The polynomial equation x^3-4x^2+2x+10=x^2-5x-3 has complex roots 3+2i What is the other root? Use a graphing calculator and a system of equations.
a –3
b –1
c 3
d 10
Answers
Answer:
The correct option is b.
Step-by-step explanation:
The given expression is
[tex]x^3-4x^2+2x+10=x^2-5x-3[/tex]
Simplify the equation.
[tex]x^3-4x^2+2x+10-x^2+5x+3=0[/tex]
[tex]x^3-5x^2+7x+13=0[/tex]
It is given that 3+2i is a root of the equation and (x-3-2i) is a factor.
By complex conjugate root theorem if a+ib is a root of an equation then a-ib must be the root of the equation.
It means 3-2i is a root of the equation and (x-3+2i) is a factor.
[tex](x-3-2i)(x-3+2i)=(x-3)^2-(2i)^2=x^2-6x+9+4=x^2-6x+13[/tex]
Divide [tex]x^3-5x^2+7x+13=0[/tex] by [tex]x^2-6x+13[/tex], to find the remaining factor.
By the long division method, the quotient is (x+1) and remainder is 0. It means (x+1) is a remaining factor of the given equation. Equate each factor equal to 0, to find the remaining roots.
[tex]x+1=0[/tex]
[tex]x=-1[/tex]
Therefore the correct option is b.
Related Questions
which function represents a vertical stretch of an exponential function
Answers
What is 16% of 43 minutes
Answers
Answer:
16% of 43 minutes are 6.8 minutes.
Step-by-step explanation:
To know the percentage of a quantity first you should divide the percentage by a hundred, then you should multiply the quantities, as follows.
1. Calculate the percentage:
[tex]\frac{16}{100}=0.16[/tex]
2. Multiply the percentage by the quantity:
[tex]0.16*43=6.88[/tex]
Therefore 16% of 43 minutes are 6.8 minutes.
Solve the inequality
5x < 16 + x.
A.) x < 1/4
B.) x > 1/4
C.) x < 4
D.) x > 4
Answers
x>4
Correct answer is D
Y= f(x) 16x find f(x) when x= 1/2
Answers
The value of f(x) when x = 1/2 is 8.
Explanation:To find the value of f(x) when x = 1/2, we need to substitute x = 1/2 into the equation y = f(x) = 16x.
Substituting x = 1/2, we get y = f(1/2) = 16(1/2) = 8.
Therefore, f(1/2) = 8.
((WILL MARK BRAINLIEST))
what is the equation of this graphed line (in slope intercept form)
thank you!
Answers
slope =
7- - 2 =9
8-0 = 8
slope = -9/8
y intercept = 7
equation: y=-9/8x+7
Two radical expressions with the same degree and the same _____ are called like terms.
Answers
Answer:
Two radical expressions with the same degree and the same radicand are called like terms.
Step-by-step explanation:
All the terms that have same power and vari ables are called like terms.
For example: 3x²y and 5x²y are like terms, 2x³ and 7x³ are like terms, etc.
The number under the root is known as radicand.
Two radical expressions are like terms if
1. They have same degree.
2. They have same radicand.
Therefore the two radical expressions with the same degree and the same radicand are called like terms.
Two radical expressions are called like terms if they have the same degree and the same:
E. radicand
Two radical expressions are called like terms if they have the same degree and the same radicand. The radicand is the number or expression inside the radical symbol. For example, in the radical expression [tex]\(\sqrt{5}\)[/tex], the radicand is 5. For two radical expressions to be like terms, they must not only have the same index (degree) of the radical but also the same radicand.
Consider the expressions [tex]\(\sqrt{3}\) and \(2\sqrt{3}\)[/tex]. These are like terms because they both have the same degree (square root, which is an index of 2) and the same radicand (3). Similarly, [tex]\(\sqrt[3]{7}\) and \(4\sqrt[3]{7}\)[/tex] are like terms because both are cube roots with a radicand of 7.
However, [tex]\(\sqrt{2}\) and \(\sqrt{3}\)[/tex] are not like terms because their radicands differ. Likewise, [tex]\(\sqrt[4]{5}\) and \(\sqrt{5}\)[/tex] are not like terms because their degrees (indices) differ. Therefore, for radical expressions to be like terms, matching radicands and degrees are essential.
The correct question is:
Two radical expressions are called like terms if they have the same degree and the same
A. denominator
B. radical
C. term
D. number
E. radicand
If h(x)= 5 for the function h(x)= 2x+1, what is the value of x?
Answers
What is 7 feet converted to miles?
