Answer:
See proofs below
Step-by-step explanation:
a) Suppose that aRb. Let y∈Sa , then y∈A and yRa. We have that yRa and aRb. Since R is a partial order, R is a transitive relation, therefore yRa and aRb imply that yRb. Now, y∈A and yRb, thus y∈Sb. This reasoning applies for all y∈Sa that is, for all y∈Sa, y∈Sb, threrefore Sa⊆Sb.
b) Suppose that Sa⊆Sb. Since R is a partial order, R is a reflexive relation then aRa. Thus, a∈Sa. The inclusion Sa⊆Sb implies that a∈Sb, then aRb.
c) Denote this set by S={Sb:b∈B}. We will prove that supS=Sx with x=supB.
First, Sx is an upper bound of S: let Sb∈S. Then b∈B and since x=supB, x is an upper bound of B, then bRx. Then b∈Sx. Now, for all y∈Sb, yRb and bRx, then by transitivity yRx, thus y∈Sx. Therefore Sb⊆Sx for all Sb∈S, which means that Sx is an upper bound of S (remember that the order between sets is inclusion).
Now, let's prove that Sx is the least upper bound of S. Let Sc⊆A be another upper bound of S (in the set F). We will prove that Sx⊆T.
Because Sc is an upper bound, Sb⊆Sc for all b∈B. Thus, if y∈Sb for some b, then y∈Sc. That is, if yRb then yRc. In particular, bRb then bRc for all b∈B. Thus c is a upper bound of B. Byt x=supB, then xRc. Now, for all z∈Sx, zRx and xRc, which again, by transitivity, implies that z∈Sc. Therefore Sx⊆Sc and Sx=sup S.
In a partial order set, if aRb, then Sa ⊆ Sb. If Sa ⊆ Sb, then aRb. If B ⊆ A and x is the least upper bound for B, then Sx is the least upper bound for {Sb : b ∈ B}.
Explanation:a) To show that if aRb, then Sa ⊆ Sb, we need to prove that if x ∈ Sa, then x ∈ Sb. Since x ∈ Sa, that means xRa holds. And since aRb, we can conclude that xRb holds as well. Therefore, x ∈ Sb, which implies that Sa ⊆ Sb.
b) To show that if Sa ⊆ Sb, then aRb, we need to prove that if aRb does not hold, then Sa ⊆ Sb does not hold. If aRb does not hold, it means that b is not in Sa. However, if Sa ⊆ Sb, it implies that every element in Sa is also in Sb. Hence, we arrive at a contradiction, which proves that if Sa ⊆ Sb, then aRb.
c) To show that if B ⊆ A and x is the least upper bound for B, then Sx is the least upper bound for {Sb : b ∈ B}, we need to prove that Sx is an upper bound for {Sb : b ∈ B} and that it is the least upper bound. Since x is the least upper bound for B, this means that every element of B is contained in Sx. Therefore, Sx is an upper bound for {Sb : b ∈ B}. Additionally, if there exists an upper bound U for {Sb : b ∈ B}, then every element of {Sb : b ∈ B} must be contained in U. Since Sb is a subset of Sa for every b ∈ B, it follows that every element of Sa is contained in U. Therefore, Sa ⊆ U for every a ∈ A. In particular, Sx ⊆ U, which proves that Sx is the least upper bound for {Sb : b ∈ B}.
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The Morrison’s car uses one gallon of gasoline for every 28 miles. If gasoline costs $1.50 per gallon, how many miles can they drive if they spend $24 on gasoline?
Given:
$ 1.50 / gallon
1 gallon = 28 miles;
Solution:
$ 24.00 / $ 1.50 = 16 gallons
16 gallons x 28 miles = 448 miles
have a nice day:)
Answer:they would drive 448 miles if they spend $24 on gasoline
Step-by-step explanation:
The Morrison’s car uses one gallon of gasoline for every 28 miles. If gasoline costs $1.50 per gallon, then the cost of driving 28 miles would be $1.5.
Therefore, the number of miles can they drive if they spend $24 on gasoline would be
(28 × 24)/1.5 = 448 miles
If one number is a multiple of 3 and the other is not, then the sum of these numbers is not a multiple of 3
A. true
B. false
Answer:
A.True
Step-by-step explanation:
Multiple of 3 is given by
3,6,9,12,15,18,,,,
Let one number a=6
6 is a multiple of 3.
Another number =5
5 is not a multiple of 3.
Sum of 6 and 5=6+5=11
We know that
11 is not a multiple of 3.
Therefore, if one number is a multiple of 3 and the other is not , then the sum of these number is not a multiple of 3 is true.
Option A is true
Sergio thinks he will need 90 cups of fruit juice to make 210 cups of punch. Explain his method. How many cups of fruit juice would Sergio need to make 154 cups of punch? Explain your calculations.
Answer:
66 cups of fruit juice will be required .
Step-by-step explanation:
According to the question ,
90 Cups of fruit juice is required for making of 210 cups of punch .
So,
For making of one cup of punch ,
[tex]\frac{90}{210}[/tex] = [tex]\frac{3}{7}[/tex] cups of fruit juice will be required ,
Thus,
For making of 154 cups of punch ,
Total number of cups of fruit juice required will be [tex]\frac{3}{7}[/tex]×154.
= 66 cups.
Thus a total of 66 cups of fruit juice will be required.
Eight women of different heights are at a party. Each woman decides to only participate in a handshake with women shorter than herself. How many handshakes take place?
Answer:
0 handshakes
Step-by-step explanation:
There are 8 women of different heights.
Let the eight women be A, B, C, D, E, F, G and H
Assume A is taller than B and A decides to shake hands with B, B will refuse because A is taller. If this happens across the eight women then there will be 0 hand shakes.
If this assumption is taken out, we have 7+6+5+4+3+2+1 = 28
Answer:
0
Step-by-step explanation:
There are 0 handshakes because if A is taller than B, then A will want to shake hands with B, but B will not participate because she is shorter.
The sum of the first 100 positive integers is 5,050. What is the sum of the first 200 positive integers?
A. 10,000B. 10,200C. 15,050D. 20,050E. 20,100
The sum of the k for k=1 to k="n"=(n*(n+1))/2 , where "n" is the total integer.
In this problem n = 200
Sum = (200*201)/2 = 20,100
State the horizontal asymptote of the rational function. F(x)=9x^2-3x-8/4x^2-5x+3
Y=3/5
Y=9/4
Y=0
None
Answer:
y=0
Step-by-step explanation:
Answer:
y = [tex]\frac{9}{4}[/tex]
Step-by-step explanation:
The horizontal asymptote is the ratio of the coefficient of the highest degree term on the numerator and denominator, that is
9x² - 3x - 8 ← coefficient 9
4x² - 5x + 3 ← coefficient 4, thus
y = [tex]\frac{9}{4}[/tex] ← equation of horizontal asymptote
1. Point A(-5,8) is reflected across the line y = x. What are the coordinates of A'? Show your work and explain.
Need help with this
Answer:
The coordinates of A'(8,-5)
Step-by-step explanation:
we know that
When you reflect a point across the line y = x, the x-coordinate and y-coordinate change places
so
The rule of the reflection across the line y=x is
(x,y) -----> (y,x)
we have the point A(-5,8)
Applying the rule of the reflection across the line y=x
A(-5,8) ----> A'(8,-5)
see the attached figure to better understand the problem
For the following frequency distribution, how many individual scores are in the entire set?
X: 5 - 4 - 3 - 2
f: 2 - 4 - 1 - 3
a. N = 54
b. N = 14
c. N = 10
d. impossible to determine
Answer:
10
Step-by-step explanation:
The individual scores in the data are represented by frequency denoted by f column. f column depicts that how many times the individual scores are occurring in the data set. Hence to calculate the amount of individual score in the data set we simply add all frequencies. n=sum of f=2+4+1+3=10. Hence there are 10 individual scores present in the entire data set.
The number of individual scores in the given frequency distribution set is 10, obtained by adding the frequencies together.
Explanation:In the given question, it's the frequency distribution that is given with scores X: 5, 4, 3, and 2 with their respective frequencies f: 2, 4, 1, and 3. To find the total number of individual scores in the entire set, you simply sum up all the frequencies. So, 2+4+1+3 equals 10. So, the number of individual scores in the entire set is 10. Hence, the correct answer is c. N = 10.
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The goals against average (A) for a professional hockey goalie is determined using the formula A = 60 a equals 60 left-parenthesis StartFraction g Over t EndFraction right-parenthesis.. In the formula, g represents the number of goals scored against the goalie and t represents the time played, in minutes. Which is an equivalent equation solved for g? StartFraction A t Over 60 EndFraction equals g.= g StartFraction A Over 60 t EndFraction equals g. = g StartFraction 60 A Over t EndFraction equals g. = g 60At = g
Answer:
Option 1 - [tex]\frac{At}{60}=g[/tex]
Step-by-step explanation:
Given : The goals against average (A) for a professional hockey goalie is determined using the formula [tex]A=60(\frac{g}{t} )[/tex]. In the formula, g represents the number of goals scored against the goalie and t represents the time played, in minutes.
To find : Which is an equivalent equation solved for g?
Solution :
Solve the formula in terms of g,
[tex]A=60(\frac{g}{t})[/tex]
Multiply both side by t,
[tex]At=60g[/tex]
Divide both side by 60,
[tex]\frac{At}{60}=\frac{60g}{60}[/tex]
[tex]\frac{At}{60}=g[/tex]
Therefore, option 1 is correct.
Answer:
a
Step-by-step explanation:
A system of inequalities is shown. Which symbol could be written in both circles in order to represent this system algebraically? y 3x x –2 ≤ ≥ < >
Answer:
"≥"
Step-by-step explanation:
1) Well, for the sake of clarity we'll use a circle on a number line to represent the point solution of each inequality.
2) Writing the system:
[tex]\left\{\begin{matrix}y\geqslant 3x&\\x\geqslant-2&\end{matrix}\right.[/tex]
3) We'll shade the circles and use "≥"
Final answer:
The correct inequality symbols that could be written in both circles for the system 'y 3x x –2' are '<=' and '>=', representing the relationships 'y <= 3x' and 'x >= -2' respectively.
Explanation:
To represent the given system of inequalities algebraically, one needs to identify the correct inequality symbols that could be used between the variables x and y. These symbols articulate the ordering and relationship between these variables.
Given the statement of the system 'y 3x x –2', the inequality symbols that could fit in the circles to complete the system algebraically could be '<=' for 'y <= 3x' and '>=' for 'x >= -2'. This means '<=' and '>=' are both inequality symbols that could be written in the circles to represent the relationship between the variables according to the rules of inequalities which define x is less than or equal to y (x <= y), and x is greater than or equal to y (x >= y).
Inequalities allow us to compare relative sizes or orders of numbers and to solve various algebraic problems dealing with quantity and relationships.
Tim's Tacos sell 57 chicken tacos a night and 89 beef tacos a night for 3 weeks. How many of each kind of taco do they sell when the three weeks are up?
Answer:
see the explanation
Step-by-step explanation:
Remember that
[tex]1\ week=7\ days[/tex]
To convert weeks to days , multiply by 7
so
[tex]3\ weeks=3(7)=21\ days[/tex]
we know that
Each night Tim's Tacos sell 57 chicken tacos and 89 beef tacos
To find out how many of each type of taco sold after three weeks, multiply the number of taco sold daily by 21 (3 weeks)
Chicken tacos
[tex]57(21)= 1,197\ chicken\ tacos[/tex]
Beef tacos
[tex]89(21)= 1,869\ beef\ tacos[/tex]
ind the probability of answering the two multiple choice questions correctly if random guesses are made. Assume the questions each have five choices for the answer. Only one of the choices is correct.a. 0.04 b. 0.4 c. 0.02 d. 0.004
Answer: a. 0.04
Step-by-step explanation:
Given : Number of multiple choice questions = 2
Choices given in each question = 5
Since only one choice is correct out of 5.
So, the probability of selecting the correct answer = [tex]\dfrac{1}{5}[/tex]
Also, both questions are independent of each other.
It means , The probability of answering the two multiple choice questions correctly if random guesses are made
=( Probability of selecting the correct answer in question 1 ) x ( Probability of selecting the correct answer in question 2 )
= [tex]\dfrac{1}{5}\times\dfrac{1}{5}= 0.04[/tex]
Hence, the required probability =0.04
The number of math problems solved in a class, ????, varies directly with the length of time x and inversely with the number of student questions in that time y. If in 6 minutes of class there were 14 student questions and a total of 5 problems that were solved, then write ???? as a function of x and y. ???? = x/y function equation editor
The function that represents the number of math problems solved in a class is given by ????(x, y) = (15/7)* x / y, where x represents time and y represents the number of student questions. The constant of variation 'k' is 15/7.
Explanation:Given that the number of math problems solved (????) in class is influenced by time duration (x) and the number of student questions (y), we can infer a relationship. We can define a constant of variation (k), which stands for the number of problems solved per time unit and per question. Based on the provided situation where 5 problems were solved in 6 minutes with 14 questions, we calculate k as k = ????(x/y) = 5(6/14) = 30/14 = 15/7.
Therefore, the function that represents this scenario is ????(x, y) = (15/7)* x / y, where x is the length of time and y is the number of student questions.
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The local amusement park was interested in the average wait time at their most popular roller coaster at the peak park time (2 p.m.). They selected 13 patrons and had them get in line between 2 and 3 p.m. Each was given a stopwatch to record the time they spent in line. The times recorded were as follows (in minutes): 118, 124, 108, 116, 99, 120, 148, 118, 119, 121, 45, 130, 118.
What is the first quartile?
a. 100.8
b. 119.8
c. 128.8
d. 112
e. 122.5
Answer: d. 112
Step-by-step explanation:
First Quartile is the median of the first half of ordered data (from smallest to largest).
The given data : 118, 124, 108, 116, 99, 120, 148, 118, 119, 121, 45, 130, 118.
Arrange in Ascending order , we get
45,99, 108,116,118, 118, 118, 119,120, 121,124,130, 148
First half = 45,99, 108,116,118, 118
No. of elements = 6
First Quartile = Median of first half = Mean of middlemost terms
=[tex]\dfrac{108+116}{2}=\dfrac{224}{2}=112[/tex]
Hence, the First quartile = 112
Correct answer = d. 112
If a fair coin is tossed three times, find the probability of getting heads on the first toss and tails on the second and third tosses.
Answer:
The answer is: [tex]\frac{1}{8}[/tex]
Step-by-step explanation:
The sample space when tossing a coin three times is [HHH, HHT, HTH, HTT, THH, THT, TTH, TTT] and the total number of occurrence is 8.
Getting Head on first toss, tail on second and third is: HTT and it occurs just once in our sample space.
Therefore, the probability of getting Head on first toss, tails on second and third tosses is: [tex]\frac{1}{8}[/tex]
Note probability = [tex]\frac{number of possible occurrence}{number of total occurrence}[/tex]
Identify the graphed linear equation.
A) y = 4x + 1
B) y = 4x - 1
C) y = -4x + 1
D) y = -4x - 1
Answer:
The answer to your question is letter C
Step-by-step explanation:
Process
1.- Find two points of the line
A ( 0, 1)
B ( 1, -3)
2.- Find the slope of the line
[tex]m = \frac{y2 - y1}{x2 - x1}[/tex]
[tex]m = \frac{-3 - 1}{1 - 0}[/tex]
[tex]m = \frac{-4}{1}[/tex]
m = -4
3.- Find the equation of the line
y - y1 = m (x - x1)
y - 1 = -4( x - 0)
y -1 = -4x
y = -4x + 1
Charles is saving $5 each week.He earns an extra $15 by mowing his neighbor's lawn.Write the inequality to show how to find how many weeks,W,will he need to save in order to save at least $75.
Answer:
Minimum number of weeks = 4
Step-by-step explanation:
Charles earns $5 each week .Also he makes $15 each week by mowing his neighbours lawn.
Thus , in total , he earns a total of $20 each week.
We have to find the minimum number of weeks needed to make $75 .
Number of weeks required = [tex]\frac{money required}{money made per week}[/tex]
= [tex]\frac{75}{20}[/tex]
=3.75
Since the number of weeks, W, is an integer, choose the next highest integer.
Hence the minimum number of weeks required = 4
Select the correct answer from each drop-down menu.
Maggie is monitoring the number of fish in a fish breeding center. The table below shows the number of fish with respect to the number of months elapsed.
Number of Months 0 1 2 3 4
Number of Fish 1,024 1,280 1,600 2,000 2,500
The independent variable in the relationship is the_____________ and should be placed on the______________ .
The dependent variable in the relationship is the_____________ and should be placed on the__________________ .
Answer:
The independent variable in the relationship is the Number of Months and should be placed on the x-axis .
The dependent variable in the relationship is the Number of Fish and should be placed on the y-axis .
Step-by-step explanation:
Independent variable is the variable that is being changed or controlled. It's the value that you would graph on the x-axis. Intuitively you would graph the months on the x-axis. I don't really know how to explain it other than that.
Dependent variable is the variable that is being measured. It's the value that is being graphed on the y-axis. You're measuring the amount of fish so that's your dependent variable.
Stephen recently purchased a camper. The value of the camper after t years is given by the following expression.
22,475(0.81)^t
Which of the following best describes the expression?
A.
the product of the initial value of the camper and its decay factor raised to the number of months since it was purchased
B.
the product of the initial value of the camper and its growth factor raised to the number of years since it was purchased
C.
the product of the initial value of the camper and its decay factor raised to the number of years since it was purchased
D.
the product of the initial value of the camper and its growth factor raised to the number of months since it was purchased
Answer:
C
Step-by-step explanation:
since the camper gets old we will choose decay factor over the years and since t is in years in the explanation so t in the expression means years as well
The expression describes the initial value of the camper multiplied by its annual decay factor raised to the power of the number of years since purchase, corresponding to option C.
The expression 22,475(0.81)^t best describes the product of the initial value of the camper and its decay factor raised to the number of years since it was purchased. The correct choice that describes the expression is C. The initial value of the camper is given as $22,475. The factor 0.81 represents the annual depreciation rate, meaning that the camper loses 19% of its value each year (100% - 81% = 19% decay). The variable t stands for the number of years since the purchase. Therefore, each year, the value is multiplied by 0.81, repeatedly, to reflect the continuous decrease in value.
A car rental costs $70 per day plus an additional $0.50 for each mile driven. The daily cost y is given by the equation y = 0.50x + 70
Answer:
Cannot give answer until Mile (x) is given
Step-by-step explanation:
Kobe attends barber school so far he has completed 612 hours if Kobe attended School the same number of hours each day for a total of 68 days how many hours did he attend school each day?
Answer:
Kobe attended barber school for 9 hours each day.
Step-by-step explanation:
Total number of hours completed by Kobe in barber school = 612 hours
Total number of days Kobe attended the school for = 68 days
We are given that Kobe attended school for same number of hours each day.
So, in order to find the number of hours Kobe attended each day we will use unitary method.
In 68 days Kobe completed = 612 hours of school
So, in 1 day he will complete = [tex]\frac{612}{68}=9[/tex] hours
Thus, Kobe attended barber school for 9 hours each day.
After sales tax your brand new car is $17,300. What is the total price of the car with DMV fees of 1.25% of the purchase price of the car?
A. $261.25
B. $17,516.25
C. $216.25
D. $17,561.25
The right answer is Option B.
Step-by-step explanation:
Given,
Purchase price of car with sales tax = $17300
DMV fees = 1.25%
Amount of DMV fees = 1.25% of purchase price
Amount of DMV fees = [tex]\frac{1.25}{100}*17300=\frac{21625}{100}[/tex]
Amount of DMV fees = $216.25
Total price = Purchase price + DMV fees
Total price = 17300 + 216.25
Total price = $17516.25
The total price of car with DMV fees is $17,516.25
The right answer is Option B.
