Which of the following equations could be th equation to represent the given graph? Make sure you explain your answer thoroughly.
Answers
Answer:
Option (C) is correct.
Step-by-step explanation:
The given options of the possible equation for the graph are as follows:
[tex](A) y=2\left(\frac{3}{2}\right)^x \\\\(B) y=-2\left(\frac{3}{2}\right)^{-x} \\\\(C) y=2\left(\frac{2}{3}\right)^x \\\\(D) y=-2\left(\frac{2}{3}\right)^{-x} \\\\[/tex]
The given graph is decreasing and at x=0, y=2.
So, first checking the value of the given options for x=0
[tex](A) y=2\left(\frac{3}{2}\right)^0=2\times 1= 2 \\\\(B) y=--2\left(\frac{3}{2}\right)^{-0}= -2\times 1= -2 \; (not\; possible) \\\\(C) y=2\left(\frac{2}{3}\right)^0= 2\times 1= 2 \\\\(D) y=2\left(\frac{2}{3}\right)^{-0} = -2\times 1= -2 \; (not\; possible)[/tex]
As, for x=0, y=2, so options (C) and (D) are not possible, so rejected.
Now, checking the nature (increasing or decreasing) of the given equation by differentiating it.
For option (A),
[tex]\frac{dy}{dx}=2\left(\frac{3}{2}\right)^{x}\times \ln\left(\frac{3}{2}\right)[/tex]
As [tex]\ln \left(\frac{3}{2}\right)=\ln(1.5)>0 \;and\; \left(\frac{3}{2}\right)^{x} >0[/tex]
So, [tex]\frac{dy}{dx}>0[/tex]
Therefore, the function in option (A) is increasing function.
Similarly, for option (C),
[tex]\frac{dy}{dx}=2\left(\frac{2}{3}\right)^{x}\times \ln\left(\frac{2}{3}\right)[/tex]
As [tex]\ln \left(\frac{2}{3}\right)=\ln(0.67)<0 \;and\; \left(\frac{3}{2}\right)^{x} >0[/tex]
So, [tex]\frac{dy}{dx}<0[/tex]
Therefore, the function in option (C) is decreasing function.
As the given graph is decreasing, so, (C) represents[tex]y=2\left(\frac{2}{3}\right)^x[/tex] the given graph.
Hence, option (C) is correct.
The equation [tex](C) y = 2(\dfrac{2}{3})^{x[/tex] could be the equation to represent the given graph is decreasing.
We have to determine, Which of the following equations could be the equation to represent the given graph.
According to the question,
The given options of the possible equation for the graph are as follows:
[tex](A)y = 2(\frac{3}{2})^x[/tex] [tex](B)y = -2(\frac{3}{2})^{-x}[/tex] [tex](C)y = 2(\frac{2}{3})^{x}[/tex] [tex](D)y = -2(\frac{2}{3})^{-x}[/tex]The given graph is decreasing and at x = 0, y = 2.
Then,
First checking the value of the given options for x = 0.
[tex](A)y = 2(\frac{3}{2})^x = 2(\frac{3}{2})^0 = 2 \times1 = 2[/tex] [tex](B)y = -2(\frac{3}{2})^{-x} = (A)y = -2(\frac{3}{2})^{-0} = -2 \times 1 = -2 (not \ possible)[/tex][tex](C)y = 2(\frac{2}{3})^x = 2(\frac{2}{3})^0 = 2 \times1 = 2[/tex] [tex](D)y = -2(\frac{2}{3})^{-x} = -2(\frac{2}{3})^{-0} = -2 \times1 = -2 (not \ possible)[/tex]For x = 0, y = 2, so options (C) and (D) are not possible, so the options are rejected.
Therefore,
To check the nature (increasing or decreasing) of the given equation by differentiating it.
For function A;[tex]\dfrac{dy}{dx} = 2(\dfrac{2}{3})^x \times ln(\dfrac{3}{2})\\\\ln(\dfrac{3}{2}) = ln(1.5) >0 \ and\ (\dfrac{3}{2})^{x} >0\\\\So, \dfrac{dy}{dx}>0\\\\[/tex]
Therefore, The function in option A is increasing function.
For function c;
[tex]\dfrac{dy}{dx} = 2(\dfrac{2}{3})^x \times ln(\dfrac{2}{3})\\\\ln(\dfrac{3}{2}) = ln(0.67) <0 \ and\ (\dfrac{3}{2})^{x} >0\\\\So, \dfrac{dy}{dx}<0\\\\[/tex]
Therefore, The function in option c is decreasing function.
The given graph is decreasing, so, the function c represents the given graph decreasing.
Hence, option (C) is correct.
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Related Questions
URGENT!!!! HELP PLEASE!!!
Answers
Please hurry! Marking beainliest!
Answers
Answer:
the ine you have selected is right
Step-by-step explanation:
we know12 inches is 1 foot we can keep going up andsee that 24 inches is 2 and so on
Answer: C correctly converts inches to feet.
Step-by-step explanation:
12 inches is one foot. 12+12 is 24. 12+12+12+12 is 48. And so on
kim weighed the dictionary and found that it had a mass of 745 grams. how many kilograms is that?
Answers
Answer:
0.745 kilograms
Find the square root of -36.
A-6
B 6
C Cannot be done
Answers
Answer: C) Cannot be done
Taking the square root of a negative number is not possible unless you involve complex numbers. If your teacher has not introduced that topic yet, then you just simply say "cannot be done" or something along those lines.
PLEASE HELP. SOON. I really need help i’m struggling a lot lol
Answers
Answer: A
Step-by-step explanation: trust me bro
Pls help me!!!!!!!!!!!!!!!
Answers
Answer:
The answer is B. and C.
Answer:
i think it will be c
Step-by-step explanation:
A dance teacher surveyed one of her classes about their favorite type of dance. Of those surveyed, 5 favored ballet, 2 favored tap, and 3 favored jazz. Based on these results, predict how many of the teacher's 90 dancers will not favor tap.
Answers
Answer:
72 students
Step-by-step explanation:
80% of the students already do not favor tap (8/10)
to get 90 students you multiply by 9.
8x9 is 72.
PLEASE HELPPPPP ME
What are the slope and y-intercept of the line?
A. The slope is approximately 3 and the y-intercept is 2.
B. The slope is approximately 1.33 and the y-intercept is 2.
C. The slope is approximately 2 and the y-intercept is 3.
D.The slope is approximately 2 and the y-intercept is 1.33.
Answers
Answer:
B.The slope is approximately 1.33 and the y-intercept is 2.
Step-by-step explanation:
On the graph we are going based off where the line starts and in this case it starts on the y line and that shows our y-intercept is 2. The line also doesn't have a rate of change that is directly being put onto an intersecting point like (2,2) which would make it a decimal 1.33.
Answer:
B. The slope is approximately 1.33 and the y-intercept is 2.
Step-by-step explanation:
We can eliminate answers C and D because the y-intercept is 2.
The slop is approximately 1.33 because if we go over 1 unit, we must go up approximately 1.33 units to follow the line.
The sum of three consecutive numbers is 84. What is the largest of these numbers? (5 points) a 28 b 26 c 29 d 27
Answers
Answer:
The answer is c.29
Step-by-step explanation:
I used Google xD
Answer:
Largest number = 29
Step-by-step explanation:
Let the consecutive numbers by (x + 1) ; (x + 2) and (x +3)
x +1 + x + 2 + x + 3 = 84 {Combine like terms}
x + x +x + 1 + 2 + 3 = 84
3x + 6 = 84
3x = 84 - 6
3x = 78
x = 78/3
x = 26
Largest number = x + 3 = 26 + 3
=29
plzzz helpppp!!!!!
How can you identify the solution to a system of inequalities?
Answers
Answer:
The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system. Graph one line at the time in the same coordinate plane and shade the half-plane that satisfies the inequality
What is the slope of the line 4x – 2y = 10? Explain your process (show your steps) for determining the slope.
Answers
subtract 4x from both sides
-2y = -4x + 10
divide everything by -2
y = 2x - 5
slope intercept form is y = mx + b, with m being the slope, so 2 is your slope
I will mark you brainiest if you answer this, please help
Answers
Answer: 216
The biggest factor is them times together
Answer:
GCF2
LCM218
EXPLANATION
The people are: Frank, Ruby, Tom, and Wendy
The cost of their food: $5.99, $6.99, $7.99, $8.99
Each person bought a different food item: banana, apple, mango, and grapefruit
Each person also bought a different drink: milk, green tea, water, and iced tea
See if you can match the person with the cost of their meal, food and drink. I will give you two free answers. The first one is Tom paid 8.99. The second one is Ruby had the grapefuit.
1. The person who had the milk paid $1 more than Wendy.
2. Ruby paid more than the person who had the milk.
3. The person who ordered the banana was either the person who had the milk or the
person who paid $5.99.
4. The four friends were the person who paid $8.99, the person who ordered the
apple, the person who ordered the grapefruit, and Wendy.
5. Tom paid $1 more than the person who ordered the grapefruit.
6. The person who ordered the grapefruit paid $2 more than the person who had the water.
7. The person who paid $7.99 was either the person who had the iced tea or the person who
had the water
Group of answer choices
wendy (cost)
[ Choose ]
wendy (drink)
[ Choose ]
wendy (food)
[ Choose ]
frank (cost)
[ Choose ]
frank (drink)
[ Choose ]
frank (food)
[ Choose ]
ruby (cost)
[ Choose ]
ruby (drink)
[ Choose ]
ruby (food)
[ Choose ]
tom (cost)
[ Choose ]
tom (drink)
[ Choose ]
tom (food)
[ Choose ]
Answers
Answer:
yo it took me 3 tires and 15 minutes, but i got it. like 5 seconds ago
Step-by-step explanation:
okay one is wrong this an 11/12, but i sped thru it to get the answers, you have to figure out which is incorrect
wendy
(cost)
5.99
wendy
(drink)
water
wendy
(food)
banana
frank
(cost)
6.99
frank
(drink)
milk
frank
(food)
apple
ruby
(cost)
7.99
ruby
(drink)
iced tea
ruby
(food)
iced tea
tom
(cost)
8.99
tom
(drink)
green tea
tom
(food)
mango
Wendy (cost) = $7.99
Wendy (drink) = water
Wendy (food) = banana
Frank (cost) = $6.99
Frank (drink) = iced tea
Frank (food) = apple
Ruby (cost) = $8.99
Ruby (drink) = milk
Ruby (food) = grapefruit
Tom (cost) = $5.99
Tom (drink) = green tea
Tom (food) = mango
Based on the given information and the provided clues, we can match the people with the cost of their meal, food, and drink as follows:
wendy (cost) = $7.99
wendy (drink) = water
wendy (food) = banana
frank (cost) = $6.99
frank (drink) = iced tea
frank (food) = apple
ruby (cost) = $8.99
ruby (drink) = milk
ruby (food) = grapefruit
tom (cost) = $5.99
tom (drink) = green tea
tom (food) = mango
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what is 4/5 ÷ 1/3 =____
Answers
charles charges $4 an hour to baby-sit. He also adds an extra $10 onto the total for families with more than three children. Write an equation for what Charles charges to baby-sit a family of 4 children.
y = 4x - 10
y = 4x + 10
y = 40x
y = 4x + 10x
Answers
Answer:
b
Step-by-step explanation:
The required expression for Charles is y = 4x + 10. Option b is correct.
An expression to be determine that explain charles charge for the families have more than 3 children.
Equation are the coded expression that describes the mathematical familiarities of the word statement.
Here, Charles charge $10 more beside of $4 an hour to baby sit for the families having more than 3 children.
⇒ let 'y' is the total charge applied and 'x' is hours of baby sit.
⇒ y = 4x + 10
Thus, the required expression for Charles is y = 4x + 10.
Learn more about equation here:
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What is the image point of (6,-4)(6,−4) after a translation left 4 units and down 5 units?
Answers
Answer:
(2,-9)
Step-by-step explanation:
6-4 = 2
-4-5 =9
so The answer is (2,-9)
helppp i don’t know the answer
Answers
Don’t forget a brainliest if this helped ;)
What is the value of 3/8 x - 4.5 when x =0.4
Answers
all of the following represents the same expression except ___.
a. -8ab
b. -8(a)(b)
c. 8 - ab
d. -8 • a • b
Answers
Answer:
What is the following expresion?
Step-by-step explanation:
Answer:
C. 8 - ab
Step-by-step explanation:
all the other represents -8 multiply by a by b.
Divide the following polynomial using synthetic division, then place the answer in the proper location on the grid. Write answer in descending powers of x. (x4+81) / (x-3)
Answers
x^4-81= x^4+0x^3+0x^2+0x-81
! 1 0 0 0 -81
x+3→-3 ! -3 9 -27 81
---------------------------------------
1 -3 9 -27 0
x^3-3x^2+9x-27
Answer: x^3-3x^2+9x-27
HELP ASAP GIVING BRAINLIEST
Solve for x if the angles are adjacent supplementary angles. Use pencil and paper. Show how to check that your value of x is correct
Answers
Answer:
x=15
Step-by-step explanation:
srry if I'm wrong =(
PLEASE HELP!! ASAP!!
Answer the following question
1. Bejar is now known as the city of San Antonio. The author says, “ As one covers the distance from Béjar to this town, he will note that Mexican influence is proportionately
diminished “What cardinal direction can you assume he has traveled from Bejar to reach “This Town"?
2. why might the influence of the Mexican government and culture diminish the further away one travels from Bejar?
3. Terran discovered that the foreigners outnumber the Mexican by what ratio?
4. Who are the “foreigners” that Teran repeatedly refers to?
5. What does Teran predict could happen in Texas if the Mexican government does not strengthen its control over Texas?
Answers
Answer: 1.Twelve months have now elapsed since the first half volume of this work was offered to the public. The favourable reception it has experienced gives the Editor reason to hope that he has fulfilled the engagements which he came under at its first appearance, and is a powerful inducement to continue his utmost exertions to preserve and improve the character of the work. In the four volumes which are now published, several extensive and important original articles are introduced, which have not hitherto appeared in any similar collection, and had not even been previously translated into English. These materially contribute towards the ample information which was formerly announced, in the Preface to the first Volume, as a leading object in this Collection. In the subsequent parts of the work, every effort shall be made to fill up its several divisions with original articles of similar interest and equal importance.
Encouraged by a satisfactory and increasing sale, the progress of publication has been somewhat hastened, beyond what was originally promised in the Prospectus and Conditions; as the whole of the fourth Volume is now published, at the period when only its first half was to have appeared. It is intended to repeat this anticipation occasionally, by the publication of two numbers or half-volumes at once, when opportunity offers. While this may gratify one portion of our readers, it is not meant to preclude others from continuing to be supplied, as before, with the numbers or half volumes at regular intervals, in their own option.
2.As the population in Texas from the United States swelled, Mexican authorities grew increasing nervous. In 1827, the Mexican government sent General Manuel de Mier y Terán to investigate the situation. He warned that unless the Mexican government took timely measures, settlers were certain to rebel. Differences in language and culture, Terán believed, had produced bitter enmity between the colonists and native Mexicans. The colonists refused to learn the Spanish language, maintained their own separate schools, and conducted most of their trade with the United States.
3.While holding out the possibility of compromise, the Texans prepared for war. The provisional government elected Sam Houston, a former Tennessee governor, to lead whatever forces he could muster. Then in early 1836, a band of three hundred to five hundred Texans captured Mexico's military headquarters in San Antonio. The Texas revolution was under way.
4.Don Manuel de Mier y Terán: As It Affected Texas-Mexican Relations (Continued)
5. THEY MARCHED AN ARMY INTO TX TO STOP THE REBELLION. THE MEXICAN GOVERNMENT “DISOWNED” SANTA ANNA AND THE TREATY; IT DID NOT RECOGNIZE TX INDEPENDENCE FORMALLY UNTIL THE END OF THE MEXICAN AMERICAN WAR.
Step-by-step explanation:
how many times does 67 117
Answers
please I need some help with both questions.
Answers
Step-by-step explanation:
which questions you were asking
Solve this math problem first you get a free crown!
what is the sum of -7/18 and -3/6
A. -4/9
B. -8/9
C. 4/9
D. 8/9
Answers
Answer:
16/18
8/9
Step-by-step explanation:
the answer is B) -8/9
Given points (-2.3) and (9.3), which expression can be used to find the distance between the two points?
191 +31
191-1-21
1-21+131
1-2 + 191
Answers
Answer:
d
Step-by-step explanation:
equalitivietion form akk absolute vaules.
dudee plz help will be given the brainlist if answered correctly
Answers
Answer:
hey im not actually here to help you, i just need points. thanks for the points
Step-by-step explanation:
The diagram below shows a map of the routes taken by Georgia Air-Taxi airline. On this diagram lengths and directions are irrelevant, all that matters is the connections between airports. Choose the adjacency matrix, name it A, that matches the scenario.
Answers
Answer: B
Step-by-step explanation: Adjacency Matrix is a square matrix representing a simple graph with 0 or 1 according to the condition given.
In this diagram, 0 corresponds to no connection between airports and 1 corresponds to connections between airports.
In other words, analysing the image, we see that:
1) Albany just have connection with Atlanta, so in the position of line Albany with column At, it must be a 1. The other columns, there are 0.
The Line for Albany in the matrix will be: [0 1 0 0 0 0]
2) Atlanta has connections with Albany, Dalton, Macon and Augusta. So corresponding position (line and column) must be 1. The only two airports Atlanta doesn't have connection with its own and Waycross, so at the corresponding column and line, it is written 0.
The line for Atlanta in the matrix is [1 0 1 1 1 0]
3) Augusta: connections with Atlanta, Macon, Waycross. At those positions, it will be written 1. At positions related to itself, Albany and Dalton is 0.
The line in the matrix will be [0 1 0 0 1 1]
4) Dalton: connection with Atlanta only. That position will be 1 while the others will be 0.
The line is [0 1 0 0 0 0]
5) Macon: connections with Atlanta, Augusta and Waycon: those positions will have 1 and the other 0.
The line is [0 1 1 0 0 1]
6) Waycross: connections with Macon and Augusta. Those positions will be 1 and the others 0.
The line is [0 0 1 0 1 0]
In conclusion, the adjacency matrix matching the scenario is
[tex]A=\left[\begin{array}{cccccc}0&1&0&0&0&0\\1&0&1&1&1&0\\0&1&0&0&1&1\\0&1&0&0&0&0\\0&1&1&0&0&1\\0&0&1&0&1&0\end{array}\right][/tex]
What is the slope of the line?
pls help I need the answer
Answers
Answer:
the slope of a horizontal line is 0
5x - 2y = 9
x + 3y = -5
Solve by Substitution
Answers
Hiiiiiiiiiiiiiiiiiiiiiiii
