for x=2....value will be 53
for x=7.....value will be 33
brainliest......
graph A represents the function f(x)=^3 graph B and C are transformations of graph A
Answer:
A3
Step-by-step explanatio
Let f(x) = x^6( x − 8 )^7 / (x^2 +2)^2
Use logarithmic differentiation to determine the derivative.
f ' (x) =________
If
f(x) = x⁶ (x - 8)⁷ / (x² + 2)²
then taking the logarithm of both sides lets us expand the right side as
ln(f(x)) = ln(x⁶ (x - 8)⁷ / (x² + 2)²)
ln(f(x)) = ln(x⁶) + ln((x - 8)⁷) - ln((x² + 2)²)
using the property ln(ab) = ln(a) + ln(b).
We can also use the property ln(aⁿ) = n ln(a), so that
ln(f(x)) = 6 ln(x) + 7 ln(x - 8) - 2 ln(x² + 2)
Then differentiating both sides using the chain rule gives
f'(x)/f(x) = 6 x'/x + 7 (x - 8)'/(x - 8) - 2 (x² + 2)'/(x² + 2)
f'(x)/f(x) = 6 (1)/x + 7 (1)/(x - 8) - 2 (2x)/(x² + 2)
f'(x)/f(x) = 6/x + 7/(x - 8) - 4x/(x² + 2)
Solve for f'(x) :
f'(x) = (6/x + 7/(x - 8) - 4x/(x² + 2)) f(x)
and replace f(x) with the given function :
f'(x) = (6/x + 7/(x - 8) - 4x/(x² + 2)) • x⁶ (x - 8)⁷ / (x² + 2)²
We can expand the product :
f'(x) = 6 x⁵ (x - 8)⁷ / (x² + 2)²+ 7x⁶ (x - 8)⁶ / (x² + 2)² - 4x⁷ (x - 8)⁷ / (x² + 2)³
then simplify by factoring :
f'(x) = x⁵ (x - 8)⁶/(x² + 2)³ • (6 (x - 8) (x² + 2) + 7x (x² + 2) - 4x² (x - 8))
Simplify the rest :
f'(x) = x⁵ (x - 8)⁶ (9x³ - 16x² + 26x - 96)/(x² + 2)³
expand the function f(x)=(x+5)^3
The function f(x) = (x + 5)³ when expanded is f(x) = x³ + 15x² + 75x + 125
How to expand the function?The function in the equation is given as
f(x) = (x+5)^3
Rewrite this function properly
So, we have the following representation
f(x) = (x + 5)³
Solving further, we need to expand the expression into factors
So, we have the following representation
f(x) = (x + 5)(x + 5)(x + 5)
Next, we expand the first two brackets in the equation
This gives
f(x) = (x² + 5x + 5x + 25)(x + 5)
Evaluate the like terms
This gives
f(x) = (x² + 10x + 25)(x + 5)
Solving further, we need to expand the last two brackets
So, we have the following representation
f(x) = (x³ + 5x² + 10x² + 50x + 25x + 125)
Evaluate the like terms
This gives
f(x) = (x³ + 15x² + 75x + 125)
Remove the brackets
So, we have
f(x) = x³ + 15x² + 75x + 125
Hence, the function is f(x) = x³ + 15x² + 75x + 125
Read more about functions at
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Find the volume of a pyramid with a square base, where the perimeter of the base is 18.1 ft and the height of the pyramid is 28.1 ft. Round your answer to the nearest tenth of a cubic foot.
Answer:
191.8
Step-by-step explanation:
Hope this helps!
Step-by-step explanation:
the volume of a pyramid is
base area × height / 3
the base area here is a square.
we know its perimeter : 18.1 ft, which is 4 times the side length.
so, one side of the square is :
18.1/4 = 4.525 ft
the area of the square is side² = 4.525² = 20.475625 ft²
we also know the height of the pyramid, so the volume is :
Vp = 20.475625 × 28.1 / 3 = 191.7883542 ft³
the rounded volume of the pyramid is 191.8 ft³
write a two column proof. given: ab is congruent to ed, ca is congruent to ce; ac bisects bd. Prove abc is congruent edc.
Given that, AB ≅ ED, CA ≅ CE, and AC bisects BD, the two-column proof that shows ΔABC ≅ ΔEDC by SSS Congruence Theorem is shown in the image attached below.
What is the SSS Congruence Theorem?The side-side congruence theorem (SSS) states that if two triangles has three pairs of sides that are congruent to each other, then both triangles are congruent.
We are given the following information:
AB ≅ EDCA ≅ CEAC bisects BDSince AC bisects BD, therefore the third pair of sides of ΔABC and ΔEDC, BC and CD, will be congruent.
Therefore, it implies that both triangles has three pairs of congruent sides (AB ≅ ED, CA ≅ CE, and BC ≅ CD), which meets the criterion of the SSS Congruence Theorem.
Therefore, ΔABC ≅ ΔEDC by SSS Congruence Theorem.
The two-column proof that shows ΔABC ≅ ΔEDC by SSS Congruence Theorem is shown in the image attached below.Learn more about the SSS Congruence Theorem on:
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HELP
find the a,b,c of this table
Answer:
a = b = 1 , c = - 8
Step-by-step explanation:
ax² + bx + c = y
( - 5 )² a - 5b + c = 12
c = - 8
3² a + 3b + c = 4
25a - 5b - 8 = 12 ⇔ 25a - 5b = 20 ⇔ 5a - b = 4 ........ (1)
9a + 3b - 8 = 4 ⇔ 9a + 3b = 12 ⇔ 3a + b = 4 .......... (2)
(1) + (2)
8a = 8 ; a = 1
b = 1
y = x² + x - 8
Lisa has $200 in her savings account. This is 40% of the money she needs to take a weekend trip. What is the total cost of the trip she wants to take?
The total cost of the trip Lisa wants to take over the weekend is $500.
Let the total cost of the trip be T.Given the following data:
Savings account balance = $200Percent of trip expenses = 40%To determine the total cost of the trip Lisa wants to take over the weekend:
Since the percentage of the money in Lisa's savings account is equal to forty percent (40%) of what is required for the total cost of the trip. Thus, we would multiply the total cost of her trip by 40% and equate it to $200.
Total cost of her trip:
[tex]\frac{40}{100} \times T = 200\\\\0.4T=200\\\\T=\frac{200}{0.4}[/tex]
Total cost, T = $500.
Read more: https://brainly.com/question/2021001
How much is 1/9 of 3/8 (in lowest terms)?
A)4/17
B)03/17
C)1/36
D)1/24
Answer:
1/24
Step-by-step explanation:
multiply 1/9 and 3/8. The product of the two factors is 3/ 72. Seeing the two factors on the other hand, we can cancel out 3. Hence the final answer to this problem in lowest terms becomes 1/24.
A student is told to work any 8 out of 10 questions on an exam. In how many different ways can he complete the exam
Answer:
Step-by-step explanation:
Assuming the order in which he answers the questions matter the answer is the number of permutations of 8 in 10.
This is 10! / (10-8)!
= 1,814.400.
If the order does not matter then the answer is the number of combinations of 8 from 10:
This is 10!/8!*2!
= 45.
which statement about decision making analysis is false
Answer: Id personally say D
Step-by-step explanation:
If you have to fly from JFK airport in New York to LAX airport in Los Angeles, you will fly 2,475 miles. If the average amount of time for a plane to fly from JFK to LAX is 5 hours and 30 minutes, what is the average speed that a plane flies on this trip? Include the appropriate units.
Answer:
450 miles / hour or 201.17 meters/second
Step-by-step explanation:
Speed = distance / time
Distance = 2475 miles
Time = 5 hours and 30 minutes
I will solve this in both miles per hour and meters per second and I am unaware of the appropriate units for your class.
Since 30 minutes = 1/2 an hour, 5 hours and 30 minutes = 5.5 hours
2475 miles / 5.5 hours = 450 miles / hour
1609.34 meters = 1 mile
3600 seconds = 1 hour
450 miles / hour * 1609.34 meters/1 mile * 1 hour/3600 seconds = 201.1675 meters/second (can round to 201.17)
Note that when multiplying, I am simply multiplying the result by 1. Since
1609.34 meters = 1 mile , 1609.34 meters/1 mile = 1 if I divide both sides by 1. Because I multiply by 1, the number is still the same. In terms of the numerator and denominator, I choose which is which by analyzing which units should cancel out. For example, I multiply by 1 hour/3600 seconds because in miles/hour, hour is on the bottom, and hour is on the top in hours/seconds.
subtract 8 and 1/5 - 4 2/5
Answer: = -3
Step-by-step explanation:
Help help help math math
Answer:
Step-by-step explanation:
You already have the slope. It is + 1 as in y = (+1)x when you have been given
y = x + b
That means all you need do is subtract to find out what b is
y = x + b
x = 5
y = 11
Difference is 11 - 5 = 6
Try it a couple more times.
x = 10
y = 16
y = x + b
16 = 10 + b Subtract 10
16 - 10 = b
b = 6 just as it did before.
y = x + b
x = 20
y = 26
26 = 20 + b Subtract 20
26-20 = b
b = 6
So ? = 6
Round 743,214 to nearest ten thousand
6. Expand the brackets: a) 3(x - y) )
Answer:
3x-3y
Step-by-step explanation:
3(x-y)
open the brackets:
(3×x)-(3×y)
= 3x-3y
JoAnn bought 18 apples for $12.42. What was the price for 1 apple?
