A fifth-degree polynomial equation with rational coefficients has the roots 3, 8i, and 7- radical 5. Which are also roots of the polynomial equation?
Answers
Using complex numbers and radicals, it is found that the correct option is C.
When a complex number is a root of a polynomial function, it's conjugate also has to be.
Hence, since 8i is a root of the function, -8i is also a root.The same is valid for radicals, as they are in the [tex]\pm[/tex] format.
Since [tex]7 - \sqrt{5}[/tex] is a root, [tex]7 + \sqrt{5}[/tex] is also a root.Hence, option C is correct.
For more on complex numbers and radicals, you can check https://brainly.com/question/25173944
Related Questions
Simply the expression. Write your answer as a power
8^9/8^7
The simplified expression is
Answers
8^9/8^7
9-7=2
8^2
PLS HELP!!! i can’t figure out this problem!!!
Answers
Answer:
7/9
Step-by-step explanation:
Evaluate the expression at x=8-. You can see from the graph that p(8-) = 3.
[tex]\displaystyle \lim_{x\to8^-}{\frac{3p(x)-2x}{15-3x}}=\frac{3(3)-2(8)}{15-3(8)}=\frac{-7}{-9}=\boxed{\frac{7}{9}}[/tex]
Add the polynomials: x2 + 2x + 1 and y2 + 2x + 3.
Answers
Therefore, the above answer is correct.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
Adding both of the polynomial equations we get [tex]x^2+y^2+4x+4[/tex].
What is a polynomial equation?A polynomial equation exists an equation where a polynomial exists set equivalent to zero. i.e., it exists an equation constructed with variables, non-negative integer exponents, and coefficients together with operations and an equal sign. It includes different exponents. The highest one demonstrates the degree of the equation.
Given: [tex]x^2 + 2x + 1[/tex] and [tex]y^2 + 2x + 3.[/tex]
Adding both of these two equations, then we get
[tex]x^2+2x+1+y^2+2x+3[/tex]
Group like terms
[tex]=x^2+y^2+2x+2x+3+1[/tex]
Add similar elements [tex]x^2+y^2+4x+4[/tex]
Adding both of the polynomial equations we get [tex]x^2+y^2+4x+4[/tex].
Therefore, the correct answer is [tex]x^2+y^2+4x+4[/tex].
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This scatter plot shows the number of baskets made and the time in minutes that has passed.
Based on the information in the scatter plot, what is the best prediction for the number of baskets made in 16 minutes?
4 baskets
7 baskets
14 baskets
20 baskets
Answers
Scatter plots are used to relate variables using scattered dots.
The best prediction for the number of baskets made in 16 minutes is (c) 14 baskets
From the graph, we can see that the number of baskets made in 14 minutes is 12.
Also, from the graph; as the minutes increases, the number of baskets either remain the same or increases.
This means that, for 16 minutes, the number of baskets would either be 12 (same as 14 minutes) or greater.
The closest to 12 baskets in the option is 14.
Hence, the best prediction for the number of baskets made in 16 minutes is (c) 14 baskets
Read more about scatter plots at:
https://brainly.com/question/6592115
38. In a certain school, 45% of the students are boys. 80% of the boys have brown hair while 50% of those with brown hair
are girls. What is the probability that a randomly selected girl does NOT have brown hair?
A) .19
B) .36
C) 55
D) .35
E) none of the above are correct
Answers
The probability that a randomly selected girl does not have brown hair is 34.54%.
Given that in a certain school, 45% of the students are boys, and 80% of the boys have brown hair while 50% of those with brown hair are girls, to determine what is the probability that a randomly selected girl does NOT have brown hair, the following calculation must be performed:
45 x 0.80 = 36% of the school are brown hair boys 36% of the school are brown hair girls 55 - 36 = 55 = 100 19 = X 19 x 100/55 = X 1900/55 = X 34.54 = X
Therefore, the probability that a randomly selected girl does not have brown hair is 34.54%.
Learn more about maths in https://brainly.com/question/25862092
Ajay is going to invest his money into 2 different stocks. Both stocks are independent, and each stock has a 50%
chance of being successful and a 50% chance of failing.
Each stock will make Ajay $500 if it succeeds or lose him $500 if it fails.
If X is a random variable that represents Ajay's profit from investing in these 2 stocks, drag the bars to graph
the probability distribution for all possible values of X.
Answers
The bar graph represents the value of Profit (X) for the different probabilities of stocks x and y.
It can be drawn as follows.
Let x and y denote the two stocks .
