Graphs of Function,
Write in interval notation the areas of increase and decrease.
I don't need all of them answered maybe 1 or 2? I want to do some myself.
Thank you for any help on this.
Answers
Answer:
A function is increasing when the gradient is positive
A function is decreasing when the gradient is negative
Question 7
If you draw a tangent to the curve in the interval x < -2 then the tangent will have a positive gradient, and so the function is increasing in this interval.
If you draw a tangent to the curve in the interval x > -2 then the tangent will have a negative gradient, and so the function is decreasing in this interval.
If you draw a tangent to the curve at the vertex of the parabola, it will be a horizontal line, and so the gradient at x = -2 will be zero.
The function is increasing when x < -2
[tex](- \infty,-2)[/tex]
The function is decreasing when x > -2
[tex](-2, \infty)[/tex]
Additional information
We can actually determine the intervals where the function is increasing and decreasing by differentiating the function.
The equation of this graph is:
[tex]f(x)=-2x^2-8x-8[/tex]
[tex]\implies f'(x)=-4x-8[/tex]
The function is increasing when [tex]f'(x) > 0[/tex]
[tex]\implies -4x-8 > 0[/tex]
[tex]\implies -4x > 8[/tex]
[tex]\implies x < -2[/tex]
The function is decreasing when [tex]f'(x) < 0[/tex]
[tex]\implies -4x-8 < 0[/tex]
[tex]\implies -4x < 8[/tex]
[tex]\implies x > -2[/tex]
This concurs with the observations made from the graph.
Question 8
This is a straight line graph. The gradient is negative, so:
The function is decreasing for all real values of x
[tex](- \infty,+ \infty)[/tex]
But if they want the interval for the grid only, it would be -4 ≤ x ≤ 1
[tex][-4,1][/tex]
Question 9
If you draw a tangent to the curve in the interval x < -1 then the tangent will have a negative gradient, and so the function is decreasing in this interval.
If you draw a tangent to the curve in the interval x > -1 then the tangent will have a positive gradient, and so the function is increasing in this interval.
If you draw a tangent to the curve at the vertex of the parabola, it will be a horizontal line, and so the gradient at x = -1 will be zero.
The function is decreasing when x < -1
[tex](- \infty,-1)[/tex]
The function is increasing when x > -1
[tex](-1, \infty)[/tex]
Related Questions
what is the cost of 23.5 gallons of gas
Answers
Answer:
Too much
Step-by-step explanation:
I did the math myself
If the discriminant is negative, you will have....
1) two irrational solutions
2) no solution
3) two real solutions
4) one solution
Answers
Answer:
Hi mate I got you
Step-by-step explanation:
A positive discriminant indicates that the quadratic has two distinct real number solutions. A discriminant of zero indicates that the quadratic has a repeated real number solution.
A negative discriminant indicates that neither of the solutions are real numbers.
PLEASE MARK ME BRAINLIEST IF MY ANSWER IS CORRECT PLEASE
The circumference of a wheel is 302 centimetres. Determine the diameter of the wheel. Round your answer to the nearest tenth.
Answers
Lisa makes $5 per hour babysitting and $12 per hour giving music lessons. One weekend, she worked a total of 18 hours and made $139. How many hours did she spend babysitting that weekend?
Answers
Answer:
11 Hours
Step-by-step explanation:
Let's say Lisa makes x hours babysitting and y hours giving music lessons.
Because she worked a total of 18 hours, we know that x + y = 18.
5 * x is how much money she earns babysitting for x hours, while 12 * y is how much money she earns giving music lessons for y hours. Adding them up gives her total revenue:
5x + 12y = 139
We now have a system of equations. Let's multiply both sides of x + y = 18 by 12:
12 * (x + y) = 18 * 12
12x + 12y = 216
Now, subtract 5x + 12y = 139 from 12x + 12y = 216:
12x + 12y = 216
- 5x + 12y = 139
_________________
7x + 0y = 77
Divide both sides by 7:
x = 11
Thus, Lisa spent 11 hours babysitting.
