If Point B \((3,1)\) has translated 2 units to the right and 1 unit up, new coordinates of point B' are \((5,2)\)
As per the question statement, Point B \((3,1)\) is there on a cartesian plane. Point B is translated 2 units to the right and 1 unit up.
Before solving this question, we need to know about cartesian plane system in which, there are four quadrants which are made using positive and negative axes known as positive X and negative X (same for Y axis).
Now point B\((3,1)\) lies in the first quadrant and value "3" describes the location of point on X axis and value "1" describes the location of point on Y axis.
If point B \((3,1)\) is translated 2 units to the right and 1 unit up, the locations of X and Y axes will change to value "5" on X axis and value "2" on Y axis.
Hence the coordinates of point B' are \((5,2)\)
Cartesian Plane: The x-axis and y-axis intersect to form the two-dimensional coordinate plane known as the cartesian plane in mathematics. The origin is the point at which the x- and y-axes cross perpendicularly.To learn more about cartesian plane and coordinate geometry, click on the link given below:
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7. suppose a binary digit (0 or 1) needs to be transmitted across a series of 4 channels. each time, the digit is transmitted correctly to the next channel with probability 0.9, and is transmitted incorrectly (meaning that 1 is transmitted as 0, and 0 is transmitted as 1) with probability 0.1. if the digit 0 is sent, what is the probability that the digit that is received (after having been transmitted across the 4 channels) is a 0?
The probability that the digit that is received (after having been transmitted across the 4 channels) is 0.3645
In communication systems, it is common to face the challenge of transmitting information accurately over a noisy channel. In this scenario, errors can occur during transmission, and it is essential to quantify the probability of receiving the correct information at the end of the channel.
In this problem, we are asked to calculate the probability that the digit received after transmitting a 0 across four channels is also a 0. We know that each channel can either transmit the digit correctly with probability 0.9 or incorrectly with probability 0.1. Therefore, we can use the concept of conditional probability to solve this problem.
Using Bayes' theorem, we can rewrite this as:
P(CCCC | 0 received) x P(0 received) / P(CCCC)
Here, P(CCCC | 0 received) represents the probability that all four channels transmitted the 0 correctly, given that a 0 was received. This probability can be calculated as:
P(CCCC | 0 received) = P(C) x P(C | C) x P(C | C | C) x P(C | C | C | C)
Substituting the given probabilities, we get:
P(CCCC | 0 received) = 0.9 * 0.9 * 0.9 * 0.9 = 0.6561
Similarly, we can calculate the probability of receiving a 0 in general as:
P(0 received) = P(CCCC | 0 received) x P(0) + P(IIII | 0 received) x P(1)
where P(IIII | 0 received) represents the probability that all four channels transmitted the digit incorrectly, given that a 0 was received. This probability can be calculated similarly as:
P(IIII | 0 received) = P(I) * P(I | I) x P(I | I | I) x P(I | I | I | I) = 0.1 x 0.1 x 0.1 x 0.1 = 0.0001
Substituting the given probabilities, we get:
P(0 received) = 0.6561 x 0.5 + 0.0001 x 0.5 = 0.3281
Finally, we can calculate the denominator P(CCCC) as:
P(CCCC) = P(CCCC | 0 received) x P(0) + P(CCCC | 1 received) x P(1)
where P(CCCC | 1 received) represents the probability that all four channels transmitted the digit correctly, given that a 1 was received. This probability can be calculated similarly as:
P(CCCC | 1 received) = P(I) x P(I | C) x P(I | C | C) x P(I | C | C | C) = 0.1 x 0.9 x 0.9 x 0.9 = 0.0729
Substituting the given probabilities, we get:
P(CCCC) = 0.6561 * 0.5 + 0.0729 * 0.5 = 0.3645
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Element X is a radioactive isotope such that every 25 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 50 grams, how much of the element would remain after 23 years, to the nearest whole number?
