brainly (dbs = drag on balls)
Answers
Answer:
5 year old cat
Step-by-step explanation:
because a kg is about a pineapple
1
N
3
5
6
B
10
56:0
What is the range of the function on the graph?
5
14
O all real numbers
O all real numbers less than or equal to -1
all real numbers less than or equal to 3
© all real numbers less than or equal to 0
-5-4-3-2-14
1 2 3 4 5 X
I
-2
-3
-4
-5
Answers
Answer:
pack you
pa brainliwa po
50 points+ Brainliest PLEASE SHOW WORK!!!!
(i can only give brainliest if at least 2 people answer)
Answers
Answer:
here
Step-by-step explanation:
we can do it by using the formula like
mean; efx÷n
median =n+1÷2
mode =which is more
range=highest-smallest
Answer:
Step-by-stwe can do it by using the formula like
mean; efx÷n
median =n+1÷2
mode =which is more
range=highest-smallestep explanation:
Solve the system of equations.
Answers
Answer:
3x+2y=24
Y=3
Substitute in the equation
3x+2(3)=24
3x+6=24
3x=24-6
3x=18
X=18/3
X=6
Which expression is equivalent to 2(5z+3)?
Answers
Answer:
D
Step-by-step explanation:
That expression equals :
10z+6
So, now we need to find one of the expressions that ALSO gives us 10z+6
D
This is because:
2*3z=6z
2*2z=4z
----------------------
6z+4z=10z, so we got that one so far.
NEXT
2*3=6.
We got the 6 too!
it is d
Hi can someone help me pls
Answers
Answer:
f(x) = 45x + 5
Step-by-step explanation:
The parking fee for a minibus at an event is $5 entering the parking lot. There is an extra charge of $45 per passenger.
The formula that simulates the parking fee for this sentence is
f(x) = 45x + 5
This is because 45x represents the charge per passenger and we are using addition because the $5 minibus parking fee; to enter the parking lot - increases the total cost of the parking fee.
Sketch advertising firm charges $150 to design a full-color flyer and 12 cents per flyer to print the flyer. Rose's Sweet Shop spent $192 on the flyers for the grand opening. How many Flyers did she buy?
Answers
Answer:
210
Step-by-step explanation:
First, we keep $150 on the back of our minds(or our paper).
Second, we would assume that Rose's would've designed the flyer at $150, making us determine how much flyers they bought for the remaining $42.
($192 - $150 = $42)
Now that we know all of this, we can begin.
12 x 5 is 60, so 60 cents makes 1 dollar.
So for every dollar, they can make 5 flyers.
If we do 5 x 42, we'll get the answer of 210, which is the amount of flyers she bought!
Which choice is the solution to the inequality below?
8x < 24
O A. x< 24
O B. x> 24
C. x>3
O D. x<3
Answers
Answer:
D
Step-by-step explanation:
8x < 24
divide both sides by the coefficient of x
8x/8 < 24/8
x < 3
How many times larger is 8 x 10^9 than 4 x 10^3
Answers
Answer:
600
Step-by-step explanation:
10x9 =90
10x3=30
8x90=720
4x30=120
720-120= 600
What is the area of this trapezoid?
Answers
Answer:
The area is [tex]80[/tex]
Step-by-step explanation:
rectangle in the middle; 24
both triangles on the side; 56
In total; 80
0.7 is equivalent to what fraction
Answers
Answer:
7/10
Step-by-step explanation:
Fractional form of 0.7 is 7/10.
[tex] \tt(6x4−2x3 +7x2 −x) + ( 7x4+ 2x3−5x + 7)[/tex]
[tex] \\ [/tex]
With Solution!!
