. Using the derivative, /'(x)=(5-x)(8-x), determine the intervals on which f(x) is increasing or decreasing. a. Decreasing on (-0,5); increasing (8,00) b. Decreasing on (5,8); increasing (-0,5) U (8,00) c. Decreasing on (-00, 5) U (8,00), increasing (5,8); d. Decreasing on (-00,-5) U (-8,00), increasing (-5,-8); e. Function is always increasing 5. Determine where g(x)= 3x³ + 2x + 8 is concave up and where it is concave down. Also find all inflection points. a. Concave up on (-00, 0), concave down on (0,00); inflection point (0,8) b. Concave up on (0,00), concave down on (-00, 0); inflection point (0,8) c. Concave up on (0,00), concave down on (-00, 0); inflection point (0,2) d. Concave up for all x; no inflection points e. Concave down for all x; no inflection points 6. Find the horizontal asymptote, if any, of the graph of h(x)=- 5x²-3 a. y = 0 b. y = C. y=-² d. y = ² e. no horizontal asymptote 4x²+3 x-x-2x 43 c. 0 d. 00 e. Limit does not exist
Answers
The answer is as follows: 5. (b) Decreasing on (5,8); increasing (-∞,5) U (8,∞). 6. (e) Concave down for all x; no inflection points. 7. (a) y = 0.
5. To determine the intervals where the function f(x) is increasing or decreasing, we need to find the critical points by setting the derivative equal to zero: (5-x)(8-x) = 0.
Solving this equation, we find x = 5 and x = 8 as critical points. Testing the intervals between and outside these points, we observe that f(x) is decreasing on the interval (5,8) and increasing on the intervals (-∞,5) and (8,∞). Therefore, the correct answer is (b) Decreasing on (5,8); increasing (-∞,5) U (8,∞).
The concavity of a function can be determined by analyzing the second derivative. Taking the derivative of g(x) = 3x³ + 2x + 8, we find g'(x) = 9x² + 2
The second derivative, g''(x) = 18x, indicates the concavity of the function. Since the coefficient of x is positive, g(x) is concave up for all x. As there are no changes in concavity, there are no inflection points. Thus, the correct answer is (e) Concave down for all x; no inflection points.
To find the horizontal asymptote of h(x) = -5x² - 3, we examine the behavior of the function as x approaches positive or negative infinity. As x becomes infinitely large in either direction, the quadratic term dominates, and the linear term becomes insignificant. Therefore, the leading term is -5x². Since the coefficient of the quadratic term is negative, the graph of the function opens downwards. As x approaches infinity, the function decreases without bound, indicating a horizontal asymptote at y = 0. Hence, the correct answer is (a) y = 0.
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Related Questions
which coordinate plane shows a polygon with four vertices graphed at (-5,5), (2,4), (6,-2), and (-3,-6)?
Answers
Based on the given coordinate points, the coordinate plane that shows the polygon would be: Graph A.
What is a Coordinate Plane?A coordinate plane can be described as a two-dimensional plane that specifies each point uniquely by a pair of numerical coordinates (x, y).
It has a horizontal axis (x-axis) and vertical axis (y-axis).
Given that a polygon has four vertices that are graphed at: (-5,5), (2,4), (6,-2), and (-3,-6), therefore, based on these coordinate points, the coordinate plane that shows the polygon would be: Graph A.
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i need help with What is the difference between marginal cost and marginal revenue?
Answers
Answer:
The marginal cost is the additional cost added by increasing the quantity. This is also known as the additional cost “at the margin.” The marginal revenue is the additional revenue added by increasing the quantity. This is also known as the additional revenue “at the margin.”
Step-by-step explanation:
Please mark as brainlist
y varies jointly as x and z. y = 36 when x= 3 and z=3. Find y when x=5 and z=2.y=
Answers
Where k is a constant
When y = 36 , x = 3 , z=3
\(\begin{gathered} k\text{ = }\frac{y}{xz} \\ k=\text{ }\frac{36}{3\times3}\text{ =}\frac{36}{9}\text{ = 4} \end{gathered}\)\(\begin{gathered} y\text{ = 4xz} \\ x=\text{ 5 , z = 2} \\ y\text{ = 4 }\times5\times2=40 \end{gathered}\)The value of y is 40
Could someone help me find the length of each segment and which statements are true?