Keywords: percentage, addition
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Final answer:
The total price of the car including DMV fees of 1.25% is (B) $17,516.25, which is found by adding the DMV fees of $216.25 to the purchase price of $17,300.
Explanation:
The question asks for the total price of a car including DMV fees, which are 1.25% of the purchase price of the car after sales tax.
To find the DMV fees, first convert the percentage to a decimal by dividing 1.25 by 100, which gives us 0.0125. Then multiply the purchase price after sales tax, $17,300, by 0.0125 to get the DMV fees.
The calculation is: $17,300 x 0.0125 = $216.25.
Finally, add the DMV fees to the purchase price to get the total price: $17,300 + $216.25 = $17,516.25. Therefore, the correct answer is B. $17,516.25.
When using your portable radio, you must push the "press to talk" button and wait one second before speaking. This is essential to effective communication because your EMS system must use:
Answer:
Repeaters.
Step-by-step explanation:
This is essential to effective communication because your EMS system must use Repeaters.
These are machines used to carry signals across a great distance. We may be in ambulances or put around an EMS network in different areas. The repeater receives and re transmits signals from lower power systems, such as mobile and handheld phones, to a higher power.
Final answer:
When using portable radios in an EMS system, waiting before speaking is necessary to prevent frequency interference with medical equipment like AEDs. This ensures effective communication and prevents disruptions with critical equipment operations.
Explanation:
When using a portable radio and instructed to push the "press to talk" button and wait one second before speaking, it is essential for effective communication because it ensures that the EMS system has time to establish a clear connection. This waiting period is crucial because communications or medical equipment may use similar radio frequencies. Interruptions and interference on these frequencies can arise from external devices, such as mobile phones operating at 1.9 GHz. Moreover, important medical devices, like automated external defibrillators (AEDs), which provide verbal instructions during cardiac emergencies, rely on these frequencies to function correctly without disruption. Therefore, allowing a small delay ensures that all emergency communication and equipment can operate without interference.
Additionally, speaking slowly and clearly is also vital to ensure that the message is conveyed accurately, especially in situations where there might be wi-fi delays or microphone malfunctions.
Tickets for a raffle costs $7. There were 640 tickets sold. One ticket will be randomly selected as the winner, and that person wins $ 1600 and also the person is given back the cost of the ticket. For someone who buys a ticket, what is the Expected Value (the mean of the distribution)?
Answer: Expected value is -4.48.
Step-by-step explanation:
Since we have given that
Cost of ticket for a raffle = $7
Number of tickets sold = 640
Amount winner wins = $1600
So, we need to find the expected value.
So, it becomes,
[tex]E[x]=\sum xp(x)\\E[x]=-7\times \dfrac{639}{640}+(1600+7)\times \dfrac{1}{640}\\\\E[x]=\dfrac{-4473+1607}{640}\\\\E[x]=\dfrac{-2866}{640}\\\\E[x]=-4.48[/tex]
Hence, Expected value is -4.48.
If each light fixture on a job requires 4 lamps and each room requires 16 fixtures, how many lamps will be required for 6 rooms?
Answer:
384 lamps
Step-by-step explanation:
This is simply a multiplication problem. From the question, we know that each fixture needs 4 lamps with a single room needing 16 fixtures.
The number of lamps required by each room is thus 16 * 4 = 64 lamps
Now, the total number of lamps required by 6 rooms is thus 64 * 6 = 384 lamps
To find the total number of lamps required for 6 rooms, multiply the number of fixtures per room by the number of rooms, then multiply the result by the number of lamps per fixture.
Explanation:To find the total number of lamps required for 6 rooms, we need to first determine the number of fixtures in 6 rooms. Since each room requires 16 fixtures, the total number of fixtures in 6 rooms would be 16 x 6 = 96 fixtures.
Each fixture requires 4 lamps, so to find the total number of lamps required for 96 fixtures, we multiply 96 x 4 = 384 lamps.
Therefore, 384 lamps will be required for 6 rooms.
