f(x)=x^3-3x^2+2
g(x)=2f(x)-1
a) describe the graph of g as a transformation of the graph of f.
write a rule for g
Answers
a) The transformations applied to the graph of f to obtain the graph of g are given as follows:
Vertical stretch by a factor of 2.Shift down of one unit.b) The rule for g(x) is given as follows: g(x) = 2x³ - 6x² + 3.
What are the transformations?The parent function f(x) is defined as follows:
f(x) = x³ - 3x² + 2.
The transformed function is given as follows:
g(x) = 2f(x) - 1.
The meaning of each transformation is given as follows:
Multiplication by 2: vertical stretch by a factor of 2.Subtraction by 1: Shift down one unit.The rule for g(x) is then obtained as follows:
g(x) = 2(x³ - 3x² + 2) - 1
g(x) = 2x³ - 6x² + 4 - 1
g(x) = 2x³ - 6x² + 3.
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Related Questions
Please help me with this question.
Answers
The complete solution to the system of equations in this problem is given as follows:
x = [-14; 5; 0; 2]
How to solve the system of equations?The system Ax = b is given in augmented matrix form, hence it is defined as follows:
[tex]x_1 + 3x_2 + 2x_3 + 2x_4 = 5[/tex][tex]2x_1 + 3x_2 - 2x_3 + 10x_4 = 7[/tex][tex]4x_1 + 13x_2 + 7x_3 - 3x_4 = 3[/tex][tex]3x_1 + 9x_2 + 5x_3 + 3x_4 = 9[/tex]Inserting the system into a calculator, the homogeneous solution is given as follows:
[tex]x_1 = -14, x_2 = 5, x_3 = 0, x_4 = 2[/tex]
The system has no given inputs, hence the particular solution is of zero.
Hence the complete solution in matrix form is given as follows:
x = [-14; 5; 0; 2]
(the ; separator means a new line).
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Jotham needs 18 liters of a 80% alcohol solution. He has a 30% and a 90% solution available. How many liters of the 30% and how many liters of the 90% solutions should he mix to make the 80% solution?
Answers
The amounts of each solution that he should use are given as follows:
30% solution: 3 liters.90% solution: 15 liters.How to obtain the amounts of each solution?The amounts of each solution are obtained by a system of equations, for which the variables are given as follows:
x: amount of the 30% solution.y: amount of the 90% solution.The total solution is of 18 liters, hence:
x + y = 18.
x = 18 - y.
The final concentration is of 80%, hence:
0.3x + 0.9y = 0.8 x 18
0.3x + 0.9y = 14.4.
As x = 18 - y, the value of y is obtained as follows:
0.3(18 - y) + 0.9y = 14.4
0.6y = 9
y = 9/0.6
y = 15.
Hence the value of x is obtained as follows:
x = 18 - y
x = 18 - 15
x = 3.
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Solve the homogeneous linear system corresponding to the given coefficient matrix. (If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, express x1, x2, and x3 in terms of the parameter t.) 1 0 1 0 1 0 0 0 0 (x1, x2, x3) =
Answers
There are indefinitely many solutions to the system.
[x(1), x(2), x(3)] = [-t, 0, t]
The matrix is:
[tex]\begin{bmatrix}1 &0 &1 \\ 0 &1 &0 \\ 0 &0 & 0\end{bmatrix}[/tex]
The system of equations' equivalent augmented matrix is
[tex]\left [ \left.\begin{matrix}1 &0 &1 \\ 0 &1 &0 \\ 0 &0 & 0 \end{matrix}\right|\begin{matrix}0\\0 \\0 \end{matrix} \right ][/tex]
The following matrix has been reduced and transformed into a set of equations.
x(1) + x(3) = 0
Subtract x(3) on both side, we get
x(1) = -x(3)
x(1) = -t
x(2) = 0
Let x(3) = t
[tex]\begin{bmatrix}x(1)\\ x(2)\\ x(3)\end{bmatrix}=\begin{bmatrix}-t\\ 0\\ t\end{bmatrix}[/tex]
There are indefinitely many solutions to the system.
[x(1), x(2), x(3)] = [-t, 0, t]
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The complete question is:
Solve the homogeneous linear system corresponding to the given coefficient matrix. (If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, express x1, x2, and x3 in terms of the parameter t.)
[tex]\begin{bmatrix}1 &0 &1 \\ 0 &1 &0 \\ 0 &0 & 0\end{bmatrix}[/tex]
(x1, x2, x3) =
12. Town A has 4.563 residents.
Town A has 127 more than
4 times the number of residents
of Town B. How many residents
does Town B have?
