Answer:
The degree of the polynomial is 3.
By the fundamental theorem of algebra, the function has three roots.
Two roots are given, so there must be one root remaining.
By the complex conjugate theorem, imaginary roots come in pairs.
The final root must be real.
Step-by-step explanation:
The number of roots remaining of the polynomial function f(x) = x³ − 7x − 6, with two roots -2, and 3 already given is 1. The nature of the root will be real.
What are polynomial functions?A polynomial function is a function (say f(x)), which is defined over a polynomial expression in x. It is of the form,
f(x) = a₀ + a₁x + a₂x² + a₃x³ + ... + aₙxⁿ, where a₀, a₁, a₂, ..., aₙ are constants, x is a variable, and n ≥ 0.
Degree of the polynomial function = n, the highest power of x.
What is the fundamental theorem of algebra?The fundamental theorem of algebra is that the number of roots or solutions of a polynomial function = The degree of the polynomial function.
What is the complex conjugate theorem?According to the complex conjugate theorem, if a polynomial function has complex roots, they will always exist in conjugate pairs, that is, if one root is of the form a + bi, the other root will be a - bi.
How will we determine the question?We are given a polynomial function f(x) = x³ - 7x - 6. Two roots of the equation are given as -2, and 3.
The degree of the equation = 3, so by the fundamental theorem of algebra number of roots = 3.
2 roots are given, so the number of roots remaining = 1.
Since none of the given roots are complex, the third root can not be complex, as complex roots always exist in conjugate pairs, coming from the complex conjugate theorem. So, the remaining root will be real in nature.
Learn more about the fundamental theorem of algebra and the complex conjugate theorem at
https://brainly.com/question/11855858
https://brainly.com/question/13792775
#SPJ2
0.5(repeated)+0.1(repeated)-0.3(repeated)?
Answer:
[tex]\dfrac{1}{3}=0.\overline{3}[/tex]
Step-by-step explanation:
Since a single digit is repeated in each case, and since the repeat starts at the decimal point, the fraction corresponding to the repeated digit is that digit divided by 9.
[tex]0.\overline{5}+0.\overline{1}-0.\overline{3}=\dfrac{5}{9}+\dfrac{1}{9}-\dfrac{3}{9}=\dfrac{5+1-3}{9}=\dfrac{3}{9}\\\\=\boxed{\dfrac{1}{3}}[/tex]
_____
Comment on equivalents to repeating decimals
The number of 9s in the denominator equals the number of repeated digits.
0.2727(repeated) = 27/99 = 3/11 . . . . . 2 repeated digits
Find the length of a rectangle with a diagonal of 10 and a height of 8.
Answer:
The length of the rectangle is 6.
Step-by-step explanation:
Given: The diagonal of a rectangle is 10 and the height is 8.
Please understand, that a diagonal, divides the rectangle into two tringles.
To find the length of the rectangle, you can use Pythagoras on one of the right sided triangles, because the length of the triangle, is also the length of the rectangle!
EXTRA:
If you know the special 3 4 5 triangle, a so called Pythagorean Triple, then you can "see" the simularity between the numbers.
Instead of 5, a diagonal of 10 is given (factor of 2 bigger).
Instead of 4, the height of 8 is given (factor of 2 bigger). By scaling the Pythagorean Triple 3 4 5 by a factor of 2, you get the numbers 6 8 10. Could it be, that the number we need to find, is six?
Try to verify, by calculating the missing number (which is the length of the rectangle we are looking for).
a² + b² = c²
a = length (and is unknown)
b = height = 8
c = hypothenusa/diagonal = 10
Substitute the numbers given:
a² + 8² = 10²
Subtract 8² left and right of the = sign.
a² +8² -8² = 10² - 8²
a² + 0 = 100 - 64
a² = 36
a = + - √36
a = + - 6
EXTRA:
You can ignore the -√36 = -6 part of the solution, because a length of -6 has no meaning here.
a = 6
So, the length of the triangle is 6 and thus, the length of the rectangle is also 6.
What was the sampling method that was used in the scenario? A study was done to determine the age, the number of times per week, and the duration (amount of time) of residents using a local park in San Antonio, Texas. The first house in the neighborhood around the park was selected randomly, and then the resident of every eighth house in the neighborhood around the park was interviewed.