Answers
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's solve ~
[tex]\qquad \tt \dashrightarrow \:\tt(6x {}^{4} −2x {}^{3} +7x {}^{2} −x) + ( 7x {}^{4} + 2x {}^{3} −5x + 7)[/tex]
[tex]\qquad \tt \dashrightarrow \:\tt6x {}^{4} −2x {}^{3} +7x {}^{2} −x + 7x {}^{4} + 2x {}^{3} −5x + 7[/tex]
Now, move all like terms aside :
[tex]\qquad \tt \dashrightarrow \:6 {x}^{4} + 7 {}x^{4} - 2 {x}^{3} + 2 {x}^{3} + 7 {x}^{2} - x - 5x + 7[/tex]
Add the like terms ~
[tex]\qquad \tt \dashrightarrow \:13 {}x^{4} + 7 {x}^{2} + 6x + 7[/tex]
Answer:
13(x)⁴ + 7(x)²-6(x) + 7
Explanation:
[tex]\hookrightarrow \sf (6x^4 -2x^3+7x^2-x)+(7x^4+2x^3-5x+7)[/tex]
remove the parenthesis
[tex]\sf \hookrightarrow 6x^4-2x^3+7x^2-x+7x^4+2x^3-5x+7[/tex]
group the variables
[tex]\hookrightarrow \sf 6x^4+7x^4-2x^3+2x^3+7x^2-x-5x+7[/tex]
add similar terms
[tex]\sf \hookrightarrow 13x^4+7x^2-x-5x+7[/tex]
simplify
[tex]\hookrightarrow \sf 13x^4+7x^2-6x+7[/tex]
Segment AB has point A located at (6, 5). If the distance from A to B is 5 units, which of the following could be used to calculate the coordinates for point B? 5 = square root of the quantity of x minus 6 all squared plus y minus 5 all squared 5 = square root of the quantity of x minus 5 all squared plus y minus 6 all squared 5 = square root of the quantity of x plus 6 all squared plus y plus 5 all squared 5 = square root of the quantity of x plus 5 all squared plus y plus 6 all squared
Answers
The distance of segment AB is the number of units on the segment
The equation that can be used to determine the coordinates of point B is [tex]5 = \sqrt{(x -6)^2 + (y - 5)^2}[/tex]
How to determine the equation?The given parameters are:
A = (6,5)AB = 5 unitsThe distance AB is calculated using:
[tex]AB = \sqrt{(x_2 -x_1)^2 + (y_2 - y_1)^2}[/tex]
This gives
[tex]5 = \sqrt{(x -6)^2 + (y - 5)^2}[/tex]
Hence, the equation that can be used to determine the coordinates of point B is [tex]5 = \sqrt{(x -6)^2 + (y - 5)^2}[/tex]
Read more about distance equations at:
https://brainly.com/question/7243416
Answer:
√(x-6)² + (y-5)²
Step-by-step explanation:
The Distance Formula is √(x2 - x1)² + (y2 - y1)²
If you plug in the known values, you get √(x - 6)² + (y - 5)²
This is our answer.
Look at this rectangle. Find the value of u.
Answers
Answer:
1 inch
Step-by-step explanation:
We know that opposite sides of a rectangle are equal to each other.
Given that,
Perimeter = 30 in
Therefore,
u + u + 14 + 14 = 30
2u + 28 = 30
2u = 30 - 28
2u = 2
Divide both sides by 2.
u = 1 in
Pick one A,b,c,d,e will give brainlest
Answers
Answer:
E (simalr to the other one you posted)
Step-by-step explanation:
Denominator cannot equal 0 so domain (x values) cannot include 2
range: all numbers, buthere is no way to make a 0
i would really like some help, factoring trinomials if you want an extra 50-100 points you could help with a previous question on my profile lol
Answers
Answer:
[tex]g) \left(5x-2\right)\left(3x+2\right)[/tex]
[tex]h)2\left(8a-9\right)\left(a-2\right)[/tex]
[tex]i)3\left(21n^2+42n+16\right)[/tex]
Step-by-step explanation:
Starting with g) [tex]15^2+4x-4[/tex]
Break the expression into group
[tex]=\left(15x^2-6x\right)+\left(10x-4\right)[/tex]
Now, Factor out [tex]3x[/tex] from [tex]15x^2-6x[/tex] which is now is [tex]3x(5x-2)[/tex]
Next, Facotr out [tex]2[/tex] from [tex]10x-4[/tex] which is now is [tex]2(5x-2)[/tex]
Thus,
[tex]=3x\left(5x-2\right)+2\left(5x-2\right)[/tex]
Factor common term 5x -2
[tex]\left(5x-2\right)\left(3x+2\right)[/tex]