Answers
Answer: We can set up an equation to represent the given information:
4.563 = 4B + 127
where B is the number of residents in Town B.
To solve for B, we can first subtract 127 from both sides:
4.563 - 127 = 4B
Then divide both sides by 4:
B = (4.563 - 127) / 4
B = 1.140775
So Town B has approximately 1.140775 residents.
Step-by-step explanation:
solve the inequality |x| < 5
Answers
The inequality is solved to x < -5/4
What is an inequality?An inequality can be defined as a mathematical relation that makes a non-equal comparison between two numbers, mathematical expressions or equations.
Inequalities are used to compare two numbers on the number line on the basis of their size.
The different inequality signs are;
< represents less than> represents greater than≤ represents greater than or equal to≥ represents less than or equal toFrom the information given, we have that;
|x| < 3x - 5
Note that the signs, "| |" represents modulus which explains that the number must be a positive number.
collect like terms
x -3x< 5
substract the like terms
-4x< 5
Make 'x' the subject
x < -5/4
Hence, the value is x < -5/4
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The complete solution is:
solve the inequality |x| < 3x - 5
select yes if the determinant shows that the matrix will reduce to an identity matrix; select no if it does not. [ 3 0 5 1 ]
Answers
No. The determinant doesn't show that the matrix will reduce to an identity matrix.
The determinant of a matrix is a scalar value that can be used to determine whether a matrix is invertible or not. If the determinant is non-zero, the matrix is invertible and can be reduced to an identity matrix through row operations. If the determinant is zero, the matrix is not invertible and cannot be reduced to an identity matrix.
In this case, the determinant of the matrix [3 0 5 1] is equal to 3 * 1 - 0 * 5 = 3, which is non-zero. Therefore, this matrix can be reduced to an identity matrix through row operations, but the determinant does not indicate this directly.
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-x (y-8) ^2 for x = -2 and y = 5 ?
Answers
This is because you wnat to plug each number in. After its plugged in you want to use the piwer of two on the numbers inside the parentheses first then whatever that is add the two numbers.
Quadrilateral BCDE is shown on the coordinate grid. Keisha reflects the figure across the line y=x to create B’C’D’E’. Use the connect line tool to draw quadrilaterl B’C’D’E
Answers
The vertices of quadrilateral B'C'D'E' are obtained exchanging the x and y-coordinates of the vertices of Quadrilateral BCDE.
Then the quadrilateral is drawn connecting the four vertices of quadrilateral B'C'D'E'.
What is the reflection rule?The rule for a reflection over the line y = x is given as follows:
(x,y) -> (y,x).
Meaning that a reflection over the line y = x will exchange the coordinates of the figure.
Then we apply this procedure to obtain the vertices of quadrilateral B'C'D'E', and in the drawing connect the consecutive vertices.
Missing InformationThe problem is incomplete, hence the answer was given in general terms.
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Box of clothes Weighting 10lbs (4.5kg) and a box of books weights 10lbs (4.5kg) was put on balance beam scales would most likely will it do
Answers
What will it cost to make 1,580 copies if the cost of 50 copies is $2.05
Answers
Answer:
=$64.78
Step-by-step explanation:
If. 50 copies. = $2.05
than. 1,580 copies = ?
1580/50 × $2.05
=3239/50
=64.78
Therefore if the cost of 50 copies is $2.05 than the cost of 1,580 copies is $64.78.
Answer:
$64.78
Step-by-step explanation:
Proportions:
50 copies >>>> $2.05
1580 copies >>>> $C
C = 1580"2.05/504
C = 64.78
i flip a coin three times and then another three times if the number of heads is the same the first and second time i win is this game worth playing
Answers
I flip a coin three times, and then another three times. If the number of heads is the same the first and second time, I win. If the number of heads is different, then I win. If I win, you pay me one dollar. If you win, I give you 3 dollars. This is worth playing game.
Let's assume that player A wins if both sets of coins are fair and have an equal number of heads.
The likelihood of this = (1/8)^2 + (3/8)^2 + (3/8)^2 + (1/8)^2
The likelihood of this = 1/64 + 9/64 + 9/64 + 1/64
The likelihood of this = (1 + 9 + 9 + 1)/64
The likelihood of this = 20/64
The likelihood of this = 5/16
If the two sets are different, let's say B triumphs.
The likelihood of this = 1 - 5/16 = 11/16
Therefore, if A wins 3 dollars and loses 1 dollar, then A's predicted net gain is
= 3 × 5/16 - 1 × 11/16
= 15/16 - 11/16
= (15 - 11)/16
= 4/16
So this game is defiantly worth playing game.