Answer:
The sampling method that was used in the scenario is systematic sampling.
Step-by-step explanation:
Systematic sampling is a kind of probability sampling method in which individuals from a larger population are nominated according to a random initial point and following a static, periodic interval.
For instance, consider a study where the researcher first selects a name randomly from the alphabetized order and then follow a fixed pattern of selecting every 10th person from the population.
In this case, a study was done to determine the age, the number of times per week, and the duration (amount of time) of residents using a local park in San Antonio, Texas.
The first house was randomly selected from the neighborhood around the park.
Then, the resident of every 8th house in the neighborhood around the park was interviewed.
So, the researcher selects a random house and then keep on selecting the houses in an interval of 8. This way the next house selected with be the 8th, the next the 16th, and so on.
Thus, the sampling method that was used in the scenario is systematic sampling.
Helen wants to buy 8 boxes of crayons at $1.94 per box for the day care center that she runs estimate the total cost of the crayons
Answer: $16
Step-by-step explanation:
1.94 * 8 = 15.52
$15.52 rounds up to $16
find the product of 4025 multiply 5 by using properties
Answer:
Change 4020 to 4000 + 25.
Then use the distributive property.
4025 * 5 = (4000 + 25) * 5 = 4000 * 5 + 25 * 5 = 20,000 + 125 = 20,125
Use a table of function values to approximate an x-value in which the exponential function exceeds the polynomial function in your final answer include the table of function values f(x)=2^x h(x)=x^3+x+8
Answer:
When x = 10, or when f(x) = 1024, or any value greater than that.
Step-by-step explanation:
For f(x): 1x = 2, 2x = 4, 3x = 8, 4x = 16, 5x = 32, 6x = 64, 7x = 128, 8x = 256, 9x = 512, 10x = 1024
for g(x) 1x = 10, 2x = 19 3x = 38, 4x = 72, 5x = 128, 6x = 230, 7x = 358, 8x = 528, 9x = 746, 10x = 1018
Answer:
When x = 10, or when f(x) = 1024, or any value greater than that.
Step-by-step explanation:
Consider the function f(x) = 3x and the function g, which is shown below. G(x)=F(x)-2=3^x-2 How will the graph of g differ from the graph of f? A. The graph of g is the graph of f shifted 2 units up. B. The graph of g is the graph of f shifted 2 units to the right. C. The graph of g is the graph of f shifted 2 units down. D. The graph of g is the graph of f shifted 2 units to the left. Reset Next
H E L P
Answer:
C. The graph of g is the graph of f shifted 2 units down
Step-by-step explanation:
The transformation ...
g(x) = f(x -h) +k
represents a translation h units right and k units up.
You have h=0 and k=-2, so the graph is shifted 0 units right and 2 units the opposite of up.
The graph of g is the graph of f shifted 2 units down.
Answer:
C
Step-by-step explanation:
I just took the test on edmentum
Pete is making decorations for a dinner party.The instructions tell him to use 9 flowers for a medium-sized decoration.Complete each statement to adjust the flowers for different-sized decorations based on these instructions.
Answer:i need points
Step-by-step explanation:bleep bop boop
Share £45 in the ratio of 2:3.
Answer:
18:27
Step-by-step explanation:
2:3= 2 parts to 3 parts
Total is 5 parts
45/5 parts- each part is 9
2(9)=18
3(9)=27
Answer:
[tex]\£ 18: \£27[/tex]
Step-by-step explanation:
[tex]\frac{45}{2+3}[/tex]
[tex]\frac{45}{5}=9[/tex]
[tex]2:3[/tex]
[tex]2 \times 9 : 3 \times 9[/tex]
[tex]18:27[/tex]
The image of ABC after a reflection across EG is ABC which statement is true about point F
Answer: First option.
Step-by-step explanation:
As the triangle is reflected over the line EG, this means that the distance between each common point of the triangles and the line must be the same for both triangles.
This means that the distance between B and E, is the same distance as the distance between B' and E.
Now, as you know, the midpoint of a segment is a point such that the distance between that point and each endpoint is the same.
