i need help with number 10. I have questions about the extreme and end behavior and symmetry
Answers
Answers:
Symmetry: about the origin
Extrema: No
End behavior: as x --> ∞, f(x) --> ∞ and as x --> -∞, f(x) --> -∞
Explanation:
The graph for f(x) = x³ is
Then, we can see that the graph is symmetric over the origin becuase
f(-x) = -f(x)
(-x)³ = -(x³)
-x³ = -x³
On the other hand, it doesn't have an extreme value, there are no maximum or minimum points in a given interval.
Finally, we can see that when x increases, f(x) increases, and when x decreases f(x) decreases. So, the end behavior is
as x --> ∞, f(x) --> ∞
as x --> -∞, f(x) --> -∞
Related Questions
What is the perimeter of a square if the hight is 5x and the length is 4x+7
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Given data:
The given height of the square is h=5x.
The given lenght of the square is l=4x+7.
In square all dimensions are equal.
5x=4+7
x=7
The
Use Law of Cosines to solve for this problem. Round your answer to the nearest TENTH.
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We can find the distance from the basket to malachi (BC) using the law of cosines. Therefore:
[tex]\begin{gathered} BC=\sqrt{AB^2+AC^2-2(AB)(AC)cos(A)} \\ BC=\sqrt{24^2+26^2-2(24)(26)cos(34)} \\ BC\approx14.7ft \end{gathered}[/tex]Answer:
The distance between the basket and Malachi is 14.7 ft
Please help I’m failing math and my quarter ends Friday
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y-intercept (0, -7) and x-intercept (5,0)
1) To find the y-intercept, let's rewrite that equation into the slope-intercept form to better do it:
2/5x -2/7y =2 Add 2/7y to both sides
-2/7y = 2 -2/5x Multiply the whole equation by 7 to get rid of the fraction x
-2y = 14 -14/7x Divide by -2
y = -7 +x
y= x -7
So the y-intercept is at y=-7
2) To find the x-intercept, let's plug into that y=0
2/5x -2/7y =2
2/5x -2/7(0) = 2
2/5x = 2
x= 2 : 2/5
x = 2 x 5/2
x= 5
3) Hence, the answer is y-intercept (0, -7) and x-intercept (5,0)
19 February 25 Review 19 What is the decimal expansion of the following fraction? A. 0.045 OB 0.22which is the decimal expansion of the following fraction 1/22
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Brandy and parents, this is the solution:
We have the fraction: 1/22
All we need to do is divide 1 by 22, and the outcome is:
A. 0.045
Hey I need a tutor the lines across the other answer choice does not mean it is wrong it is glitched out and I can’t change it back please help thank you
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Explanation
In order to answer the question, we will have to get the mode, median, and range of both stores
mode: The mode is the value that appears most frequently in a data set.
Range: The Range is the difference between the lowest and highest values.
median: The Median is the "middle" of a sorted list of numbers.
For store 1
[tex]\begin{gathered} mode:2 \\ range=\text{ 6- 0=6} \\ median\text{ =2} \end{gathered}[/tex]For store 2
[tex]\begin{gathered} mode:1 \\ range=6-0=6 \\ median=\frac{1+2}{2}=1.5 \end{gathered}[/tex]The mode of store 1 is greater than store 2: TRUE
The range of store 1 is greater than store 2: FALSE
The range of store 1 and store 2 is the same: TRUE
The median of data store 2 is greater than data store 1: FALSE
Find outside surface area and volume of the solid object assume that the base is regular
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The solid object shown is the frustum of a square based pyramid..