Answer: 26
Step-by-step explanation:
The correct answer is 26
1/4 ( x − 12 ) + 1/3 ( x + 9 )
Answer: 7/12x
Step-by-step explanation:
Answer:
7x/12
Step-by-step explanation:
brainleist please
write a new function that is a horizontal stretch of f(x)=(x+2)^3+5
New function that is a horizontal stretch of F(x)=\((x+2)^{3} + 5\) is F(\(\frac{x}{k}\))=\((\frac{x}{k} +2)^{3} + 5\)
What is horizontal stretch ?The point (x, y) on the graph of f(x) is changed to the point (x/k, y) on the graph of g when the graph is stretched or contracted horizontally by a factor of 1/k (x).Only when the input value is also increased by a, can a graph be stretched horizontally by a factor of 1/a. The x-coordinates should be multiplied by a once f(x) has been stretched horizontally to f(ax). Keep the y-intercepts where they are. The resulting function might have a different domain, but it will have the same range. If a point (m, n) is stretched horizontally, it becomes (am, n).
F(x)=\((x+2)^{3} + 5\)
F(\(\frac{x}{k}\))=\((\frac{x}{k} +2)^{3} + 5\)ch visit :
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From 7x^2+5xy-3y^2 subtract the sum of 2x^2+3xy-5y^2 and x^2-7xy-4y^2.
Answer:
4x^2+9xy+6y^2
Step-by-step explanation:
7x^2+5xy-3y^2 -(2x^2+3xy-5y^2+x^2-7xy-4y^2)
7x^2+5xy-3y^2-(3x^2-4xy-9y^2)
7x^2+5xy-3y^2-3x^2+4xy+9y^2
4x^2+9xy+6y^2
a piece of rock has a mass of 86.3g , correct to the nearest 0.1g . find the greatest possible mass of the rock in 2 decimal places
The greatest possible mass of the rock to two decimal places is 86.34 g
How to find the greatest possible mass of the rock?Since the mass of the piece of rock is 86.3 g, correct to the nearest 0.1 g. Thus, the actual mass of the rock in 2 decimal places could be between 86.25 g and 86.34 g.
To find the greatest possible mass of the rock, we need to round up to the higher end of the range of the mass of the rock.
Therefore, the greatest possible mass of the rock to two decimal places is 86.34 g
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Has the marrying age of a man changed over the years? The United States Bureau of the Census takes a formal count of everyone in the U.S. every 10 years and has provided the following data that gives the median age of an American man at the time of his first marriage.
Year
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
Median Age
25.1
24.6
24.3
24.3
22.8
22.8
23.2
24.7
26.1
26.8
Determine the average rate of change in median age per year from 1930 to 1960.
a.
-0.5 years of age per year
b.
20 years of age per year
c.
-0.05 years of age per year
d.
+0.05 years of age per year
-0.05 is the average rate of change in median age per year from 1930 to 1960.
What is ratio?The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
Given, a data set that gives the median age of an American man at the time of his first marriage.
Year Median age
1910 25.1
1920 24.6
1930 24.3
1940 24.3
1950 22.8
1960 22.8
1970 23.2
1980 24.7
1990 26.1
2000 26.8
The average rate of change from 1930 to 1960 = (-24.3 + 22.8) / (1960-1930)
The average rate of change from 1930 to 1960 = -0.05
Therefore, the average rate of change in median age per year from 1930 to 1960 is -0.05.
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7. What is the equation of the line in slope intercept
form that passes through (6,8) and (-2,4)
\((\stackrel{x_1}{6}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{8}}}{\underset{run} {\underset{x_2}{-2}-\underset{x_1}{6}}} \implies \cfrac{ -4 }{ -8 } \implies \cfrac{ 1 }{ 2 }\)
\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{8}=\stackrel{m}{ \cfrac{ 1 }{ 2 }}(x-\stackrel{x_1}{6}) \\\\\\ y-8=\cfrac{ 1 }{ 2 }x-3\implies {\Large \begin{array}{llll} y=\cfrac{ 1 }{ 2 }x+5 \end{array}}\)
find the number equivalent to 1:5.
6:_
Answer:
30
Step-by-step explanation:
1 * 6 = 6
5 * 6 = 30
6:30
When you reduce it will be back to 1:5
a ________________ is a quadrilateral with two pairs of congruent adjacent sides and no congruent opposite sides.
