If a polynomial function, f(x), with rational coefficients has roots 3 and startroot 7 endroot, what must also be a root of f(x)?
Answers
The conjugate which is 3 - √7 is also a root of f(x).
What is the root of a polynomial function?The root of a polynomial function f(x) is the value of x for which f(x) = 0.
Now if a polynomial function has a root x = a + √b then the conjugate of x which is x' = a - √b is also a root of the function, f(x).
What must also be a root of f(x)?
Given that the polynomial function, f(x), with rational coefficients has roots
3 + √7, then by the above, the conjugate which is 3 - √7 is also a root of f(x).
So, 3 - √7 is also a root of f(x).
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Related Questions
If the trip from Paris, France, to Geneva, Switzerland, takes 5 hours, and the train travels at 130 miles per hour, how many miles from Paris is Geneva?
Answers
Answer: 650 miles
Step-by-step explanation:
If it takes 5 hours to go from Paris to Geneva and a train is travelling at 130 miles per hour then multiply the total number of miles per hour by 5 to find how many miles you will have to travel from Paris to Geneva.
130 * 5 = 650
A politician estimates that 61% of his constituents will vote for him in the coming election. how many constituents are required for a random sample to obtain a margin of error of at most 0.03 with 95% confidence
Answers
many constituents are required for a random sample to obtain a margin of error of at most 0.03 with 95% confidence is 1016.52
What is the margin of error?The margin of error is a measure of the precision of a sample estimate. It reflects the level of uncertainty associated with a statistical estimate and is typically expressed as a percentage or a decimal fraction.
To obtain a margin of error of at most 0.03 with 95% confidence, we need to use a sample size that is large enough to ensure that the sample proportion of constituents who will vote for the politician is close to the true population proportion of 61%. We can use the following formula to calculate the required sample size:
n = (z^2 * p * (1 - p)) / (e^2)
where n is the sample size, z is the z-score corresponding to the desired level of confidence (1.96 for 95% confidence), p is the estimated population proportion (0.61 for this problem), and e is the desired margin of error (0.03 for this problem).
Substituting the given values into the formula gives:
n = (1.96^2 * 0.61 * (1 - 0.61)) / (0.03^2)
n = (3.8436 * 0.61 * 0.39) / (0.0009)
n = (2.3473 * 0.39) / (0.0009)
n = 0.91837 / 0.0009
n = 1016.52
Thus, the required sample size is 1016.52. Since the sample size must be a whole number, we can round this value up to 1017.
Hence, a random sample of at least 1017 constituents is required to obtain a margin of error of at most 0.03 with 95% confidence.
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Plsssss I need help! I don’t want any BS Answers I need an answer to EACH part. This is rlly important, absurd answers WILL be reported it’s that simple. Best answer gets Brainliest <3
Answers
meh, I'm borred rn, and 15p are 15p. maybe some1 will get something out of this someday :p
Part A
Option 1 is exponential (steps get bigger)
Option 2 is linear (steps stay the same)
Part B
f1(x) = 1000 * 1.1^x
f2(x) = 1000 + 100x
Part C
f1(20) = 1000 * 1.1^20 = 6727.50
f2(20) = 1000 * 100*20 = 3000
Someone plz just answer these correct thx
(Ignore the circle) lol
Answers
Answer:
5. thirty-four thousand five hundred
6. seven hundred three and two hundred forty-six thousandth
7. seventy-six million eighty thousand
Step-by-step explanation:
These are the answers because:
1) Word form is translating the numbers into words
2) Basically, all you have to do is write the word form the way you pronounce the number
3) Whenever you are round decimals, make sure to have an "and" for the decimal point and "ths" at the end of the value of the number (look at question 6 for reference)
Hope this helps!
\(\frac{10ax^{2} bc^{3}}{ 12ab{2} }\)
Answers
![[tex]\frac{10ax^{2} bc^{3}}{ 12ab{2} }[/tex]](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/ny3QasFM5nGGsT5EAlEwyMoWzk7DRptR.png)
Evaluate the expressions. 32) 12+ 32÷3-6
Answers
Answer:
16.66666667
Step-by-step explanation:
=12+10.66666667-6
=22.66666667-6
=16.66666667
3 Diversify Your Hand You are dealt 5 cards from a standard 52 card deck. Let X be the number of distinct values in your hand. For instance, the hand (A, A, A, 2, 3) has 3 distinct values. (a) Calculate E[x] (b) Calculate Var[x].
Answers
The expected value of X is 2.6, and the variance of X is 0.972. This can be answered by the concept of Probability.
