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.
To know more about the Graphs click the link given below.
https://brainly.com/question/16351335
Related Questions
write the equation of the line that passes through the point (2,-1) and has a slope of -3
Answers
Answer:
y=2/-1 -3
Step-by-step explanation:
Which of the following is true? (1 point) Group of answer choices |−6| < 5 |−6| < |5| |−5| < |−6| |−5| < −6
Answers
Answer:
|−5| < |−6|
Step-by-step explanation:
The symbols around the numbers signify that you must switch the negative to a positive or vice versa. So, in this case, this equation is actually 5 < 6.
PLEASE HELP ME
Matt wants to spend no more than 120 minutes watching TV on his day off. It takes 40 minutes to watch one episode of his favorite show, The Office, and half that amount of time to watch one episode of his other favorite show, Seinfeld.
Which inequality represents all possible combinations of x, the number of episodes of The Office, and y, the number of episodes of Seinfeld, that Matt can watch on his day off?
A:20x+40y>_120
B:20x+40y _120
D40x+20y<_120
Answers
Answer:
D "Matt wants to spend no more than" That indicates that it would be Less Than or = to
Step-by-step explanation:
what is - 10 = w - 2 ?
Answers
Answer:
W= - 8
-10 + 2 = w
-8 = w
W = -8
Answer:
w = -8
Step-by-step explanation:
1. Add 2 to the -10
2. -10 + 2 = -8
W = -8
Find the slope for the given points. A. (4,3) B. (5,-2)
Answers
Answer:
This free slope calculator solves for multiple parameters involving slope and the equation of a line. It accepts inputs of two known points, or one known point
Step-by-step explanation:
there is no need to that and I'm in 5th grade and that is easy peasy lemon squeezy cuz my last name is lemon
EASY POINTS FOR Y'ALL!!!!!!!!!!
Answers
Answer:
a
Step-by-step explanation:
Answer:
the answer is A
Step-by-step explanation:
happy new year
Pls help ASAP thanks :P
Answers
write a table of value from 0 to 5 with this equation: x^2-x-12, how can i do that ?
Answers
Answer is picture. The table and work
help pls pls asap i need this
Answers
Answer:
B
Step-by-step explanation:
there are 36 carpenters in a crew. On a certain, 29 were present. What percent showed up for work? (round to the nearest tenth)
Answers
Answer:
30
Step-by-step explanation:
What is the average rate of change of f over the interval -7 < or equal to x
Give an exact number
Answers
Answer:
[tex]\frac{4}{3}[/tex]
Step-by-step explanation:
The average rate of change can be found by using the following formula
[tex]\frac{f(x_{2}) - f(x_{1}) }{x_{2} - x_{1}}[/tex]
Since the interval goes from -7 to 2, we should find the y-values that correspond to x=-7 and x=2.
By inspection of the graph, we can clearly see that when x is -7, y is -7 as well and when x is 2, y is 5.
Now that we know this, we can simply plug these values into the formula!
[tex]\frac{f(2) - f(-7) }{2 - (-7)} = \frac{5 - (-7)}{2 - (-7)} = \frac{5 +7}{2+7} = \frac{12}{9} = \frac{4}{3}[/tex]
Good luck!
Karissa earns $200 per week plus $25 per item she sells. Which
equation models the relationship between her pay p per week and the
number of items n she sells?
A. p = 200n + 25
C. n = 25p + 200
B. p = 25n + 200
D. n = 200p + 25
Answers
Answer:
Step-by-step explanation:
p=200+25(n)
please help! i’ll mark brainliest!!!
Answers
Answer:
(6+x)(5+x)
Step-by-step explanation:
Where is the point (0, -4) located on the coordinate plane?
Answers
Answer:
Start from coordinate 0, the exact center where the lines meet, then count down four, leave your point at -4 on the middle line.
If this answer was helpful pls mark as brainliest. <3
Find the slope and the y-intercept of the line.
- 9x+3y=-6
Answers
Answer:
slope is 3 and y intercept of -2
Step-by-step explanation:
Does the point (-3,-1) lie on the line with the equation y = 10 - 3x ? Be sure to show your work.
Answers
Replace x in the equation with the x value from the point and solve. If the equation equals the y value from the point the point lies in the line, if it doesn’t equal the y value then it doesn’t lie on the line.
Y = 10 -3(-3) = 10 + 9 = 19
19 doesn’t equal -1 so the point does not lie on the line.
Hurry I will mark brainlyest and 20 points!!!
What division problem can be represented using the number line?
Answers
Answer:
c can br used using the number line
Answer:
I believe its A
Step-by-step explanation
HOPE THIS HELPS
−3(2a−14)−3a=24
what is a
Answers
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
[tex] - 3(2a - 14) - 3a = 24[/tex]
[tex] - 6a + 42 - 3a = 24[/tex]
[tex] - 9a + 42 = 24[/tex]
Subtract sides 42
[tex] - 9a + 42 - 42 = 24 - 42[/tex]
[tex] - 9a = - 18[/tex]
Divide sides by - 9
[tex] \frac{ - 9a}{ - 9} = \frac{ - 18}{ - 9} \\ [/tex]
[tex]a = 2[/tex]
_________________________________
CHECK :
[tex] - 3(2(2) - 14) - 3(2) = 24[/tex]
[tex] - 3(4 - 14) - 6 = 24[/tex]
[tex] - 3( - 10) - 6 = 24[/tex]
[tex]30 - 6 = 24[/tex]
[tex]24 = 24[/tex]
Thus the solution is correct.....
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Suppose you are told that 1/2 = 3' on a scale drawing. If there is an object that measures 5" in the drawing, what would its actual length be?
Answers
5”= 10/2
1/2x10= 10/2 so you have to times 3 by 10 to get the answer 3x10=30’
Scale drawings are used to represent a large drawing using smaller measurements
The equivalent of 5" in the drawing is 30' i.e. 30 feet
The scale is given as:
[tex]\mathbf{\frac 12" = 3'}[/tex]
A single quote means feet, while a double quote means inches
So, the scale can be rewritten as:
[tex]\mathbf{\frac 12\ inches= 3\ feet }[/tex]
Multiply both sides by 10
[tex]\mathbf{\frac 12\ inches \times 10 = 3\ feet \times 10}[/tex]
Simplify
[tex]\mathbf{5\ inches = 30\ feet }[/tex]
Rewrite as:
[tex]\mathbf{5" = 30'}[/tex]
Hence, the equivalent of 5" in the drawing is 30' i.e. 30 feet
Read more about scale drawings at:
https://brainly.com/question/22627686
Which expression is equivalent to 2(a+3) when a= 3?
A 2(3)
B 5(3)
C 2(3)+3
D 2(3)+6
Answers
Answer:
D
Step-by-step explanation:
2(a+3), a=3
2(3+3)
2(6)
12
A) 2(3)=5 (not equivalent)
B) 5(3)=15 (not equivalent)
C) 2(3)+3=9 (not equivalent)
D) 2(3)+6=12 (equivalent)
Answer:
I believe it'll be D.
Step-by-step explanation:
2(a+3) would be 2(3+3). Following PEMDAS, it'll be 2(6), or in other words 12.
In the answer D, 2(3) would equal 6. And 6 + 6 equals 12.
Sorry if this explanation isn't proper enough.
help me plzzzzzzzzzz
Answers
Answer: Not congrute
Step-by-step explanation:
Answer:
B (SSS)
Step-by-step explanation:
Congruent by postulate side side side.
Leon tried to solve an equation find leons mistake 1/2w-12=18
Step one : 1/2w=30
Step two: w=15
Answers
Answer:
They made a mistake of the value of W. If half of W is 30, then 1/1 should thus be 60, but it's 15. Leon made a mistake on the value of W. 1/2w-12=18 would actually be 3 based of background information.
Step-by-step explanation:W-
Answer:
Step two
Step-by-step explanation:
step one isn't wrong
and he infact made a mistake
7 − 58z = −23 ASPA
A. 9.38
B. 48
C. −24
D. 24
Answers
Answer:
the given are not correct the real answer is 15/29 or 0.517...
Step-by-step explanation:
7-58z = -23
-58z = -23 -7
-58z =-30 the negatives will cancel each other out
-58. -58
z = 30/58 divide both by 2
z= 15/29 which can also be equal to 0.517...
who plays forza horizon 3
Answers
Answer:
I recently got it on my xbox
Step-by-step explanation:
I usually play with the family my name on xbox is wood
Answer:
me
Step-by-step explanation:
Which sentence is written correctly?
O A
No one know who hid the book in the desk.
OB.
Whoever sent me flowers are my new best friend.
O C.
Everyone is invited to Anne's party next week.
OD. All of my friends is going to the big dance.
Answers
What is the y-intercept of the equation?
Answers
Answer:
The answer would be 0
Step-by-step explanation:
Use y = m x + b :)
Hello I don't know what I'm doing can someone please help.
I don't know how to solve a standard form slope equation can you please explain what I have to do.
The slope of the line 5x + y = 15 is___
Answers
Answer:
x = -1/5y +3
Step-by-step explanation:
add -y to both sides
5x + y + -y = 15 + -y
5x = -y + 15
step 2 divide both sides by 5
5x/5 = -y +15/5
x= -1/5 y +3
Answer
x= -1/5 y + 3
Find the slope of the line
Answers
Answer:
The line has a slope of Zero.
Step-by-step explanation:
Answer:
The answer is zero
Step-by-step explanation:
The answer is zero because the line is straight it's not positive or negative.
Help me PLEASE!
2. When Deema begins her drive, she is 400 mi from home. She drives at an average rate of 50 mph until she gets
home. Draw a graph to represent this situation?
Answers
Answer: I can give coordinates (0,400) (1,350) (2,300) (3,250) (4,200) (5,150) (6,100) (7,50) (8,0)
Step-by-step explanation:
Deema starts at 400 which is y-intercept and goes down on a slope of -50 cause we are decreasing 50 mi for every hour she drives.
Hope this helped :) !!!!!!!
The coordinates of the graph representing the given situation are listed below
A (0 ,400)
B ( 1 ,350 )
C (2,300)
D(3,250)
E(4, 200)
F(5, 150)
G(6, 100)
H(7, 50)
I (8, 0)
The graph attached shows the nature of the graph.
Total distance traveled by Deema = 400 miles
The average speed of Deema = 50 mph
In each 1 hour, 50 miles of distance will be covered
So by the rate of 50 miles per hour the coordinates in this situation are given as follows
Time (X axis) Distance (Y axis)
0 400
1 350
2 300
3 250
4 200
5 150
6 100
7 50
8 0
The coordinates of the graph are listed above and the nature of graph is shown in the figure attached in the solution.
The graph of this situation has a constant negative slope.
For more information please refer to the link given below
https://brainly.com/question/12322912
Which value is included in the solution set for the inequality graphed on the number line?
A. -5
B. -2
C. 0
D. 3
Answers
Answer:
since the graph is in the direction it is the only number choice it acctually passes through would be -2.