Answers
Explanation
It is the only one that makes sense
The interval of the domain of the considered function for which the function is decreasing is none. The function is strictly increasing: Option D: The function is increasing only.
When do we say that a function is decreasing?Suppose that the function is y = f(x)
If for an interval I, when x increases meanwhile staying in the interval I, the function's output decreases (or can stay same), then we say that the function is decreasing in the interval I.
This interval I was of values that x can take for this function, which is the domain of the considered function, so we say:
y = f(x) is decreasing function in an interval I if:
[tex]f(x+\delta) \leq f(x) \: \forall x \in I : x+\delta \in I[/tex]
If we have:
[tex]f(x+\delta) < f(x) \: \forall x \in I : x+\delta \in I[/tex], then the function is called strictly decreasing in the interval I.
Similarly, there increasing( [tex]f(x+\delta) \geq f(x) \: \forall x \in I : x+\delta \in I[/tex] ) and strictly increasing([tex]f(x+\delta) > f(x) \: \forall x \in I : x+\delta \in I[/tex] ) functions.
For this case, the function is:
[tex]h(x) = \left \{ {{2^x, x < 1} \atop \: \atop {\sqrt{x+3}, x \geq 1}} \right.[/tex]
The function is differentiable in either side of 1.
Sign of rate of function at a point tells whether its increasing or decreasing.
For x < 1:[tex]h'(x)= 2^x ln(2)[/tex]
We know that:
[tex]2^x > 0 \: \rm \forlall x \in \mathbb R[/tex]
And [tex]ln(2) \approx 0.69 > 0[/tex]
Thus, [tex]h'(x)= 2^x ln(2) > 0 \: \forall x \in \mathbb R[/tex]
So, rate is positive, the function is strictly increasing for this case.
For x > 1:[tex]h'(x) = \dfrac{1}{2\sqrt{(x+3)}}[/tex]
For all x > 1, [tex]\sqrt{x+3} > 0[/tex], and so as h'(x)
So rate is positive and therefore strictly increasing for this case too.
For x = 1:[tex]h(1+\delta) - h(1)= \sqrt{1+\delta + 3} - \sqrt{1+3} = \sqrt{4+\delta} - \sqrt{4} > 0 \forall \delta > 0[/tex]
So rate of the considered function is positive,so function is strictly increasing all over the domain.
Thus, the interval of the domain of the considered function for which the function is decreasing is none. The function is strictly increasing: Option D: The function is increasing only.
Learn more about increasing functions here:
https://brainly.com/question/14330051
#SPJ2
Related Questions
What is the equation of a horizontal line that passes through (6,8)
Answers
Answer:
y=8
Step-by-step explanation:
All horizontals lines are going to be equations of y=y
(6,8)
(x,y)
y=8
Ariel bought a 6-cup bag of dough for $6.34. She used 1.45 cups to make rolls and 3.45 cups to make bread. How much dough is left? PLEASE HEELP
Answers
Answer:
1.1 cups. Hope this helps.
Step-by-step explanation:
Which table contains a set of non-linear ordered pairs?
Answers
Answer:
The second option is your answer
Step-by-step explanation:
The functions are not aligned here.
They are not even ordered in a function.
Your answer is the second option.
Answer: The bottom right graph
Step-by-step explanation: The increase in Y values is not consistent so the non-linear ordered pairs are in the bottom right graph.
Hope this helps!
Select the correct answer. If 20% of a number is 35, what is 50% of that number?
Answers
Due Sunday by 11.59pm
Points 10
Submitting an external tool
Question
Translate the English phrase into an algebraic expression: the quotient of A and the difference of 3 and B.
Provide your answer below:
WS FEEDBACK
MORE INSTRUCTION
SUBM
Answers
Answer:
A÷(3-B)
quotient means division
when they say and, that means you need to divide between the two values
Can someone please help, ty!!
(Will mark brainliest)
Answers
Answer:
Arcadia
Step-by-step explanation:
the line in the box is the median and Arcadia is bigger than Millersburg
Please help me don’t know how to do it,
Answers
Answer:
7=60
6=60
5=120
4=120
2=60
1=120
Answer:
angle 4 and angle 5 is = 120degree
Step-by-step explanation:
2(2x + 3) = -4 + 2(2x + 5)
Answers
Answer:
All real numbers are solutions for this problem.
Step-by-step explanation:
Is this problem correct?
Answers
Answer:
Yes that is correct. B is correct.
Step-by-step explanation:
When you plug 0 in for x, the result is 3.
When you plug 1 in for x, the result becomes 1.
The equation matches up correctly.
f(x) = -2x + 3
#teamtrees #WAP (Water And Plant)
You got it right. Try to substitute x values in there to check your answer.
Here's an example
f(x) = -2x + 3
f(1) = -2(1) + 3 = -2+3 = 1
.
.
.
f(4) = -2 (4) + 3 = - 8 + 3= - 5
Keep up the good work!!
A bird flies south. Its distance from its nest, as a function of time, is modeled by y=20x+1.
What statement best describes the function?
A. The function is linear at some points and nonlinear at others.
B. Not enough info to decide.
C. Linear
D. Nonlinear
Answers
Answer:
might be c
Step-by-step explanation:
intuition
Answer: c
Step-by-step explanation: the function is linear
Help me with this question pleaseee
Answers
Answer:
< 1 = 26 degrees
< 2 = 154 degrees
< 3 = 26 degrees
< 4 = 26 degrees
< 5 = 154 degrees
< 6 = 154 degrees
< 7 = 26 degrees
Step-by-step explanation:
Because of angles opposed by the vertex, <2 = 154 degrees
Because of corresponding angles between parallel lines, <5 = <6 = <2 = 154 degrees.
Because of supplementary angles,
< 1 = < 3 = < 4 = < 7 = 180 - 154 = 26 degrees
What is 9 x 100 + 8 x 10 + 7 x 1000
Answers
Answer:
9 x 100 + 8 x 10 + 7 x 1000 = 7,980
can someone pleaseee help me and btw dont mind my answers
Answers
Answer:
Substract by 2: n+8, 2n+8, 2n+8
Divide by 2: (n+8)/2, (n+8)/2, (n+8)/2
Step-by-step explanation:
if a/3 = b/2 then what is the following ratio
a+b/5a
Answers
Answer:
1/3
Step-by-step explanation:
a=6
b=4
a+b=6+4=10
5.6=30
10/30=
1/3
I hope that it was helpful
~best wishes
1. Evaluate 4x' + 7xy - 5y for x = 5, and y = 3.
Answers
Answer:
110 is your answer
You are most likely to encounter an irrational number when you are
Answers
Answer:
dealing with circles (using pi for circumference, area, arc angle, etc)
Answer:
Well, you can finding the area of a circle
Step-by-step explanation:
Explain how the location of the vertex and the direction of the opening (upwards or downwards) affects the domain and range of the quadratic function. Use complete sentences.
Answers
Answer:
Following are the solution to this question:
Step-by-step explanation:
Its vertex position, as well as the position of its opening, influence its quadratic function set. Its y-coordinate of its vertex (v) and then all values of current above it are included in scope whenever the direction of openings becomes up therefore, the lowest y-value becomes possible.
It implies the scope is y >=v. If it sets up, then, y-coordinate of its vertex was its highest y value available, from all y-values above too y <= v. The scope of a quadratic function, as it will continue forever to left and right, from the negative to positive infinity.Will mark brainliest:)
Answers
Answer:
Step-by-step explanation:
nice
A particular fruitâs weights are normally distributed, with a mean of 598 grams and a standard deviation of 6 grams. The heaviest 8% of fruits weigh more than how many grams? Give your answer to the nearest gram.
Answers
Answer:
The 8% of the fruit weigh more than [tex]x=606.43 \ g[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 598 \ g[/tex]
The standard deviation is [tex]\sigma = 6 \ g[/tex]
Generally the 8% is mathematically represented as
[tex]P(X > x) = 0.08[/tex]
=> [tex]P(X > x) = P ( \frac{X - \mu}{\sigma }>\frac{x - 598}{6} )=0.08[/tex]
[tex]\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )[/tex]
[tex]P(X > x) = P ( Z >\frac{x - 598}{6} )=0.08[/tex]
From the normal distribution table the critical value corresponding area representing 0.08 towards the right tail of the curve is
[tex]z = 1.405[/tex]
So
[tex]\frac{x- 598}{6} = 1.405[/tex]
=> [tex]x=606.43 \ g[/tex]
Leon has a container filled with 450 grams of tea leaves. Each morning, he uses 3 grams to make a cup of tea. Which expression can be used to represent the amount of tea leaves remaining after x days?
A. 450 – 3x
B. 450 + 3x
C. 3 + 450x
D.3 – 450x
Answers
Answer:
(A) 450-3x
Step-by-step explanation:
Cuz I know the answer.
Find the slope of the line that passes through the ordered pairs (-2,8) and (-9,19)
Answers
Answer:
slope: -11/7
Step-by-step explanation:
Slope is equal to the change in yy over the change in xx, or rise over run.
m=change in ychange in xm=change in ychange in x
The change in xx is equal to the difference in x-coordinates (also called run), and the change in yy is equal to the difference in y-coordinates (also called rise).
m=y2−y1x2−x1m=y2-y1x2-x1
Substitute in the values of xx and yy into the equation to find the slope.
m=19−(8)−9−(−2)m=19-(8)-9-(-2)
Simplify.
m=−11/7
Answer:
[tex]m=-1\frac{4}{7}[/tex]
Step-by-step explanation:
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\\\\\left(x_1,\:y_1\right)=\left(-2,\:8\right),\:\\\left(x_2,\:y_2\right)=\left(-9,\:19\right)\\\\m=\frac{19-8}{-9-\left(-2\right)}\\\\m=\frac{11}{-9+2}\\\\m=\frac{11}{-7} \\\\m=-\frac{11}{7}\\\\m=-1\frac{4}{7}[/tex]
Need help ASAP !!!!!!!!!!!!! Which statements describe the graph of f(x) = -1/4x as a transformation of the graph of g(x) = 1/x? Check all that apply.
A- the graph includes a vertical stretch.
B- the graph includes a compression.
C-the graph remains on the same side of the x-axis. D- the graph reflected across the x-axis ?
Answers
Answer:
It's B - The graph includes a compression
and D - The graph is reflected across the x-axis
Step-by-step explanation:
I got those right
B is right because f(ax) if a is greater than 1, then it includes a horizonal compression and 1/4x = f(4x)
D is right because -f(x) reflects across the x-axis. -f(x)= -1/x.
So -f(4x) = -1/4x
Answer:
b and d on edge
Step-by-step explanation:
just took the test
Alicia runs for exercist. If Alicia runs 8 miles in 6 days, how many days does it take her to run 36 miles? A 32 b 48 c 24 d 27
Answers
Answer:
It takes 27 days
Step-by-step explanation:
We will cross multiply
8/36 = 6/x
216= 8x --- next we will isolate our variable x, therefore you'll divide both sides by 8
216/8 = 8x/8
x = 27
(2(3^2+1)^2÷(5^2×4÷2))^3÷2^4
Answers
Answer:
Step-by-step explanation:
Use PEDMAS
P - Parenthesis
Exponents
D - DIvision
M - Multiplication
A - Addition
S - Subtraction
[2 (3² + 1)² ÷ (5²*4÷2)]³÷ 2⁴ = [2 (9 + 1)² ÷ (25*4÷2)]³÷ 2⁴
= [2 (10)² ÷ (25*2) ]³÷ 2⁴
= [2*100 ÷ 50]³÷ 2⁴
= [2*2]³÷ 2⁴
= 4³÷ 2⁴
= 64 ÷ 16
= 4
A new company is hiring employees rapidly. Everyday the number of employees doubles in size. If it takes 48 days for the company to be at full capacity, how many days would it take for the company to be at half capacity?
Answers
Answer:
It would take the company 47 days to be at half capacity.
Step-by-step explanation:
From the question, it is stated that the number of employees doubles in size everyday. This implies that the current day capacity is equal to the previous day capacity. This can be written in a mathematical form as follows:
Current day capacity = Previous day capacity * 2 ......................... (1)
We can assume that the current day capacity which is 48th day in this question is equal to 100 employees. That is;
Current day capacity = 48th day capacity = 100
Substituting this into equation (1) above and solve for the previous day capacity, we have:
100 = Previous day capacity * 2
Previous day capacity = 100 / 2 = 50
Since 50 is half of 100 and the previous day is 47th day, it therefore implies that It would take the company 47 days to be at half capacity.
(YOU WILL BE MARKED BRAINLIEST IF YOU WRITE A SHORT STORY FOR THIS MATH PROBLEM!!)
Write a short story that could represent this math problem.
Answers
Answer:
Once upon a time a troll was walking down a deep dark hallway, there was no light anywhere that he could see and he was starting to get scared of what could happen to him. But then out of the blue he saw something, something was would change his life forever, he saw a pigeon. Now you might think "Oh, a pigeon, how could that have changed his life?' Now the answer is kind of mundane but is deeper than you might think. The simple answer as to why the pigeon would change his life is because it gave the troll hope, hope that there is an exit. You see, the troll thought if the pigeon found there way into this pitch black hallway, then there must be a way in and hence a way out.
Now listen here, there's something that I wasn't telling you at the beginning of the story about the pigeon, the pigeon was also glowing. This is very useful obviously because it gave the troll some kind of light. Again, it gave the troll hope. Now, being a troll you might think that he would just snatch the pigeon and hold it for light, but this troll wasn't like other trolls, he had the capability to think before he used brute force to change something. So what the troll though was "If I just follow the pigeon then it might lead me to the exit because they have natural navigation in their brains"
Let's skip a while into the future, the troll followed and followed the pigeon for what felt like days, but in reality it was more like 3 hours. But then, the troll saw something that he thought he would never see again; sun light. As soon as the troll saw this, he started running and running towards the light, but as fast as he was running, the light seemed to get farther and farther away from him, then... POOF the troll was gone...
The troll found himself in a very lit up room, almost pure white all around him, which scorched his eyes because he was just in a pitch black room for hours. His ears were ringing and he was in pain, after a while all of that stopped, he was able to see clearly, he felt great, and his ears stopped ringing. What he saw was a very tall thin figure looking down at him from a room of pure white. The figure bent their neck and got right in the trolls face. The figure brought his left hand up to the trolls face, right next to his ear and snapped. The sound of a monstrous click sound right in the trolls ears hurt. The troll jumped back in fear but as soon as the click happened he saw a thing in his vision, a thing he new wasn't actually in the real world as it seemed to follow his eyes where ever he looked. It was, now i know this might sound stupid, I'm not here to imagine a story, I'm simply here to reenact the story of the troll. What he saw was a math problem, a grid was in his vision. It was a 4 by 6 grid.
The tall shadow figure was now back where the troll saw him originally, he was no longer bent and he seemed to not have arms anymore, just a tall dark figure with a cloak. The troll then began to hear a voice which seemed to come from everywhere. It was a deep voice that was very muffled, it said "Do this math problem and go back to your world. Get it correct and everything will go back to normal, but fail; and I'll have your soul" The troll was about to have an adventure of a lifetime...
Step-by-step explanation:
I legit came up with this on the spot, did you like it? XD
May I have brainliest please :)
cloud is a vegetable grower, has 8 4/15 plots of pechay, 5 1/3 plots of eggplants and 5 2/5 of okra . how many plots of vetable do cloud has?
Answers
Answer:
The total plots of vegetable cloud will be: 19
Step-by-step explanation:
From the question statement, it is clear that the cloud has [tex]8\frac{4}{15}[/tex] plots of pechay, [tex]5\frac{1}{3}[/tex] plots of eggplants and [tex]5\frac{2}{5}[/tex] plots of okra.
so, Just add all the plots to get the total plots of the vegetable cloud.
i.e.
[tex]8\frac{4}{15}+5\frac{1}{3}+5\frac{2}{5}=\frac{124}{15}+\frac{16}{3}+\frac{27}{5}[/tex]
[tex]=\frac{124}{15}+\frac{80}{15}+\frac{81}{15}[/tex]
[tex]=\frac{124+80+81}{15}[/tex]
[tex]=19[/tex]
Therefore, the total plots of vegetable cloud will be: 19
Complete the sentence.
9 is 18% of
Answers
Answer: 50%
Step-by-step explanation:
Answer:
50
Step-by-step explanation:
50/100 = .5
.5*18 = 9
HOPE THIS HELPS
PLZZ MARK BRAINLIEST
Rob lost 77 pounds in the 1st 6 months of his diet then 16 pounds in the next 2 months find his average change in way each month
Answers
Answer:
7 is a good answer. Do you know how good of an answer 7 is. I don't think you do. If you don't know the answer always choose 7.
0.5 ft of snow melts to 2inches of H2o. To how many inches will 4.5 ft of snow melt?
Answers
Answer:
4.5 feet of snow = 27 inches H2o. Please read the explanation for better details
Step-by-step explanation:
if 0.5 feet of snow melts into 2 inches of water, then that means that 6 inches of snow melts into 2 inches of water. This means that for every 2 inches of snow you melt, it will become 1 inch of water. If 4.5 ft = 54 inches, you simply divide by 2, getting your answer of 27 inches of snow. Hope this helps! :)