So, in the linea AA', the points A and A' are the endpoints, and because F lies in the line of reflection, the distance between A and F is the same distance than in between A' and F.
So F is the midpoint in the line AA'
The correct option would be the first one, F is the midpoint of AA' because the line EG bisects AA', and F is colinear to E and G.
Arrange the equations in the correct sequence to rewrite the formula for displacement, d = vt-at?, to find a. In the formula, dis
displacement, vis final velocity, a Is acceleration, and t is time.
2(vt -d)=at^2
a=2(d – vt)/12
2(d-vt) = at^2
vt-d=1/2 at^2
d-vt = 1/2at^2
a=2(vt-d)/t^2
Options
[tex]2(vt -d)=at^2[/tex]
[tex]a=\frac{2(d - vt)}{t^2}[/tex]
[tex]2(d-vt) = at^2[/tex]
[tex]vt-d=\frac{1}{2} at^2[/tex]
[tex]d-vt = -\frac{1}{2}at^2[/tex]
[tex]a=\frac{2(vt-d)}{t^2}[/tex]
Answer:
See Explanation below
Step-by-step explanation:
Given
[tex]d = vt - \frac{1}{2}at^2[/tex]
Required
Steps to find a
To solve for a;
The step 1 is :
[tex]d-vt = -\frac{1}{2}at^2[/tex]
This is achieved by adding vt to both sides
The step 2 is:
[tex]vt-d=\frac{1}{2} at^2[/tex]
This is achieved by multiply both sides by -1
The step 3 is:
[tex]2(vt -d)=at^2[/tex]
This is achieved by multiplying both sides by 2
The step 4 is:
[tex]a=\frac{2(vt-d)}{t^2}[/tex]
This is achieved by dividing both sides by t²
Note that, not all steps in the option are used because they are either incorrect or not necessary
Answer:
for edmentum the answer is
Box 1: d-vt=1/2at^2
Box 2: vt-d=1/2at^2
Box 3: 2(vt-d)/t^2
Step-by-step explanation: Almost certain after scrounging Brainly.
Good luck!
If sin(18+x)=cos58 find value of x
Answer:
14
Step-by-step explanation:
Since sine and cosine are cofunctions of each other:
[tex]\sin (\theta)= \cos (90-\theta)[/tex]
and vice versa. Therefore:
[tex]18+x=90-58 \\\\18+x=32 \\\\x=32-18=14[/tex]
Hope this helps!
Which is the better buy?. Store A $180 at 1/3 off Or Store B $110 at 10% off
Answer: Store B
Step-by-step explanation:
180 / 3 = 60. 180 - 60= $120. Store A cost is $120.
110 * 0.9 = $99. Store B's cost is $99.
Answer:
Store B
Step-by-step explanation:
Store A the price would be about $120.60
Store B price would be about $99
To find store a price, you first find the discount, so
0.33 x 180 = 59.40
Then subtract this from the original price to know the total after the discount
180-59.40=120.60
Do the same thing with the other Store
110 x 0.10 = 11
110-11=99
100 POINTS!!!!! PlZ help Find all possible values of the digits Y, E, A, R if YYYY - EEE + AA - R = 1234, and different letters represent different digits.
Answer:
Y = 1, E = -1, A= 1, R = -1
Step-by-step explanation:
YYYY - EEE + AA - R = 1234
First we would break down the digits in the whole numbers into their place value (thousands, hundreds, tens and units).
YYYY = 1000Y + 100Y +10Y + Y
EEE = 100E + 10E + E
-EEE = -100E - 10E - E
AA = 10A + A
R = R
-R = -R
1234 = 1000+200+30+4
Let's equate each place value for each of the numbers.
Thousands: 1000Y = 1000
Y = 1000/1000 = 1
Hundreds: 100Y - 100E = 200
100(1) - 100E = 200
-100E = 200-100
-100E= 100
E = -1
-EEE = -E(111)
Tens: 10Y - 10E + 10A = 30
10(1) - 10(-1) + 10A = 30
20+ 10A = 30
A = 10/10
A= 1
Units: Y - E + A - R = 4
1 - (-1) + 1 - R = 4
3-R = 4
R = 3-4 = -1
YYYY - EEE + AA - R = 1234
1111 - (-111) + 11 - (-1) = 1111+111+11+1 = 1234
All possible values of the digits Y, E, A, R are Y = 1, E = -1, A= 1, R = -1
Answer:
Y=2
E=9
A=1
R=0
Step-by-step explanation:
Let's check our work.