Answer:
11 hours baby sitting and 7 hours music lessons
Step-by-step explanation:
you have to solve:
x + y = 18
and
5x + 12y= 139
assuming that x is the total hours of baby sitting and y is the total hours of music lessons
What is the volume of the rectangular prism?
Will mark brainlyest!
Answers
(-3)+5+(-5)+12=
Can someone break this down for me?
I just wanted to get some help ...
Thank you !
Answers
Answer:
[tex]9[/tex]
Step-by-step explanation:
[tex](-3)+5+(-5)+12=\\-3+5-5+12=\\5-5-3+12=\\-3+12=\\12-3=\\9[/tex]
Whenever you are doing a problem that says [tex]+(-n)[/tex] (n for number), it's the same as subtracting that number.
help!! Graph y>−5/4x+5
Answers
Answer:
it's the top right.
Step-by-step explanation:
hope this helps.
I did an exam I think 3 months ago and I got F Yesterday I did the same exam I did 3 months ago and got C+ is that good or bad?
Answers
Answer:
It's good. Because over those 3 months your grade increased.
Step-by-step explanation:
Answer: hii
Thats really good, That means you have improved a lot!
Step-by-step explanation:
If you got a f and then get a c later on it means you gotten better at the topic for the exam.
Hopefully this helps you!
- Matthew :)
A researcher estimates that a fossil is 3200 years old. Using carbon-14 dating, a procedure used to determine the age of an object, the researcher discovers that the fossil is 3600 years old.
Find the percent error
What other estimate gives the same percent error
Answers
Answer:
11.1%
Step-by-step explanation:
% error = [(3600-3200)/3600] * 100
= 11.1%
An apartment building contains 100 units. The one-bedroom units rent for $600 per month. When all the units are rented out, the total monthy rent paid by the tenants is $55,275. How many two-bedroom apartments are there?
O 45
O 66
O 55
O 50
Answers
Answer:
55
Step-by-step explanation:
Let x represent the number of one bedroom units and y represent the number of two bedroom units.
Since the apartment building contains 100 units:
1) x + y = 100
The total monthly rent paid by the tenants is $55,275, so:
2) 495x + 600y = 55275
Solving equation 1 and 2 gives:
x = 45, y = 55
So, there are 55 two-bedroom units in the apartment.
A farmer plants five apple trees in 25 minutes. If he continues to work at a constant rate, how long will it take him to plant 200 trees?
Answers
five apple trees in 25 mins.
to find:the duration he'll take to plant 200 trees.
solution:let the time taken to plant 1 tree be x.
5x=25
=>x=25/5-5 mins
time taken to plant 200 trees:
trees=200*5
=1000mins
=16.67 hours.
therefore, he'll take 16.67 hours to plant 200 trees.
trees=200*5
=1000 mins
=16.67 hours.
he will take 16.67hours to plant 200 trees.
what is the solution of y=-2x+4
Answers
Answer:
2x+4=y
Step-by-step explanation:
Y equals 2*x+4/2x+4 so you figure out what x equals the multiply it by 2, then add 4 and the number you get is how much y is.
If you didnt understand I am very sorry. I am trying my best to explain.
If 65 is 20% of x, then x = ?
Answers
Answer:
325
Step-by-step explanation:
I got it right before
Answer:
325
Step-by-step explanation:
You are analyzing the survey results tabulated below. The first survey question (yes/no) is whether the respondent is over 40, and the second survey question (low-cal, regular) is whether the respondent prefers your low-cal butter or the regular.
Answers
Answer:
Step-by-step explanation:
Select the place where the digit 6 sits in this number. 607,182
Answers
Answer:
Hundred Thousand
Step-by-step explanation:
Hundred Thousand
I hope it helped you
Answer:
Hundred thousand
Step-by-step explanation:
The digit 6 is in the hundred thousand place.
To understand place values, see the attached file.
[tex]\rule[225]{225}{2}[/tex]
The ratio of the number of peanuts to the number of cashews in a trail mix recipe is 5:3.
Complete the table to show the relationship between peanuts and cashews in the trail mix recipe. Enter a number in each box.
Answers
Answer:
40 and 16 for 8 servings
25 and 10 for 5 servings
15 and 6 for 3 servings
Step-by-step explanation:
Which of the following would best be solved using completing the square?
A) 2x^3 - 12x^2 + 5x - 30 = 0
B)5x^2 + 7x = 12
C) x^2 = 81
D) x^2 + 4x - 21 = 0
Answers
x over 4 space equals space 6 over 8 ; x=
Answers
Answer: x=3
Step-by-step explanation: This is a porportion, meaning that the numbers are set equal to each other. Look at your denominators, 4 and 8? What do they have in common? In this case, they have a factor of 2 in common, and 8 is 4x2. So then we look at the numerators now. What times 2 equals to 6? Your answer then becomes 3.
Please help I really need to know the answer or how to find the answer for this question
Answers
Upper left corner
==========================================================
Explanation:
There are 2 red out of 1+2+2 = 5 total. The fraction 2/5 represents the probability of picking red on the first selection.
Assuming the marble picked is not put back, we have 2 green out of 5-1 = 4 left over. So 2/4 = 1/2 is the probability of picking green as the second selection, based on the previous event in the first paragraph.
Multipling those fractions gets us (2/5)*(1/2) = (2*1)/(5*2) = 2/10 = 1/5 as the probability of picking red, then green with no replacement.
Are you getting enough sleep? Many kids aren’t getting enough sleep, and TV might be part of the problem. Among 2002 randomly selected 8- to 18-year-olds in the United States, 71% had a TV in their bedroom. What is the lower boundary of our confidence interval at the 99% level?
a. 6547
b. 6714
c. 6677
d. 6839
Answers
Using the z-distribution, it is found that the lower bound of the 99% confidence interval is given by:
d. 68.39%.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.In this problem, we have a 99% confidence level, hence[tex]\alpha = 0.99[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.
The sample size and estimate are given by:
[tex]n = 2002, \pi = 0.71[/tex]
Hence, the lower bound is given by:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.71 - 2.575\sqrt{\frac{0.71(0.29)}{2002}} = 0.6839[/tex]
Hence the lower bound is of 68.39%, which means that option D is correct.
More can be learned about the z-distribution at https://brainly.com/question/25890103
#SPJ1
PLEASE HELP ME!!!!! GIVING (17 POINTS)
Answers
Answer:
61.) A, B, A
62.) 120 minutes
Step-by-step explanation:
61.) 48 is a multiple of 6. A multiple is a number which can be fully divided into another number (divded without remainder). Therefore, 48 is a multiple of 6 because 6 * 8 = 48 meaning that 48/6 would equal 8. Because there is no remainder, Carly can put the beads into 6 equal groups.
62.) This is a simple conversion problem. Since they are asking the amount of minutes, you need to convert 2 hours to minutes. You do not need to calculate it or set up a formula because there are 60 minutes in one hour, therore, in 2 hours there are 120 minutes (60 minutes + 60 minutes).
At Freddy’s fro yo shop 25 percent of the 44 frozen yogurt flavors are sugar free how many frozen yogurt flavors are sugar free
Answers
need help will give brainlist
Answers
Answer:
3rd option
Step-by-step explanation:
- 1 ( [tex]\frac{3x}{2y}[/tex] )
- 1 is multiplying the complere fraction , not just 1 part of it , so
= - [tex]\frac{3x}{2y}[/tex]
An object was launched from the ground. The graph below shows the path that the object took. Use the graph to answer questions 9-10.
What is the domain?
What is the range?