The probability of success of x is p=50%= 50/100=1/2 = 0.5
The probability of failure of x is q= 50%= 50/100= 1/2= 0.5
Similarly
The probability of success of y is p=50%= 50/100=1/2 = 0.5
The probability of failure of y is q= 50%= 50/100= 1/2= 0.5
Then their joint distribution can be calculated from the following table.
x 0.5 0.5 h(y)
y
0.5 0.25 0.25 0.5
0.5 0.25 0.25 0.5
g(x) 0.5 0.5 1.0
It is evident from the data that x and y have the same probability at each point when both x and y are at
successfailuresuccess and failurefailure and successBut the random variable X will have different values for
both success = $500+ $500= $ 1000 both failure = -$500+ -$500= $- 1000success and failure = $500+ $-500= $0failure and success = $-500+ $500= $ 0For the bar graph click
https://brainly.com/question/25196929
https://brainly.com/question/25718527
The bar graph will appear as follows.
Answer:
Step-by-step explanation:
Pls Help! Which graph A,B or C?
Answers
Answer:
Answer=C
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
Parallel lines hAve no solutions
Option A omittedTwo lines intersection point gives one solution only
Option B omittedOne single line denotes to infinite solutions
Option C is correct
Converting 60 minutes to seconds gives you how many seconds
Answers
Answer:
3600 seconds
Step-by-step explanation:
where is it located on the number line
Answers
move it 0.25 units right
Hep I’ll choose brainliest!!
Answers
Answer:
7
Step-by-step explanation:
3x - y = 1
2x + 2y = 14
x = 2
y = 5
x + y = 2 + 5 = 7
7. Reesa's sister is a salesperson at Old Navy.
a. Reesa's sister earns $15 per hour. The store
offers her a raise-a 6% increase per hour.
After the raise, how much will Reesa's sister
make per hour?
HELP
Answers
Answer: 24$
Step-by-step explanation:
help please! a is wrong, that was my initial answer.
Answers
Answer:
D -1
Step-by-step explanation:
[tex]-6(3a+4)=3a-3[/tex]
[tex]-18a-24=3a-3[/tex]
[tex]-18a-3a=-3+24[/tex]
[tex]-21a=21[/tex]
a = [tex]\frac{21}{-21} =-1[/tex]
Hope this helps
Graph the line y= 2/3x +1
Answers
Step-by-step explanation:
Given the linear equation, y = ⅔x + 1, where the slope, m = ⅔, and the y-intercept, (0, 1) where b = 1.
Start at the y-intercept:In order to graph the given linear equation, start by plotting the coordinates of the y-intercept, (0, 1). As we know, the y-intercept is the point on the graph where it crosses the y-axis. It coordinates are (0, b), for which the value of b represents the value of the y-intercept in slope-intercept form, y = mx + b.
Plot other points using the slope:From the y-intercept, (0, 1), we must use the slope, m = ⅔ (rise 2, run 3) to plot the other points on the graph. Continue the process until you have sufficient amount of plotted points on the graph that you could connect a line with.
Attached is a screenshot of the graphed linear equestion, which demonstrates how I plotted the other points on the graph using the "rise/run" techniques" discussed in the previous section of this post.
[tex]\huge\boxed{Hello,\:hope\:you\:are\:having\:a\:wonderful\:day.}[/tex]We are asked to graph the line y=2/3x+1.
2/3 is the slope of this line (Rise/Run)
The rise is how many units we move up; the run is how many units we move left or right.
For this line, 2 is the rise, and 3 is the run.
Now, 1 is the y-intercept. (where the graph touches the y-axis)
First, plot this point: (0,1)
Then, move 2 units up and 3 to the left (Up 2, over 3, up 2, over 3)
When you have a line, take a ruler and connect these points, and you will have the graph of y=2/3x+1.
[tex]\huge\bold{Hope\:it\:helps!}[/tex]
[tex]\huge\mathfrak{LoveLastsAllEternity}[/tex]
[tex]\huge\sf{Good\:luck}[/tex]
Answer the following questions. Make sure to show all your work.
1. In each case below, show if the point given is a solution to the system of
equations.
a.)
Point (-0.8,-0.6)
Equation 1 - y = 2x + 1
Equation 2 - y = -3x - 3
b.)
Equation 1 - x + y = 3
Equation 2 - y + 2 / 2 = x
POINT - (1/3, 2)
PLZ HELP ME
Answers
a) Since the corresponding y-value is -0.6, hence the point (-0.8, -0.6) is a solution to the system of equations
b) since the corresponding x-value is not 1/3, hence the point (1/3, 2) is not a solution to the system of equation
In order to show if the given point corresponds to the given function, we will have to substitute the value of x into the function to see if we will have its corresponding y-value
For the point (-0.8, -0.6), substitute x = -0.8 into both functions as shown:
f(x) = 2x + 1
f(-0.8) = 2(-0.8) + 1
f(-0.8) = -1.6 + 1
f(-0.8) = -0.6
Simiarly;
y = -3(-0.8)- 3
y = 2.4 - 3
y = -0.6
Since the corresponding y-value is -0.6, hence the point (-0.8, -0.6) is a solution to the system of equations
For the point (1/3, 2), substitute x = 1/3 into both functions as shown:
x = (y+2)/2
x = (2+2)/2
x = 4/2
x = 2
Simiarly;
x + 2 = 3
x = 3-2
x = 1
Since the corresponding x-value is not 1/3, hence the point (1/3, 2) is not a solution to the system of equations
Learn more on systems of equation here: https://brainly.com/question/847634
show that
[tex] \frac{2}{3 + \sqrt{7} } = 3 - \sqrt{7} [/tex]
I don't know what to do
please help with the steps.
for brainliest
Answers
Answer:
multiply by (3-√7)/(3 -√7) and simplify
Step-by-step explanation:
When there are radicals or complex numbers in the denominator, you can rewrite the expression so it has a real, rational denominator. You do this by multiplying numerator and denominator by the conjugate of the denominator. That value is the denominator with its sign changed.
This takes advantage of the factoring of the difference of squares.
(a -b)(a +b) = a² -b²
__
[tex]\dfrac{2}{3+\sqrt{7}}=\dfrac{2}{3+\sqrt{7}}\times\dfrac{3-\sqrt{7}}{3-\sqrt{7}}=\dfrac{2(3-\sqrt{7})}{3^2-(\sqrt{7})^2}=\dfrac{2}{9-7}\times(3-\sqrt{7})\\\\=\boxed{3-\sqrt{7}}[/tex]
compare the quantities in column A and Columb B,
column A.
4x-y=11
3x+y=3
column B
x-5y=-8
-x+4y=5
Answers
Answer:
A
Step-by-step explanation:
can't tell you
Need Help....
I can't understand the question so please help me.....
[tex]for \: x \: such \: that \: 0 < x < \frac{\pi}{2}[/tex]
It is the expression
[tex] \frac{ \sqrt{1 - {cos}^{2}x } }{sin \: x} \:- \frac{ \sqrt{1 - {sin}^{2}x } }{cos \: x} \\ \\ is \: equivalent \: to:[/tex]
[tex]f.0 \\ g.1 \\ h.2 \\j. - tan \: x \\ k. \: sin \: 2x[/tex]
Don't spam and Don't copy
Don't answer if you don't know
Thank You!
Answers
If 0 < x < π/2, then both sin(x) and cos(x) are positive.
From the Pythagorean identity, we then have
cos²(x) + sin²(x) = 1
⇒ cos(x) = + √(1 - sin²(x)) and sin(x) = + √(1 - cos²(x))
Then
√(1 - cos²(x))/sin(x) = sin(x)/sin(x) = 1
and
√(1 - sin²(x))/cos(x) = cos(x)/cos(x) = 1
so that the overall expression reduces to
1 - 1 = 0
Tyson is 6 feet 2 inches tall. There are 2. 54 centimeters in 1 inch. What is Tyson's height in centimeters?.
Answers
Answer:
187.96cm
Step-by-step explanation:
first convert 6 feet to cm=182.88
then convert 2 inches to cm=5.08
add your answers together=187.96
Use the linear combination method to solve the system of equations. â€"2. 1x 4y = 5. 3 2. 1x â€" 5. 5y = â€"0. 2 What is the solution to the system? ( , ).
Answers
The solution to the systems of equations is (7, 3)
Given the systems of equations expressed as:
-x + 4y = 5 ....................1
x - 5y = -2 ...................... 2
Add both equations to have:
-x+x + 4y - 5y = 5 - 2
4y-5y = -3
-y = -3
y = 3
Substitute y = 3 into equation 1:
-x + 4(3) = 5
-x + 12 = 5
-x = 5 - 12
-x = -7
x = 7
Hence the solution to the systems of equations is (7, 3)
Learn more on simultaneous equations here: https://brainly.com/question/148035
Find the gradient of the line segment between the points (-6,2) and (4,10).
Give your answer in its simplest form.
Answers
Answer:
3
Step-by-step explanation:
gradient/slope/m formula:-
(-6,2) (4,10).
m=(10-4)/(-4-6)
m=6/2
m=3
CAN SOMEONE HELP ME PLEASE ASAP!?
Answers
Answer:
<
Step-by-step explanation:
tickets at a particular movie theater have different rates for adults and children. On tuesday the theater sold 8 adult tickets and 9 tickets for 174. the next day the theater sold 5 adult tickets and 7 children tickets for 117. What is the price for the adult ticket and the price for the child ticket
Answers
Answer:
Adult = $15 pp
Child = 46 pp
Step-by-step explanation:
Let A and C be the price of Adult and Child's tickets, respectively.
