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
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Answer:
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Step-by-step explanation:
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Answers
Answer:
y = -1/2 x
Step-by-step explanation:
slope = Δy / Δx
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Answers
Answer:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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How much money will Bob in December have if his bank account growth stays at the same rate?
Month Bank-Acc
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January | $5,000
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Dion can type 155 words in 6 minutes. Assuming that he can type at a
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Answers
Answer:
1162.5 words
Step-by-step explanation:
6m = 155 words
45m = [tex]\frac{45}{6}[/tex] × 155 words
= 1162.5 words
Answer:
Step-by-step explanation:
If:
155 words = 6 minutes :
Then:
1 minute = 155/6 = 25.8 words
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45 × 25.8 = 1,162.5
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3x - 3
x^3 - 1
on someone plz help it is timed i will give Brainliest if correct
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Answer:
D.
Step-by-step explanation:
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Answer:
The answer you have checked is the correct one.
SV is an angle bisector of ∠RST. If m∠RSV = (3x + 9)° and m∠RST = (8x − 26)°, find x.
Answers
Answer:
C) Definition of Angle Bisector, x=22
Step-by-step explanation:
[tex]As\ we\ the\ question\ relates\ only\ about\ SV\ bisecting\ \angle RST,\ We\ may\ use\ the\\[/tex][tex]C)Angle\ Bisector[/tex]
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Answers
Answer:
T=3r+20 for the children and T=4r+28 for the adults
Step-by-step explanation:
Let r equal the amount of rides the person took, let T equal the total cost of the trip
What is the y-intercept of 2y=-3x+18
Answers
Answer:
18
Step-by-step explanation:
y = mx + b
m = slope
b = y-intercept
2y = -3x + 18
The -3x crosses
2y = 18
———— Y=9
2 2
I hope that helps.
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Answers
Answer: y = 4
Step-by-step explanation:
The equation y = 3 represents a vertical line. Thus, any equation in which y = m = 0 would be parallel to this line. Pick a random b-value and plug it into the equation with a slope of 0 and you should have a parallel line equation.
How do you solve this?
Look at attached file please...I'm really confused!
Answers
Answer:
X=18, Y=6
Step by Step Explanation:
This is a little long winded.. Let's solve for Y first.
First looking at the problem, you can note a few things. First of all, there is an Isosceles triangle, and there is an equilateral triangle. Where they connect, there is a 90° angle.
Now, all equilateral triangles have the same angle measurement. 60°. Now, if you look where the right angle is, it is showing a 60° angle, a total of 90°, and an unknown area. So simply subtract. 90-60=30. Divide that by 5, and you have your answer of 6.
Now let's solve X. X is very simple. On an isosceles triangle, the two top sides are the same length. And one of the top sides is the same size as the equilateral triangle. And on equilateral triangles, all sides are the same.
So the 11 transfers over to the X side. So let's make a small equation. 11=X-7. To make it even, let's add 7 to both sides. 11+7=X+7-7. Simplify to get 18=X, which is your answer.
Answer:
X=18 y=6
Step-by-step explanation:
explain and solve
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Answers
Answer:
4.7 inches
Step-by-step explanation:
The original is 12.5, and it was shortened to 7.8. So take the original, subtract the result, and you will get the answer.
12.5-7.8=4.7
Answer:
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EASY MATH PROBLEM!
Please help me! Will mark brainliest for sure!
Answers
Answer:
A
Step-by-step explanation:
Answer:
The answer would be A
Step-by-step explanation:
Use the formula for |A| <= B which is: -B <= A <= B
For this example you would do:
1. Insert the numbers into the formula: -6 <= 2x - 8 <= 6
2. first do the math for -6 <= 2x-8 which is 1 <= x
3. then do the math for 2x - 8 <= 6 which is x <= 7
4. Put that together and you get 1 <= x <= 7
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You bought a can of black beans last week that cost $1.34. This week, the store advertised a sale where 5 cans of beans cost $6.00. You bought one can of beans this week as well. Find the cost per can, and determine how much less the can of beans cost this week compared to last week.
Answers
Answer:
1. $1.2
2. $0.14
Step-by-step explanation:
Step one:
given data
Black beans last week that cost $1.34
Step two:
This week's price
5 cans of beans cost $6.00
The cost per can is
= 6/5
=$1.2
The difference in price
=1.34-1.2
= $0.14
Pluto has an average distance from the sun of 3.6 x 10^8 miles venus has an average distance from the sun of 9.0 x 10^6. How many times greater is pluto's average distance from the sun than venus?
Answers
Answer:
40 times greater
Step-by-step explanation:
Given the following:
Pluto average distance from the sun Ps = 3.6 x 10^8 miles
venus average distance from the sun Vs = 9.0 x 10^6miles
Take the ratio:
Ps/Vs = 3.6 x 10^8/9.0 x 10^6
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(I’ve tried everything I can think of, but I still haven’t been able to solve this. Please help!)
Answers
Answer:
x = 6
∠2 = 75
Step-by-step explanation:
In the given triangle two sides are equal and so it is an isosceles triangle. So, the angles opposite to equal sides are equal
11x + 9 + 11x + 9 + 30 = 180 {Angle sum property of triangle}
11x + 11x + 9 +9 +30 = 180
22x + 48 = 180
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x = 132/22
x = 6
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Answer:
C
Step-by-step explanation:
This is your answer because when you do the math you get c as your answer.
Hope this help:)
pls mark brainly
Answer:
The answer is C
Step-by-step explanation:
You had $72.31 at the beginning of the month but you deposited $11.27 and $14.76 so if you add all of those you get $19.84
Have a great day!
Please consider marking brainliest
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Olivia filled 4 baskets of apples. Her friend filled up one additional basket of apples. if all of the baskets sold for a total of $160, how much money did each basket of apples cost?
Answers
Answer:
$32
Step-by-step explanation:
Since the question says that all the apples were sold for a total of $160, this means that you have to add the additional basket of the friend's to Olivia's. Since Olivia has 4 baskets of apples and her friend has 1, 4+1=5. Since you're trying to find the unit price for 1 basket, you take the total of $160 and divide it by 5 to find how much each basket of apples costed. Since 160/5 is 32, $32 is your answer.
I know I haven't been on this app for a long time but can ya'll help me
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Answer:
2774
Step-by-step explanation:
start by multiplying 2 by 7, the answer is 14 put the 1 above the 8 in 1387 then put the 4 under the equation, similar to addition. repeat but next time when you multiply 2 by 8 add the 1 (from the previous multiplication) to the answer under and put the 1 from 17 on top of the 3. you get it?
Please Help please please
Answers
Answer:
5.25
Step-by-step explanation:
Take the distance between the two points and divide by 2.
The distance between the two is 10.5 (9.1-(-1.4))
Divide by two to find the midpoint.
Answer: 3.85
Step-by-step explanation:
find the mean of the 2 numbers, that is the midpoint.
Given the function defined in the table below, find the average rate of change, in
simplest form, of the function over the interval 0 < x < 2.
20
0
58
2
46
4
34
6
22
Answers
Answer:
- 0.4 (in decimal)
Step-by-step explanation:
Here "x" is input and "f(x)" is output
Average Rate of Change is = change in output / change in input
At x = 0, the output is 41
At x = 60, the output is 17
= (17-41)/(60-0) = -24/60 = -0.4
The function f(x) = –2x2 + 32 represents the height of an object, f(x), after x seconds. How many seconds does it take for the object to hit the ground?
Answers
Given:
The height of an object, f(x), after x seconds is
[tex]f(x)=-2x^2+32[/tex]
To find:
The time taken be object to hit the ground.
Solution:
We have,
[tex]f(x)=-2x^2+32[/tex]
The object will hit the ground if the height is 0, i.e., f(x)=0.
[tex]0=-2x^2+32[/tex]
[tex]2x^2=32[/tex]
Divide both sides by 2.
[tex]x^2=\dfrac{32}{2}[/tex]
[tex]x^2=16[/tex]
Taking square root on both sides.
[tex]x=\pm 4[/tex]
Time cannot be negative. So, x=4.
Therefore, the object will hit the ground after 4 seconds.
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Simplify completely 4m^3 over 3m^2n X 9n^2 over 30m^2n^2
Answers
Answer:
The answer is 2/405Xmn with an exponent of 5 at the end
3. The price of a pair of shoes is $64.00 plus 9% sales tax. What is the sales tax on this pair of shoes in dollars and cents? A. $5.76 B. $57.60 $69.716) D. $78.00
Answers
Step-by-step explanation:
To figure out this answer, you need to figure out how much 9% is in $64.00
? 9
------- = --------
64 100
Now to solve this you have to multiply diagonally and divide the neighbor
(let me explain)
basically in this case, you would multiply 64 and 9, then divide by 100
64 * 9 = 576
576 / 100 = $5.76
In short: your answer is 'A' $5.76
Hope this helps <3
Identify the variable in the following situation. Mr. Gopal goes to the store and has 25 dollars. He has to buy some candy bars for 10 dollars total. How water bottles can he buy with his remaining money if each water bottle costs 5 dollars
Answers
Answer:
3 water bottles
Step-by-step explanation:
25-10=15
15/5=3