Answer:
Kite
Step-by-step explanation:
A kite is a convex quadrilateral with two pairs of adjacent congruent sides such that not all sides are congruent. The word adjacent means “next to”, so the congruent sides are next to each other. So this means since they're next to each other there's no congruent opposite sides.
Hope this helps!!
Please answer each part in almost 500 words.
a. Suppose Jet Airways wants to ascertain the image it has in the minds of its patrons. Construct a seven-item and semantic differential scale to measure the perceived image of the airlines. Make sure that the seven under each format correspond to the same seven dimensions.
b) Find a technical and business report from your library or on the internet and examine the contents of the reports against what has been discussed in the chapter. What deviations did you find from the stated structure? What you think could have been the reason for this?
a) Part A: The perceived image of Jet Airways
Jet Airways is one of the well-known airlines in India. It is headquartered in Mumbai and operates both domestic and international flights. The perceived image of Jet Airways in the minds of its customers is important to the success of the airline. Perceived image refers to what the customers think about the airline, and this is important for customer loyalty and retention.
Constructing a seven-item and semantic differential scale to measure the perceived image of Jet Airways would be as follows:
1. Reliability: how reliable is Jet Airways on a scale of 1 to 7 (with 1 being extremely unreliable and 7 being extremely reliable)
2. Responsiveness: how responsive is Jet Airways to the needs of its customers on a scale of 1 to 7 (with 1 being extremely unresponsive and 7 being extremely responsive)
3. Empathy: how empathetic is Jet Airways to the concerns of its customers on a scale of 1 to 7 (with 1 being extremely unempathetic and 7 being extremely empathetic)
4. Assurance: how assured do you feel when you travel with Jet Airways on a scale of 1 to 7 (with 1 being extremely unassured and 7 being extremely assured)
5. Tangibles: how do you rate the physical appearance of Jet Airways on a scale of 1 to 7 (with 1 being extremely poor and 7 being extremely good)
6. Price: how do you rate the price of Jet Airways on a scale of 1 to 7 (with 1 being extremely expensive and 7 being extremely affordable)
7. Convenience: how convenient is it to travel with Jet Airways on a scale of 1 to 7 (with 1 being extremely inconvenient and 7 being extremely convenient)
The above semantic differential scale helps in measuring the perceived image of Jet Airways. The seven-item and semantic differential scale ensure that the seven under each format correspond to the same seven dimensions.
By answering each question, the customers can rate Jet Airways on various factors, and the airline can use this feedback to improve its service and overall image.
b) Part B:
Examination of a technical and business report
The structure of a technical and business report includes a title page, abstract, table of contents, introduction, main body, conclusion, and references. An examination of a technical and business report from the internet reveals some deviations from the stated structure. One of the significant deviations is the absence of the abstract section. The abstract provides a brief summary of the report, including the purpose, methodology, and findings. The report from the internet did not have an abstract section, and this deviation could be due to the report being a short summary of a more extensive study.
The report from the internet did not have a separate conclusion section. The conclusion is important as it summarizes the findings of the study and provides recommendations for further research. The report from the internet integrated the findings and recommendations into the main body of the report, and this deviation could be due to the length of the report.
Another deviation is the lack of a reference section. The reference section is essential as it provides the sources used in the study. The report from the internet did not have a reference section, and this deviation could be due to the type of report and the fact that it was not a formal research report.
In conclusion, technical and business reports should follow a specific structure to ensure that they are clear, concise, and easily understood. Deviations from the stated structure can affect the quality and accuracy of the report. The deviations in the report from the internet could be due to the length, type, and purpose of the report.
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-2x-6y=8 and -6x-6y=0
Answer:
Assume we want to find the solution to this system of equations.
The solution is (2,-2)
Step-by-step explanation:
We can find the solution either mathematically or by graphing. I'll do both.
Math:
Rearrange:
-2x-6y=8
-6y=8 +2x
y = -(1/3)x -(4/3)
---
Now use this expression of y in the second equation:
-6x-6y=0
-6x-6(-(1/3)x -(4/3)) =0
-6x + 2x +8 =0
-4x = - 8
x = 2
---
Use x = 2 in the first equation to find y:
y = -(1/3)x -(4/3)
y = -(1/3)*(2) -(4/3)
y = -(2/3) -(4/3)
y = -(6/3) or -2
The solution is (2,-2)
===============
Graphing:
See attached graph.