Answers
Answer:
see explanation
Step-by-step explanation:
(a)
calculate the lengths using the distance formula
d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)
with (x₁, y₁ ) = J (- 3, - 7 ) and (x₂, y₂ ) = K (3, - 8 )
JK = \(\sqrt{(3-(-3))^2+(-8-(-7))^2}\)
= \(\sqrt{(3+3)^2+(-8+7)^2}\)
= \(\sqrt{6^2+(-1)^2}\)
= \(\sqrt{36+1}\)
= \(\sqrt{37}\)
repeat with (x₁, y₁ ) = M (8, 3 ) and (x₂, y₂ ) = N (7, - 3 )
MN = \(\sqrt{(7-8)^2+(-3-3)^2}\)
= \(\sqrt{(-1)^2+(-6)^2}\)
= \(\sqrt{1+36}\)
= \(\sqrt{37}\)
repeat with (x₁, y₁ ) = P (- 8, 1 ) and (x₂, y₂ ) = Q (- 2, 2 )
PQ = \(\sqrt{-2-(-8))^2+(2-1)^2}\)
= \(\sqrt{(-2+8)^2+1^2}\)
= \(\sqrt{6^2+1}\)
= \(\sqrt{36+1}\)
= \(\sqrt{37}\)
(b)
JK ≅ MN ← true
JK ≅ PQ ← true
MN ≅ PQ ← true
If you are standing 75 ft away from a tree and looking up at the top at a 40° angle, what is the height of the tree?
Answers
Answer:
Step-by-step explanation:
Solve the following expression when g = 7 and e = 5
4e+g²-3e-9-g
Answers
Answer:
38
Step-by-step explanation:
4e + g² - 3e - 9 - g ( collect the e- terms together )
e + g² - 9 - g ( substitute g = 7, e = 5 into the expression )
= 5 + 7² - 9 - 7
= 5 + 49 - 16
= 54 - 16
= 38
Jessica needs 6 5/8 cups of flour for her recipe. The box she has only has 7/8 cup of flour left in it.
How many more cups of flour does she need?
Enter your answer as a mixed number in simplest form
Answers
Answer:
5 6/8 cups
Step-by-step explanation:
1 cups equal 8/8
simply one cup from the 6 and add to 5/8;8/8 +5/8 =13/8
13/8 -7/8=6/8
add the remaining 5 cups
totalling 5 6/8
Answer: 5 3/4
Step-by-step explanation:
Find the circumference of a circle with diameter 66cm(Take π=22/7)
Answers
Answer:207
Step-by-step explanation: circumference = to 2πr or πd
substitute the diameter into the equation πd (22/7)(66) and you get 207.4285...
And Bill collect coin. Karen ha x coin. Bill ha 6 coin fewer than two time the number of coin Karen ha. Write and implify an expreion for the total number of coin Karen and Bill have
Answers
The total number of coins Karen and Bill have is 4x-6.
An equation is a mathematical statement, which has an equal sign (=) between the algebraic expression. Linear equations are the equations of degree 1. It is the equation for the straight line. The solutions of linear equations will generate values, which when substituted for the unknown values, make the equation true. In the case of one variable, there is only one solution. For example, the equation x + 2 = 0 has only one solution as x = -2. But in the case of the two-variable linear equation, the solutions are calculated as the Cartesian coordinates of a point of the Euclidean plane.
Given that,
Karen has x coins.
Bill has 6 coins fewer than three times the number of coins Karen has.
Hence,
The number of coins Bill has =3x-6
The total number of coins Karen and Bill have is.
=x+(3x-6)
= 4x-6
Therefore, the total number of coins Karen and Bill have is 4x-6.
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Complete question: Karen and Bill collect coins. Karen has x coins. Bill has 6 coins fewer than three times the number of coins Karen has. Write and simplify an expression for the total number of coins Karen and Bill have.
Note: enter your answer and show all the steps that you use to solve this problem in the space provided. jebb is the tallest player on the basketball team. he is 1 1 2 times as tall as the shortest girl in the sixth grade, who is 4 1 4 feet tall. how tall is jebb?
Answers
Jebb is 6 feet 4.5 inches tall.
What is height?
The distance between the bottom and top of an object or person is a measurement of its height.
Height, altitude, and elevation all refer to the vertical distance, either between the top and bottom of something or between its base and something above it. Height is a term for something that can be high or low and is measured vertically.
Given: Jebb is the tallest player on the basketball team.
He is 1 1 /2 times as tall as the shortest girl in the sixth grade, who is 4 1 /4 feet tall.
Here
1 1/2 times 4 1/4
change to improper fractions
\(1\frac{1}{2} = \frac{(2)(1)+1}{2}= \frac{3}{2}\)
\(4\frac{1}{4}= \frac{(4)(4)+1}{4} = \frac{17}{4}\)
⇒ 1 1/2 times 4 1/4 is (3/2)*(17/4)
\(\frac{3}{2}(\frac{17}{4})=\frac{51}{8}\)
Convert 51/8 into improper fraction.