To calculate E[X], we can use the formula for the expected value of a discrete random variable:
E[X] = ∑ x × P(X = x)
Here, x represents the possible values that X can take, which are integers from 1 to 5. P(X = x) is the probability that X takes the value x. To calculate this probability, we need to count the number of ways we can get a hand with x distinct values and divide it by the total number of possible hands.
The number of ways to get a hand with x distinct values is given by:
(13 choose x) × ((4 choose 1)ˣ) × ((48 choose 5-x)/(4 choose 1)⁽⁵⁻ˣ⁾)
The first term represents choosing x distinct values out of 13 possible values. The second term represents choosing one card from each of the x distinct values. The third term represents choosing the remaining 5-x cards from the remaining 48 cards (excluding the x distinct values), with each card having 4 possible suits to choose from.
Using this formula and summing over x from 1 to 5, we get E[X] = 2.6.
To calculate Var[X], we can use the formula for the variance of a discrete random variable:
Var[X] = E[X²] - (E[X])²
To calculate E[X²], we need to modify the formula for E[X] as follows:
E[X²] = ∑ x² × P(X = x)
Using the same method as before, we can calculate P(X = x) for each value of x and use it to calculate E[X²]. Substituting these values into the formula for Var[X], we get Var[X] = 0.972.
Therefore, the expected value of X is 2.6, and the variance of X is 0.972.
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7 1/2- 3 7/10 or Seven and a half subtract three and seven tenths.
Answers
Answer:
3.8 is the answer to your problem. Happy Holidays!
The functions f(x) and g(x) are graphed.
Which represents where f(x) = g(x)?
Of(0) = g(0) and f(2)= g(2)
Of(2)= g(0) and f(0) = g(4)
Of(2)= g(0) and f(4) = g(2)
Of(2)= g(4) and f(1) = g(1)
Answers
The correct statement regarding f(x) = g(x) is given as follows:
f(0) = g(0) and f(2)= g(2).
How to solve a system of equations graphically?We solve the system graphically, hence the solution is given by the point of intersection of the graphs of the two functions.
When two functions intersect, they have the same numeric value.
The two functions intersect at x = 0 and at x = 2, hence the correct statement is given as follows:
f(0) = g(0) and f(2)= g(2).
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Plz write it for me how u got it ❤️On paper then send it to me
Answers
Answer:
See below in bold.
Step-by-step explanation:
1. x^2 - 13x - 30
We need 2 numbers whose product is -30 and whose sum = -13.
They are -15 and + 2:
Answer is (x - 15)(x + 2).
2. 2x^2 + 4x - 126
First we can take 2 out to give:
2(x^2 + 2x - 63)
Now we need 2 numbers whose product is - 63 and sum = +2.
These are +9 and - 7 so
Answer is 2(x - 7)(x + 9).
3. -30x^3 + 3x^2 + 9x
First we can take out -3x to give
-3x(10x^2 - x - 3)
Now we want 2 numbers whose product is 10*-3 = -30 and whose sum is -1. They are -6 and +5 so we write the above as:
-3x(10x^2 + 5x - 6x - 3)
Now we factor the parentheses by grouping:
= -3x( 5x(2x + 1) - 3(2x + 1)
= -3x(2x + 1)(5x - 3) Answer.
The answer to the second part is 12x^2 - 13x - 21.
Part 3
1, 18.
2. 6.
3. = 5(2(-3)^2 - 3*3*4 + 4^2) - 3)) - 2(-3)(-3 + 7(4) - 1) - 3*4^2
= 5*(67) - 2(72) - 48
= 143.
4. (11m^2 - 7) - (6m^2 + 3m - 11) + (3m^2 - m - 9)
= 11m^2 - 7 - 6m^2 - 3m + 11 + 3m^2 - m - 9
= 8m^2 - 4m - 5
A = 8, B = 4 and C = 5.
A restaurant used 231 eggs last week. Of these, 46 were brown in color. The remainder of the eggs were white in color. Which equation can be used to solve for w, the number of white eggs used last week?
Answers
so
W = 185
Answer:
46 + w = 231
hope this helped
a pizza delivery chain advertises that it will deliver your pizza in 35 minutes from when the order is placed. being a skeptic, you decide to test and see if the mean delivery time is actually more than 35 minutes. for the simple random sample of 13 customers who record the amount of time it takes for each of their pizzas to be delivered, the mean is 39.4 minutes with a standard deviation of 6.4 minutes. assume that the population distribution is approximately normal. perform a hypothesis test using a 0.05 level of significance. step 1 of 3: state the null and alternative hypotheses for the test. fill in the blank below.
