Answer:
x = {1, 1.5, 2}Step-by-step explanation:
GivenPolynomial f(x) = 2x³ - 9x² + 13x - 6, One of the factors x - 1.Factorize the polynomial using the given details.
Since one of the factors known, try to factor it out and futher:
2x³ - 9x² + 13x - 6 = 2x³ - 2x² - 7x² + 7x + 6x - 6 = 2x²(x - 1) - 7x(x - 1) + 6(x - 1) = (x - 1)(2x² - 7x + 6) = (x - 1)(2x² - 3x - 4x + 6) = (x - 1)[x(2x - 3) - 2(2x - 3)] =(x - 1)(x - 2)(2x - 3)Find its zero's:
x - 1 = 0 or x - 2 = 0 or 2x - 3 = 0x = 1 or x = 2 or x = 1.5Answer:
[tex]x=1, \quad x=\dfrac{3}{2}, \quad x=2[/tex]
Step-by-step explanation:
Factor Theorem
If f(x) is a polynomial, and f(a) = 0, then (x – a) is a factor of f(x).
If the coefficients in a polynomial add up to 0, then (x - 1) is a factor.
Given polynomial function:
[tex]f(x)=2x^3-9x^2+13x-6[/tex]
Sum the coefficients:
[tex]\implies 2-9+13-6=0[/tex]
As the sum of the coefficients is zero, (x - 1) is a factor.
Therefore:
[tex]\implies f(x)=(x-1)(ax^2+bx+c)[/tex]
Expand the brackets:
[tex]\implies f(x)=ax^3+bx^2+cx-ax^2-bx-c[/tex]
[tex]\implies f(x)=ax^3+(b-a)x^2+(c-b)x-c[/tex]
Compare the coefficients with the given polynomial.
As the coefficient of the leading term of the polynomial is 2:
[tex]\implies a=2[/tex]
As the coefficient of the term in x² is -9:
[tex]\implies b-a=-9[/tex]
[tex]\implies b-2=-9[/tex]
[tex]\implies b=-7[/tex]
As the constant of the given polynomial is -6:
[tex]\implies c=6[/tex]
Substitute the found values of a, b and c into the factored form of the polynomial:
[tex]\implies f(x)=(x-1)(2x^2-7x+6)[/tex]
Factor the quadratic:
[tex]\implies 2x^2-7x+6[/tex]
[tex]\implies 2x^2-4x-3x+6[/tex]
[tex]\implies 2x(x-2)-3(x-2)[/tex]
[tex]\implies (2x-3)(x-2)[/tex]
Therefore, the fully factored polynomial is:
[tex]\implies f(x)=(x-1)(2x-3)(x-2)[/tex]
To find the zeros, set the function to zero:
[tex]\implies f(x)=0[/tex]
[tex]\implies (x-1)(2x-3)(x-2)=0[/tex]
Apply the zero-product property:
[tex]\implies x-1=0 \implies x=1[/tex]
[tex]\implies 2x-3=0 \implies x=\dfrac{3}{2}[/tex]
[tex]\implies x-2=0 \implies x=2[/tex]
Therefore, the real zeros of the given polynomial are 1, ³/₂ and 2.
What is 3 2/5 plus 2 1/5?
Answer: 5 3/5
Step-by-step explanation:
3 + 2 = 5
2/5 + 1/5 = 3/5
5 + 3/5 = 5 3/5
Hope this helps!
Kayla is 1.85 meters tall. At 12 noon, she measures the length of a tree's shadow to be 28.15 meters. She stands 23.1 meters away from the tree, so that the tip of her shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter. -28.15 m (Diagram is not to scale.) T 1.85 m 23.1 m-
The height of the tree is approximately 2.11 meters if Kayla is 1.85 meters tall. At 12 noon, she measures the length of a tree's shadow to be 28.15 meters.
What is the similarity law for triangles?It is defined as the law to prove that two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.
It is given that:
Kayla is 1.85 meters tall. At 12 noon, she measures the length of a tree's shadow to be 28.15 meters.
D = 39.75 m
d = 34.9 m
H:h = D:d
H/1.85 = 39.75/34.9
H = 2.11 m
Thus, the height of the tree is approximately 2.11 meters if Kayla is 1.85 meters tall. At 12 noon, she measures the length of a tree's shadow to be 28.15 meters.
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You will have $ in five years if you set aside $1,000 a year at 8%.
printer a can print a 300 page document in 10 minutes. printer b can print a 400 page document in 8 minutes. Both printers were run until a total of 1000 pages were printed. How many pages did printer b print?
Answer:
625 pages
Step-by-step explanation:
Rate x time of the one printer + the rate x time of the second printer = 1000 pages
t= time
([tex]\frac{300}{10}[/tex] )t +( [tex]\frac{400}{8}[/tex]) t = 1000
30t + 50t = 1000
t(30 + 50) = 1000
80t = 1000 Divide both sides by 80
t = 12.5
It took 12.5 minutes to get this job done with both printers.
Look at printer b
[tex]\frac{400}{8}[/tex] (12.5) = pages
50 x 12.5 = 625 pages
to determine the number of trout in a lake, a conservationist catches 200 trout, tags them and throws them back into the lake. Later, 56 trouts are caught; 14 of them are tagged. how many trout would the conservationist expect to be in the lake
The conservationist expects to be in the lake would be; 142 trouts.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given, that determine the number of trout in a lake, a conservationist catches 200 trout, tags them, and throws them back into the lake.
We have to find conservationists who expect to be in the lake.
Now, initially, trout count = 200
Then, again 56 trouts caught then, trout count = 200 + 56
But 14 of them are tagged that means; they are part of 200 trouts so we should not count again in 56 trouts.
So, trout count = 200 + 56 – 14 = 142.
Hence, the conservationist expects would be; 142 trouts.
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Answer the question below in the picture please and thank you
Depending on the particular isotope, this process can take a variety of times. While for some it will take years and decades, it will just take a microsecond for individuals. Usually, the isotope will decay into a different element or isotope.
What is meant by isotope?Isotopes are two or more different atom types that share the same atomic number and place in the periodic table but have different quantities of neutrons in their nuclei, resulting in various nucleon numbers.
If we start with 180 g of the isotope, after one half-life the quantity will diminish to 180 g/2 = 90 g which exists half the original quantity.
This can be written mathematically as: [tex]$180 g\left(\frac{1}{2}\right)^1$[/tex]
After the second half life: [tex]$\frac{90 g}{2}=45 g=\frac{180 g}{4}=(180 g)\left(\frac{1}{2}\right)^2$[/tex]
After the third half life: [tex]$\frac{45 g}{2}= 22.5 g=\frac{180 g}{8}=(180 g)\left(\frac{1}{2}\right)^3$[/tex]
But now that we are dividing the amount by 2 to a power that grows as the number of half-lives, we can start to notice a pattern.
The original quantity can then be rapidly computed for six half-lives using the formula below:
[tex]$(180 g)\left(\frac{1}{2}\right)^6=(180 g)\left(\frac{1}{64}\right)=\frac{180 g}{64}=2.8 g$$[/tex]
Depending on the particular isotope, this process can take a variety of times. While for some it will take years and decades, it will just take a microsecond for individuals. Usually, the isotope will decay into a different element or isotope.
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suppose that a high school marching band has 108 members. of these 108 band members, 39 are seniors, 23 play the trumpet, and 8 are seniors who play the trumpet. what is the probability that a randomly selected band member is a senior given that he or she plays the trumpet? give your answer as a percentage, rounded to one decimal place.
The probability that a randomly selected band member is a senior given that he or she plays the trumpet is 34.78%.
Probability is defined as the likeliness of an event to happen. It can be calculated by dividing the total desired outcomes by the total outcomes.
P = desired outcomes / total outcomes
Of the 108 band members, if 23 play the trumpet, and 8 are seniors who play the trumpet, then the probability that a randomly selected band member is a senior given that he or she plays the trumpet is 8 divided by 23.
P = 8/23 x 100
P = 34.78%
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Sal earns $480 per week. Lidia earns $300 per week. Are their salaries proportional if Sal works 40 hours per week and Lidia works 25 hours per week?
True or false?
The given statement "Sal earns $480 per week. Lidia earns $300 per week. Are their salaries proportional if Sal works 40 hours per week and Lidia works 25 hours per week" is true.
As given in the question,
If one amount is proportional to another, the two amounts increase and decrease at the same rate so there is always the same relationship between them
a:b = c:d
a ÷b = c ÷d
ad = bc
let Sal earns $480 per week and he works 40hours per week
480÷40 = 12
Lidia earn $300 per week and she works 25 hours per week
300÷25 = 12
Cross product of their salaries is
480×25=1200
300×40=1200
The ratio of their salaries and their product are equal.
Hence, The given statement "Sal earns $480 per week. Lidia earns $300 per week. Are their salaries proportional if Sal works 40 hours per week and Lidia works 25 hours per week" is true
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Let f(x) = -3x³ + 9x² - 5x + 15. Use the Factor Theorem to help answer the
following questions.
a) Is a
O Yes
O No
b) Is x + 1 a factor of f(x)?
O Yes
No
1 a factor of f(x)?
c) Is a 3 a factor of f(x)?
O Yes
O No
Answer:
See below. I added words tro the first question "Is a" so that I could answer it.
Step-by-step explanation:
f(x) = -3x³ + 9x² - 5x + 15
f(x) = -(x-3)(3x² + 5)
x((9-3x)x-5)+15
-3(x-1)[tex]x^{3}[/tex] + 4(x-1) + 16
=======
a) Is a [ghost happy]?
O Yes Yes, as long as it can haunt.
O No
b) Is x + 1 a factor of f(x)?
O Yes Yes
No
1 a factor of f(x)?
Always
c) Is a 3 a factor of f(x)?
O Yes
O No No, as far as I can see.
(2,-9) reflected over the y-axis
The new point is (-2, -9).
What happens when a point is reflected about an axis?
The x-coordinate remains constant when a point is reflected across the x-axis, but the y-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the x-axis as (x, -y).
The y-coordinate stays the same when a point is reflected across the y-axis, but the x-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the y-axis as (-x, y).
Given, the point to be reflected is : A : (2, -9)
Also, the axis through which the point is to be reflected is y-axis.
Following the statement established in the literature, we have:
The point (2, -9) when reflected over the y-axis, the x-coordinate is assumed to be the additive inverse, thus the new co-ordinate is (-2, -9).
The new point is (-2, -9).
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write the answer in standard form(-3x^4 + x^6 – 9x^5+ 2x^2– 7) + (-2x^5 + x - 4x^2– x^4 + 12)
Simplify the expression and express in standard form.
[tex]\begin{gathered} (-3x^4+x^6-9x^5+2x^2-7)+(-2x^5+x-4x^2-x^4+12) \\ =-3x^4+x^6-9x^5+2x^2-7-2x^5+x-4x^2-x^4+12 \\ =x^6-11x^5-4x^4-2x^2+x+5 \end{gathered}[/tex]So answer is,
[tex]x^6-11x^5-4x^4-2x^2+x+5[/tex]Finding Slope
HELP ME
Answer: slope is -3
Step-by-step explanation: (-5,6) and (-9,-6)
Take your Y values and subtract them -6-6=-12
Take your X values and subtract them -9-(-5) or -9+5= -4
Then your -12 will be your numerator and your -4 will be your denominator
Then Divide
-12/-4= -3
I hope this helps!
You have a goal to practice the guitar for an average of at least 45 minutes per day for one week
An inequality that represents the number of minutes m you need to practice on the seventh day is m≤70.
Given that, You have a goal to practice the piano for an average of at least 45 minutes per day for one week.
What is a inequality?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Let m be the number of minutes you need to practice on the seventh day
The inequality for the given situation is
245+m≤315
⇒ m≤315-245
⇒ m≤70
Therefore, an inequality that represents the number of minutes m you need to practice on the seventh day is m≤70.
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"Your question is incomplete, probably the complete question/missing part is:"
You have a goal to practice the piano for an average of at least 45 minutes per day for one week. The first six days you practice a total of 245 minutes.
Write and solve an inequality that represents the number of minutes m you need to practice on the seventh day.
Convert the decimals below into fractions.
Use the symbol to represent the fraction bar. For example, you can expressas 2/3. Where necessary, express answers as improper fractions and in simplest
form.
0.25=
Type answer here. Be careful with spelling.
0.36
Type answer here. Be careful with spelling.
1.04 =
Type answer here. Be careful with spelling
sketch the graph or the inverse of the function pictured
Step 1:
Draw the table for the input x and output y.
Step 2:
From the table, we can see that the function is an exponential function.
[tex]\begin{gathered} y=x^2 \\ \text{for x = 0, y = 0} \\ \text{for x = 1, y = 1} \\ \text{for x = 2, y = 4} \\ \text{for x = 3, y = 9} \\ \text{Hence, y = x}^2 \end{gathered}[/tex]Step 2:
Find the inverse of the function.
[tex]\begin{gathered} y=x^2 \\ \text{The inverse of } \\ y=x^2 \\ is \\ y\text{ = }\pm\sqrt[]{x} \end{gathered}[/tex]Step 3:
The two graphs below, show the graph of the inverse for both negative and positive square roots of x.
[tex]\text{The blue graph above shows the graph for y = +}\sqrt[]{x}[/tex][tex]\text{The blue graph above shows the graph of y = -}\sqrt[]{x}[/tex]Final answer
The blue graph is the inverse of the red graph.
4x^2 -18x-5 factored form by grouping
4x² - 18x - 5 cannot be factored by grouping.
How to factor quadratic equations?Factoring a polynomial involves writing it as a product of two or more polynomials.
In other words, it is a process of finding the factor.
Therefore, let's factor the quadratic equation as follows:
4x² - 18x - 5
Factorization by grouping means that we need to group the terms with common factors before factoring.
The grouping method can be used to factor polynomials whenever a common factor exists between the groupings.
Hence,
4x² - 18x - 5 cannot be factorise by grouping because it has no common factor.
in other word, we cannot, however, use the grouping method to factor 4x² - 18x - 5 because factoring out the GCF from both groupings does not yield a common factor.
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What is the equation of the line that passes through the point (-6, 5) and has a
slope of - 3/2
Answer:
y = - [tex]\frac{3}{2}[/tex] x - 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = - [tex]\frac{3}{2}[/tex] , then
y = - [tex]\frac{3}{2}[/tex] x + c ← is the partial equation
to find c substitute (- 6, 5 ) into the partial equation
5 = 9 + c ⇒ c = 5 - 9 = - 4
y = - [tex]\frac{3}{2}[/tex] x - 4 ← equation of line
Find the tangent of the angle whose measure is negative pi. (-pi)
First convert the angle measure from radians to degrees using the formula
[tex]\theta\cdot\frac{180}{\pi}[/tex]Were θ represents the angle of interest
So for this exercise the angle is pi, so:
[tex]\pi\cdot\frac{180}{\pi}=180[/tex]Now using the calculator you can determine tha tangent of negative 180º
tan(-180º)=0
So the tangent of negative pi should also be zero
The angles of a triangle are in the ratio 2:8:5 find the size of each side
Answer:
24° , 60° , 96°
Step-by-step explanation:
sum the parts of the ratio, 2 + 8 + 5 = 15 parts
divide the sum of the angles in a triangle by 15 to find the value of one part of the ratio.
180° ÷ 15 = 12° , then
2 parts = 2 × 12° = 24°
5 parts = 5 × 12° = 60°
8 parts = 8 × 12° = 96°
the 3 angles in the triangle are 24° , 60° , 96°
a certain store has 3,000 employees working at its main location in a city and 100 employees working at a smaller location outside the city. the store manager will select a sample of 50 employees from all the employees to ask their opinions about extending store hours during the holidays. what is the advantage of selecting a stratified random sample, with location as strata, instead of a simple random sample? responses
The answer is the stratified sample assures that the opinions of employees from both locations will be represented..
The survey results will accurately reflect the opinions of both urban and rural employees if you choose this option. By soliciting feedback from employees in both regions, it will be possible to ensure that any policy based on the results of this survey not only represents the interests of urban employees, who make up the bulk of the workforce, but also those of rural employees.
Option B is untrue since a stratified sample will cost more to implement than a straightforward random sample and won't always result in financial savings.
Option C does not applicable because it is just a supposition without any supporting data.
Choice D is False, since a stratified sample in this situation produces results that are more typical of the store's employees from both locations than a random sample.
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Three-inch pieces are repeatedly cut from a 42-inch string. The length of the string after x cuts is given by y = 42-3x. Find and interpret the x- and y-intercepts. The x-intercept is 14 The y-intercept is 42 ✓ This means that after Select Choice cuts, the length of the string is Select Choice ✓ This means that the Select Select Select Choice Choice inches. inches.
1) The x-intercept lies at (1, 14), and the y-intercept lies at (3, 42).
2) This means that after 3 cuts, the length of the string is 33 inches.
3) Therefore, the 42-inch string can be cut into 14 pieces of 3 inches each.
What are the x- and y-intercepts?The x-intercept is the point on the graph where a line crosses the x-axis.
The y-intercept is the point on the graph where a line crosses the y-axis.
The x- and y-intercepts are the coordinate points for graphing data.
Thus, the x- and y-intercepts are coordinate points where the graph of a function or an equation touches the two axes.
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Which expression is equivalent to the following?
(5×10−3)+(6×10−3)2.2×104
5 × 10-7
5 × 10-1
5 × 10-10
5 × 107
Answer:
[tex]5 \times 107 = 535[/tex]
This is equivailent to the following
if covariance between two variables is near 0, it implies that group of answer choices a positive relationship exists between the variables. none of the choices. the variables are not linearly related. the variables are negatively related. the variables are strongly related.
If covariance between two variables is near 0, it implies that the variables are not linearly related.
In probability theory and statistics, covariance is a measure of the combined variability of two random variables in probability theory. The covariance is positive if the larger values of one variable mostly correlate with the greater values of the other variable, and vice versa for the smaller values.It is given that the covariance between two variables is near zero.In mathematical modelling, statistical modelling, and experimental sciences, dependent and independent variables are variables. Dependent variables are so named because their values are explored in an experiment under the assumption or requirement that they are dependent, by some law or rule, on the values of other variables.It clearly implies that the variables are not linearly related.To learn more about covariance, visit :
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If you love codes answer this question!
Answer:
Your answer would be
(a) FPUGT.
out of 100 people which are either tall or fat or both, 62 are tall, and 55 are fat. if i select one random person out of the 100 what is the probability, he is both tall and fat?
The probability a selected person is both tall and fat is 0.341
How to determine the probability?From the question, the given parameters are
People = 100
Fat = 55
Tall = 62
So, the individual probabilities are
P(Fat) = 55/100
P(Tall) = 62/100
Evaluate
P(Fat) = 0.55
P(Tall) = 0.62
The probability a person is both tall and fat is
P(Fat and Tall) = P(Fat) * P(Tall)
So, we have
P(Fat and Tall) = 0.55 * 0.62
Evaluate
P(Fat and Tall) = 0.341
Hence, the probability is 0.341
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A die is rolled and the spinner is spun. Find each probability.
Hello!
First, let's write the possible options:
Dice: 6 different results.
• 1, 2, , 4, 5, 6.
Spinner: 4 different results.
• A, B, C, D.
Knowing it, let's solve each alternative of your exercise:
a. 1 and AIn the dic, we have 6 possible results and we want a specific number. SOo, we can write it as 1/6.
In the spinner, we have 4 possible results and we want a specific one too. So, we have 1/4.
Now, remember he r"and" rule: when we consider two events happening simultaneously, we must multiply their probabilities.
Solving:
[tex]\frac{1}{6}\times\frac{1}{4}=\frac{1\times1}{6\times4}=\frac{1}{24}[/tex]b. odd score and B.We'll solve it in a similar way.
We have three possible odd numbers (1, 3, 5) in a total of 6 options. So, 3/6 = 1/2.
For the spinner, the reasoning will be the same: 1/.
Let's calculate:
[tex]\frac{1}{2}\times\frac{1}{4}=\frac{1\times1}{2\times4}=\frac{1}{8}[/tex]c. number less than 5 and a consonant.In a dice, we have four numbers less than 5: 1, 2, 3,4.
In the spinner, there are 3 consonants (B, C, D).
Let's calculate:
[tex]\frac{2}{3}\times\frac{3}{4}=\frac{2\times3}{3\times4}=\frac{6}{12}=\frac{1}{2}[/tex]
24. Oranges were packed in boxes of 90. There were 5 packed boxes. 1/5 of the oranges were rotten How many oranges were not rotten? |giving 30 pints!!
Answer:
Find the total number of oranges.
Total oranges = 90 × 5
= 450
Since 1/5 were rotten oranges,
Fraction of oranges that were not rotten
= Fraction of total oranges - Fraction of rotten oranges
= 5/5 - 1/5
= 4/5
Number of oranges not rotten = 4/5 × 450
= 360
Complete the flow proof of the converse of the corresponding angles theorem. Fill in the blanks.
When two lines and a transversal form comparable angles that are congruent, the lines are parallel, which is the converse of the corresponding angles theorem's flow proof. Which means that line c ║ to line d.
What are perpendicular lines?The two different lines that meet at an angle of 90 degrees are called perpendicular lines. Do your walls' connecting corners—or the letter "L"—share any similarities? They are the straight lines, referred to as perpendicular lines, that intersect at the proper angle. An angle of 90 degrees between two straight lines is known as a perpendicular. The illustration depicts a little square in between two perpendicular lines to indicate the 90° angle, which is also known as a right angle. Here, a right angle between the two lines Two lines that cross each other at a 90° angle are referred to as perpendicular lines in mathematics. I
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Could someone please help me this is due at 3 pm and it's allready 2:18 and i only need these questions and i am done please help me. if you answer all you get 20 points! PLEASE HELP
These are the solutions of all the questions
Answer the A, B or C from the image. I understand it will be challenging… so I will be giving brainliest to whoever answers more than one. And many points to whoever answers even one.
!Any fake answers; ex. Blank answers. Will be reported!
Take as much time as you need, I will be trying to answer them myself in the meantime.