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What is the effect on the graph of the parent function f(x) = x when f(x) is replaced with f(x) - 4? A) shifts the line 4 units up B) shifts the line 4 units down C) increases the slope of the line by a factor of 4 D) decreases the slope of the line by a factor of 4
Answer:
B) shifts the line 4 units down
Step-by-step explanation:
The point (x, f(x)) is moved to the point (x, f(x)-4), one with a y-coordinate 4 units lower. The line is shifted down 4 units.
Answer:
B) shifts the line 4 units down.
Step-by-step explanation:
The constant negative number makes a vertical translation of the parent function in the -y direction. Slope keeps intact. So, the right answer is B.
Find the Values of k for which the following simultaneous equations have no solutions:
2x - 3ky = 1
4x + (k + 2)y = 5
Answer:
[tex]k=-\frac{2}{7}[/tex]
Step-by-step explanation:
The two equations given represent two straight lines in 2-D graph.
The two lines will not intersect if they are parallel.
Hence the two equations will not have solution if the lines are parallel and not coincident.
The condition for 2 lines given by the equations :
ax+by+c=0
dx+ey+f=0 to be parallel but not coincident is:
[tex]\frac{a}{d}=\frac{b}{e}\neq\frac{c}{f}[/tex]
here a=2 b=-3k c=-1 d=4 e=k+2 f=-5
[tex]\frac{2}{4}=\frac{-3k}{k+2}\\k+2=-6k\\k=-\frac{2}{7}[/tex]
But also:
[tex]\frac{-3k}{k+2}\neq\frac{1}{5}[/tex]
Hence the value of k is -2/7.
Explain the rules for multiplication and division to convert units. How do you know when to multiply and when to divide to convert units of measurement?
Write three to four sentences.
Answer:
To convert larger units to smaller units, multiply. When the units are smaller, you need more of them to express the same measure. To convert smaller units to larger units, divide. When the units are larger, you need fewer of them to express the same measure.
Multiply to convert larger units to smaller units.
Divide to convert smaller units to larger units.
When the units are smaller, you need more of them to express the same measure.
When the units are larger, you need fewer of them to express the same measure.
Answer:
To convert between units, you're usually given one measure and asked to convert to another measure.
Step-by-step explanation:
Going to smaller units means going to bigger numbers so you multiply and going to bigger units means going to small. or in other words if you need to convert from a larger unit to a smaller unit Multiply. and if you need to convert from a smaller unit into a larger unit Divide. When converting customary units of measure from a larger unit to a smaller unit, multiply the the larger unit by its smaller equivalent unit.
Line segment AB is dilated to create line segment A'B' using point Q as the center of dilation. Point Q is the center of dilation. Line segment A B is dilated to create line segment A prime B prime. The length of Q A is 1.25 and the length of A A prime is 1.25. What is the scale factor?
Answer:
2
Step-by-step explanation:
A is on the line QA', which is 1.25+1.25 = 2.50 units long*. Thus the scale factor is ...
QA'/QA = 2.50/1.25 = 2
The scale factor is 2.
_____
* There are two points on the line QA that are 1.25 units from A. One of them is point Q. If A' is coincident with Q, then the scale factor is 0, and line segment A'B' is the single point Q. We don't believe that is intended to be the case, so we assume that point A' is farther along AQ, hence 2.5 units from Q.
1. Use the graph of the rational function
to complete the following statement.
As x → -3*, f(x) →
N
Answer:
As [tex]x \to -3^{+}, f(x) \to -\infty[/tex]
Step-by-step explanation:
Given:
From the graph, we can conclude that:
The function has vertical asymptotes at [tex]x=-3\ and\ x=2[/tex]
The function has horizontal asymptote at [tex]f(x)=0[/tex]
Vertical asymptotes are those values of 'x' for which the functions tends towards infinity. Horizontal asymptote is the value of the function as the 'x' value tends to infinity.
Now, as [tex]x \to -3^{+}[/tex] means the right hand limit of the function at [tex] x=-3[/tex]
From the graph, the right hand limit is the right side of the asymptote of the function at [tex] x = -3[/tex]. The right side shows that the function is tending towards negative infinity.
Therefore, As [tex]x \to -3^{+}, f(x) \to -\infty[/tex]