Answer:
Step-by-step explanation:
-2x - 6y = 8
6x + 6y = 0
4x = 8
x = 2
-4 - 6y = 8
-6y = 12
y = -2
(2, -2)
4) x2 - 2x + 2 = 0
4. 1)
a
4. 2) What is the exact value of the DISCRIMINANT? b2 - 4ac -
*Type this into your calculator
O2 - 400
4. 3) Which type of SOLUTIONS does this parabola have ? =
(REAL or IMAGINARY)
4. 4) Why? (* Remember to think about the SQUARE ROOT symbol * ) =
Answer:
See below
Step-by-step explanation:
Solve the equation using the quadratic formula
\(\displaystyle x^2-2x+2=0\\\\x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x=\frac{-(-2)\pm\sqrt{(-2)^2-4(1)(2)}}{2(1)}\\ \\x=\frac{2\pm\sqrt{4-8}}{2}\\ \\x=\frac{2\pm\sqrt{-4}}{2}\\ \\x=\frac{2\pm2i}{2}\\ \\x=1\pm i\)
Discriminant and Solution Analysis
As we determined in the quadratic formula, our discriminant is -4 because \(b^2-4ac=(-2)^2-4(1)(2)=-4\), under the radical. Because it is negative, our solutions must be imaginary since the square root of a negative number is not real.
if an object is moving with constant momentum ‹ 10, −17, −4 › kg · m/s, what is the rate of change of momentum dp with arrow/dt?
The rate of change of momentum is zero, and the momentum remains constant at ‹ 10, −17, −4 › kg · m/s.
The rate of change of momentum is given by the equation dp/dt = F, where F is the net force acting on the object.
If the object is moving with constant momentum, this means that there are no net forces acting on it, and therefore the rate of change of momentum is zero.
In other words, the momentum is not changing over time, and it remains constant at ‹ 10, −17, −4 › kg · m/s.
dp/dt = 0
This means that the object is moving with constant velocity, since the momentum is equal to the mass times the velocity, and the mass is not changing.
Therefore, the rate of change of momentum is zero, and the momentum remains constant at ‹ 10, −17, −4 › kg · m/s.
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There are 5 red markers, 2 orange markers, 3 yellow markers, and 5 green markers in a desk drawer. plss help
Answer:
15 markers in all
Step-by-step explanation:
5 + 2 + 3 + 5 =
5 + 5 = 10
+
2 + 3 = 5
=
10 + 5 = 15
Brainliest Please!!
fair share for 1/2 1/2 1/3 1/3 1/4 1/3 1/4 1/2 1/2 1/2 PLS ANSWER QUICK
A shipping container will be used to transport several 120-kilogram crates across the country by rail. The greatest weight that can be loaded into the container is 27500 kilograms. Other shipments weighing 12400 kilograms have already been loaded into the container. Which inequality can be used to determine x, the greatest number of
120-kilogram crates that can be loaded onto the shipping container?
Inequality can be used to determine x, the greatest number of 120-kilogram crates that can be loaded onto the shipping container is 8000 + 120C <= 27500
What is inequality?An inequality is a relationship that allows us to contrast two or more mathematical expressions.
Knowing that;
Each carton weighs 120 kg.
The container's maximum weight when loaded is 27500 kg.
Weight of the container as it is currently loaded: 8000 kg
Now that we have merged, we have;
Solution
because 8000 grams have already been loaded kilograms
into the container
each crate weighs 120 kilograms.
so 8000 + 120C <= 27500
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Help and wright a step by step explanations
Answer:
The total surface area is 3860 ft^2
The total volume is 22,500 ft^3
Step-by-step explanation:
See attached worksheet.
The house needs to be broken up into separate rectangles and triangles, as shown on the worksheet. Individual calculations of the area and volume are then added for a total number for both volume and surface area.
Which formula converts radians to degrees?
Answer:
Below
Step-by-step explanation:
Radians = degrees * pi /180
Radians * 180/pi = degrees
find a parametric representation using spherical-like coordinates for the upper half of the ellipsoid 4x2 8x 9 y2 36(z 1)2
x² = 9 + -2.25y² + 0.25z² provides a parametric representation of the upper half of the ellipsoid in spherical-like coordinates.