-------------------------------------------------------------------------------------------------------------
Next we have [tex]h)16a^2-50a+36[/tex]
Factor out common term thus we have [tex]2(8a^2-25a+18)[/tex]
Factor again: [tex]8a^2-25a+18[/tex] now turn into [tex](8a-9)(a-2)[/tex]
[tex]=2\left(8a-9\right)\left(a-2\right)[/tex]
-------------------------------------------------------------------------------------------------------------
Lastly we have [tex]i)63n^2+126n+48[/tex]
Rewrite the following:
63 as 3 * 21
126 as 2 * 42
48 as 3 * 16
[tex]63n^2+126n+48[/tex]
Now cut out common term:
[tex]=3\left(21n^2+42n+16\right)[/tex]
-------------------------------------------------------------------------------------------------------------
~lenvy~
Answer:
(g) [tex](5x-2)(3x+2)[/tex]
(h) [tex](16a-18)(a-2)[/tex]
(i) [tex]3(21n^2+42n+16)[/tex]
Step-by-step explanation:
To factor a quadratic in the form [tex]ax^2+bx+c[/tex]
Find 2 two numbers ([tex]d[/tex] and [tex]e[/tex]) that multiply to [tex]ac[/tex] and sum to [tex]b[/tex]Rewrite [tex]b[/tex] as the sum of these 2 numbers: [tex]d + e = b[/tex]Factorize the first two terms and the last two terms separately, then factor out the comment term.Question (g)
[tex]15x^2+4x-4[/tex]
[tex]\implies ac=15 \cdot -4=-60[/tex]
[tex]\implies d+e=4[/tex]
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Therefore, the two numbers (d and e) that multiply to -60 and sum to 4 are:
10 and -6
Rewrite [tex]4x[/tex] as [tex]+10x-6x[/tex]:
[tex]\implies 15x^2+10x-6x-4[/tex]
Factories first two terms and last two terms separately:
[tex]\implies 5x(3x+2)-2(3x+2)[/tex]
Factor out common term [tex](3x+2)[/tex]:
[tex]\implies (5x-2)(3x+2)[/tex]
Question (h)
[tex]16a^2-50a+36[/tex]
[tex]\implies ac=16 \cdot 36=576[/tex]
[tex]\implies d+e=-50[/tex]
Factors of 576: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 144, 192, 288, 576
Therefore, the two numbers that multiply to 576 and sum to -50 are:
-32 and -18
Rewrite [tex]-50a[/tex] as [tex]-32a-18a[/tex]:
[tex]\implies 16a^2-32a-18a+36[/tex]
Factories first two terms and last two terms separately:
[tex]\implies 16a(a-2)-18(a-2)[/tex]
Factor out common term [tex](a-2)[/tex]:
[tex]\implies (16a-18)(a-2)[/tex]
Question (i)
[tex]63n^2+126n+48[/tex]
Factor out common term 3:
[tex]\implies 3(21n^2+42n+16)[/tex]
This cannot be factored any further.
what is the answer 2⅓+⅚
Answers
Answer:
3 1/6
Step-by-step explanation:
2+1/3+5/6
(1/3=2/6)
so 3/6+5/6 = 7/6
-15 divided by -1 2/3
Answers
Answer:
9
Step-by-step explanation:
15 / 5/3 = 15 x 3/5=9
Because a negative numebr divided by a negative number is always positive.
Answer:
9
Step-by-step explanation:
6 Jenny is y2 years old and her daughter Allyson is y years old, If Jenny lives to the age of 13y,
Allyson will be y years old. How old is Allyson now? (Note: the difference in ages must
remain constant.)
Answers
Answer:
Allison is 7 years now, Jenny is 49 yeas now. Check. 13y = 13*7 = 91 will happen in 91-49 = 42 years. Jenny will be 7 + 42 = 49 years old at that time.
Step-by-step explanation:
What formula can we use to find the surface area of a rectangular prism?
Answers
Answer:
○ [tex]\displaystyle SA = 2lw + 2lh + 2wh[/tex]
Explanation:
A rectangle has four right angles, including two pairs of congruent edges, only containing two dimensions – height and length. Therefore, going three-dimensional, a rectangular prism has three dimensions – width, height, length. With this information, you should know what the answer is.
I am joyous to assist you at any time.