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The complete question is:
I flip a coin three times, and then another three times. If the number of heads is the same the first and second time, I win. If the number of heads is different, then I win. If I win, you pay me one dollar. If you win, I give you 3 dollars. Is this game worth playing?
Write down the percentage multiplier to find 26% of an amount
pls do simple steps/working out :)
Answers
Answer:
To find 26% of an amount, you would use the percentage multiplier of 0.26.
Step-by-step explanation:
To use the multiplier, you would simply multiply the amount by 0.26.
For example:
26% of $100 = $100 x 0.26 = $26.
Alternatively, you can also express the percentage as a decimal by moving the decimal point two places to the left. In this case 26% is equal to 0.26
So, to find 26% of an amount you would multiply the amount by 0.26
For example:
26% of $100 = $100 x 0.26 = $26.
Need help ASAP will reward
Answers
Answer: 24.35333333
Step-by-step explanation:
Derrick would like to explore his area. He estimates that his walking speed is 3.5 mph in the difficult terrain he has been given. If Derrick leaves at around 12 pm, and the sun sets at 4:45 pm, how far can he explore and still make it back by sunset?
Answers
Answer:
16.625 miles
Step-by-step explanation:
The time elapsed between 4:45 pm and 12 noon is 4 hours and 45 minutes
45 minutes is equivalent to 45/60 = 0.75 hour
Total elapsed time = 4.75 hours
At a speed of 3.5 mph the distance that can be covered
= 3.5 x 4.75 = 16.625 miles
Solve the equation.
2x² +6=-34
The solutions are x =
and x =
Answers
The solution of the equation 2x² + 6 = - 36 is x = √20i or x = -√20i, where i is equal to -1.
How to evaluate for the solution of the equation2x² + 6 = - 36
2x² = - 36 - 6 { subtract 6 from both sides of the equation }
2x² = - 40
x² = -40/2 {divide through by the coefficient of x² which is 2}
x² = -20
we take the square root of both sides
x = ± √-20
√-20 = √20 x √-1 { -1 = I an imaginary number}
so;
x = √20i or x = -√20i
Therefore, the solution of the equation 2x² + 6 = - 36 is x = √20i or x = -√20i, where i is equal to -1.
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Please help me with this question.
Answers
In the given case- An inverse of a Laplace transform, which is the sum of two distinct components, is the sum of the inverse transforms of each term separately.
What does inverse Laplace transform refer to?
A Laplace transform that is the sum of two different terms has an inverse that is the sum of the inverse transforms of each term taken separately. A Laplace transform, which also has an inverse of the constant multiplied by the inverse of the function, is produced when a constant is multiplied by a function.
A given derivative function with a real variable (t) is transformed into a complex function with a variable (s) by the Laplace transform, which is an integral transformation. Assuming that f(t) complies with a number of later-explained conditions,
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HELPP!!
One rental store charges a one time fee of $12 plus $3 per hour to rent a power washer. A
second rental store charges $15 plus $2 per hour to rent a power washer. For what number
of hours is the rental cost the same?
Answers
Answer:
3 hours
Step-by-step explanation:
First, we need to set up an equation with a variable representing the time.
12 + 3x = 15 + 2x
Then you solve.
12 + 3x = 15 + 2x
-2x-12 -2x-12
x = 3
geometry unit 7 : angles of polygons & parallelograms
find the value of x
Answers
Using the relationships between the angles of a parallelogram, the value of x is 12.55°.
Finding the value of x:A parallelogram has opposite angles that are equal, and adjacent angles that add up to 180°.
We can start with angles a and c. Since they are both equal to 90°, that means that angle b must also be 90°.
We can now use this information to find the value of x.
We can use the fact that angles a, b, and c add up to 270° to find x.
Since angles a and c are both 90°, that means that angle b must be 90°.
We can then solve for x by subtracting 190° (90° + 100°) from 270° and dividing by 7.
In order to solve for the value of x, we must use the properties of a parallelogram.
Since a parallelogram has four sides and four angles, the sum of the interior angles must equal 360°.
Therefore, we can set up an equation using the given angles and the unknown angle of x to solve for the value.
95° + (7x - 4)° + 90° + (3x + 23)° + (9x - 6)° = 360°
20x + 109° = 360°
20x = 251°
x=12.55°
Therefore, the value of x is 12.55°.
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EASY POINTS!
What is the total cost of groceries if the state sales tax of 6.4% added $9.60 to the original cost?
$9.60
$172.93
$72.93
$159.60
Answers
Answer:
The total cost of groceries if the state sales tax of 6.4% added $9.60 to the original cost would be $159.60. To calculate this, multiply the original cost by 1.064, which is the amount of the sales tax in decimal form. For example, if the original cost was $150, then the total cost would be $150*1.064 = $159.60.