To calculate the total surface area, we shall follow the procedure below;
[tex]\begin{gathered} \text{Total Surface Area}=TSA \\ \text{TSA}=\lbrack\frac{1}{2}(P_1+P_2)L\rbrack+B_1+B_2 \\ \text{Where the variables are;} \\ P_1=Perimeter\text{ of base 1} \\ P_2=\text{Perimeter of base 2} \\ L=Slant\text{ height} \\ B_1=\text{Area of base 1} \\ B_2=\text{Area of base 2} \end{gathered}[/tex]We shall now solve as follows;
[tex]\begin{gathered} P_1=2(l+w) \\ P_1=2(14+14) \\ P_1=2(28) \\ P_1=56in \end{gathered}[/tex][tex]\begin{gathered} P_2=2(l+w) \\ P_2=2(24+24) \\ P_2=2(48) \\ P_2=96in \end{gathered}[/tex][tex]\begin{gathered} B_1=l\times w \\ B_1=14\times14 \\ B_1=196in^2 \end{gathered}[/tex][tex]\begin{gathered} B_2=l\times w \\ B_2=24\times24 \\ B_2=576in^2 \end{gathered}[/tex]The total surface area would now be;
[tex]\begin{gathered} \text{TSA}=\lbrack\frac{1}{2}(P_1+P_2)L\rbrack+B_1+B_2 \\ \text{TSA}=\lbrack\frac{1}{2}(56+96)19\rbrack+196+576 \\ \text{TSA}=\lbrack\frac{1}{2}(152)19\rbrack+772 \\ \text{TSA}=\lbrack76\times19\rbrack+772 \\ \text{TSA}=1444+772 \\ \text{TSA}=2216in^2 \end{gathered}[/tex]The volume of a frustum of a square based pyramid is given as;
[tex]\begin{gathered} Vol=\frac{1}{3}h(B_1+B_2+\sqrt[]{B_1B_2}) \\ \text{Where;} \\ h=vertical\text{ height (altitude)} \end{gathered}[/tex]The volume would now be;
[tex]\begin{gathered} \text{Vol}=\frac{1}{3}\times15(196+576+\sqrt[]{196\times576}) \\ \text{Vol}=5(772+\sqrt[]{112896}) \\ \text{Vol}=5(772+336) \\ \text{Vol}=5(1108) \\ \text{Vol}=5540in^3 \end{gathered}[/tex]ANSWER:
Therefore, we have
Total surface area = 2,216 inches squared
Volume = 5,540 inches cubed
find the missing measure in the triangle with the given angle measures.100°, x°, 40°a. 40b.90c.220d.30
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For this exercise you need to remember that, by definition, the sum of the interior angles of any triangle is 180 degrees.
In this case, you know the following interior angles of the triangle given in the exercise:
[tex]\begin{gathered} 100\degree \\ 40\degree \end{gathered}[/tex]Then, based on the explained above, you can set up the following equation:
[tex]40\degree+100\degree+x=180\degree[/tex]Finally, you must solve for the variable "x" in order to find the measure of the missing angle of the triangle. You get that this is:
[tex]\begin{gathered} 140\degree+x=180\degree \\ x=180\degree-140\degree \\ x=40\degree \end{gathered}[/tex]The answer is: Option a.
5. A science museum opened its butterfly exhibit in January 1996 with an initial population of 30 butterflies. The population doubles in size every 6 months. Which value of x, the number of doubling cycles, should be used to determine the number of butterflies in the exhibit in January 2000?C. 32A 4B. 8D. 64
Answers
Given that
A science museum opened its butterfly exhibit in January 1996 with an initial population of 30 butterflies. The population doubles in size every 6 months. And we need to find the number of doubling cycles till January 2000.
Explanation -
To find the doubling rate we will divide the initial population by the time in which it is getting doubled.
So, the initial population is 30 and the time is 6 months.
The doubling rate will be = 30/6 = 5
So the value of x will be
[tex]x=2^5=32[/tex]So the correct option is C.
And the final answer is 32.
i really need help pleaseThe floor plan of a school auditorium is shown. What is the area of the auditorium?
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The area of the auditorium is given by:
Will be the area of the blue rectangle minus the area of the red triangles, so:
The area of the rectangle is:
[tex]\begin{gathered} Ar=w\cdot l \\ where\colon \\ w=32 \\ l=13+3=16 \\ Ar=512ft^2 \end{gathered}[/tex]The area of each triangle is:
[tex]\begin{gathered} At=\frac{b\cdot h}{2} \\ where\colon \\ b=\frac{32-20}{2}=6 \\ h=3 \\ so\colon \\ At=\frac{6\cdot3}{2} \\ At=\frac{18}{2} \\ At=9ft^2 \end{gathered}[/tex]Therefore, the area of the auditorium:
[tex]\begin{gathered} A=Ar-2At \\ A=512-2(9) \\ A=512-18 \\ A=494ft^2 \end{gathered}[/tex]Select the correct answer from the drop-down menu.You are conducting a survey on the best beaches in the world. The group that would probably give you the most reliable data is_________
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In order to collect information about the best beaches, it's more reliable to survey people that already visited the beaches, so they can give you information about what they experienced.
It's not good to survey officials who manage the beaches, because they will be biased to say to you that their beaches are the best ones.
Therefore the correct option is the third one.
< Tank A initially contained 124 liters of water. It is then filled with more water, at a constant rate of 9 liters per minute. How many minutes have passed, m, when Tank A contains 151 liters How many minutes have passed, m, when Tank A contains 191.5 liters How many minutes have passed,y, when Tank A contains x liters
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we get that the equation that models this situation is:
[tex]L=9m+124[/tex]where L is the number of liters and m the minutes. So we have that
[tex]151=124+9m\rightarrow m=\frac{151-124}{9}=3[/tex]so after 3 minutes the tank jas 151 liters
[tex]191.5=124+9m\rightarrow m=\frac{191.5-124}{9}=7.5[/tex]so after 7.5m the tanks has 191.5 liters
and for the last one we get
[tex]x=9y+124\rightarrow y=\frac{x-124}{9}[/tex]Help please been trying to figure these out and I want to learn
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Given:
Two binomials are given.
[tex](2A+3B)(2A-3B)[/tex]Required:
Find the product of the binomials.
Explanation:
The given binomials are:
[tex](2A+3B)(2A-3B)[/tex]Use the following identity
[tex](a+b)(a-b)=a^2-b^2[/tex][tex]\begin{gathered} (2A+3B)(2A-3B)=(2A)^2-(3B)^2 \\ (2A+3B)(2A-3B)=4A^2-9B^2 \end{gathered}[/tex]This matches with option D.
Final Answer:
Option D is the correct answer.
the graph of a function f(x) passes through the following points: (0, 0), (1, -2), (2, 0) which of the following could be f(x) f(x)= 2x^2-4x f(x)= -2x^2f(x)= -2x f(x)= 2 √x-4x
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Recall that the x-intercepts of a graph are of the form:
[tex](x,0)\text{.}[/tex]Since the graph of f(x) passes through (0,0), (1, -2), and (2,0), then its x-intercepts are (0,0) and (2,0).
Therefore f(x) must be as follows:
[tex]\begin{gathered} f(x)=k(x-0)(x-2) \\ =kx(x-2)\text{.} \end{gathered}[/tex]Where k is a constant.
Since f(x) passes through (1,-2), then:
[tex]-2=f(1)\text{.}[/tex]Then:
[tex]-2=k\cdot1(1-2)\text{.}[/tex]Simplifying the above equation we get:
[tex]\begin{gathered} -2=k(-1), \\ -2=-k\text{.} \end{gathered}[/tex]Therefore:
[tex]k=2.[/tex]Therefore f(x) could be as follows:
[tex]\begin{gathered} f(x)=2x(x-2) \\ =2x^2-4x\text{.} \end{gathered}[/tex]Answer: First option.
What is the correct answer to this question A 40B 44 C24D 52
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Given:
The parallelogram PQRS is a square.
The length of PQ = 2x+8
Perimeter = 96
Required:
Find the length of the side PQ.
Explanation:
Given that perimeter = 96
[tex]\begin{gathered} 4(2x+8)=96 \\ 8x+32=96 \\ 8x=96-32 \\ 8x=64 \\ x=\frac{64}{8} \\ x=8 \end{gathered}[/tex]The value of x is 8.
The length of the side PQ
[tex]\begin{gathered} =2(8)+8 \\ =16+8 \\ =24 \end{gathered}[/tex]Final Answer:
Last question choose from the correct choice A,BC, or D
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Given the function
[tex]R(x)=\frac{7x+7}{6x+12}[/tex]we have to determine the behavior of the graph on either sides of the vertical asymptotes. if one exists.
Remember that vertical asymptotes occur when in a rational function, that is a function of the form
[tex]R(x)=\frac{f(x)}{g(x)}[/tex]The denominator, g(x), becomes 0.
In our case, the denominator of the rational function is
[tex]g(x)=6x+12[/tex]therefore
[tex]6x+12=0\text{ }\Rightarrow\text{ }x=-2[/tex]we conclude that there is a vertical asymptote at x=-2.
Now we will determine the behavior on both sides of the asymptote
One possible approach to discover this behavior is to pick up close to x=-2 values on both sides and evaluate it to determine the sign. Let us take
[tex]x=-2.01\text{ and }x=-1.99[/tex]Evaluation the first one
[tex]R(-2.01)=\frac{7(-2.01)+7}{6(-2.01)+12}=117.83[/tex]since the result is big and positive we conclude that on the left side of the asymptote the function approach to + infinity.
Now we will evaluate on the other side to determine the sign
[tex]R(-1.99)=\frac{7(-1.99)+7}{6(-1.99)+12}=-115.5[/tex]Therefore, the on the right the function approach to - infinity as the numbers approach to x=-2
Looking at the options we see that the correct option is the option c).
In ALMN, the measure of ZN=90°, LM = 68 feet, and MN = 38 feet. Find themeasure of ZL to the nearest tenth of a degree.
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The sine of an angle(in a right triangle) is given by the the ratio of the opposite side with the hypotenuse, so the sine of (xº) is given by:
[tex]\frac{38}{68}=\sin (x^o)[/tex]Using the arcsin(x) function we can find the measure of the angle:
[tex]\begin{gathered} \sin ^{-1}(\frac{38}{68})=x^o=33.9744759503\ldots \\ \Rightarrow x^o\approx34^o \end{gathered}[/tex]On a number line, where would 3/10 be located? Choose all answers that makea true statement.A. To the right of 1/10B. In the same place as 6/10C. To the left of 8/10D. To the left of 2/10
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Consider the number line drawn below
Statement A is correct since 3/10 is located to the right of 1/10.
Statement B is false because 6/10 is located to the right 3/10.
Statement C is correct because 3/10 is placed to the left of 8/10.
Statement D is false because 2/10 is located to the right of 3/10.
Answers: A and C
Need help solving this math class work I don’t understand it
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Given:
[tex]\frac{2+i}{1-2i}[/tex][tex]\frac{2+i}{1-2i}=\frac{2+i}{1-2i}\times\frac{1+2i}{1+2i}[/tex][tex]\frac{2+i}{1-2i}=\frac{2+4i+i-2}{1+4}[/tex][tex]\frac{2+i}{1-2i}=\frac{5i}{5}[/tex][tex]\frac{2+i}{1-2i}=i[/tex]0 to 1, or Never to AlwaysFor each probability given below, think up two situations that havethat probability.In one of those two situations, the probability should be based on atheoretical model. In the other situation, the probability should bebased on observed results. Be imaginative!1. Probability = 02. Probability = 13. Probability = 75%4. Probability = 15. Probability = 2.36. Probability = .01
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The probability or likelihood of an event happening or not is usually based on a percentage expressed as 1.0 for "DEFINITELY GOING TO HAPPEN" and 0 for "DEFINITELY CANNOT HAPPEN" and then some in between measuring from 0.1 to 0.9
[tex]undefined[/tex]1.3b Practice Your teacher has limited times you may check yo this item i Determine whether the equation 2(h+1) = 5h – 7 has one solution, no solution, or infinitely many solutions. The equation has If the equation has a solution, enter it below. If the equation has no solution or infinitely many solutions, leave the solution field blank. h= 201 PREV 1 2 3 4 5 6 NEXT > Check ? Help
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1) Let's check that by solving it
2(h+1) = 5h – 7 Distribute the factor
2h +2 = 5h -7 Subtract 2 from both sides
2h -5h = -7 -2 Combine like terms
-3h= -9
3h=9 Divide both sides by 3
h=3
This equation has one solution. h=3
julia is going to invest $860 in an account and leave it for 8 years. assuming the interest rate is compounded continuously, What interest rate To the nearest Hundresth of a percent Would be required in order for julia To end up with $1190?
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Brian decides to mix grades of gasoline in his truck. He puts in7 gallons of regular and5 gallons of premium for a total cost of$45.14. If premium gasoline costs$0.22 more per gallon than regular, what was the price of each grade of gasoline?
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In this problem we have two variables, so we need two equation to solve the system.
The first equation comes from the gasoline he puts in his truck so: (R mean the regular gasoline, and P means the premium gasoline)
[tex]7R+5P=45.14[/tex]And the secon equation comes from the value of a individual gallon:
[tex]P=R+0.22[/tex]Now to find the value of the regular gasoline we can replace the second equation into the first equation:
[tex]\begin{gathered} 7R+5(R+0.22)=45.14 \\ 7R+5R+1.1=45.14 \\ 12R=44.04 \\ R=\frac{44.04}{12} \\ R=3.67 \end{gathered}[/tex]Now with the value of R we can rplace that into the second equation:
[tex]\begin{gathered} P=3.67+0.22 \\ P=3.89 \end{gathered}[/tex]You have decided to purchase a home that has an asking price of $159,900. You wish to put a down payment is the percent equivalent to the date you were born on (for example I was born on the 29th of the month so I would have a 29% down payment). Explain how you would determine the amount that you would be financed for your mortgage. (The amount financed is the is the amount of the asking price that would be left after the down payment is paid.) Your explanation should include the mathematical support.
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You have decided to purchase a home at $159,900.
I was born on the 28th so I choose to put a 28% down payment.
The amount I would be financed for my mortgage would be 100 - 28 = 72% of $159,900.
This can be simplified as;
[tex]\begin{gathered} =\frac{72}{100}\times159900 \\ =\text{ \$115128} \end{gathered}[/tex]Therefore, the amount that I would be financed for my mortgage is $115,128
One figure is a rotation image of the other One figure is a translation image of the other Neither figure is a translation or rotation image of the other
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Given:
Two figures are congruent.
Required:
We need to find the correct statement.
Explanation:
One figure is rotated and we get the image.
One figure is a rotation image of the other
We know that rotation transformation preserved the sides.
Final answer:
One figure is a rotation image of the other
you want to buy some noodles A 6 ounce package costs $1.92 A 16 ounce package costs $5.28 A 22 ounce package costs $6.82 which package is the best buy
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Given that a 6 ounce package costs $1.92,
the cost per ounce is
= $1.92/6
= $0.32
If a 16 ounce package costs $5.28 ,
the cost per ounce will be
= $5.28/16
= $0.33
Given that aA 22 ounce package costs $6.82
Write a equation in slope intercept form using the following informationslope: 1 y- intercept : (0,-1)
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The crackers in a box have three shapes. Max randomly choose one cracker at a time 40 times, returning the cracker to the box each time.Crackers (Shape/frequency)Oval: 18Rectangle: 14Star: 8Find the experimental probability of choosing a cracker that is not star-shaped.
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Can you see my message now?
Alright, give me one moment to read the exercise, please.
I'll type the explanation now. I'll bold the explanation so that you can tell it appart from my messages.
There are 3 shapes of crackers in the box, oval, rectangular and star. Max took one cracker at a time, 40 times, recorded its shape and put it back in the box.
To calculate the experimental probability of getting each shape, you have to divide the number of times he got that determined shape (frequency of the cracker shape) by the total number of times he repeated the experiment.