We can set up equations for each of the two days, Tuesday and Wednesday. Each equation adds the totals paid for the two ticket levels and set it equal to the total income for that day:
Tues: 8A+9C=174
Wed: 5A+7C=117
We have two equations and two unknowns. Let's manipulate one of the equations in a way that allows us to eliminate one of the two variables, A or C. [One can also solve either equation to isolate one of the variables, and then use that in the second equation.]
I chose to multiply the first by 5 and the second by -8, in order to make the coefficients for A the same value in both equations, but opposite in sign:
Tues: 40A+45C = 870 [Multiply by 5]
Wed: -40A -56C = -936 [Multiply by -8]
-11C = -66 [Add the two equations]
C = 6 [Ta Da. Now use this price for a child's ticket in either of the original equations to find the cost of an adult ticket.]
8A+9C=174
8A+9*(6)=174
8A+54=174
8A = 120
A = 15
====
Use these two prices in the original equations to see if they indeed add up to the correct totals for each day.
Total Sales
Price Tues Wed Tues Wed
A 15 8 5 120 75
C 6 9 7 54 42
174 117 174 117 [The prices are correct]
Adult is $15 and child is $6
Use a Quadratic formula to solve for X
3x^2+9x=-4
Round to the nearest hundreth.
Answers
That should by the answer but I couldn’t find how to round it up sorry
The cost of a bottle of water is (w – 1) cents.
The cost of a bottle of milk is (2w – 11) cents.
A certain number of bottles of water costs $4.80.
The same number of bottles of milk costs $7.80 .
Find the value of w
Answers
Answer:
w= 25
Step-by-step explanation:
Cost of water= (w -1)¢
Cost of milk= (2w -11)¢
Let the certain number be x.
x(w -1)¢= 480¢ -----(1)
x(2w -11)¢= 780¢ -----(2)
From (1):
wx -x= 480 -----(3)
From (2):
2wx -11x= 780 -----(4)
(3) ×2:
2wx -2x= 960 -----(5)
(5) -(4):
(2wx -2x) -(2wx -11x)= 960 -780
Expand:
2wx -2x -2wx +11x= 180
9x= 180
Divide both sides by 9:
x= 180 ÷9
x= 20
Substitute x= 20 into (3):
w(20) -20= 480
20w -20= 480
20w= 480 +20
20w= 500
w= 500 ÷20
w= 25
If -11 + N = -11, then N is the
a. additive identity
b. additive inverse
c. multiplicative inverse
d. multiplicative identity
Answers
Answer:
Step-by-step explanation:
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A 20-foot piece of metal is cut INTO pieces that each measure 1 1/4 feet. How many pieces are there after the cut?
A. 16
B. 25
C. 18.75
D. 5
Answers
Answer:
I believe the answer is 16 Don't get mad if incorrect just trying my best
Answer:
A. 16
Step-by-step explanation:
If a 20 ft piece of metal is cut in 1 1/4 feet pieces you would divide the total length (20) by each of the pieces length (1 1/4) to find the answer. 20 ÷ 1 1/4 = 16.
Select the situation that can be represented by 9 x 4.
a
Yuri and his family buy 9 loaves of white bread and 4 loaves of wheat bread.
b
Yuri and his family buy 9 loaves of bread. They give their neighbor 4 loaves.
c
Yuri and his family eat 9 loaves of bread each week for 4 weeks.
d
Yuri and his family eat 9 slices of bread on Monday and 4 slices on Tuesday.
Answers
Answer:
C is the answer because it makes the most sense
A box contains 8 red balls and 8 black balls. A
woman takes balls out at random without looking at
them. Once a ball is taken out it is not replaced back in
the box. How many balls must she select to be sure of
having at least three balls of the same color?
Answers
Answer:
At least 5 times
Step-by-step explanation:
Number of balls to be selected for having assurance of at least three balls of the same colour is equals to 5 balls.
What is without replacement ?" Without replacement means if an item is drawn from the set of items it is not kept back which represents sample space is decrease by as per the number of selection is done in first draw."
According to the question,
Number of red balls in a box = 8
Number of black balls in a box =8
As per the condition of without replacement we get,
In this case worst selection case could be
Alternate balls are of different colour
Black →Red → Black → Red → fifth ball is either Red or Black
Hence, 5balls must be selected for assuring at least three balls of the same colour .
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Why are all of the equivalent ratios for 1 to 105
Answers
Answer: it’s infinite
Step-by-step explanation:
What is the value of r in the equation −4/3r − 1 = −2 ?
Answers
Answer:
r = 3/4
Step-by-step explanation: