given the function f(x)=-2x^4-16x^3-36x^2, determine all intervals on which f is both decreasing and concave down
Answer:
(0, ∞)
Step-by-step explanation:
The only maximum, local or otherwise, is at x=0. Since the leading coefficient is negative, the function is decreasing and concave down for x-values greater than 0.
0 < x < ∞ . . . . . decreasing and concave down
__
Since the leading coefficient of this even-degree function is negative, it will have a generally ∩ shape. It will be decreasing to the right of any local maximum.
The first derivative is negative only for x > 0, so that is the only region where the function is decreasing. Since that x=0 is a local maximum, the function must be concave downward in that neighborhood.
__
The attached graph shows the function and its first and second derivatives. The function is concave down where the second derivative is negative, to the right of the right-most point of inflection.
_____
Additional comment
A graphing calculator provides a quick answer to a question like this. You can find the same answer algebraically.
The first derivative is ...
f'(x) = -8x^3 -48x^2 -72x = -8x(x^2 +6x +9) = -8x(x+3)^2
This has a zero at x=-3 where the graph of it touches the x-axis, but does not change sign. That means f(x) has a flat spot at x=-3, but is not decreasing except to the right of x=0.
The second derivative is ...
f''(x) = -24x^2 -96x -72 = -24(x^2 +4x +3) = -24(x +1)(x +3)
The second derivative will be negative for x < -3 and x > -1, to the left and right of the points of inflection. This means f(x) is concave upward only for -3 < x < -1, and concave downward everywhere else.
The function is concave downward and decreasing for x > 0.
What is the answer for 3x-7y=4 solve for y
y = [tex]\frac{4-3x}{7}[/tex]
Answer:
[tex]y = \frac{ - 4 + 3x}{7} [/tex]
Step-by-step explanation:
follow the steps in the previous answer, but
negative divided by a negative is positive
what is the answer for 4x<-28
Answer:
x < -7
Step-by-step explanation:
Divide both sides of the equation by the coefficient of x.
(4x)/4 < (-28)/4
x < -7
Answer:
x<-7
Step-by-step explanation:
Sheri is making 4 pounds of mixed nuts. She will use One-third the amount of macadamia nuts as she does almonds. A graph titled Sheri's Mixed Nut Recipe has pounds of macadamia nuts on the x-axis, and pounds of almonds on the y-axis. 2 lines intersect at (1, 3). How many pounds of each nut will she use? 1 pound of macadamia nuts; 3 pounds of almonds 3 pounds of macadamia nuts; 1 pound of almonds 4 pounds of macadamia nuts; no almonds 4 pounds of almonds; no macadamia nuts.
1 pound of macadamia nuts; 3 pounds of almonds of each nut will she use.
Given that,
Sheri is making 4 pounds of mixed nuts.
She will use One-third the number of macadamia nuts as she does almonds.
A graph titled Sheri's mixed nut recipe has pounds of macadamia nuts on the x-axis, and pounds of almonds on the y-axis. 2 lines intersect at (1, 3).
We have to find,
How many pounds of each nut will she use?
According to the question,
Total mixed nuts are 4 pounds,
She will use One-third the number of macadamia nuts as she does almonds.
2 lines intersect at (1, 3).
Therefore,
Sheri's mixed nut recipe has pounds of macadamia nuts on the x-axis,
At x-axis, the point 1 lies.
So, macadamia nuts have 1 pound.
And pounds of almonds on the y-axis,
At y-axis, the point 3 lies.
So, almond nuts have 3 pounds.
Hence, 1 pound of macadamia nuts; 3 pounds of almonds of each nut will she use.
For more details about Graphs refer to the link given below.
https://brainly.com/question/9351049
Answer:
A/ the first one
Step-by-step explanation:
Did the edg
Right Triangle ABC has sides of length 5 units, 12 units and 13 units. The triangle is dilated by a scale factor of 3 around point B. What is the area of triangle A'B'C'?
Answer:
Step-by-step explanation:
Multiply each # by 3 so 15 36 39
(15x36)/2=270
I'm sorry if its wrong.
The area of the right-angle triangle A'B'C' will be 450 square units.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.
Right Triangle ABC has sides of length 5 units, 12 units, and 13 units. The triangle is expanded by a scale element of 3 around point B.
Then the dimension of the right triangle is given as,
A'B' = 3 x 5 = 15 units
B'C' = 12 x 5 = 60 units
A'C' = 13 x 5 = 65 units
The area of the right-angle triangle A'B'C' will be given as,
A = (1/2) x 15 x 60
A = 15 x 30
A = 450 square units
The region of the right-point triangle A'B'C' will be 450 square units.
More about the dilation link is given below.
https://brainly.com/question/2856466
#SPJ2
Sally earns commission for selling cars at the Nissan dealership. She earns 5.5% on
every car she sells. Last month, she sold 7 cars for a total of $160,000. What was
Sally's commission last month?
Answer:
8800
Step-by-step explanation:
Question is on the pic!
Answer:
C
Step-by-step explanation:
C has 2 negative 2's on it, and 2 numbers on the x side cannot be the same.
Answer:
C
Step-by-step explanation:
If your x Collum has more than one of the same numbers so in this case -2 is there twice it's not a function
X 1 1 2 3 4
________________________________________________________
Y 0 3 4 2 6
this would not be a function because the one is at two different heights.
if you think of every number as a person and the y axis as height. two different people can be the same height but one person cannot be two different heights at the same time. if it's on a graph use the vertical line test take a vertical edge of a paper and run it across the graph if the edge of paper goes through more than one point it's not a function
?????????????????????
Step-by-step explanation:
Distributive property
(repost) Please help! It involves inequalities! Also please include a number line.
Answer:
-5 ≤ x
Step-by-step explanation:
2(x -3) -5x ≤ 9 . . . . . given
2x -6 -5x ≤ 9 . . . . . . eliminate parentheses
-3x -6 ≤ 9 . . . . . . . . combine like terms
-6 ≤ 9 +3x . . . . . . . add 3x
-15 ≤ 3x . . . . . . . . subtract 9
-5 ≤ x . . . . . . . . . divide by 3
__
The point x=-5 is included in the solution set, so there is a sold dot at that point. The rest of the solution set is values of x that are greater than that value, so the number line is shaded to the right of that point. Your number line should show an arrow at the right end of the graph to indicate it extends that direction indefinitely. (My graphing program doesn't draw arrows easily.)
_____
Additional comment
Perhaps the most straightforward way to solve this would have been to add 6 instead of 3x. That would give ...
-3x ≤ 15
Then dividing by -3 would give x. That operation would reverse the inequality symbol (because the divisor is negative). Then you would have ...
x ≥ -5
Either way works. We judge it to be less confusing when we don't have to change the direction of the inequality symbol.
it takes a 1/4 bottle glue to make slime if teacher has 15 bottles of glue how many bottles of slime can the 5th graders make
Answer:
60students
Step-by-step explanation: 4 x 15=60
This is because each bottle can make 4 slimes and if there are 15 bottles you multiply 4 by 15. Now you will receive 60.
a water tank can hold up 80 gallons of water. if it is 40% full now. how many gallons of water does the tank contain?
Answer:
32 gallons of water
Step-by-step explanation:
If the total tank can hold up to 80 gallons of water, it is considered full when it contains 80 gallons. When the tank is 40% full, it has 40% of 80 gallons in the tank. 40% of 80 is 40/100*80=8*4=32 gallons of water.
Find the area of ΔABC.
A)21.93
B) 37.20
C) 29.77
D) 18.6
Answer:
Option D is correct
Step-by-step explanation:
First, let's find side BC by using Pythagoras theorem.
Given:
Hypotenuse = 9 unitsSide 1: 7.8 unitsSide 2: BC=> 9² = 7.8² + x²
=> 81 = 60.84 + BC²
=> BC² = 20.16
=> √BC² = √20.16
=> BC = √20.16
=> BC = 4.48998886413 (Using calculator)
=> BC ≈ 4.49 (Estimated)
Therefore, side BC ≈ 4.49 units. Now, let's find the area by using hero's formula.
=> 1/2(Perimeter) = S
=> Perimeter: Hypotenuse + Side 1 + Side 2
=> 7.8 + 9 + 4.49
=> 21.29 = Perimeter
=> 1/2(21.29) = S
=> 10.645 = S
=> √s(s - a)(s - b)(s - c) = Area of triangle
=> √10.645(10.645 - 9)(10.645 - 4.49)(10.645 - 7.8)
=> √10.645(1.645)(6.155)(2.845)
=> √10.645 x 1.645 x 6.155 x 2.845
=> √306.635120999 (Using calculator)
=> √306.64 (Estimated)
=> 17.5111393119 (Using Calculator)
=> 17.51 units² (Estimated)
We can see that option D is the closest option. Therefore, Option D is correct.
If Option D was incorrect, then my second opinion is A.
If both are wrong, I deeply apologize for the inconvenience caused by me. Hoped this helped.
Answer:
answer is d) 18.6
Step-by-step explanation:
area = 1/2ab sin ∅
a= 9
b = 7.8
so it's
1/2 ×7.8 × 9 sin 32
use your calculator to get 18.600 unit squared
*we can also use the heroes formula*...
Find the area of the shape
Answer:
400 [tex]ft^{2}[/tex] (Don't forget the square symbol!)
Step-by-step explanation:
For the triangle:
Base times height divided by 2.
8 x 25 = 200
200/2 = 100
For the regtangle:
Width times height.
25 x 12 = 300
Add them together, and you get:
100 + 300 = 400.
Answer:300
Step-by-step explanation:25*12=300
25
x12
50
250+50=300
Order the following numbers from least to greatest:
30% 3% 0.003 1/300 1.3 30,000/100 30
Step-by-step explanation:
30%=0.3
3%=0.03
1/300=0.003333
30000/100=300
Therefore the order is:
0.003;1/300;3%, 30%;1.3;30;30000/100
Answer:
Step-by-step explanation:
30%=0.3
3%=0.03
1/300=0.003333
30000/100=300
Therefore the order is:
0.003;1/300;3%, 30%;1.3;30;30000/100
Round 2593.6781 to nearest thousandths.
Answer:
The answer is 2593.678
Step-by-step explanation:
A function f() is graphed on the coordinate plane.
What is the function rule in slope-intercept form?
Enter your answer in the box
Answer:
i dont know but some one will help freeee points
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
Find each percent increase round to the nearest percent from 86 books to 140 books
Answer: 61%
Step-by-step explanation:
Drake is playing basketball. He knows that he can score one, two, or three-point shots in a game, and he has already scored 5 points this game. He wants to score at least 20 points before the game ends.
Answer: He needs to splash the threes
Step-by-step explanation: He dosent have the vertical so he just needs to have a splashy 3 pointer
smiplify 3^2 x 3^4 x 3^6
PLEASE ANSWER QUICKLY
[tex] {3}^{2} \times {3}^{4} \times {3}^{6} [/tex]
[tex] = {3}^{2 + 4 + 6} [/tex]
[tex] = {3}^{2 + 10} [/tex]
[tex] = {3}^{12} [/tex]
(-3x+4)+(x-9) help please.
Answer:
- 1 · (2×±5)Step-by-step explanation:
Answer:
−2−5
Step-by-step explanation:
(-3x+4)+(x-9)
−3x+4+x−9
Subtract
−3x+4+x−9
-3−5+
Combine terms
−3x−5+x
−2−5
Pls po pahelpp ..... Kahit po paturo lng pra po matapos ko po
Answer:
ngee hirap Naman niyan sayang
1. Each of 9 friends chooses her favorite positive integer
a. The median of the chosen number is 91, what is the smallest the average of the 9 chosen numbers could be?
b. The median of the chosen number is 91, is there an limit to how large the aerge of the chosen numbers can be? If so, what is the largest the average can be?
c. The average of the chosen number is 91, what is the smallest the median of the 9 chosen numbers could be?
d. The average of the chosen numbers is 91. What is the largest the median of the chosen numbers could be?
Answer:
a) 1
b) There is no limit to which the largest number can be because we are only given information about the median.
c) 1
d) 90
A glass top of an office table has sides of 21 inches. What is its area?
Answer:
441 [tex]inches^{2}[/tex]
Step-by-step explanation:
If this is a rectangle, meaning the width and the legnth is different, there is no way in solving this.
However, if it is a square, meaning all the sides are the same,
we can know that every side is 21 inches long.
An area is the width times the length, which is both 21 in this case.
21 times 21 = 441.
441 inches squared.
Aaron noticed that he caught 8 pidgeys for every Squirtle when he played Pokémon Go. If Aaron caught 104 Pidgeys how many Squirtles did he catch?
Answer:
He caught 13 squirtles
Step-by-step explanation:
104/8 = 13 squirtles
Squirtles divided by pidgeys
A bakery sells glazed donuts for $1.09 each. Cinnamon bagels and onion bagels are $1.59 each. Max buys x donuts, y cinnamon bagels, and z onion bagels. Which expression represents the total amount Max spent at the bakery?
A.
1.09x + 1.59yz
B.
1.09x + 1.59y + 1.59z
C.
1.09x + 3.18(y + z)
D.
(1.09 + 1.59)(x + y + z)
Answer:
B
Step-by-step explanation:
For each glazed donut, Max spends $1.09. Therefore, if he buys x donuts, he pays $1.09 x times, or $1.09 * x. Similarly, for cinnamon bagels, he pays $1.59 * y, and for onion bagels, he pays $1.59 * z. Adding these up, we get
1.09x + 1.59y + 1.59z
A plumber charges a $25 flat rate. If he works for 6 hours, how much does he charge per hour if the total is $67?
Answer:7
Step-by-step explanation:(67-25) divided by 6
mark as brainliest
Subtract the flat rate from the total first:
67-25 = 42
Now divide that by total hours:
42/6 = 7
Answer: $7 per hour
Can someone help me out?
Answer:
d
Step-by-step explanation:
Combine the like terms to create an equivalent expression.
\large{9y+y}9y+y
Answer:
20y
Step-by-step explanation:
t - 2 2/3 = - 5/2
A. 1/6
B. -1/6
C. 4 1/3
D. -4 1/3
2/3x + 5/6=3 1/3 I need it in as a mixed number in it's simplest form please
Answer:
3 3/4
Step-by-step explanation:
