Answers
Answer:
[tex]\frac{dy}{dx}[/tex] = 8(2x + 3)³
Step-by-step explanation:
Differentiate using the chain rule
Given
y = f(g(x)) , then
[tex]\frac{dy}{dx}[/tex] = f'(g(x)) × g'(x)
Here
f(x) = [tex](2x+3)^{4}[/tex] ⇒ f'(x) = 4(2x + 3)³
g(x) = 2x + 3 ⇒ g'(x) = 2
Thus
[tex]\frac{dy}{dx}[/tex] = 4(2x + 3)³ × 2
= 8(2x + 3)³
Related Questions
the volume of a box is 45x^3 + 198x^2 + 189x. find expressions for the possible dimensions of the prism
Answers
Answer:
length, width, and height are (b+2), (b-2), (b+3)
Step-by-step explanation:
Doing what the problem statement tells you to do, you get ...
(b^3 +3b^2) -(4b +12)
= b^2(b +3) -4(b +3) . . . factor each pair of terms
= (b^2 -4)(b +3) . . . write as a product
= (b -2)(b +2)(b +3) . . . use the factoring of the difference of squares
The three factors are (b-2) , (b+2) , and (b+3). We have no clue as to how to associate those with length, width, and height. We just know these are the dimensions of the box.
The possible dimensions of the prism are:
Length: 9x, 5x + 7, or x + 3
Width: 5x + 7, x + 3, or 9x
Height: x + 3, 9x, or 5x + 7
What is a prism?A prism is a three-dimensional object.
There are triangular prism and rectangular prism.
We have,
To find the possible dimensions of the prism, we need to factor the given volume expression into three factors, each representing the length, width, and height of the box.
We start by looking for common factors among the coefficients of the three terms:
45x³ + 198x² + 189x
= 9x (5x² + 22x + 21)
Now we can factor the quadratic expression inside the parentheses:
5x² + 22x + 21
= 5x² + 15x + 7x + 21
= 5x(x + 3) + 7(x + 3)
= (5x + 7) (x + 3)
The volume expression can be factored as:
45x³ + 198x² + 189x
= 9x (5x + 7) (x + 3)
Thus,
The possible dimensions of the prism are:
Length: 9x, 5x + 7, or x + 3
Width: 5x + 7, x + 3, or 9x
Height: x + 3, 9x, or 5x + 7
Learn more about prism here:
https://brainly.com/question/12649592
#SPJ2
What number is missing from the table of equivalent ratios?
A. 2
B. 5
C. 7
D. 13
Answers
Answer:
Step-by-step explanation:
The answer would be 5 because 14/7=2 and 6/3=2 and 10/ 2 =5 so 5
Identify the slope in the equation y=-7/3x +5 5 -5 7/3 -7/3
Answers
Answer:
-7/3
General Formulas and Concepts:
Algebra I
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptStep-by-step explanation:
Step 1: Define
y = -7/3x + 5
Step 2: Break Function
Identify Parts
Slope m = -7/3
y-intercept b = 5
i don’t know how to do this and it’s due in an hour someone help please
Answers
Answer:
912 divided byt he square root of AB to 5^2
Step-by-step explanation:
Answer:
AB to 5^2
Step-by-step explanation:
Flattykawa -_-
The table shows the balance of an account each year.
Years Balance
0 $40
1 $42
2 $44
3 $46
What is the interest rate of the account?
Answers
Answer:
+2 each year. 40+(2+y), y being years.
4. Chrissy had 4 gallons of gas in her tank when she arrived at the
gas station. She pumped gas into her car at a rate of 0.3 gallon per
second. How many gallons of gas were in the tank after s seconds?
Answers
Here is a list of numbers:
4.6, 3.9, 6.8, 8.6, 3.5, 0.8, 8.5, 2.8, 2.6
State the mediant
Answers
Answer:
median is 3.9
Step-by-step explanation:
You arrange them all from the smallest to the biggest, then cross out pairs from each side till you get the one in the middle
0.8, 2.6, 2.8, 3.5, 3.9, 4.6, 6.8, 8.5, 8.6
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
Norma is looking for a job cutting hair. One option is self-employment at The Seaside Salon, where she would pay $534 per month to rent a station and keep all of her earnings. Another option is to work at a franchise, where she would just have to pay the salon $3 for every haircut. If she performed a certain number of haircuts every month, the amount paid to either salon would be the same. How many haircuts would that be? How much would Norma pay?
If Norma performed__________ haircuts in a month, she would pay $____________ to either salon.
Answers
Answer:
If Norma performed 178 haircuts in a month, she would pay $534 to either salon
Step-by-step explanation:
Saloon 1:
Cost of saloon 1 = $534
Saloon 2:
Cost of saloon 2 = 3h
Where,
h = number of haircut
Equate the cost of renting either saloon
534 = 3h
h = 534 / 3
h = 178 hair cut
If Norma performed 178 haircuts in a month, she would pay $534 to either salon.
What is the range of the following numbers:
12,20,18,25,6
Answers
Answer:
19
Step-by-step explanation:
You need to find the biggest and smallest number; 25,6
Then you subtract 6 from 25
25-6=19
I hope this helps!!!!!!!
Answer:
19
Step-by-step explanation:
The range is the difference between the highest and the lowest number
So 6, 12, 18, 20, 25 and 25-6 = 19
(2k^3 - 7k^2 + 3k) - (-4k^2 + 5k) in polynomial standard form PLEASE HELP
Answers
Answer:
2 k 3 − 3 k 2 − 2 k
Step-by-step explanation:
Answer: ...