A city currently has 132 streetlights. As part of an urban renewal program, the city council has decided to install 4 additional streetlights at the end of each week for the next 52 weeks. Use this information to complete the following statements. Round to the nearest whole number as needed.
The city will have (blank) streetlights at the end of 46 weeks.
The city will have 232 streetlights at the end of (blank) weeks.
Answers
Answer:
316 street lights.
25 weeks.
Step-by-step explanation:
Linear Equations:We can set up a linear equation with the information provided expressed in slope intercept form: [tex]y=mx+b[/tex], where "m" is the slope, and "b" is the initial value.
We're given the initial amount, or what the city already has is 132 street lights, that's our "b" value and they will install 4 each additional week which is our slope. So we have the equation: [tex]y=4x+132[/tex]
To find how many streetlights the city will have at the end of 46 weeks, we can plug in 46 as "x" to give us:
[tex]y=4(46)+132\\y=316[/tex]
To find when the city will have 232 streetlights we can set the equation equal to 232 and solve for "x" the number of weeks.
[tex]232=4x+132[/tex]
Subtract 132 from both sides
[tex]100=4x[/tex]
Divide both sides by 4
[tex]25=x[/tex]
So this will occur after 25 weeks.
6x x 6 + 75 = 10x - 9
Answers
Therefore, in the previous equation, 6x + 75 = 10x -9, the value of x is 4. It's really common to contrast expressions and phrases.
what is expression ?It is necessary to duplicate, divide, add, or subtract in mathematics. The following is how an expression are put together: Number, expression, and mathematical operator The components of a numerical method include numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) It's really common to contrast expressions and phrases. An language, often known as an algebraic expression, is any mathematical statement that rating systems, numbers, and then an arithmetic function between them. For instance, the word m in the given equation is separated from the terms 4m and 5 by the arithmetic symbol +, as is the variable m in the expression 4m + 5.
given
6x + 75 = 10x -9
Because 6x + 75 = 10x -9
6x -10 x = -9 - 75
-4x = -84
x = 21; the value of x is 4.
Therefore, in the previous equation, 6x + 75 = 10x -9, the value of x is 4.
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A single card is drawn from a standard 52-card deck. What is the probability that the card is either a)a jack, or a five, or a king? b)a heart, or a club, or a spade? c)an ace, or a queen, or a heart? d)a seven, or a queen, or a heart, or a diamond?
Answers
Probability on cards.
(a) P(Jack or five or King) = 12/52 = 3/13
(b) P(heart or club or spade) = 39/52 = 3/4
(c) P(Ace or Queen or heart) = 19/52
(d) P(seven or Queen or heart or diamond) = 30/52 = 15/26
What is probability?Probability is a numerical description of how possible an event to happen. Probability of an event can be expressed as
P(A) = n(A) / n(S)
Where
P(A) is the probability of an event An(A) is the number of favorable outcomesn(S) is the total number of events in the sample spaceA single card is drawn from a standard 52-card deck. Find the probability that the card is either
a) a Jack, or a five, or a Jing?
b) a heart, or a club, or a spade?
c) an Ace, or a Queen, or a heart?
d) a seven, or a Queen, or a heart, or a diamond?
The four suits for a standard deck of 52 cards are hearts, diamonds, clubs, and spades of 13 cards each. The hearts and diamonds are red. While, the clubs and spades are black. The 13 cards are Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King.
The total number of events is n(S) = 52.
Let's count each number of favorable outcomes, then the probability of the event!
(a) The number of Jack is 4, five is 4, and King is 4. They are 12.
P(Jack or five or King) = 12/52 = 3/13
(b) The number of hearts is 13, clubs is 13, and spade is 13. They are 39.
P(heart or club or spade) = 39/52 = 3/4
(c) The number of hearts is 13, other Aces is 3, other Queens is 3. They are 19.
P(Ace or Queen or heart) = 19/52
(d) The number of diamonds is 13, hearts is 13, other seven is 2, other Queen is 2. They are 30.
P(seven or Queen or heart or diamond) = 30/52 = 15/26
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Twenty members of an athletic club are studying the relationship between the time it takes an individual athlete to reach a given level of fatigue during exercise (time to fatigue, measured in minutes) and athletic performance. For each member, time to fatigue and a performance score were recorded. The computer output of the regression analysis is shown in the table.
TermCoefSE CoefTConstant39.884.249.41Time to fatigue3.920.715.52
Which of the following is a 90 percent confidence interval for the slope of the regression line relating performance score and time to fatigue? Assume that the conditions for inference are met.
