The polynomial (A) f(x)=x³-2x²-3x+6 has the zeros 2, radical 3, and negative radical 3 thanks to the factor theorem.
What is Factor Theorem?A factor theorem is a tool used in mathematics to thoroughly factor polynomials.
It is a theorem that connects the polynomial's zeros and factors.
The factor theorem states that (x-a) is a factor of f(x) if f(a)=0 and f(x) is a polynomial of degree n 1 and 'a' is any real number.
So, the Factor Theorem states that P(k) must equal zero if (x - k) is a factor of polynomial P(x).
A polynomial function with the zeros 2, 3, and -3 is provided to us. As a result, we can set k = 2, 3, -3.
The Factor Theorem states that P(2), P(3,) and P(-3) must all equal 0.
Tests of each option reveal that only option A is accurate:
f(x) = x³ – 2x² – 3x + 6
Testing each of the three results in:
[tex]\begin{aligned}f(2) & =(2)^3-2(2)^2-3(2)+6 \\& =(8)-(8)-(6)+(6) \\& =0 \stackrel{\checkmark}{=} 0 \\f(\sqrt{3}) & =(\sqrt{3})^3-2(\sqrt{3})^2-3(\sqrt{3})+6 \\& =(3 \sqrt{3})-(6)-(3 \sqrt{3})+6 \\& =0=0 \\f(-\sqrt{3}) & =(-\sqrt{3})^3-2(-\sqrt{3})^2-3(-\sqrt{3})+6 \\& =(-3 \sqrt{3})-(6)+(3 \sqrt{3})+6 \\& =0=0\end{aligned}[/tex]
Therefore, with the help of the factor theorem, polynomial (A) f(x)=x³-2x²-3x+6 has the zeros 2, radical 3, and negative radical 3.
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Complete question:
Using the Factor Theorem, which of the polynomial functions has the zeros 2, radical 3, and negative radical 3?
a. f(x) = x3 – 2x2 – 3x + 6
b. f(x)= x3 – 2x2 + 3x + 6
c. f(x) = x3 + 2x2 – 3x + 6
d. f(x) = x3 + 2x2 – 3x – 6
-3x-4y=12 solve for Y
What is the area of triangle ABC if a = 7, c = 11, and B = 55°?
Round the answer to the nearest hundredth.
The area of the triangle is 31.54 square units
How to determine the area of the triangleFrom the question, we have the following parameters that can be used in our computation:
We have the following values
a = 7 units
c = 11 units
B = 55 degrees
The area of the triangle is calculated using the following area formula
Area = 1/2absin(C)
Substitute the known values in the above equation, so, we have the following representation
Area = 1/2 * 7 * 11 * sin(55 degrees)
Evaluate
Area = 31.54
Hence, the area is 31.54 square units
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(a) at point a or point b is the gradient vector more horizontal? why? (b) at point a or point b is the gradient vector longer? why?
The definition of the gradient vector for point a to b is defined below.
Vector:
In math vector value consists of magnitude and direction.
Given,
Here we need to find the gradient vector of point a or point b.
According to the definition of vector, a multidimensional input have partial derivatives, you might wonder what the full derivative of such a function is. Here in the case of scalar-valued multivariable functions, meaning those with a multidimensional input but a one-dimensional output, the answer is the gradient.
Where as the gradient of a function f, denoted as ∇f,
Where f, is the collection of all its partial derivatives into a vector.
Here the point a and b is more horizontal because of the partial derivative nature of vector.
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Christina's Pizza sells pizza by the slice for lunch. Today, they sold 76 slices, including 20 slices of pepperoni pizza. What is the experimental probability that the first slice sold during lunch tomorrow will be a slice of pepperoni pizza?
Write your answer as a fraction or whole number.
P(pepperoni)=
Answer:
Step-by-step explanation:
2/6
consider the following binomial experiment: the probability that a cell phone manufactured at electronics unlimited is defective is 0.11. if a sample of 6 cell phones is selected at random, what is the probability that at least one is defective? a) 0.4423 b) 0.5030 c) 0.4970 d) 0.5584 e) 0.4416 f) none of the above.
Using the binomial distribution, it is found that there is a 0.5954 = 59.54% probability that at least 1 is defective.
What is the binomial distribution?
A collection of numerous independently distributed Bernoulli trials with equal distributions results in the binomial distribution. The experiment in a Bernoulli trial is said to be random and can only result in one of two outcomes: success or failure.
For each phone, there are only two possible outcomes, either it is defective, or it is not. The probability of a phone being defective is independent of any other phone, which means that the binomial distribution is used to solve this question.
Binomial probability distribution
[tex]P(X = x) = C_n, x. p^{x.(1-p)^n-x}[/tex]
[tex]C_n, x = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.
n is the number of trials.
p is the probability of success on a single trial.
In this problem:
0.11 probability of a single phone is defective, hence
6 phones are selected at random, hence
The probability that at least 1 is defective is:
P(X >= 1) = 1 - P(X = 0)
In which
[tex]P(X = x) = C_n, x. p^{x.(1-p)^n-x}[/tex].
P(x = 0) = C₆,₀.(0.11)⁰ (0.86)⁶ = 0.4046
Then:
P(X >= 1) = 1 - P(X = 0) = 1 - 0.4046 = 0.5954
Hence, the 0.5954 = 59.54% probability that at least 1 is defective.
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11. There is a $10 monthly membership fee to download music. There is
a $0.50 fee for each song downloaded.
a. Write a linear equation that models the cost of downloading x songs
per month.
b. Graph the equation.
c. What is the cost of downloading 15 songs?
Answer:
A) y=0.5x+10 C) 17.5 dollars (don't forget your units)
Step-by-step explanation:
a) 0.5 is the price paid per song, or x, and 10 is the price that does not change for a month, so we can say that y=0.5x+10
c) to download 15 songs, we substitute x by 15
y=0.5(15)+10
y=7.5 + 10
y=17.5
and for b, im sorry but I cannot graph here.
let $w 1, w 2, \dots, w n$ be complex numbers. a line $l$ in the complex plane is called a mean line for the points $w 1, w 2, \dots, w n$ if $l$ contains points (complex numbers) $z 1, z 2, \dots, z n$ such that \[\sum {k
The slope of the line is going to be m = 163.
Here, we have been told that the sum of the numbers is going to be -
= ∑[tex]w _{k}[/tex]= 3 + 504i (i)
The other set of complex numbers is (z₁, z₂, ....[tex]z_{k}[/tex]) and their sum is going to be = ∑[tex]z_{k}[/tex]= 3 + 504i (ii)
If we write the number 3+504i in the standard form for complex numbers i.e., a+bi with respect to the summations, we get -
= ∑[tex]a_{k}[/tex]= 3 (III)
= ∑[tex]b_{k}[/tex]= 504 (Iv)
The standard equation is of the form, y = mx+3. Substituting the polar coordinates, we get -
= [tex]b_{k}[/tex] = m[tex]a_{k}[/tex] + 3
Now, if we use all of the given values in equations (iii) and (iv) for k, we get -
= 504 = 3m + 15
Now, on simply solving for m, we get -
= 3m = 504 - 15 = 489
= m = 489/3
= m = 163
Henceforth, we find out that the slope of the line, m is 163.
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y normally distributed with a standard deviation of 40 hours. how large a sample is needed if we wish to be 96% confident that our sample mean will be within 10 hours of the true mean?
A sample of 68 is needed if we wish to be 96% confident that our sample mean will be within 10 hours of the true mean for the standard deviation of 40 hours
Since a level =1-0.96/2 =0.02, here the Z value of 1-a = 1-0.02= 0.98 , for which z=2.055 .Now we know that the formula for margin is:
M = z*σ/√n, where σ is the standard deviation and n is the sample size since we are provided with the standard deviation of 40 and M=10. so,
=> 10= 2.055*40/√n
=>10√n= 2.055*40
=>√n = 82.2/10
=>n=67.6 ,which is almost 68
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Round the decimal 213.21 to the nearest whole number.
Answer: 213
Step-by-step explanation:
Answer: 213
Step-by-step explanation:
find the temperature (in k) at which the root-mean-square speed of ch4 molecules is the same as the root-mean-square speed of o2 molecules at 448.8 k.
Temperature of ch4 will be 150K
given :-
[tex]\sqrt{2} speed of 02 = 448.8[/tex]
u.avg. = [tex]\sqrt{8rt/\pi m} \\[/tex]
u.avg ch4 = [tex]\sqrt{8rt1/\pi 16}[/tex]
hence , mass of ch4 = 12 +4 = 16
Methane (US: MEH-thayn, UK: MEE-thayn) is a chemical compound with the chemical formula CH4 (one carbon atom bonded to four hydrogen atoms). It is a group-14 hydride, the simplest alkane, and the main constituent of natural gas.
The molar mass of oxygen atom O
O
is 15.99
This is only the mass of 1 oxygen atom so the molar mass of oxygen molecule O is 15.99
is double the number, i.e. approximately 32
u.avgO2 = [tex]\sqrt{8r(300)/\pi (32)}[/tex]
u.avgch4 = u.avgo2
[tex]\sqrt{8rt1/\pi 16}[/tex] = [tex]\sqrt{8r(300)/\pi (32)}[/tex]
==> t1/16 = 300/32
==> t1 = 150 K
They have same average velocity when the temperature of CH4 is 150 K
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Write the equation of the line that passes through the points (2, 7) and (5,-2).
Answer:
y = -3x + 13
Step-by-step explanation:
Assuming the line is linear, you can use the point-slope equation of a line.
(y - y) = m (x - x)
The y and x variables come from the points on the line. Points are written in the form (x, y). In the point (2,7), 2 is x and 7 is y.
1. Plug your points in.
(7 - - 2) = m (2 - 5)
2. Solve for m (the slope)
(7 + 2) = m (2 - 5)
(9) = m (-3)
9 = -3m
m = -3
3. Write an equation of the line with the slope you found.
You can write this equation in different forms, but I'll use the slope-intercept form.
y = mx + b
You'll have to find b, the y-intercept. You can plug one of your points in for x and y as well as your slope, m, and solve for b.
7 = -3(2) + b
7 = -6 + b
b = 13
Therefore, the equation is y = -3x + 13
only six and seven needed
6- G and P are collinear
7- Points D,H and P are collinear
Answer: 67 87 34
Step-by-step explanation:
To prepare for the drama club's upcoming musical performance, Ms. Melody is printing programs on the school's copier. The number of programs Ms. Melody has printed increases over time. This situation can be modeled as a linear relationship.
What does the slope of the line tell you about the situation?
The slope of linear graph is 4 which means the rate of prinitng program copies is 4 copies per minute.
What is formula for slope?
The slope of the line between two points (x₁, y₁) and (x₂, y₂) is
m = (y₂ - y₁)/(x₂ - x₁)
Slope of a line signifies rate of change between two quantities.
According to the given question:
(Check the graph attached below)
From the graph the two points we can consider for finding the graph are (0,0) and (3, 120)
Putting these values in the formula for slope
m = (y₂ - y₁)/(x₂ - x₁)
= (120 -0)/(30 - 0)
= 4
Hence slope of the line in the situation tells that the rate of printing program is 4 copies per minute.
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Endure all, a manufacturer of batteries claims that the lifetime of their batteries is normally distributed with a mean of 500 hours and a standard deviation of 40 hours. What is the probability that an endure all battery selected at random will last more than 550 hours?.
A random selection of an Endure All battery has a 10.56% probability of lasting more than 550 hours.
Explain the term z score?A Z-score is a metric that quantifies how closely a value relates to a mean of a set of values. Standard deviations as from mean are used to measure Z-score. A Z-score of zero means the data point is entirely score is the same as the mean score.The Z score is utilized to calculate how far the raw score deviates from the mean.
The Z score is calculated as follows:
z = (x - μ)/σ
Given that x > 550 and μ = 500, σ = 40:
z = 550 - 500 / 40
z = 1.25
Following the normal distribution chart,
P(z > 1.25) = 1 - P(z < 1.25)
P(z > 1.25) = 1 - 0.8944
P(z > 1.25) = 0.1056
Therefore, there is a 10.56% chance that a randomly chosen Endure All battery would survive longer than 550 hours.
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my regular recipe for cream of potato soup makes 50 8-ounce servings. i need to make potato soup for 200, but i want to increase the portion size to 12 ounces. what conversion factor should i use to adjust my recipe for the new amount?