So for the oval crackers, the probability will be:
[tex]P(oval)=\frac{\text{frequency}}{\text{Total}}=\frac{18}{40}=0.45[/tex]For the rectangular crackers the probability will be
[tex]P(rec\tan gular)=\frac{\text{frequency}}{\text{Total}}=\frac{14}{40}=0.35[/tex]For the star-shaped crackers the probability will be:
[tex]P(star)=\frac{\text{frequency}}{\text{Total}}=\frac{8}{40}=0.20[/tex]Now you have to determine the probability of the event "NOT star shaped" this occurs when you get either rectangular or oval shaped crackers. This event is complementary to the event "Star shaped" and you can calculate it as:
[tex]\begin{gathered} P(Star^c)=1-P(Star) \\ P(Star^c)=1-0.20 \\ P(Star^c)=0.80 \end{gathered}[/tex]You have to express it as a percentage so multiply the result by 100
[tex]0.80\cdot100=80[/tex]The experimental probability of not geting a star shaped cracker is 80%
Done!
Tell me if you have any doubts regarding the explanation.
11.) f(x) = 2 |x + 2| + 8 Transformation 1: Transformation 2: Transformation 3: 13.) f(x) = -|x |- 5 Transformation 1: Transformation 2:
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f(x) = 2 (x + 2)^2 + 8
Transformation 1: If we start with y = x^2 and replace x by x + 2, it has the effect of shifting the graph 2 units to the left.
Transformation 2: Then if we multiply the right side by 2, it turns the parabola upside down and gives a vertical expansion by a factor of 2.
Transformation 3: Finally, if we add 8 to the right side, it shifts the graph to 8 units up.
please help me work through this thank you! read the question carefully since it can be confusing
Answers
ANSWER
636,255 cubic centimeters
EXPLANATION
Given:
Thickness = 0.02 cm
Diameter = 45m = 4500cm
Recall, Volume of a sphere is:
[tex]V=\frac{4}{3}\pi r^3[/tex]Determine change in V by differentiating the Volume:
[tex]\begin{gathered} \Delta V=dV=3\times\frac{4}{3}\pi r^{3-1}dr \\ dV=4\pi r^2dr \end{gathered}[/tex]Note: from the given question
dr = 0.02cm
r = 4500/2 = 2250 cm
Recall: for Hemisphere
[tex]\begin{gathered} dV=\frac{1}{2}\times4\pi r^2dr \\ dV=2\pi r^2dr \end{gathered}[/tex]Substitute the values:
[tex]\begin{gathered} dV=2\times3.142\times(2250)^2\times0.02 \\ dV=6.284\times5062500\times0.02 \\ dV=636255cm^3 \end{gathered}[/tex]Hence, the amount of paint needed is 636,255 cubic centimeters.
In a class of 26 students, 17 have a brother and 12 have a sister. There are 5 students who do not have any siblings. What is the probability that a student has a brother given that they have a sister?
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The number of students have a brother is 17.
The number of students have a sister is 12.
The number of students who donot have any siblings are 5.
The total students are 26.
Let there are x students who have both brother and sister. So number of students with only brother s (17 - x), number of students with sister only is (12 - x).
Determine the number of students have both brother and sister.
[tex]\begin{gathered} 17-x+12-x+x+5=26 \\ -x=26-17-12-5 \\ x=8 \end{gathered}[/tex]So probability for students with both brother and sister is,
[tex]P(\text{ Brother and sister)=}\frac{8}{26}[/tex]Probability for student have sister is,
[tex]P(\text{ sister)=}\frac{12}{26}[/tex]Determine the probability that a student has a brother given that they have a sister.
[tex]\begin{gathered} P\text{ (Brother and sister|sister)=}\frac{P\text{ (Brother and sister)}}{P\text{ (Sister)}} \\ =\frac{\frac{8}{26}}{\frac{12}{26}} \\ =\frac{8}{26}\cdot\frac{26}{12} \\ =\frac{8}{12} \\ =\frac{2}{3} \end{gathered}[/tex]Answer: 2/3