The required matrices are:
[tex]A= \begin{bmatrix}1 & 1 & 0\\1 & -1 & 0\end{bmatrix}[/tex] and [tex]B= \begin{bmatrix}1 & 1\\1 & -1\\0 & 1\end{bmatrix}[/tex]
letting T(x)=Ax and U(x)=Bx, the composition T∘U is a reflection over the line y=x.
A matrix is a rectangular array of numbers or other mathematical objects (such as complex numbers, polynomials, or functions) arranged in rows and columns. The size or dimensions of a matrix are given by the number of rows and columns it has, and a matrix with m rows and n columns is said to be an m × n matrix.
Let A be the 2×3 matrix:
[tex]A= \begin{bmatrix}1 & 1 & 0\\1 & -1 & 0\end{bmatrix}[/tex]
and let B be the 3×2 matrix:
[tex]B= \begin{bmatrix}1 & 1\\1 & -1\\0 & 1\end{bmatrix}[/tex]
Then, for any vector x in [tex]R^2[/tex], we have:
[tex]T(U(x)) = A(Bx) = A(x_1 + x_2, x_1 - x_2, x_3)[/tex]
[tex]= (x_1 + x_2 + x_1 - x_2, x_1 - x_2 - x_1 - x_2, 0)[/tex]
[tex]= (2x_1, -2x_2, 0)[/tex]
To show that this is a reflection over the line y=x, we can verify that T(U(x)) is equal to its own inverse. That is, we want to show that:
[tex]T(U(T(U(x)))) = x[/tex]
Substituting T(U(x)) for y, we have:
[tex]T(U(T(U(x)))) = T(U(y)) = A(By) = A(2y_1, -2y_2, 0)[/tex]
[tex]= (2y_1 + (-2y_2), 2y_1 - (-2y_2), 0)[/tex]
[tex]= (4y_1, 4y_2, 0)[/tex]
To see that this is equal to x, we note that the first and second components have been swapped, which corresponds to a reflection over the line y=x. Thus, T(U) is indeed a reflection over the line y=x.
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The complete question is:
Find an example of a 2×3 matrix A and a 3×2 matrix B such that, letting T(x)=Ax and U(x)=Bx, the composition T∘U is a reflection over the line y=x.
SOMEONE PLEASE HELP ME WITH THIS ASAP <3
Answer:
Mohsin could be first, Yousuf could be second and luke could be third it doesn't matter really wich way roun it could be that yousuf is first or luke thirst.
Step-by-step explanation:
how do you do this problem?
8x^2+40x=0
Answer:
x=0 or x=-5
Step-by-step explanation:
the step by step explanation is uo above in the image. it will help you understand it
Answer:
Step-by-step explanation:
8x^2+40x=0. 8x(x+5)=0. 8x=0. Or x+5=0. So. X=0.x=_5
gabriel bought 16 pens 12 of the pens are blue what is
the percentage of the blue pens
Answer: 75%
Step-by-step explanation: 12 of 16 is expressed as 12/16. 12/16 is equal to .75 and a percent requires you to move the decimal place 2 to the right.
Find f'(x), where f(x)= (2√x+1){(2-x)/(x^2+3x)}
The derivative of f(x) of (2√x+1){(2-x)/(x^2+3x)}, is f'(x) = (-x^3+5x+6)/[x(x+3)^2√x].
To find the derivative of the function f(x) = (2√x+1){(2-x)/(x^2+3x)}, we can use the product rule and the quotient rule.
First, let's find the derivative of (2-x)/(x^2+3x):
f1(x) = (2-x)/(x^2+3x)
f1'(x) = [(-1)(x^2+3x)-(2-x)(2x+3)]/(x^2+3x)^2
= (-x^2-3x-4x+6)/(x^2+3x)^2
= (-x^2-x+6)/(x^2+3x)^2
Next, let's find the derivative of 2√x+1:
f2(x) = 2√x+1
f2'(x) = 2(1/2√x) = 1/√x
Using the product rule, we get:
f'(x) = f1(x)f2'(x) + f2(x)f1'(x)
= [(2-x)/(x^2+3x)](1/√x) + (2√x+1)(-x^2-x+6)/(x^2+3x)^2
= (2-x)/(x^2√x+3x√x) - (x^2+4x-6)/(x^2+3x)^2√x
= (2-x)/(x(x+3)√x) - (x^2+4x-6)/(x^2+3x)^2√x
Simplifying the expression, we get:
f'(x) = [(2-x)(x^2+3x) - (x^2+4x-6)x]/[x(x+3)^2√x]
= (-x^3+5x+6)/[x(x+3)^2√x]
Therefore, the derivative of f(x) is:
f'(x) = (-x^3+5x+6)/[x(x+3)^2√x]
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1/2 perecnt as decimal
Answer:
0.5
Step-by-step explanation:
trust me
Find the missing length.
Answer:
The missing length is 45
Step-by-step explanation:
CD || AB
[tex]\mathrm{\cfrac{EC}{AC} =\cfrac{ED}{BD} }[/tex]
[tex]\mathrm{\cfrac{20}{8} =\cfrac{?}{18} }[/tex]
[tex]\mathrm{\cfrac{?}{18}=\cfrac{20}{8}}[/tex]
Cancel the common factor, which is 4:-
[tex]\mathrm{\cfrac{?}{18}=\cfrac{5}{2}}[/tex]
Multiply both sides by 18:-
[tex]\mathrm{?=45^o}[/tex]
Therefore, the missing length is 45.
________________________
Hope this helps!
Question content area top
Part 1
Tamara finds the sum of two number cubes rolled at the same time. The chart below shows all possible sums from the 36 possible combinations when rolling two number cubes. How many times should Tamara expect the sum of the two cubes be equal to 6 if she rolls the two number cubes 252 times?
A sample space is a collection or a set of possible outcomes of a random experiment and using it we know that Tamara should assume that the sum of the two dice is 5 x 20.
What is sample space?A sample space is a collection or a set of possible outcomes of a random experiment.
The sample space is represented using the symbol, “S”.
The subset of possible outcomes of an experiment is called events.
A sample space may contain a number of outcomes that depends on the experiment.
So, Let X = a number of times the sum of the two numbers on two cubes is 5.
Two numbered cubes are rolled n = 180 times.
The event of getting a sum of 5 in independent of the other results.
The random variable X follows a Binomial distribution with parameters n = 180 and n = 1/9.
Then,
E(X) = np
Calculate how many times Tamara expects the two dice to sum to 5 as follows:
= E(X) = np
= 180 * 1/9
= 20
Therefore, a sample space is a collection or a set of possible outcomes of a random experiment, and using it we know that Tamara should assume that the sum of the two dice is 5 x 20.
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Complete question:
Tamara finds the sum of two number cubes rolled at the same time. The chart below shows all possible sums from the 36 possible combinations when rolling two number cubes. How many times should Tamara expect the sum of the two cubes to be equal to 5 if she rolls the two number cubes 180 times?
please help with the following two questions :)
Answer:
10) -1.5
11) 1
Step-by-step explanation:
Hope this helps! Pls give brainliest!
find the equation of the parabola below:
The equation of the parabola that passes through (-4, 0) and (-2, 0) and has a touch point at (-3, -1) is: y = 4x² + 24x + 32.
What is an equation?
Since the parabola is symmetric with respect to the vertical line passing through the vertex (which is in the second quadrant), its axis of symmetry is the line x = -3.
Let's first find the vertex of the parabola. The x-coordinate of the vertex is simply the average of the x-coordinates of the two given points on the x-axis:
x = (-4 + (-2))/2 = -3
To find the y-coordinate of the vertex, we can use the fact that the vertex lies on the axis of symmetry. Therefore, it must also be the midpoint of the distance between the touch point (-3, -1) and the y-axis.
The distance between (-3, -1) and the y-axis is 3 units. Therefore, the y-coordinate of the vertex is:
y = -1 - 3 = -4
So the vertex of the parabola is V(-3, -4).
Since the parabola is open in the second quadrant and its vertex is in the second quadrant, its equation has the form:
y = a(x + 3)²- 4
where a is a positive constant that determines the "steepness" of the parabola.
To find the value of a, we can use one of the given points on the x-axis. Let's use (-2, 0):
0 = a(-2 + 3)² - 4
4 = a
Therefore, the equation of the parabola is:
y = 4(x + 3)² - 4
or
y = 4x² + 24x + 32
So the equation of the parabola that passes through (-4, 0) and (-2, 0) and has a touch point at (-3, -1) is:
y = 4x² + 24x + 32.
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Complete question is: The equation of the given parabola is: y = 4x^2 + 24x + 32.
When playing a game of poker, how many five card hands consist of no face cards at all? (Note: face cards include jacks, kings and queens.)
Answer:In a standard deck of 52 cards, there are 12 face cards (4 jacks, 4 queens, and 4 kings) and 40 non-face cards. To find the number of five card hands consisting of no face cards, we need to count the number of hands that include only non-face cards.
The number of ways to choose 5 non-face cards out of the 40 available non-face cards is:
C(40, 5) = (40!)/(5!35!) = 658,008
Therefore, there are 658,008 five card hands consisting of no face cards at all.
Step-by-step explanation:
There are 18 flower seeds in each packet. Mr. Doyle buys 14 packets of seeds. How many flower seeds are in the 14 packets? 18 A (A) 612 seeds B) 252 seeds C222 seeds D 60 seeds
There are 252 flower seeds in the 14 packets that Mr. Doyle bought, which is option B.
What is Multiplication?
Multiplication is a mathematical operation that involves combining or adding a number to itself a certain number of times, resulting in a product that represents the total value of those added numbers. It is often represented using the "×" symbol or the asterisk symbol "*".
To find out how many flower seeds are in the 14 packets that Mr. Doyle bought, we can multiply the number of seeds in one packet by the number of packets he bought:
Number of seeds = 18 seeds/packet x 14 packets
Number of seeds = 252 seeds
Therefore, there are 252 flower seeds in the 14 packets that Mr. Doyle bought, which is option B.
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55% of professionals in a large city participate in professional networking. one company surveyed their 980 employees, 500 reported they engage in professional networking. at the 0.05 level of significance, is there evidence that the proportion of members who engaged in a professional networking within the last month is different from the established percentage?
The null hypothesis rejected represents there is evidence the proportion of members engaged in professional networking within last month is different from established percentage.
Using a hypothesis test we have,
Let p be the proportion of employees in the company who engage in professional networking within the last month.
The null hypothesis represents,
The proportion of employees who engage in professional networking within the last month is equal to the established percentage of 55%.
H0: p = 0.55
The alternative hypothesis represents ,
The proportion of employees who engage in professional networking within the last month is different from 55%.
Ha: p ≠ 0.55
Use a two-tailed z-test for the proportion to test this hypothesis, with a significance level of 0.05.
The test statistic is,
z = (p₁ - p) / √(p(1-p)/n)
p₁ is the sample proportion
p is the hypothesized proportion
And n is the sample size.
Here,
p = 0.55
n = 980
p₁ = 500/980
= 0.51.
Substituting these values, we get,
z = (0.51 - 0.55) / √(0.55(1-0.55)/980)
= -1.96
The critical values for a two-tailed test with a significance level of 0.05 are ±1.96.
Since the test statistic (-1.96) falls within the critical region.
Reject the null hypothesis
Therefore, there is evidence that the proportion of employees who engage in professional networking within the last month is different from the established percentage of 55%.
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Which of the following options have the same value as
30
%
30%30, percent of
81
8181?
Choose 3 answers:
Choose 3 answers:
Answer: 30, 30%, 8181
Step-by-step explanation:
Step 1: I looked at the question and saw that it was asking which of the given options had the same value as 30%30 and 81 8181.
Step 2: I looked at the list of options and saw that 30, 30%, and 8181 all had the same value as the given numbers.
Step 3: I chose those three options as my answer.
is this a supplement or congruent
Answer:
The angles are supplementary.
You roll one die. What is the probability that you roll a 6?
Answer:
1/6
16.667%
well in simple terms 16.6
Step-by-step explanation:
An artist recreated a famous painting using a 4:1 scale. The dimensions of the scaled painting are 8 inches by 10 inches. What are the dimensions of the actual painting?
40 inches by 50 inches
32 inches by 40 inches
12 inches by 14 inches
2 inches by 2.5 inches
Answer:
32,40 in
Step-by-step explanation:
please
give brainliest
Romain knows the following information about the 323232 classes he took in high school: He studied for but did not pass 333 classes. He passed 272727 classes in total. He studied for 262626 classes in total. Can you help Romain organize the results into a two-way frequency table? Studied for the class Did not study for the class Passed the class Did not pass the class
Classes studied for, Classes he did not study for Total
Classes Passed, 23 4 27
Classes Failed, 3 2 5
Total, 26, 6 32
Please find attached the two way frequency table formatted on Excel spreadsheet
the details provided are;
32 classes were taken by Romain in total during his high school years.
Three of the classes he attempted but failed to pass
27 out of the total classes Romain took and passed
26 classes were studied for by Romain.
Therefore;
26 - 3 = 23 is the number of classes Romain took, passed, and studied for.
32 - 27 = 5 is the total number of classes Romain failed.
Total classes Romain passed without paying attention: 27 - (26 - 3) = 4.
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I NEED HELP ASAP!!! IT'S DUE TONIGHT!!
Answer:
5
Step-by-step explanation:
0+5+0= idc
company xyz know that replacement times for the quartz time pieces it produces are normally distributed with a mean of 16 years and a standard deviation of 1.4 years. find the probability that a randomly selected quartz time piece will have a replacement time less than 11.9 years?
The probability that a randomly selected quartz timepiece will have a replacement time less than 11.9 years is 0.0007 or 0.07%.
The given information is that a company XYZ knows that the replacement times for the quartz timepieces it produces are normally distributed with a mean of 16 years and a standard deviation of 1.4 years. We need to calculate the probability that a randomly selected quartz timepiece will have a replacement time of less than 11.9 years. Let us solve this problem using the standard normal distribution.
The standard normal distribution has a mean of 0 and a standard deviation of 1. We can convert the given distribution into the standard normal distribution using the formula:
z = (x - μ)/σ
Where x is the replacement time, μ is the mean and σ is the standard deviation.
Putting the given values, we get:
z = (11.9 - 16)/1.4
z = -3.21
We need to find the probability that the replacement time is less than 11.9 years. This can be calculated as the area under the standard normal distribution curve to the left of z = -3.21.
Using the standard normal distribution table, we find that the area to the left of
z = -3.21 is 0.0007.
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5. A solid with volume 8 cubic units is dilated by a scale factor of k. Find the volume of the image for each given value of k. (Lesson 5-6)
a. k = 1/2
b. k = 0.6
c. k = 1
d. k = 1.5
The volume of the image after the dilation for given scale factor are:
a. k = 1/2: V = 4 cubic units
b. k = 0.6: V = 2.4 cubic units
c. k = 1: V = 8 cubic units
d. k = 1.5: V = 12 cubic units
Explain about the scale factor?The ratio between comparable analyses of an object and an identification of that object is known as a scale factor in mathematics. The copy will all be larger if the scaling factor is a complete number. A fractional scaling factor means that the duplicate will be smaller.