Answers
The null and the alternative hypothesis for the test are given as follows:
Null hypothesis: \(H_0: \mu \leq 35\).Alternative hypothesis: \(H_1: \mu > 35\)How to identify the null and the alternative hypothesis in the context of this problem?To identify each hypothesis, first the claim needs to be identified, which is given as follows:
The mean delivery time is more than 35 minutes.
(your claim).
At the null hypothesis, it is supposed that there is not enough evidence to conclude that the claim is true, that is, there is not enough evidence to conclude that the mean mean delivery time is more than 35 minutes, hence:
\(H_0: \mu \leq 35\)
At the alternative hypothesis, it is tested if there is enough evidence to conclude that the claim is true, that is, there is enough evidence to conclude that the mean mean delivery time is more than 35 minutes, hence:
\(H_1: \mu > 35\)
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two containers are used to hold liquid. these containers have exactly the same shape. the first container has a height of 20 cm, and it can hold 320 m3 of liquid. if the second container has a height of , how much liquid can it hold?
Answers
The second container can hold approximately 1715 m³ of liquid.
Two containers have exactly the same shape, we can use their height ratio to determine the liquid capacity ratio.
Let's denote the height of the first container as H1 = 20 m and its liquid capacity as C1 = 320 m³.
We want to find the liquid capacity of the second container, C2, given its height H2 = 35 m.
The ratio of the heights is H2 / H1 = 35 m / 20 m = 7/4.
The ratio of the liquid capacities is equal to the ratio of the volumes, since the containers have the same shape. Therefore, we have:
C2 / C1 = (H2 / H1)³
Substituting the given values:
C2 / 320 m³ = (7/4)³
Simplifying the exponent:
C2 / 320 m³ = 343 / 64
To find C2, we can cross-multiply:
C2 = (343 / 64) × 320 m³
Calculating the result:
C2 ≈ 1715 m³
Therefore, the second container can hold approximately 1715 m³ of liquid.
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The question is incomplete the complete question is :
two containers are used to hold liquid. these containers have exactly the same shape. the first container has a height of 20 m, and it can hold 320 m³ of liquid. if the second container has a height of 35 m, how much liquid can it hold?
This table shows values that represent an exponential function.
What is the average rate of change for this function for the interval from x = 2
to X = 42
A.6
B.12
C.1/12
D.1/6
Answers
Answer:
A
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is
\(\frac{f(b)-f(a)}{b-a}\)
Here [ a, b ] = [ 2, 4 ], thus
f(b) = f(4) = 16 ← corresponding value of y from table
f(a) = f(2) = 4 ← corresponding value of y from table , thus
average rate of change = \(\frac{16-4}{4-2}\) = \(\frac{12}{2}\) = 6 → A
The average rate of change of function f(x) in the interval from x = 2 to x = 4 is 6.
What is the average rate of change of a function?
The average rate of change of a function is defined as the average rate at which one quantity is changing with respect to something else changing.
Formula for finding the average rate of change of a function\(A([a, b]) = \frac{f(b)-f(a)}{b-a}\)
Where,
A([a, b]) is the average rate of change of function A(x) in the closed interval [a, b].
According to the given question
We have an interval [2, 4]
⇒ [a, b] = [2, 4]
Now,
f(b) = f(4) = 16 (corresponding value of f(4) from table)
and, f(a) = f(2) = 4 (corresponding value of f(2) from table)
Therefore average rate of change of f(x) in the closed interval [ 2, 4 ] is
⇒ Average rate of change of f(x) = \(\frac{f(4)-f(2)}{4-2}\)
⇒ Average rate of change of f(x) = \(\frac{16-4}{2}\)
⇒ Average rate of change of f(x) = \(\frac{12}{2}\)
⇒ Average rate of change of f(x) = 6
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Which of the following statements accurately describes the expressionx +3x² - 4?A. The quotient of x+3 and x2 - 4B. The quotient of you - 4 and you - 4OC. The product of x+3 and 2 - 4OD. The product of x+3 and x+3
Answers
-Recall that the statement:
The quotient of a and b,
in algebraic notation is:
\(\frac{a}{b}\text{.}\)-Therefore, the expression:
\(\frac{x+3}{x^2-4},\)as a statement is:
The quotient of x+3 and x²-4.
Answer: Option A.
13. Zahra likes to go rock climbing with her friends. In the past, Zahra has climbed to the top of the
wall 7 times in 28 attempts. Determine the odds against Zahra climbing to the top.