2k^3−3k^2−2k
2x-4(x-1)=10
I keep getting -3 but I know it's not right
Answers
I do think that it is -3 tho
Answer:
Step-by-step explanation:
2x=10+4
2x=14
14/2 = 7
X=7
Please help me with the questions please
Answers
Answer:
50,373 feet
Step-by-step explanation:
tan 15° = 13500 / x
.268 = 13500 / x
x = 50,373
How many 1/2's are in 3 1/2? *
Answers
Answer:
Step-by-step explanation:
7
Answer:
7
Step-by-step explanation:
3.5 divided by .5
What is the volume of a rectangular box that measures 3 by 8 by 20 inches?
488 cubic inches
0 480 cubic inches
O 31 cubic inches
O 44 cubic inches
Answers
What is the slope of the line
Answers
Answer:
Positive, Upward Slope.
Step-by-step explanation:
Answer:
the slope of a line shows how steep a straight line is, or the direction of a straight line
C=S + 16
The variable s represents the number of additional sticks of butter Max buys, and the variable
c represents the total number of cakes he can bake. How many additional sticks of butter
does Max need in order to bake a total of 17 cakes?
Answers
what is the value of (f – 9)(144)?
Answers
144(f-9)
144f- (144•9)
144f-1296
The Benton family uses up a 1/2 gallon jug of milk every 3 days. At what rate do they drink milk?
Answers
Answer:
1/6
Step-by-step explanation: in a rate you need to make it a one so you double the 1/2 gallon to make it one gallon then since you doubled that you have to double the days to 6. So they drink 1 gallon per 6 days.
2x-8y=16 solve for x
Answers
Answer:
x=8+4y
Step-by-step explanation:
Add 8y to both sides:
2x=16+8y
Divide both sides by 2:
x=8+4y
A spinner is divided into 10 congruent sections. Each section is labeled with a number as shown. The spinner will be spun one time. What is the probability that the arrow will land in a section that is labeled with a number that is a multiple of 2? 1 A U 9 un 6 3 B 1 10 2 09 4 1 1 / 2 UN
Answers
Answer:
b
Step-by-step explanation:
The five marathon runners weigh an average weight of 92 pounds, Nicole weighs 89 pounds, Jon weighs 95 pounds, Jenny and Kim weigh 90 pounds each, How much does Jordin weigh?
Answers
Answer:
Jordin weighs 96 pounds
Step-by-step explanation:
The Mean Value of a Data Set
The mean or average of a data set is found by adding all numbers and then dividing by the number of values in the set. Written as a formula:
[tex]\displaystyle \bar x=\frac{\sum x_i}{n}[/tex]
Where xi is the value of each data and n is the total number of values.
We are given the average weight of n=5 marathon runners:
[tex]\bar x=92[/tex]
Multiplying the formula by n and expanding the sum:
[tex]n\bar x=\sum x_i=x_1+x_2+x_3+x_4+x_5[/tex]
We are given the weighs of four of the runners:
[tex]5*92=89+95+90+90+x_5[/tex]
[tex]460=364+x_5[/tex]
Solving for x5:
[tex]x_5 = 460-364=96[/tex]
Jordin weighs 96 pounds
-324/18
Plz show all the steps of how you got the answer.
Answers
Answer:
-18
Step-by-step explanation:
Step 1 - divide the numerator and denominator by 18
-324÷18 / 18÷18
Step 2 - divide the numbers
-18 / 18÷18
-18/1
any expression divided by 1 remains the same
-18
Isabel ran for president of the chess club, and she received 12 votes. There were 15 members in the club. What percentage of the club members voted for Isabel?
Answers
Answer:
80%
explanation:
just looked up "what percentage is 12 out of 15 and it gave me an answer"
just do this for all ur other questions like this
y=x+3
y=x-3
Solve these equations
Answers
Answer:
what is x?
Step-by-step explanation:
Answer:
No solutions
Step-by-step explanation:
Lin and Elena have discovered they have so much in common. They each have a fish tank holding 20 units of water. Whose tank holds 20 gallons, and whose holds 20 cups?
Answers
Answer: a. Lin's tank hold 20 cups and Elena's tank hold 20 gallons; I know this because gallons are greater than cups.
Step-by-step explanation:
Gallons are greater than cups so the fish tank that will hold 20 gallons would have to be the bigger one which in this case is Elena's.
With cups being lesser in quantity than gallons, the fish tank that will hold 20 cups of water will definitely have to be the smaller one which in the case is Lina's.
Solve for n: 2n < 6
Math pls answer this
Answers
Answer:
n can be a number less than 3
Step-by-step explanation:
Hope this helps!
Answer:
N<3
Step-by-step explanation:
Solve for x. I need help :,) thank you if you help!
Answers
Answer: if its a multiple of a 345 triangle then its congruent x is 36 if othersides ate multiples of 20 ie
Sides are
60 80 100 is a 345 right triangle
Step-by-step explanation:
Lance has 12 boxes of comic books. Each box has 40 comic books in it.
How many comic books does Lance have?
Answers
Answer:
480
Step-by-step explanation:
12*4=48 then add a zero to the end of it
hope that helps!
happy new year!
Answer:
Lance has 480 comic books.
Step-by-step explanation:
Multiply 12 by 40:)
what is the answer to 5--4
Answers
Answer:
9
Step-by-step explanation:
if you have two negatives next to eachother, the equation now adds like 5+4. 5+4=9
Identify the like terms.
7 + 4p - 5 + p + 2y
A: 4p, -5, 2y
B: 4p, p, 2y
C: 7, 5 AND 4p, p
D: 7, -5 AND 4p, p
Answers
Answer:
D:7, -5 AND 4p,p
Step-by-step explanation:
B/c like terms are terms with the same variable and exponent.
If it's helpful ❤❤
THANK YOU.