3.92±1.734(0.71)
Answers
The confidence interval for the slope of the regression line relating performance score is 0.71
sample size (n) = 20
slope (b1) = 3.92 and SE of slope = 0.71
Degrees of freedom = 20 - 2 = 18
Using t-table we get, t-critical value at significance level of 0.10 with 18 degrees of freedom is,
tα/2=1.734
The 90% confidence interval for the slope of the regression line relating performance score and time to fatigue is,
B1±Tα/2*SE
3.92±1.734(0.71) (c)
Regression analysis is a statistical measure that is used in many different fields, including investing, finance, sales, marketing, science, mathematics, and others. It tries to figure out how closely one dependent variable is related to a set of other changing variables. They are commonly referred to as independent variables.
For example, how commodity prices relate to the shares of companies that trade in those commodities.
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Which point is a solution to the system of linear equations? y = −x + 2 x − 3y = 6
Answers
If x and y are positive integers x/y=2, and (x^2+y^2)=z, which of the following cannot equal z?
Answers
Step-by-step explanation:
I'm not sure if there were answer choices, but the smallest possible positive integers for x/y=2 is x=2 and y=1
If we plug those in to the other equation
(x^2+y^2)=z
(2^2+1^2)=z
(4 + 1) = z
5=z
Indicating that any number less than 5 cannot equal Z
Which of these is the note A?
A.
OB.
O C.
O D.
Co
6.
fo
Answers
Answer:
the correct answer is A
Step-by-step explanation:
A correspond to Note La
Find the area of the sector of the circle with central angle of 195° and radius of 7 cm. Use 3.14 for pi(π) and round to the nearest hundredth.
Group of answer choices
23.81 cm2
166.68 cm2
27.86 cm2
83.34 cm2
Answers
Answer:
A ≈ 83.34 cm²
Step-by-step explanation:
the area (A) of the sector is calculated as
A = area of circle × fraction of circle
= πr² × [tex]\frac{195}{360}[/tex] ( r is the radius of the circle )
= 3.14 × 7² × [tex]\frac{13}{24}[/tex] ( cancelling by 15 )
= [tex]\frac{3.14(49)(13)}{24}[/tex]
≈ 83.34 cm² ( to the nearest hundredth )
Find the values of x , y and z .
Answers
Answer:
x = 144y = 60z = 156Step-by-step explanation:
Given two segment measures in a right triangle diagram, you want the values of the other measures.
Pythagorean theoremThe Pythagorean theorem can be used to find y:
BC² = BD² +CD²
65² = y² +25²
y² = 65² -25² = 3600
y = √3600 = 60
Similar trianglesThe proportionality of corresponding sides in similar triangles can be used to find the remaining measures.
short side/hypotenuse = 25/65 = 65/(25+x)
25 +x = 65²/25 = 169
x = 144
And for z, we can use ...
long side/hypotenuse = AB/AC = BD/BC
z/169 = 60/65
z = 169(12/13) = 156
The triangle measures are ...
x = 144y = 60z = 156Please help me with the following question.
Answers
The probabilities for this problem are given as follows:
a) At least five: 0.4909 = 49.09%.
b) Less than five: 0.4091 = 40.91%.
c) Between five and ten: 0.585 = 58.5%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].The parameters of the binomial distribution are given as follows:
n = 100, p = 0.05.
Hence the mean and the standard deviation of the approximation are given as follows:
Mean: [tex]\mu = 100 \times 0.05 = 5[/tex]Standard deviation: [tex]\sigma = \sqrt{100 \times 0.05 \times 0.95} = 2.18[/tex]Then the probability of at least five successes, using continuity correction, is P(X > 4.5), which is one subtracted by the p-value of Z when X = 4.5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (4.5 - 5)/2.18
Z = -0.23.
Z = -0.23 has a p-value of 0.4091. (probability of less than five successes).
1 - 0.4091 = 0.4909 = 49.09%.
The probability of between five and ten successes is the p-value of Z when X = 10.5 subtracted by the p-value of Z when X = 4.5, hence:
Z = (10.5 - 5)/2.18
Z = 2.52
Z = 2.52 has a p-value of 0.9941.
Z = (4.5 - 5)/2.18
Z = -0.23.
Z = -0.23 has a p-value of 0.4091.
Hence:
0.9941 - 0.4091 = 0.585 = 58.5%.
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b) The growth rate of covid patient is 5% per hour. If the number of covid patients in the morning 9am is 44,100, what was the number of patient 7am sharp?
Answers
Answer:
36,900
Step-by-step explanation:
it's right I just do not know how to explain lol