The conversion factor you should use to adjust your recipe for the new amount is 6.
What is conversion factor?
A conversion factor is a number that is used to multiply or divide one set of units into another. If a conversion is required, it must be done using the correct conversion factor to get an identical value.
Equating the conversion factor :
Given: original serving = 50 8-ounce serving
required new serving = 200 12-ounce serving
To find: conversion factor?Original serving = 50×8 ounce = 400 ounce
Required serving = 200×12 ounce
= 2400 ounce
As we know, conversion factor = {Required Yield} ÷ {Original Yield}
∴ Conversion factor =2400 ÷ 400
∴ Conversion factor = 6
Conversion factor is greater than 1 when required yield is supposed to be greater than original yield and conversion factor is less than 1 when required yield is less than original yield.
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Find the missing angle measures.
The value of x is 122°.
The value of y is 130°.
What are corresponding angles?The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.
Corresponding angles are equal.
We have,
The figure has two parts.
One part is a triangle.
Another part is a heptagon.
We see that,
The three angles sum 180 degrees.
Two angles are equal inside the triangle.
2m + 80 = 180
2m = 180 - 80
2m = 100
m = 50
Now,
y + 50 = 180
y = 180 - 50
y = 130
Now,
The sum of the heptagon angles is 900.
Three angles are the same.
i.e 3x
Two angles are the same.
i.e 130 + 130 = 260
260 + 3x + 135 + 140 = 900
3x + 535 = 900
3x = 900 - 535
3x = 365
x = 365/3
x = 122
Thus,
The value of x is 122°.
The value of y is 130°.
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28 Find the area of the figure below.
2(2x-4)om
(2x+10) cm
A. 528cm²
C. 480cm²
B. 92cm²
D. 46cm²
(x +13)cm
*
35
Answer:
A=L*W2x-4=2x+10x=14ans=912the volume of a gas in a container varies inversely with the pressure on the gas. if a gas has a volume of 500 cubic inches under a pressure of 14 pounds per square inch, what will be its volume if the pressure is increased to 19 pounds per square inch? (round off your answer to the nearest cubic inch.)
If the pressure is increased to 19 pounds per square inch, then the volume is 368.42 cubic inches
The volume of the gas = 500 cubic inches
The pressure = 14 pounds per square inch
The volume of a gas in a container varies inversely proportional with the pressure on the gas.
V ∝ 1/P
Where V is the volume and P is the pressure
Then,
V = k/P
Where k is the constant
500 = k/14
k = 500 × 14
k = 7000
The pressure of the gas = 19 pounds per square inch
Volume = 7000 /19
= 368.42 cubic inches
Therefore, the volume is 368.42 cubic inches
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hypotheses: h0: pass/fail rates are school. h1: pass/fail rates are school. which of the following best fits the blank spaces above?
The correct option is independent of, dependent on for the given sets of hypothesis H0: Pass/fail rates are _____ school. H1: Pass/fail rates are _____school.
What is hypothesis?A hypothesis is a statement that makes sense in light of the available information but hasn't been proved true or wrong. A hypothesis in statistics is a claim that will serve as the foundation for hypothesis testing (also known as a statistical hypothesis). A straightforward hypothesis is a claim that expresses the relationship between precisely two variables. a dependant and a single independent. Take the statement "Smoking is a significant cause of lung cancer" as an example. Smoking is an independent variable that influences the dependent variable, lung cancer.
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Use the ruler to measure the length of RS to the nearest centimeter.
The length of RS is __ Centimeters.
The answer should be 18cm
Here is why I think that:
On the ruler, you should count from 9 to 26
9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26.
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18.
The total tick marks from 9 to 26 is = to 18
(I know that R is resting above the number eight, do not count that one, many people make that mistake)
Please let me know in the comments if
somehow my calculation is wrong.
If a = 3 and b = 5, find a/(a+b)=.
Answer: 5/3 or 1.67
Step-by-step explanation:
what is
c=2.80g c=8.30g
Which of the following would best describe the situation that a second-degree polynomial regression equation would be used to model?
A) An exponential growth trend
B) A cosine function
C) A parabola
D) It depends on the number of independent variables.
(C) A parabola is the best representation of the situation that a second-degree polynomial regression equation would be used to mimic.