Answers
Answer:
Step-by-step explanation:
Use the factor-label method you learned in chemistry (also known as dimensional analysis), keeping in mind 2 things:
the label you want needs to be on the top of the equivalent ratio, and
that there are 5280 feet in 1 mile. Having said that:
[tex]7feet*\frac{1mile}{5280 feet}=[/tex]
The math tells us to divide 7 by 5280. That means that
7 feet = .0013257576 miles, to however many decimal places you need. That 7575 is repeating, btw.
Solve 2a − 5d = 30 for d
Answers
-5d = -2a + 30....divide both sides by -5
d = (-2a + 30) / -5 or d = 2/5a - 6
Can somebody PLEASE help me on this question, I really need an answer. What are the reasons for a,b,c, and, d?
Answers
Reason A: Distributive Property
Reason B: Additive Property of Equality
Reason C: Combine like terms
Reason D: Additive Identity Property
----------------------------------------------------------
Further Explanation:
Reason A: The distributive property is the idea where we multiply a number by a block of values inside a parenthesis. In this case we have 3 outside the parenthesis multiplied by the x inside and the -4 inside as well. So 3 times x = 3x and 3 times -4 = -12 indicating that 3*(x-4) = 3*x+3*(-4) = 3x-12. Be sure to multiply the outer 3 by EVERY term inside the parenthesis. Often it is easy to forget a term inside.
Reason B: We are adding 12 to both sides. The goal is to have the -12 go away. Notice in the next line -12+12 = 0 which is effectively canceled out. Adding the same value to both sides is the Additive Property of Equality. It must be done to both sides to balance things out. The general rule is that if a = b, then a+c = b+c. We have added c to both sides.
Reason C: We just do arithmetic here. On the left side -12+12 turns into 0. On the right side 33+12 turns into 45. This is considered "combine like terms" as all of these terms have something in common: they don't have variables attached to them. Which is why they are common or like terms
Reason D: The additive identity property says that adding 0 to anything leads to the same thing as before. For example, adding zero to 5 gets us 5+0 = 5. Nothing has changed, which is what we expect. That's why 3x+0 turns into 3x. At this point, the -12 a few steps prior has been canceled out. In general, the additive identity property is x+0 = x or 0+x = x
Isabella competed in a triathlon. She completed the swimming event in 12.9 minutes, the biking event in 13.05 minutes, and the running event in 23.125 minutes. What was Isabella’s total time in the triathlon?
Answers
Add up (12.9 + 13.05 + 23.125)
12.9 + 13.05 + 23.125
25.95
25.95 + 23.125
49.075
Answer:
49.075 minutes
HOPE I HELPED!!!!!!!!!!!!!!!!!!!!
P.S. If you need anymore help do not hesitate to ask!!!!!
Answer:
49.075 minutes
Step-by-step explanation:
Your welcome :]
WILL MARK BRAINLIEST ANSWER
2x^2+20x=-38
show work
Answers
2x^2 + 20x + 38 = 0
Divide both sides by 2.
x^2 + 10x + 19 = 0
The quadratic formula works very well here.
Let a = 1, b = 10 and c = 19
x = [-b +- sqrt{b^2 - 4ac}]/(2a)
Plug those values into the formula to find two answers for x.
One is negative and the other positive.
Good luck.
2x ^2 + 20x + 38 = 0
Use the quadratic formula to find the solutions.
−b±√b^2 − 4 (ac)/2a
Substitute a = 2, b = 20, and c = 38 into the quadratic formula and solve for x.
−20±√20 ^2 − 4⋅(2⋅38)/2⋅2
Simplify. x = −5±√6
The result can be shown in both exact and approximate form.
x = −5±√6
x ≈ −2.55051025, −7.44948974
What is f(–3) if f(x) = |2x – 1| – 5?
Answers
f(-3) = |2x - 1| - 5
f(-3) = |-6 - 1| -5
f(-3) = |-7| - 5
f(-3) = 7 - 5 Absolute value of -7 = 7
f(-3) = 2
f(-3) = |2(-3) – 1| – 5
f(-3) = |-6 - 1| - 5
f(-3) = |-7| - 5
f(-3) = 7 -5
f(-3) = 2
Find the special product (5s-3)^(2)
A. 10s2 - 9
B. 25s2 -30s - 9
C. 25s2 - 9
D. 25s - 9 30x + 9
Answers
=> (5s - 3)^2 = (5s)^2 - 2(5s)(3) + (3)^2 = 25s^2 - 30s +9
The list of options is mistyped, so you must use the right list of choices and find which is 25s^2 - 30s + 9.
Answer: 25s^2 - 30s + 9
In the diagram below, ∠Q is bisected.
Find the perimeter of ΔPQS.