Answers
Answer:
See below ~
Step-by-step explanation:
Domain
Range of x values in the graphIt is from 0 to 4⇒ 0 ≤ x ≤ 4Range
Range of y values in the graphIt is from 0 to 64⇒ 0 ≤ y ≤ 64Answer:
range is 4 domain is 64 i think
Step-by-step explanation:
Jerry is mowing his lawn.It takes him 1/6 of an hour to mow 3/20 of his yard. What proportion of the yard does jerry mow per hour
Answers
Answer:
If he mows 3/20 in 1/6 of an hour he'll mow 18/20 or 9/10 in one hour
which means the ratios are equal
1/6:3/20 = 1:18/20 = 1:9/10
Therefore, Jerry will mow 90% of the lawn in one hour
Step-by-step explanation:
Hope this helps:)...if not then sorry for wasting your time and may GOd bless you
Find the equation of the line shown
Answers
Answer:
the equation of the line is 2y-x-1
pls give brainliest
The tallest of a collection of wooden dolls stands 1 meter tall, and each successive doll is half as tall as the one before it. If there are 8 dolls in the collection, which is closest to the combined height of the dolls?
A. 1.5 meters
B. 2 meters
c. 3.1 meters
D. 4 meters
Answers
Answer:
the answer is a for approval
From an electronic shop, 34 washing machines were sold on a particular day. The price of one washing machine was 8,400. Find the total amount collected by selling the washing machines on that day
Answers
Answer:
$201,600
Step-by-step explanation:
Multiply 34 and 84, which is 2016. Then add 2 zeros at the end because there are 2 zeros in 8400. So, the answer is 201,600 dollars.
Help me guys!
Show that the locus of the middle points of normal chords of the parabola y² = 4ax is
y⁴ - 2a(x - 2a)y² + 8a⁴=0
Answers
Chord of Contact:-
The chord joining the points of contact of two tangents drawn from an external point to a parabola is known as the chord of contact of tangents drawn from external point.Equation of the normal chord at any point (at², 2at) of the parabola y² = 4ax is
y + tx = 2at + at³ ....(i)
Look at the attached figure
But if M (x₁, y₁) be it's middle point its equation must be also,
T = S₁
:⟹ yy₁ - 2a (x + x₁) = y₁² - 4ax₁
:⟹ yy₁ - 2ax = y₁² - 2ax₁ .....(ii)
Therefore, from eqs. (i) and (ii) are identical, comparing, them
[tex] \sf \frac{1}{y_1} = \frac{t}{ - 2a} = \frac{2at + {at}^{3} }{ {y_1}^{2} - 2ax} \\ \\ \sf \: from \: first \: two \: relations \: ,t = - \frac{2a}{y_1} ....(iii)\\ \\ \sf \: from \: first \: two \: relations \: , \: \frac{t}{ - 2a} = \frac{2at + {at}^{3} }{{y_1}^{2} - 2ax_1} [/tex]
[tex] \implies \sf \: \frac{{y_1}^{2} - 2ax_1}{ - 2a} = 2a + {at}^{2} \: \\ \\ \implies \sf \: \frac{{y_1}^{2} - 2ax_1}{ - 2a} = 2a + a \bigg \lgroup \frac{ - 2a}{y_1} { \bigg \rgroup}^{2} \qquad\{ \: from \: eqs. \: (iii) \} \\ \\ \implies \sf \:\frac{{y_1}^{2} - 2ax_1}{ - 2a} = \frac{2a{y_1}^{2} + 4 {a}^{3} }{{y_1}^{2}} \\ \\ \implies \sf \: {y_1}^{4} - 2ax_1 {y_1}^{2} = - 4 {a}^{2} {y_1}^{2} - 8 {a}^{4} \\ \\ \implies \sf \: {y_1}^{4} - 2a(x_1 - 2a){y_1}^{2} + 8 {a}^{4} = 0[/tex]
[tex] \sf hence, \: the \: locus \: of \: middle \: point \: (x_1,y_1) \: is \: \\ \\ \qquad \qquad \: \sf \: {y_1}^{4} - 2a(x_1 - 2a){y_1}^{2} + 8 {a}^{4} = 0[/tex]
What slope would make the lines
perpendicular?
y = -1/3x +5
y = [?]x+2
Answers
3
Step-by-step explanation:
When it comes to perpendicular lines, the slopes must be opposite reciprocals of one another. The reciprocal of -1/3 is -3, and the opposite of -3 is 3.