What is a Parabola?A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics.
It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves.
A parabola can be described using a point and a line.
The situation that a second-degree polynomial regression equation would be used to simulate is best described by a parabola.
The phrase "parabolic move" originated as trader jargon.
It describes when a stock experiences an increase in price that resembles the right side of a parabolic curve: A parabolic move happens when the stock's price rises at an exponentially faster rate.
Therefore,(C) a parabola is the best representation of the situation that a second-degree polynomial regression equation would be used to mimic.
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How many eighty-fours are in 672?
Answer: 8
Step-by-step explanation:
We only need to take 672/84 = 8
So there are 8
If you can please give me a Brainliest, I only need 1 more to become an Ace, thank you!
Answer:
x=8
Step-by-step explanation:
Lets assume that the number of 84 is x
as given in this equation
total values given in the question be 672
then the equatiuon becomes
84 multiplied by x is 672
simplify above the equation
84x=672
[tex]x=\frac{62}{84}[/tex]
x=8
Therefore, the number of 84 is 672 is 8.
(Hope this helped! :D)
Use the number line to represent the solution to 2.4x−6>−13.2.
Answer:
The answer should be (8,0)
In PQR, QR PQ and m/Q = 159°. Find m/P.
Applying the definition of an isosceles triangle, the measure of angle P = 10.5°.
What is an Isosceles Triangle?If a triangle has two sides that are of the same length, then the triangle is an isosceles triangle. Thus, the angles that are opposite the two equal sides of an isosceles triangle are called the base angles, and they are therefore congruent to each other.
Given that triangle PQR has two equal sides, QR ≅ PQ, it means it is an isosceles triangle, therefore its base angles, ∠P ≅ ∠R.
Therefore:
m∠Q = 159° [given]
m∠P = 1/2(180 - 159)
m∠P = 1/2(21)
m∠P = 10.5°
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HELP MEEEEEE bc y’all are slay
The correct relation is that both the angles are corresponding angles.
What are corresponding angles?Corresponding angles are angles that occur on the same side of the transversal line and are equal in size.
Given is an arrangement of streets in the form of two parallel lines and a street acting as a transversal.
The angle of library and angle of school are corresponding angles, and corresponding angles between parallel lines are congruent.
Since, angle of library = 42°
angle of school = angle of library
Therefore, angle of school = 42°
Hence, The correct relation is that both the angles are corresponding angles.
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is the pareto distribution a member of a location family? a member of a scale family? a member of a location-scale family? none of the above? explain.
Pareto distribution is a member of a scale family referring fixed values of the shape parameter, it is trivially closed under scale transformations.
The Pareto distribution is a power-law probability distribution used in description of social, quality control, scientific, geophysical, actuarial, and many other types of observable phenomena. It was initially applied to demonstrate the distribution of wealth in a society, fitting the trend that a large portion of wealth is held by a small fraction of the population. The pareto principle or 80-20 rule states that 80% of outcomes are due to 20% of causes. Pareto distribution is a member of the scale family distribution which is parameterized by a scale parameter. The larger the scale parameter, the more spread out the distribution.
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is the square root of open paren x negative 3 close paren squared equals 3 negative x ? (1) x is not equal to 3 (2) negative x times the absolute value of x is greater than 0
The square root of open paren x negative 3 close paren squared =
3 negative x negative x times the absolute value of x is greater than 0.
Let the equation be: |x−3|=3−x|x−3|=3−x
When x>3x>3, then RHS is negative, but LHS (absolute value) is never negative, hence in this case equations doesn't hold true.
When x≤3x≤3, then LHS=|x−3|=−x+3=3−x=RHSLHS=|x−3|=−x+3=3−x=RHS
x≠3x≠3
Thus,
−x|x|>0−x|x|>0, this inequality implies that x<0x<0, hence x<3x<3.
Hence option b becomes the correct option i.e, negative x times the absolute value of x is greater than 0.
Square root of a number is a value, which on multiplication by itself, gives the original number. The square root is an inverse method of squaring a number. Hence, squares and square roots are related concepts.
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Shane can hike 10 miles in 5 hours. If he hikes for 8 hours, then how many miles will he travel
Answer: 13.33
Step-by-step explanation: I could be wrong