2,222 - 999 + 11 - 0
1,223 + 11 - 0
1,234 - 0
1,234
Also previous answerer how can digits be negative?
Please answer this correctly
Answer:
5/7
Step-by-step explanation:
There are 7 cards, all of which have an equal chance of being chosen.
And in this case, because there are 7 cards in total, they each have a 1/7 chance of being chosen. Because there are 5 cards greater than 4, you have a 5x1/7 chance =5/7 chance of choosing a number greater than 4.
P.S. If you need it as a percentage, then it is 71.428571%.
P.P.S. Remember if you like the answer then mark as brainliest thank you!
Pleasssseeee hheeelllppp
Answer:
No
Step-by-step explanation:
They are not congruent or similar because the figures themselves indicate no similar or congruent parts. Although they may seem congruent or similar, without telling us one thing, we cannot assume that they are similar or congruent.
4. (07.04 MC)
An observer (0) spots a plane (P) taking off from a local airport and flying at a 23° angle horizontal to her line of sight and located directly above a tower (T). The observer also notices a bird (B)
circling directly above her. If the distance from the plane (P) to the tower (T) is 5,000 ft., how far is the bird (B) from the plane (P)? Round to the nearest whole number.
Answer:
11779 ft
Step-by-step explanation:
We are given that
[tex]\theta=23^{\circ}[/tex]
Distance between tower and plane,d=5000 ft
We have to find the distance between the plane and bird.
Let x be the distance between bird and plane
We know that
[tex]tan\theta=\frac{perpendicular\;side}{Base}[/tex]
Using the formula
[tex]tan23=\frac{5000}{x}[/tex]
[tex]x=\frac{5000}{tan23}=11779.3 \approx 11779ft[/tex]
Hence, the distance between the plane and bird=11779 ft
Answer:
11779 ft
Step-by-step explanation:
We are given that
Distance between tower and plane,d=5000 ft
We have to find the distance between the plane and bird.
Let x be the distance between bird and plane
We know that
Using the formula
Hence, the distance between the plane and bird=11779 ft
How many arrangements of the letters in the word olive can you make if each arrangement must use three letters
Answer:
60
Step-by-step explanation:
There are 5 letters that can be first.
There are 4 letters that can be second.
There are 3 letters that can be third.
The number of permutations is 5×4×3 = 60.
6 people will attend a lunch 2 cans of juice should be provided per person determine the total number of cans of juice required
Answer:
12
Step-by-step explanation:
it's 6 people and 2 cans of juice goes to each person so you can multiply 6× 2 and you get 12 . 12 cans of juice would be required to provide 6 people with 2 cans each .
A large school district notices that about 26% of its sophomore students fail Algebra I. An online education supplier suggests the district try its new technology software, which is designed to improve Algebra 1 skills and, thus, decrease the number of students who fail the course. The new technology software is quite expensive, so the company offers a free, one-year trial period to determine whether the Algebra 1 pass rate improves. If it works, the district will pay for continued use of the software. What would happen if the school district makes a Type I error
Answer:
In the case of a Type I error, the null hypothesis would be wrongly rejected and the school district will conclude that the new technology is effective when it is not.
They will start to pay for the software when in fact it does not improve Algebra 1 skills.
Step-by-step explanation:
A Type I error happens when a true null hypothesis is rejected.
The probability of a Type I error is equal to the significance level, as it is the probabilty of getting an sample result with low probability but only due to chance, as the null hypothesis is in fact true.
In this scenario, the null hypothesis would represent the claim that the new technology does not make significant improvement.
In the case of a Type I error, this null hypothesis would be wrongly rejected and the school district will conclude that the new technology is effective when it is not.
They will start to pay for the software when in fact it does not improve Algebra 1 skills.
a personality test maybe given to assess what
Answer:
A personality test may be given to assess individual behavior patterns. A personality test may be given to assess individual behavior patterns. This answer has been confirmed as correct and helpful.