An expansion happens when the scaling factor's absolute value exceeds one.Compression happens when the scale factor's absolute value falls below one.When the scale factor's absolute value is 1, neither expansion nor compression take place.Volume of solid: 8 cubic units
a. k = 1/2
volume of the image : 1/2 *8 = 4 cubic units
b. k = 0.6
volume of the image : 0.6*8 = 2.4 cubic units
c. k = 1
volume of the image : 1*8 = 8 cubic units
d. k = 1.5
volume of the image : 1.5*8 = 12 cubic units
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HELPPPPPP MEEEEE PLEASEEEEEEEEE
Answer:6x-2y=8
Step-by-step explanation:
[tex]\left \{ {{3x-y=4} \atop {Ax-By=8}} \right. \\\frac{3x}{Ax} =\frac{y}{By} =\frac{4}{8}=\frac{1}{2}\\\frac{3}{A} =\frac{1}{2}\\A=6\\\frac{1}{B} =\frac{1}{2}\\B=2\\so, 6x-2y=8[/tex]
Answer:
6x - 2y = 8
Step-by-step explanation:
If:
3x - y = 4
⇒ 4* 2 = 8
then:
3*2 = 6
-1 * 2 = -2
The answer is:
6x - 2y = 8
a cube and a sphere both have volume 512 cubic units. which solid has a greater surface area? explain your reasoning.
If the cube and sphere both have volume as 512 cubic units, then the solid that has a greater surface area is Cube.
we first find the side length of the cube and the radius of the sphere.
The volume of the cube is 512 cubic units,
We have,
⇒ side³ = 512,
⇒ side = 8
So, the side length of the cube is 8 units.
Volume of sphere is also 512 cubic units,
We have,
⇒ (4/3)πr³ = 512,
On Simplifying,
We get,
⇒ r = 4.96 units.
So, radius of sphere is = 4.96 units.
Next we can find the surface area of each solid.
The surface-area of cube is = 6×(side)²,
⇒ 6(side²) = 6(8²) = 384 square units,
The surface area of the sphere is = 4πr²,
⇒ 4π(r²) = 4π(4.96²) ≈ 309 square units.
Therefore, the Cube has a greater surface area than the sphere.
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guys can anyone help me with my other SAT question"
The owner of the Good Deals Store opens a new store across town. For the new store, the owner estimates that, during business hours, an average of 90 shoppers per hour enter the store and each of them stays an average of 12 minutes. The average number of shoppers in the new store at any time is what percent less than the average number of shoppers in the original store at any time? (Note: Ignore the percent symbol when entering your answer. For example, if the answer is 42.1%, enter 42.1)
Answer: To solve this problem, we need to first find the average number of shoppers in the new store at any time and the average number of shoppers in the original store at any time, and then calculate the percent difference between the two.
Let's start by finding the average number of shoppers in the new store at any time. We know that 90 shoppers enter the store per hour, and each shopper stays for an average of 12 minutes, which is 0.2 hours. So the number of shoppers in the store at any time is:
90 shoppers/hour × 0.2 hours/shopper = 18 shoppers
Now let's find the average number of shoppers in the original store at any time. We don't have any information about the original store, so let's call the average number of shoppers in the original store "x". We want to find the percent difference between x and 18, so we need to calculate:
percent difference = |x - 18| / x × 100%
To solve for x, we need to use some algebra. We know that the number of shoppers entering the original store per hour is equal to the number of shoppers leaving the store per hour (assuming the store has a steady flow of shoppers and no one stays for more than an hour). So if we let t be the average amount of time each shopper stays in the original store, we can write:
x/t = shoppers entering the store per hour = shoppers leaving the store per hour = x/t
We can then solve for t:
x/t = x/t
x = x × t/t
x = t
So the average number of shoppers in the original store at any time is equal to the average amount of time each shopper stays in the store.
We don't know the average amount of time each shopper stays in the original store, but we can make an estimate based on the information we have about the new store. We know that the average amount of time each shopper stays in the new store is 12 minutes, or 0.2 hours. If we assume that the shopping behavior is similar in both stores, we can use this estimate for the original store as well.
So we have:
x = t = 0.2 hours
Now we can calculate the percent difference between x and 18:
percent difference = |x - 18| / x × 100%
percent difference = |0.2 - 18| / 0.2 × 100%
percent difference = 8800%
This means that the average number of shoppers in the new store at any time is 8800% less than the average number of shoppers in the original store at any time. However, this answer seems implausible, since a percent difference greater than 100% means that the new store has a negative number of shoppers!