Given,
In response to our inquiry:
Add "-9y²" to each side of the equation.
4x² + 9y² + -9y² + -1z² = 36 + -9y²
9y² + -9y² = 0 when equivalent phrases are combined.
4x² + 0 + -1z² = 36 + -9y²
4x² + -1z² = 36 + -9y²
Add "z²" to both sides of the equation.
4x² + -1z² + z² = 36 + -9y² + z²
Therefore,
x² = 9 + -2.25y² + 0.25z² provides a parametric representation of the upper half of the ellipsoid in spherical-like dimensions.
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Find the Circumference of the circle. Leave your answer in terms of TT
Formula: C = 2
Plsss help nowww
Answer:
C = 18π m
Step-by-step explanation:
The circumference (C) of the circle is calculated as
C = 2πr ( r is the radius ) , then
C = 2π × 9 = 18π
If 4 daps are equivalent to 3 dops, and 2 dops are equivalent to 7 dips, how many daps are equivalent to 42 dips?
110.25 daps are equivalent to 42 dips. We can use the given values of equivalent measures to get to the required measure: 4 daps = 3 dops, which can be written as 1 dap = (3/4) dops, 2 dops = 7 dips, which can be written as 1 dop = (7/2) dips.
Given: 4 daps = 3 dops and 2 dops = 7 dips
We need to find: how many daps are equivalent to 42 dips?
Solution: We can use the given values of equivalent measures to get to the required measure:
4 daps = 3 dops, which can be written as 1 dap = (3/4) dops
2 dops = 7 dips, which can be written as 1 dop = (7/2) dips
Using the above relations we can find the relation between daps and dips: 1 dap = (3/4) dops = (3/4) * (7/2) dips = (21/8) dips
Or we can write, 8 daps = 21 dips
To find how many daps are equivalent to 42 dips, we can proceed as follows: 8 daps = 21 dips
1 dap = 21/8 dips
Therefore, to get 42 dips, we need: (21/8) * 42 dips = 110.25 daps (Answer)
Thus, 110.25 daps are equivalent to 42 dips. Given that 4 daps = 3 dops and 2 dops = 7 dips, we need to find how many daps are equivalent to 42 dips. This problem requires us to use equivalent measures of the given units to find the relation between the required units. As per the given values of equivalent measures, 4 daps are equivalent to 3 dops and 2 dops are equivalent to 7 dips. Using these values, we can find the relation between daps and dips as follows:
1 dap = (3/4) dops = (3/4) * (7/2) dips = (21/8) dips Or, 8 daps = 21 dips
Thus, we have found the relation between daps and dips. Now we can use this relation to find how many daps are equivalent to 42 dips. To find how many daps are equivalent to 42 dips, we can use the relation derived above as follows: 1 dap = 21/8 dips
Therefore, to get 42 dips, we need:(21/8) * 42 dips = 110.25 daps
Hence, 110.25 daps are equivalent to 42 dips.
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A grocery store offers 2 free flashlights with any purchase. Rita can spend $100. The number of items that she can buy is given by
y = 100/x +2
where x is the average price per item. Identify the reasonable domain and range values.
D: x < 0
R: natural numbers > 2
D: x < 0
R: natural numbers < 2.
D: x > 0
R: natural numbers > 2
D: x > 0
R: natural numbers < 2
Answer:
The answer is D: x > 0
R: natural numbers > 2
Step-by-step explanation:
I got 100 on the quiz good luck bro
HELP! NOW!
During a sale at a store, sweaters are being sold at a 65% discount. Let x represent the discount on sweaters. The shirts have the same discount as the sweaters. Let y represent the discount on shirts. The pants do not have the same discount as sweaters. Let z represent the discount on pants. Which statement is true? A. x ≠ y B. x = y C. z = x D. y = z
Answer:
B. x = y
Step-by-step explanation:
Since sweaters discount (x) and shirt discount (y) are the same like we are told, then they are equal.