A. 3:1
B. 4:1
C. 3:11
D. 3:4
Answers
Answer:
the odds against Zahra climbing to the top are,
B. 4:1
Step-by-step explanation:
Since she has climbed 7 times in 28 attempts,
the probability of a successful climb is,
P = 7/28
P = 1/4
So, the odds against Zahra climbing to the top are 4:1
1 point) solve the system using elimination. ⎧⎩⎨⎪⎪−6x3x−4x−5y−6y−3y−3z−6z 2z===39314 {−6x−5y−3z=393x−6y−6z=3−4x−3y 2z=14 x=x= y=y= z=z=
Answers
Equation 6: x = (11y + 3z - 303) / 16
Equation 9: 811y + 387z = 2,745
What is Elimination?
The method of elimination is where you actually eliminate one of the variables by adding two equations. In this way, you remove one variable in order to solve for the other variable. In a system of two equations, since you have two variables, eliminating one greatly simplifies the process of solving for the other.
To solve the system of equations using elimination, we'll eliminate one variable at a time until we find the values of x, y, and z.
Multiply the second equation by 2 and the third equation by -3 to make the coefficients of z the same in both equations:
Equation 2: 2x - 12y - 12z = 6
Equation 3: 12x - 9y - 6z = -42
Add the first equation to the modified second equation and the modified third equation:
Equation 1 + Equation 2: -6x - 5y - 3z + 2x - 12y - 12z = 393 + 6
=> -4x - 17y - 15z = 399 (Call this Equation 4)
Equation 1 + Equation 3: -6x - 5y - 3z + 12x - 9y - 6z = 393 - 42
=> 6x - 14y - 9z = 351 (Call this Equation 5)
Multiply Equation 5 by 2 and subtract Equation 4 from it:
2 * Equation 5 - Equation 4: 12x - 28y - 18z - (-4x - 17y - 15z) = 702 - 399
=> 16x - 11y - 3z = 303 (Call this Equation 6)
Multiply Equation 4 by 16 and add it to Equation 6:
16 * Equation 4 + Equation 6: -64x - 272y - 240z + 16x - 11y - 3z = 16 * 399 + 303
=> -48x - 283y - 243z = 6,399 (Call this Equation 7)
Divide Equation 7 by -1 to simplify the coefficients:
Equation 7: 48x + 283y + 243z = -6,399
Now we have the following system of equations:
Equation 6: 16x - 11y - 3z = 303
Equation 7: 48x + 283y + 243z = -6,399
We can solve this system using further elimination or substitution. Let's solve it using substitution.
From Equation 6, solve for x:
16x = 11y + 3z - 303
x = (11y + 3z - 303) / 16
Substitute this value of x into Equation 7:
48[(11y + 3z - 303) / 16] + 283y + 243z = -6,399
Simplify the equation:
528y + 144z - 9,144 + 283y + 243z = -6,399
Combine like terms:
811y + 387z = 2,745 (Call this Equation 8)
Now we have the following system of equations:
Equation 6: x = (11y + 3z - 303) / 16
Equation 8: 811y + 387z = 2,745
We can solve this system by further substitution or using a numerical method. Let's solve it using substitution.
From Equation 6, solve for x:
x = (11y + 3z - 303) / 16
Substitute this value of x into Equation 8:
811y + 387z = 2,745
Simplify the equation:
811y + 387z = 2,745 (Call this Equation 9)
Now we have the following system of equations:
Equation 6: x = (11y + 3z - 303) / 16
Equation 9: 811y + 387z = 2,745
We can solve this system by further substitution or using a numerical method. Let's solve it using a numerical method such as Gaussian elimination or matrix inversion.
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There are 3 basketball teams. Each team has 10 players. All of the teams are used to make 6 groups during practice. How many players are in each group.
Answers
3x10=30.
30/6=5
David's minimum payment is 2.5% of his new balance. His new balance is 820.00. What is the minimum payment?
Answers
Answer:
20.50
Step-by-step explanation:
2.5/100 * 820.00
= 20.50
Each hamburger patty is 18
pound. Drag the correct equation to each amount to show how many 18
pound hamburger patties can be made.
Answers
There are 56 hamburgers in 7 pounds of hamburgers.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given that, each hamburger patty is 1/8 pound.
Hamburger Weight: 3 pounds
Number of Hamburgers = Total Weight of hamburger ÷ Weight each hamburger
= 3 ÷ 1/8
= 3×8
= 24
Hamburger Weight: 7 pounds
Number of Hamburgers = 7 ÷ 1/8
= 7×8
= 56
Therefore, there are 56 hamburgers in 7 pounds of hamburgers.
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Find an expression which represents the difference when (-6x + 5) is subtractedfrom (-X – 8) in simplest terms.