Step-by-step explanation:
hopes this helps
Answer:
Interests, values, skill set and basic personality
Step-by-step explanation:
Personality tests are mostly used as an assessment tool be HR managers and employers during the interview process. They can provide a potential employer with information about your interests, values, skill set and even basic personality, which can be very useful to help an employer make a decision about whether you are the best fit for a position.
I hope this helped. I am sorry if you get this wrong.
5:36, 2:9, 3:18, 1:3 what is the largest ratio? please help me!
Answer:
[tex]1:3[/tex]
Step-by-step explanation:
[tex]5:36=5/36[/tex]
[tex]\approx 0.13888888888[/tex]
[tex]2:9=2/9[/tex]
[tex]\approx 0.22222222222[/tex]
[tex]3:18=1/6[/tex]
[tex]\approx 0.16666666666[/tex]
[tex]1:3=1/3[/tex]
[tex]\approx 0.33333333333[/tex]
Answer:
1:3
Step-by-step explanation:
GCF of 36, 9, 18, 3 is 36
5:36
2:9= 8:36
3:18= 6:36
1:3= 12:36
1:3 is the largest ratio.
justify each step x/3-7=11 x/3=18 x=6
This is the steps for equation solving for the value of x,
x/3-7 = 11
now 7 goes to the other side of equation by changing the sign from - to +,
x/3 = 11 + 7
x/3 = 18
now when we multiply both sides of equation with 3 or 3 goes to the other side of equation and multiply with 18 leaving x alone here for finding the value of x,
and we get, x = 54
at the end of equation we get x = 54, if the equation was in the form 3x - 7 = 11, then we will get x = 6
HELP ME PLS I DO NOT UNDERSTAND A random number generator is used to create a real number between 0 and 1, equally likely to fall anywhere in this interval of values. (For the instance, 0.3794259832... is a possible outcome). a. Sketch a curve of the probability distribution of this random variable, which is the continuous version of the uniform distribution. b. What is the mean of this probability distribution?
f(x)=1, 0 < x < 1 is the probability density function of the random variable x.
generally, it is f(x)=1/(b-a) a < x < b;
where b=1 and a=0.
b) mean = integral (0 to 1) xdx = (0 to 1) = 1/2
c)integral( 0.35 to 0.6) dx =x (between 0.35 and 0.6) = 0.6-0.35=0.25
d) integral(less than 0.82)dx = x (between 0 and 0.81) = 0.81 - 0 = 0.81
Please mark me brainliest!
Which are the possible side lengths of a triangle?
O 3 cm, 5 cm, 9 cm
O 4 cm, 8 cm, 10 cm
O 6 cm, 9 cm, 17 cm
O 8 cm, 10 cm, 18 cm
Answer:
4 cm, 8 cm, 10 cm
Step-by-step explanation:
For a triangle to exist, two sides added up must be greater than the third side. The only quantities that satisfy this relationship is the second option.
Flight 4581 travels daily from Pittsburgh to San Antonio. The flight is due into San Antonio at 5:07 p.m. The following list gives the Flight 4581 arrival time relative to 5:07 p.m. (in minutes) for a selection of 9 days. (A negative number means that the flight arrived early.) 21, 39, 37, 25, 6,-6, -4, 40, 37 Send data to Excel
(a) What is the mean of this data set? If your answer is not an integer, round your answer to one decimal place. an integer, round your answer to one decimal place.
zero modes
(b) How man ndicate the number of mo vasluers) of the mode modes does the data set have, and what are eir values?
Question:
Flight 4581 travels daily from Pittsburgh to San Antonio. The flight is due into San Antonio at 5:07 p.m. The following list gives the Flight 4581 arrival time relative to 5:07 p.m. (in minutes) for a selection of 9 days. (A negative number means that the flight arrived early.) 21, 39, 37, 25, 6,-6, -4, 40, 37 Send data to Excel
(a) What is the mean of this data set? If your answer is not an integer, round your answer to one decimal place. an integer, round your answer to one decimal place.
b) How many modes does the data set have? and what are their values
Answer:
a) 21.2
b) Value of mode = 37
It contains just one mode
Step-by-step explanation:
Given:
x = 21, 39, 37, 25, 6,-6, -4, 40, 37
n = 9
a) Find the mean
Mean is the average value of a dataset.