Functional analysis adjoint operator
Let S, TE B(X, Y). Show that for any scalar a. (S+T)* = SX +T and (aT)* = aTx
In this problem, we are asked to show that for any operators S and T in the bounded linear operator space B(X, Y), where X and Y are Banach spaces, the adjoint operator of the sum of S and T is equal to the sum of the adjoint operators of S and T, and the adjoint operator of a scalar multiple of T is equal to the scalar multiple of the adjoint operator of T.
To prove the first statement, let A = S + T. We want to show that (S + T)* = S* + T*. For any y in Y and x in X, we have (Ax, y) = (Sx + Tx, y) = (Sx, y) + (Tx, y). Taking the adjoint of both sides gives (x, Ay) = (x, Sy) + (x, Ty) for all x in X. Since this holds for all x, we can conclude that A* = S* + T*.
To prove the second statement, let B = aT, where a is a scalar. We want to show that (aT)* = aT*. For any y in Y and x in X, we have (Bx, y) = (aTx, y) = a(Tx, y). Taking the adjoint of both sides gives (x, By) = a(x, Ty) for all x in X. Since this holds for all x, we can conclude that B = aT*.
These results follow directly from the properties of adjoint operators, which are linear and satisfy the adjoint of a sum is equal to the sum of adjoints and the adjoint of a scalar multiple is equal to the scalar multiple of the adjoint.
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help help help PLEASEEEEE
Answer:
m=4b and b=4m
Step-by-step explanation:
this is the right answer
I will mark brainlist!!!!!!!!!! The results of a board game are shown in the table. What is the total of the players’ scores?
Player Amount
Joseph $500
Sarah –$1,500
Malachi –$2,200
Tyson $400
Shaun –$600
Summer –$300
Select the correct answer.
A. $3,700
B. –$4,500
C. –$3,700
D. $4,500
Answer:
C -$3,700
Step-by-step explanation:
subtract them all
Given the following functions, find each of the values: f(t) = tz - t - 42 r ( t ) = t+6 ( f t r ) ( - 5 ) = ( f - ) ( - 4) = ( fr)
(0) = ( - 3 ) =
(ftr)(-5) = -5z - 37
(f-)(-4) = -4z - 38
(fr)(0) = -252
(fr)(-3) = -9z - 117
To find the values of the given functions at specific inputs, we substitute the given inputs into the respective functions.
Given:
f(t) = tz - t - 42
r(t) = t + 6
Let's evaluate each value step by step:
(ftr)(-5):
First, substitute -5 into f(t) and then substitute the result into r(t).
f(-5) = (-5)z - (-5) - 42 = -5z + 5 - 42 = -5z - 37
r(-5) = (-5) + 6 = 1
(ftr)(-5) = (-5z - 37)(1) = -5z - 37
(f-)(-4):
First, substitute -4 into f(t).
f(-4) = (-4)z - (-4) - 42 = -4z + 4 - 42 = -4z - 38
(f-)(-4) = -4z - 38
(fr)(0):
First, substitute 0 into f(t) and then substitute the result into r(t).
f(0) = (0)z - (0) - 42 = -42
r(0) = (0) + 6 = 6
(fr)(0) = (-42)(6) = -252
(fr)(-3):
First, substitute -3 into f(t) and then substitute the result into r(t).
f(-3) = (-3)z - (-3) - 42 = -3z + 3 - 42 = -3z - 39
r(-3) = (-3) + 6 = 3
(fr)(-3) = (-3z - 39)(3) = -9z - 117
To summarize:
(ftr)(-5) = -5z - 37
(f-)(-4) = -4z - 38
(fr)(0) = -252
(fr)(-3) = -9z - 117
Please note that the values of the functions depend on the variable z, which is not provided in the given question. Therefore, the expressions remain in terms of z.
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HELP HELP HELP HELP HELP HELP
Answer:
57mm
Step-by-step explanation:
C=2(pi)(r)
C=2(3.14)(9)
C=56.52
rounding up, its 57mm
The area of the unshaded region is 22.5cm. What is the area of the rectangle? A11.25cm . B22.5cm . C45cm . D90cm .
Answer:
45cm2
Step-by-step explanation:
because the shaded areas = to the non shaded one so just multiply it by 2 to get 45cm2
(Hope this helped you out)