Answers
(-x - 8) - (-6x + 5)
open the parenthesis
-x - 8 + 6x - 5
Re-arrange
-x + 6x -8 -5
5x - 13
Pls help me the answer
Answers
Answer:
The slope is 5/3
Step-by-step explanation
The slope formula is \(\frac{rise}{run}\)
If you take 2 points on the line, the rise is 5 and the run is 3.
Determine the amplitude of the function y = negative one-half cosine x. On a coordinate plane, a function curves up from (0, negative 0.5) through (1.5, 0) to (3, 0.5). a. -1 c. One-half b. -Negative one-half d. 2
Answers
Step-by-step explanation:
The amplitude is the value that the cosine is being multiplied by.
The general equation of a sinusoid is
\( a \cos(b(x + c) ) + d\)
where a is the amplitude
\( \frac{2\pi}{ |b| } \)
is the period
-c is the phase shift
d is the midline(vertical shift)
Here the amplitude is -1/2 so b is the correct answer.
Answer:
the amplitude of the function that is y= -1/2 cos x, is 1/2.
Step-by-step explanation:
A square is made using four rods of equal length joined end to end.
the perimeter of this square is 72 cm. Three of these rods are now joined end to end to make an equilateral triangle.
What is the perimeter of this equilateral triangle
Answers
Answer:54 cm
Step-by-step explanation:
Given
Rods are joined to form a square
Perimeter of square is \(72\ cm\)
Suppose a is the length of each rod so
Perimeter is \(4 a\)
\(\therefore 4a=72\)
\(\Rightarrow a=\frac{72}{4}\)
\(\Rightarrow a=18\ cm\)
Now if rods are joined to form a square then
Perimeter is the sum of sides
Perimeter of (equilateral)triangle\(=3a\)
\(\Rightarrow =3\times 18\)
\(\Rightarrow =54\ cm\)
... 948x47929=45,436. It’s already answered so guess wht tht means!!!!
Answers
Answer:
45436
Step-by-step explanation:
Triangle PQR is formed by the three squares A, B, and C:
A right triangle PQR is shown. On the side PQ of this triangle is a square. Inside the square is written Square A, Area equal to 9 square units. On the side QR of this triangle is another square. Inside the square is written Square B, Area equal to 16 square units. On the side PR of this triangle is another square. Inside the square is written Square C, Area equal to 25 square units.
Which statement best explains the relationship between the sides of triangle PQR?
(PQ)2 + (QR)2 = (PR)2, because 9 + 16 = 25
PQ + QR = PR, because 9 + 16 = 25
(PQ)2 + (QR)2 = (PR)2, because 52 + 32 = 42
PQ + QR = PR, because 52 + 32 = 42
Answers
Answer: I believe A is the correct answer
Step-by-step explanation:
This is a sketch of the curve with equation y = f(x).
The vertex of the curve is at (2, -3)
V
X
(2, -3)
Write down the coordinates of the vertex of the curve with equation
a) f(x + 7)
b) f(-x)
I’m
Answers
Answer:
We have to use the formule to calculate the vertex which is: V(-b/2a;4ac-b^2/4a)
A) y=x+7 where a=1 b=0 and c=7
By replacing we have: V(0;28/4) V(0;7)
B) y=-x where a=-1 b and c=0 so V(0,0)
THIS IS SO HARD HELP PLEASE
Answers
Answer:
second one: EFG NML
THIRD: 82°
Find the measure of the indicated angle.
Answers
Answer:
Angle FDG is 42°
Step-by-step explanation:
the whole angle GDE is an obtuse angle (greater than 90° but less than 180°), but a line is drawn at the middle to split it into 2.Each will be an acute angle.This means our answer must be acute.Mathematically ,
x+86=128
X=128-86
X=42°
to be sure,when an obtuse angle is split into two angles,it becomes 2 acute angles.
A theater has 1,464 seats. The seats are arranged into 62 equal-sized "regular" sections plus one "premium" front-row section. How many seats are in a regular section? How many seats are in the premium front-row section? Explain.
Answers
In the theater, that have 1,464 seats.
1426 seats are in "regular" sections
38 seats are "premium" front-row section
How to find the number of seats in the "regular" sectionsThe seat arrangement is solved by division. In this case the 62 equal spaced is the divisor while the number of seats is the in each row is the quotient
The division is as follows
1464 / 62
= 23 19/31
The number of seats in the regular section is 23 * 62 = 1426
The remainder will be arranged in premium front row
using equivalent fractions
19 / 31 = 38 / 62
the remainder is 38 and this is the seat for the premium front row section
OR 1464 - 1426 = 38 seats
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