Answers
QP/QR = SP/SR
To be able to calculate the perimeter we need to know SP, which can be extracted from the formula QP/QR = SP/SR
QP/QR = SP/SR → 36/15 =SP/11 ; SP = (11x36)/15 = 26.4
And the perimeter is : 36+15+ (11+26.4) = 77.4 units
Evaluate the numerical expression. 4.2 − 3.5 ÷ 0.7 + 2.4 A) −3.2 B) 1.6 C) 11.6 D) 3.4
Answers
= 4.2 − 5 + 2.4
= -1.6
answer
- 1.6
4.2 -3.5/0.7+2.4
order of operations, do division first
-3.5/0.7 = -5
now you have:
4.2-5 +2.4
now just add/subtract from left to right
4.2-5 = -0.8 + 2.4 = 1.6
Answer is B
What number can you add to √7 to get a rational number?
−7√
7√
7
0
Answers
So if a=0 the answer is -√7, option answer 1.
Why are black people always watched so closely at a liquor store?
Answers
A lot of people assume that because of the forced situations blacks have been in the past, that they're all bad people. Which is not always true. Although black people can still steal(like any other capable human being), so can white people. And hispanics, and middle easterns. But based on the history of America, specifically, black people have been the most common to shoplift or vandalize. But that was in the past, anyone today can easily steal a bottle of beer or a pack of gum from any store just like everyone else. I think the issue is that most priveledged people haven't let go of the past. Or at least what the media filtered as the past.
Hope this helps. :)
John and 3 friends are going out for pizza for lunch. They split one pizza and 4 large drinks. The pizza cost $13.00. After using a $6.00 gift certificate, they spend a total of $13.20. Write an equation to model this situation, and find the cost of one large drink. a. 3d + $13.00 – $6.00 = $13.20; $2.07 b. 4d + $13.00 – $6.00 = $13.20; $1.55 c. 4d – $13.00 + $6.00 = $13.20; $6.73 d. 4d + $13.00 – $6.00 = $13.20; $1.60
Answers
4d +13.00 -6.00 = 13.20
4d = 7.00 = 13.20
4d = 6.20
d - 6.20/4 =1.55
answer is B
The quotient of a number and 4, minus 1, equals 5/4. find the number
Answers
(x/4) - 3 = 5/4
x/4 - 12/4 = 5/4
x - 12 = 5
x = 17
Final answer:
The equation (x / 4) - 1 = 5/4 is solved by isolating x and simplifying, which reveals that the number sought is 9.
Explanation:
To solve the equation where the quotient of a number and 4, minus 1, equals 5/4, we can set up the following algebraic expression:
Let x = the number we want to find.
Now, we translate the problem into an equation:
(x / 4) - 1 = 5/4
To find the value of x, follow these steps:
Add 1 to both sides of the equation to get the fraction by itself:
(x / 4) - 1 + 1 = 5/4 + 1
Simplify both sides:
(x / 4) = 5/4 + 4/4
Add the fractions on the right side:
(x / 4) = 9/4
Multiply both sides of the equation by 4 to solve for x:
4 * (x / 4) = 4 * (9/4)
Simplify both sides:
x = 9
Therefore, the number we are looking for is 9.
What is the measure of ∠ABC?
Enter your answer in the box.
Answers
The measure of the angle ∠ABC will be 95 degrees.
What is a quadrilateral?A quadrilateral is a shape made up of four sides having the sum of the angles 360 degrees. The given shape is like a parallelogram in which two sides are equal and at the same angles.
Given that angle A in the quadrilateral is 85 degrees. The value of the angle B will be calculated as:-
∠A + ∠B +∠C + ∠D = 360
85 + ∠B + 85 + ∠B = 360 ∠B = ∠D
170 + 2∠B = 360
2∠B = 360 - 170
2∠B = 190
∠B = 190 / 2
∠B = 95
Therefore, the measure of the angle ∠ABC will be 95 degrees.
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If you need how many days between two dates what function should be used
Answers
Your next problem is to work out the day number from the beginning of the year. On average there are between 30.4 and 30.5 days in a month, but this is only an approximation because the length of each month varies. So to aid in the calculation you need a table which gives you the day number for every date in the year, and the table is different for leap years.
So, you start by subtracting the years and counting how many leap years there are between. You consult the day number table for working out how many days there are from the beginning of the year.
Another way is to have a smaller table with just the months, so in a non-leap year Jan 1 would be 1, Feb 1 would be 32, Mar 1 would be 60, Apr 1 would be 91, and so on. Then we have to add in the day date. Mar 20 would be 19 days after Mar 1 so would have a day number of 79, not 80. Some diaries and calendars include the day number.
You can speed up the calculation by using one day number table or calculation and then adding in a day for each leap year between two dates. I hope this helps.
To calculate the number of days between two dates, subtract the start date from the end date and add 1.