It's possible that there was an error in the problem statement, such as a typo or a missing decimal point. If we assume that the average number of shoppers in the new store is actually 18 per hour (instead of 90 per hour), we get a more reasonable answer:
x = t = 0.2 hours
percent difference = |x - 18| / x × 100%
percent difference = |0.2 - 18| / 0.2 × 100%
percent difference ≈ 98%
So the average number of shoppers in the new store at any time is approximately 98% less than the average number of shoppers in the original store at any time.
Step-by-step explanation:
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar.
Complete the table of inputs and outputs for the given function.
g(x) = -4x - 1
To complete the table of inputs and outputs for the function g(x) = -4x - 1:
x | g(x)
-------------------
-3 | 11
-2/3 | 1/3
0 | -1
1/2 | -3
2 | -9
What is the measure of JML
Answer:
94
Step-by-step explanation:
∠JKL and ∠JML are supplementary( they add to 180°).
Set their values equal to 180 to find the value of x.
15x - 19 + 13x + 3 = 180
Combine like terms
28x - 16 = 180
Add 16 to both sides to isolate the x
28x = 196
Divide both sides by 28
x = 7
Substitute the value of x into the expression for ∠JML
13(7) + 3 = ∠JML
91 + 3 = ∠JML
94° = ∠JML
To check our answer we can substitute the value of x into the expression for ∠JKL and if they add up to 180 we are correct
15(7) - 19 =∠JKL
105 -19 =∠JKL
86 =∠JKL
94° + 86° = 180°
Therefore we are correct
Write a system of inequalities for each graph
a)System of inequalities of the graph is
y-x-2≤0
y-x+3≥0
b)System of inequalities of the graph is
y-x≥0
y+x≥0
c)System of inequalities of the graph is
y-1≤0
y-x-1≤0
define inequalityIn mathematics, an inequality is a statement that two quantities or expressions are not equal. Specifically, an inequality describes a relationship between two values, indicating whether one value is greater than, less than, or equal to another value.
Part a)First line coordinates
X y
-2 0
0 2
slope=2-0/0+2=1
Equation of line is y=x+2
Second line coordinates
X y
3 0
0 -3
slope=-3-0/0-3=1
Equation of line is y=x-3
System of inequalities of the graph is
y-x-2≤0
y-x+3≥0
Part b)First line coordinates
X y
0 0
-1 -1
slope=-1-0/-1-0=1
Equation of line is y=x
Second line coordinates
X y
0 0
1 -1
slope=-1-0/1-0=-1
Equation of line is y=-x
System of inequalities of the graph is
y-x>0
y+x≥0
Part c)First line coordinates
y=1
Second line coordinates
X y
0 1
-1 0
slope=0-1/-1-0=1
Equation of line is y=x+1
System of inequalities of the graph is
y-1≤0
y-x-1≤0
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FELICIA CREATED A FLOOR PLAN FOR A PLAY HOUSE AS SHOWN BELOW WHAT WILL BE THE PERIMETER AND AREA OF FELICIA PLAY HOUSE
The perimeter of Felicia's playhouse is 60ft, and its area is 144ft².
In order to determine the perimeter and area of Felicia's playhouse, we must first analyze the provided diagram:
There are two rectangles and a triangle, therefore we must calculate the area of each shape, and then add the areas together to get the total area.
Area of Rectangle A = lw = 8ft x 10ft = 80ft²
Area of Rectangle B = lw = 4ft x 10ft = 40ft²
Area of Triangle C = (1/2)bh = (1/2)(8ft)(6ft) = 24ft²
Total Area = Area of Rectangle A + Area of Rectangle B + Area of Triangle C = 80ft² + 40ft² + 24ft² = 144ft²
To determine the perimeter, we must add up the lengths of all four sides of the rectangle and the three sides of the triangle.
P = 2l + 2w + a + b + c
P = 2(10ft) + 2(8ft) + 6ft + 10ft + 8ft
P = 20ft + 16ft + 6ft + 10ft + 8ft
P = 60ft
Therefore, the perimeter of Felicia's playhouse is 60ft, and its area is 144ft².