Mean = Σx/n
Mean = [tex] \frac{21+39+37+25+6+(-6)+(-4)+40+37}{n} [/tex]
[tex] = \frac{195}{9} [/tex]
[tex] = 21.667 [/tex]
The question says one decimal place.
Therefore, mean = 21.7
b) The mode of a dataset is the value that appears most frequently.
We have the following datasets:
21, 39, 37, 25, 6,-6, -4, 40, 37
The value that appears most frequently here is 37.
37 appeared twice while the rest appeared just once.
Therefore the dataset contains just one mode
A quality control inspector has drawn a sample of 14 light bulbs from a recent production lot. If the number of defective bulbs is 1 or less, the lot passes inspection. Suppose 20% of the bulbs in the lot are defective. What is the probability that the lot will pass inspection
Answer:
0.1979 or 19.79%
Step-by-step explanation:
If 20% of all bulbs are defective, there is a 20% chance of each bulb being defective and an 80% chance of each bulb not being defective.
This is a binomial probability model with probability of success (bulb being defective) of p=0.20.
In order for the lot to pass inspection, it must contain either zero or one defective bulb, the probability of one of these scenarios occurring is:
[tex]Pass= P(d=0)+P(d=1)\\Pass= 0.80^{14}+14*0.20*0.80^{13}\\Pass=0.1979[/tex]
The probability that the lot will pass inspection is 0.1979 or 19.79%.
write an equation for an ellipse centered at the origin, which has foci at (+-3,0) and co vertices at (0+-4)
Answer:
The equation for an ellipse centered at the origin with foci at (-3, 0) and (+3, 0) and co-vertices at (0, -4) and (0, +4) is:
[tex]\frac{x^{2}}{7} + \frac{y_{2}}{16} = 1[/tex]
Step-by-step explanation:
An ellipse center at origin is modelled after the following expression:
[tex]\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1[/tex]
Where:
[tex]a[/tex], [tex]b[/tex] - Major and minor semi-axes, dimensionless.
The location of the two co-vertices are (0, - 4) and (0, + 4). The distance of the major semi-axis is found by means of the Pythagorean Theorem:
[tex]2\cdot b = \sqrt{(0-0)^{2}+ [4 - (-4)]^{2}}[/tex]
[tex]2\cdot b = \pm 8[/tex]
[tex]b = \pm 4[/tex]
The length of the major semi-axes can be calculated by knowing the distance between center and any focus (c) and the major semi-axis. First, the distance between center and any focus is determined by means of the Pythagorean Theorem:
[tex]2\cdot c = \sqrt{[3 - (-3)]^{2}+ (0-0)^{2}}[/tex]
[tex]2\cdot c = \pm 6[/tex]
[tex]c = \pm 3[/tex]
Now, the length of the minor semi-axis is given by the following Pythagorean identity:
[tex]a = \sqrt{b^{2}-c^{2}}[/tex]
[tex]a = \sqrt{4^{2}-3^{2}}[/tex]
[tex]a = \pm \sqrt{7}[/tex]
The equation for an ellipse centered at the origin with foci at (-3, 0) and (+3, 0) and co-vertices at (0, -4) and (0, +4) is:
[tex]\frac{x^{2}}{7} + \frac{y_{2}}{16} = 1[/tex]
Square 100 * square 25 simplified
Answer:
50
Step-by-step explanation:
Both √100 and √25 are perfect squares:
√100 = 10
√25 = 5
10(5) = 50
EXREAMLY URGENT!! WILL FOREVER THANK YOU!!!! PLS JUST TAKE A LOOK!!!!!
17. Find the measure of DE
A) 14.5
B) 13.4
C) 12.3
D) 15.9
Answer:
C. 12.3
Step-by-step explanation:
We should use Law of Cosines: c² = a² + b² -2abcosC
If that is the case, then EF is a, DF is b, and ∠F is c. We then plug the known variables in:
c² = 12² + 13² - 2(12)(13)cos59°
Plug that into the calc and you should get 12.2313, rounded to 12.3 as your final answer!