\(\frac{51}{8} = 6\frac{3}{8}\) feet tall.
3/8 of 12 inches is,
\(\frac{3}{8}(12) = \frac{36}{8}\)
Convert 36/8 into improper fraction
\(\frac{36}{8} = 4\frac{4}{8}\) inches
Here 4/8 = 0.5
⇒ \(4\frac{4}{8} = 4.5\)
Hence, Jebb is 6 feet 4.5 inches tall.
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How many solutions does the following equation have?
-5(z+1)=-2z+10−5(z+1)=−2z+10
Answers
Step-by-step explanation:
the answer is 13 when we evaluate it
Answer:
The given equation has exactly one solution.
Write the equation of a line parallel to the line determined by the points( -2,1) and (0,5 ) passing through the point (1,4)
Answers
Answer:
y = 2x + 2
Step-by-step explanation:
Find the slope of the line that passes through the points (-2, 1) and (0, 5):
\(\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{5-1}{0-(-2)}=\dfrac{4}{2}=2\)
If two lines are parallel they have the same slope.
Therefore, the slope of the other line that passes through point (1, 4) is also 2.
To find the equation of the parallel line that passes through the point (1, 4), substitute the found slope of 2 and the point (1, 4) into the point-slope formula:
\(\implies y-y_1=m(x-x_1)\)
\(\implies y-4=2(x-1)\)
\(\implies y-4=2x-2\)
\(\implies y=2x+2\)
Use the following function rule to find f(–4).
f(x) =
–4 +
4
|x|
f(–4) =
Answers
By evaluating the function in x = -4, we will get:
f(-4) = 12
How to evaluate the function f(x)?Here we have the following function:
f(x) = -4 + 4*|x|
So we have an absolute value function.
We want to find f(-4), so we want to evaluate the function in x = -4, to do that, just replace the variable by that number.
We will get:
f(-4) = -4 + 4*|-4|
Remember that the absolute value of a negative number gives the opposite:
|-4| = 4
Then:
f(-4) = -4 + 4*|-4|
f(-4) = -4 + 4*4
f(-4) = -4 + 16 = 12
f(-4) = 12
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An item on sale costs 30% of the original price. The original price was $83.
Use the ALEKS calculator to find the sale price.
Will Mark brainliest!!!! ASAP
LOTS OF POINTS
Answers
Answer:
This equals 58.10. The difference would be 24.90. Hope that helps :)
Step-by-step explanati
4)
If the circumference of a circle measures 37 cm, what is the area of the circle in terms of it?
A)3/4 cm
B)3/2cm
C)9/4cm
D9/2cm
Answers
Answer:
The answer is C.
Step-by-step explanation:
Also circumference formula is: 2 x pi (3.14 or 3.142) x r (radius)
So opposite method
When do u evaluate exponents in the order of operations??
Pls help I got 9 minutes to do this
Answers
Answer:
2nd
Step-by-step explanation:
Perenthasis
Exponets
Multiply
Divide
Add
Subtract
a hat company charges a design fee plus $4 per hat. the total cost of 5 hats is $30. how much will it cost for 3 hats?
Answers
Using Algebraic expression solution ,
The cost of three hats is $18 .
We have given that,
A hat company charge for design fee $4 per hat .
i.e design fee of one hat = $4
total cost of 5 hats = $30
let the cost of one hat without design fee be $x and total cost of one hat is $(x+4) .
using the above statement, we get an algebraic expression,
5( x+ 4)= 30
we solve the above algebra expression,
=> 5x + 20 = 30
=> 5x = 10
=> x = 2
so, cost of a hat without design fee is $2
and total cost of one hat is $6.
we have to calculate cost of 3 hats .
cost of one hat in hat company= $ 6
cost of three hats in hat company= $(6×3)
= $18
Hence, the total cost of 3 hats is $18.
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find the complement of 63°
Answers
Answer:
63=90-63= 27
Bye
Alice and Bob each have a coin. For Alice's coin, the probability of a head is 1/2. For Bob's coin, the probability of a head is 1/3. If each of them tosses their coin once, the probability that they will have different outcomes is
Answers
To find the probability that Alice and Bob will have different outcomes when tossing their coins once, we need to consider the possible combinations of outcomes.
Alice's coin can result in two outcomes: heads (H) with a probability of 1/2 and tails (T) with a probability of 1/2.
Bob's coin can also result in two outcomes: heads (H) with a probability of 1/3 and tails (T) with a probability of 2/3.
The possible combinations of outcomes are:
1. Alice gets H (1/2) and Bob gets T (2/3)
2. Alice gets T (1/2) and Bob gets H (1/3)
The probability that they will have different outcomes is the sum of the probabilities of these two cases.
Probability of different outcomes = (1/2) * (2/3) + (1/2) * (1/3)
= 2/6 + 1/6
= 3/6
= 1/2
Therefore, the probability that Alice and Bob will have different outcomes when tossing their coins once is 1/2 or 50%.
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Last month, customers at a gift shop bought 40 birthday cards,
19 congratulations cards, 20 holiday cards, and 21 thank you
cards. Suppose 125 customers buy greeting cards next month.
How many would you expect to buy a birthday card?
Answers
Answer:
32 People
Step-by-step explanation:
I put 40 (Number of birthday cards bought previously) over 125 (Number of expected costumers) and multiplied it by 100 (Total number of card bought previously) to get my answer. Hopefully that helps :)
A population of 100 frogs has a growth rate of 1.25% each month. At this growth rate,
the function f(x) = 100(1.25)* gives the population in x months. In how many months
will the population first reach 500?
Answers
Answer: 7.2 months
Step-by-step explanation:
Hi, to answer this question we have to substitute f(x) =500 in the equation given:
f(x) = 100(1.25)^x
500= 100(1.25)^x
Solving for x (number of months)
500/100 = 1.25^x
5 = 1.25^x
log 5 =log 1.25^x
log 5 =x (log 1.25)
log 5 /log 1.25 =x
x = 7.2 months
Feel free to ask for more if needed or if you did not understand something.
PLEASE HELP ME WITH FUNCTIONS I REALLY NEED IT
Answers
Answer:
D
Step-by-step explanation:
Range is on the y-axis & Domain sits on the x-axis
Answer: 1 , 3 , 4 , 5
Question: Which of the following sentences are written in dialect? Check the four boxes that apply.
“It was the most thrillingist one that ever was; and so he went on a-bragging.”
“I stood by the duke at the door.”
“He will be deeply obleeged if they will mention it to their friends.”
“We are sold – mighty badly sold.”
“What they wanted was low comedy.”
“These Arkansaw lunkheads couldn’t come up.”
Answers
I assume that it is 1, 3, 4, and 5. Correct me if I'm wrong. Plz give brainliest if I'm right.
Answer:
1. “It was the most thrillingist one that ever was; and so he went on a-bragging
3 “He will be deeply obleeged if they will mention it to their friends.”
4.“We are sold – mighty badly sold.”
6. “These Arkansaw lunkheads couldn’t come up.”
Step-by-step explanation:
Edge-2021
Math on the Spot Mark said that the speed of a
housefly rounded to the nearest tenth was 1.9 meters
each second. Is he correct? If not, what is his error?
insect Speeds (meters each second)
Insect
Speed
Dragonfly
6.974
Horsefly
3.934
Bumblebee
2.861
Honeybee
2.548
Housefly
1.967
Answers
Answer:
He is incorrect
Step-by-step explanation:
In 1.967, the hundredth is greater than 5. That means you'd round up! So, the correct answer would be 2.
(I tried my best to explain)
Which two of the following are continuous data?
A) concert attendance
B) age of a student
C) number of pens in a box
D) time taken to run 1 mile
Answers
Answer:
Age of a student (B) and Time taken you run 1 mile (D)
Step-by-step explanation:
Only the age of a student and the time taken to run 1 mile are continuous data.
What are the types of data?
The data is classified into majorly four categories:
Nominal data: Nominal Data is used to label variables without any order or quantitative value.Ordinal data: Ordinal data have natural ordering where a number is present in some kind of order by their position on the scale. Discrete data: The term discrete means distinct or separate. The discrete data contain the values that fall under integers or whole numbers.Continuous data: Continuous data are in the form of fractional numbers. It can be the version of an android phone, the height of a person, the length of an object, etc. Continuous data represents information that can be divided into smaller levels. The continuous variable can take any value within a range.As per the given definitions above we can state that Continuous data is (B) the Age of the students (D) the Time taken to run 1 mile
Therefore, the Answer is (B) and (D)
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Drag the correct tiles to the boxes. Each tile can be used more than once.
Match each scenario to the type of relationship it represents.
Linear
Exponential
Quadratic
In a shotput competition anything with a shock from a height of 6 feet the shower because a maximum height of 9 feet after covering a distance of 29 fee the total distance covered by the shot is 58 feet Time years 01234 number of pigs on the form 30 9 200 7 81 2430. The government plans to decrease the number of automobiles imported from a certain country by 10% each year. Ronald is descending from the 50th floor anyway elevator the elevator moves up or down eight floors per minute. Time second 02468 height of a toy jet feet 5 101310 five
Answers
Answer:
Step-by-step explanation:
constraints aregroup of answer choicesquantities to be minimized in a linear programming model.restrictions that limit the settings of the decision variables.input variables that can be controlled during optimization.quantities to be maximized in a linear programming model.
Answers
Constraints are restrictions that limit the settings of the decision variables in a linear programming model.
Constraints in a linear programming model are restrictions that limit the settings of the decision variables, which are input variables that can be controlled during optimization.
These decision variables are often defined by specific quantities to be maximized or minimized in the model.
Therefore, constraints are a group of answer choices or restrictions that must be considered when developing a mathematical model to optimize certain variables or quantities.
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In each of Problems 38 through 42, a differential equation and one solution yı are given. Use the method of reduction of or- der as in Problem 37 to find a second linearly independent solution y2. . x2y" + xy' – 9y = 0 (x > 0); yı(x) = x3
Answers
A second linearly independent solution of y₂ is \(-\frac{1}{6x^3}\)
The general Equation is y" + P(x)y' + q(x)y = 0 ...............(i)
where P(x), Q(x) are continues in the internal I ≤ R.
If y₁(x) is a solution of equation 1 in I then y₁(x) ≠ 0.
Then y₂(x) = y₁(x)\(\int{\frac{e^{-\intP(x)dx}}{(y_{1}x)^2}}dx\) is another solution.
The differential equation is x²y" + xy' – 9y = 0 where x > 0.
As y₁(x) = x³ is one solution of differential equation.
Divide throughout by (x²) to given differential equation.
1/x² (x²y" + xy' – 9y = 0)
y" + (y'/x) – (9/x²)y = 0 ................(ii)
By comparing equation (i) & (ii) we get:
p(x)=1/x , q(x)= –are continuous for x>0
So, another solution,
y₂(x) = y₁(x)\(\int{\frac{e^{-\intP(x)dx}}{(y_{1}x)^2}}dx\)
Now putting the values of P(x) And Q(x)
y₂(x) = \(x^3\int\limits {\frac{e^{\int(1/x)dx} }{(x^3)^2}} \, dx\)
y₂(x) = \(x^3\int\limits {\frac{\frac{1}{x} }{x^6} }} \, dx\)
y₂(x) = \(x^3\int\limits {\frac{1}{x^7} }} \, dx\)
y₂(x) = \(x^3\int\limits {x^-7} } \, dx\)
y₂(x) = \(x^3\left[\frac{x^{-7+1}}{-7+1}\right]\)
y₂(x) = \(-\frac{1}{6}(x^3\times x^{-6})\)
y₂(x) = \(-\frac{1}{6x^3}\)
So, the answer of this question is \(-\frac{1}{6x^3}\).
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HURRY ONLY HAVE A FEW MINUTES
If SDE ~ SWT, find the value of x.
SHOW YOUR WORK FOR CREDIT!
Answers
Answer:
It’s 12 just because I’m smart
The value of the x in the given similar triangle is 12.
What are similar triangles?Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.
Given that, two similar triangles, Δ SDE ~ Δ SWT
Since, Δ SDE ~ Δ SWT
Therefore, according to the definition of similar triangles,
SE / DE = ST / WT
Putting their given values,
40 / 56 = (4x-3) / (5x+3)
5 / 7 = (4x-3) / (5x+3)
5(5x+3) = 7(4x-3)
25x + 15 = 28x - 21
3x = 36
x = 12
Hence, the value of the x in the given similar triangle is 12.
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Given ABC with coordinates A(1,3). B(4,5), and C(5,2). what are the coordinates of A'BC after the glide reflection described by T(-1,1)Ry-axis?A =B =C=
Answers
Let's begin by listing out the information given to us:
\(A\mleft(1,3\mright);B\mleft(4,5\mright);C\mleft(5,2\mright)\)When this is glided by T(-1, 1); ry−axis(x, y) → (−x, y)
\(\begin{gathered} A\mleft(1,3\mright)\rightarrow A^{\prime}(^{}-1,3) \\ B(4,5)\rightarrow B^{\prime}(-4,5) \\ C(5,2)\rightarrow C^{\prime}(-5,2) \end{gathered}\)