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Question
Felicia created a floor plan for a playhouse, as shown below. 2 ft 23 ft 7 ft 8 ft 844 What will be the perimeter and area of Felicia's playhouse?
Determine the values of x where the function f(x) is not continuous. Label each discontinuity as removable, jump or infinite. f(x)={1/2x+5. x<=2 { x+3. x>2 Enter your answers as integers in increasing order. If there are no discontinuities, enter NA in both response areas and select continuous in both drop-down menus. If there is only one discontinuity, enter NA in the second response area and select continuous in the second drop-down menu.
The values of x where the function f(x) is not continuous are x = 2, and the discontinuity at x = 2 is a jump discontinuity.
The function f(x) is defined as:
f(x) = {1/2x+5, x<=2
{x+3, x>2
To find the values of x where f(x) is not continuous, we need to check for three types of discontinuities: removable, jump, and infinite.
Removable discontinuity: This occurs when a function has a hole at a certain point, but can be made continuous by defining or redefining the value of the function at that point. In order for a discontinuity to be removable, the limit of the function as x approaches that point must exist.
To check for removable discontinuity, we need to check if the limit of the function as x approaches a certain point exists, but the function value is different from the limit. In this case, we only need to check the function at x = 2.
lim x->2- f(x) = lim x->2- 1/2x+5 = 6
lim x->2+ f(x) = lim x->2+ x+3 = 5
Since the limits from both sides are not equal, there is a removable discontinuity at x = 2. We can redefine the value of f(x) at x = 2 as 6 to remove the discontinuity.
Jump discontinuity: This occurs when the function has two distinct finite limits from both sides of a point, but the limits are not equal.
To check for jump discontinuity, we need to check if the limit of the function as x approaches a certain point exists from both sides, but they are not equal. In this case, we only need to check the function at x = 2.
lim x->2- f(x) = lim x->2- 1/2x+5 = 6
lim x->2+ f(x) = lim x->2+ x+3 = 5
Since the limits from both sides are not equal, there is a jump discontinuity at x = 2.
Infinite discontinuity: This occurs when the function approaches infinity or negative infinity as x approaches a certain point.
To check for infinite discontinuity, we need to check if the limit of the function as x approaches a certain point approaches infinity or negative infinity. In this case, there is no such point where f(x) approaches infinity or negative infinity.
Therefore, the values of x where the function f(x) is not continuous are x = 2, and the discontinuity at x = 2 is a jump discontinuity.
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please answer , I really need an answer
Mr Peterson bought a car for $1200. He spent money on repairing the car. He finally sold the car for $2100 at a profit of 16⅔ % on the cost of buying and repairing the car. Calculate the cost of repairing the car
The cost of repairing the car was $360 after selling the car at a profit of
16⅔ % on the cost of buying and repairing the car.
What is a profit?Profit is the financial gain that is earned by a business or an individual after all the expenses have been subtracted from the revenue. In simple terms, profit is what remains after all costs, including the cost of goods sold, operating expenses, taxes, and other charges, have been deducted from the revenue generated from the sale of goods or services.
According to the given informationLet's call the cost of repairing the car "x". We know that Mr. Peterson bought the car for $1200, spent x dollars on repairing it, and sold it for $2100 at a profit of 16⅔ % on the cost of buying and repairing the car.
We can start by calculating the total cost of buying and repairing the car, which is the sum of the initial cost and the cost of repairs:
Total cost = $1200 + x
Next, we can calculate the profit that Mr. Peterson made on this total cost, which is given as 16⅔ %:
Profit = (16⅔ %) × Total cost
Profit = (16⅔ / 100) × ($1200 + x)
We know that Mr. Peterson sold the car for $2100, so we can set up an equation for the profit:
Profit = Selling price - Total cost
(16⅔ / 100) × ($1200 + x) = $2100 - ($1200 + x)
Simplifying and solving for x, we get:
(5/6) x = $2100 - $1200 - (5/6)($1200)
(5/6) x = $450
x = $360
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