Explanation:To find the number of days between two dates, you can use the formula:
Number of days = (End date) - (Start date) + 1
For example, if the start date is July 10, 2022, and the end date is July 15, 2022, the number of days between them would be:
Number of days = (15) - (10) + 1 = 6
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TDC, Inc's . net profits were $-2000 each month last year . What was TDC's net profits for the year ?
Answers
The TDC's net profits for the year were -$24,000 if TDC, Inc's. net profits were $-2000 each month last year option (A) is correct.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
TDC, Inc.'s net profits were $-2000 each month last year.
Let x be the net profit for the year
As we know there are 12 months in 1 year.
So the net profit:
x = $-2000×12
x = -$24,000
Thus, the TDC's net profits for the year were -$24,000 if TDC, Inc. net profits were $-2000 each month last year option (A) is correct.
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Deshawn multiplies 236 by 9. Which are the three partial products he could add to find the final product?
Answers
6 × 38 in parts,
writing the
numbers under
each other.3 8
× 6
4 8 First multiply
6 × 8.3 8
× 6
4 8
1 8 0
Then multiply 6 × 30 and
write the result under the 48.
Remember, the "3" is in the
tens place in the number 38
so it actually means 30.3 8
× 6
4 8
+ 1 8 0
2 2 8Lastly, add.
if a = 0.6(the 6 repeating) and b= 0.75, then a·b= (blank) and a/b=(blank)
Answers
0.6666 (repeating) / 0.75 = 0.8888888 (repeating)
Sequence 13, 39, 65, 91,
Answers
hmmm, add 26? yep
the sequence is
[tex]a_n=a_{n-1}+26[/tex] when [tex]a_1=13[/tex]
or
[tex]a_n=13+26(n-1)[/tex] or [tex]a_n=26n-13[/tex]
The function f(x)= -6x+11 has a range given by {-37,-25,-13,-1}.Select the domain values of the function from the list 1,2,3,4,5,6,7,8. explain how you arrived at your answer
Answers
function, ( f(x)=-6x+11 ), equals these numbers that are in the range {-37,-25,-13,-1}.
So you apply each of these numbers (1,2,3,4,5,6,7,8) into the function (f(x)=-6x+11)
one by one.
f(1)=-6(1)+11=5
f(2)=-6(2)+11= -1
f(3)=-6(3)+11= -7
f(4)=-6(4)+11= -13
f(5)=-6(5)+11= -19
f(6)=-6(6)+11= -25
f(7)=-6(7)+11= -31
f(8)=-6(8)+11= -37
As you can see, f(2),f(4),f(6),and f(8) equal the numbers that are in the range {-37,-25,-13,-1}.
The domain of the given function f(x)= -6x+11 for the given range is
{2,4,6,8}
Given :
The function f(x)= -6x+11
range given by {-37,-25,-13,-1)
Range is the f(x) values . Domain are the x values .
To find out domain , we substitute the values of f(x) that is range and solve for x
First we substitute -37 for f(x) in the given function and solve for x
[tex]f(x)= -6x+11 \\x=-37\\-37=-6x+11\\-37-11=-6x\\-48=-6x\\x=8[/tex]
Now substitute -25 for f(x)
[tex]x=-25\\-25=-6x+11\\-25-11=-6x\\-36=-6x\\x=6\\\\\\x=-13\\-13=-6x+11\\-13-11=-6x\\-24=-6x\\x=4\\\\\\x=-1\\-1=-6x+11\\-1-11=-6x\\-12=-6x\\x=2[/tex]
x values are the domain
Domain is {2,4,6,8}
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The price of grapes at the grocery store is $1.44 per pound. There are approximately 0.45 kilograms in a pound. To the nearest cent, what is the price of grapes in dollars per kilogram?
Answers
1 lb / 0.45 = 2.22
so approximately 2.22 kilograms per pound
divide price per pound by kilometers per pound
1.44 / 2.22 = 0.648
round to 0.65, so it costs $0.65 per kilogram
Answer:
1 lb / 0.45 = 2.22
so approximately 2.22 kilograms per pound
divide price per pound by kilometers per pound
1.44 / 2.22 = 0.648
round to 0.65, so it costs $0.65 per kilogram
Step-by-step explanation:
got it right on the quiz
how can you use a number to explain what an integer and rational number are??
Answers
The terms even and odd only apply to integers; 2.5 is neither even nor odd. Zero, on the other hand, is even since it is 2 times some integer: it's 2 times 0. To check whether a number is odd, see whether it's one more than some even number: 7 is odd since it's one more than 6, which is even.
Another way to say this is that zero is even since it can be written in the form 2*n, where n is an integer. Odd numbers can be written in the form 2*n + 1. Again, this lets us talk about whether negative numbers are even and odd: -9 is odd since it's one more than -10,which is even.
Write the ratio of dogs to cats in simplest form. 12 dogs, 16 cats