Answer: $1.45
Step-by-step explanation:
18/12.42 = $1.45
165 of the city library members are children if there are 750 total members
Answer:
Step-by-step explanation:
Not sure what you require but (165/750) * 100
= 0.22 * 100
= 22% are children
Fid the value of the expression
Answer:
2
Step-by-step explanation:
The question askes what is k divided by m (k/m) when k is equal to 8 and m is equal to 4. So, plug the values into the original questions 8÷4. This means that the number 8 is being split into 4 groups. When 8 is divided into 4 groups each group is left with 2. Therefore, the answer is 2.
Another way to solve this is to make a fraction. 8÷4 is the same as 8/4. If you simplify that fraction you also get 2.
Circle A was dilated with the origin as the center of dilation to creat circle b
Answer: The answer is B.)
Have a great Day/Night!
A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 3 large boxes and 2 small boxes has a total weight of 59 kilograms. A
delivery of large boxes and 4 small boxes has a total weight of 149 kilograms. How much does each type of box weigh?
a
Victoria wants to purchase a skateboard. She has $125 to spend. She finds one that regularly sells for $140 and is on sale for 15% off. Sales tax is 7%.
Victoria says that she has enough money to buy the skateboard. Is she correct?
What is the height of a cylinder if the radius is 6 cm and volume is 904.78
Answer:
8 cm
Step-by-step explanation:
h = v/(pi r^2)
h = 904.78/ (3.1415 * 6^2)
America says that the point (0,0) on the graph below means that you use no sugar if you make 1 pie. Is America correct?
Answer:
America is correct
Step-by-step explanation:
it says 0,0 and then it would mean it wouldn't have any sugar in the pies
Answer:
No, America's wrong.
If you look on the graph, as the line increases you can see one pie needs around 3/4(not accurate). (0,0) is the origin point. No sugar is used, and no pie was made.
What is 5 x 2 3/10 as a mixed number in the simplest form
?
Answer:
11 1/2Step-by-step explanation:
5 × 2 3/10 = 5 × (2 + 3/10) =5 × 2 + 5 × 3/10 = 10 + 3/2 = 10 + 1 1/2 =11 1/2[tex]\large{{\sf{5 \times 2 \frac{3}{10} = \frac{115}{10} = \frac{115 \div 5}{10 \div 5} = \frac{23}{10} = {\large{\underline{\boxed{\sf{\green{11 \frac{1}{2} }}}}}}}}} \\ [/tex]
Larry wishes to invest $1500. he can invest in an investment club which pays simple interest of 8% for 3 years. what is the amount in his account after three years?
A. $1830
B. $1860
C. $5024
D. $1524
Ten men and ten women are to be put in a row. Find the number of possible rows if Beryl, Carol, and Darryl want to stand next to each other in some order (such as Carol, Beryl, and Darryl, or Darryl, Beryl and Carol).
Answer: 6 possibilities.
Carol, Beryl, and Darryl
Carol, Darryl, and Beryl
Darryl, Carol, and Beryl
Darryl, Beryl, and Carol
Beryl, Darryl, and Carol
Beryl, Carol, and Darryl
Hope this helps :)
Solve for x (13x + 2) (5x - 7) (3x - 4)
Thank you
[tex]\huge \bf༆ Answer ༄[/tex]
As we know, sum of interior angles of a triangle is 180°
that is ~
[tex] \sf13x + 2 + 5x - 7 + 3x - 4 = 180[/tex][tex] \sf21x - 9 = 180 [/tex][tex] \sf21x = 180 + 9[/tex][tex] \sf x = \dfrac{189}{21} [/tex][tex] \sf x = 9 \degree[/tex]
Hence, value of x is 9°
Answer:
x = 9Step-by-step explanation:
Sum of interior angles is 180:
(13x + 2) + (5x - 7) + (3x - 4) = 18021x - 9 = 18021x = 189x = 189/21x = 9What's the missing addend 634 + =644
Answer:
10
Step-by-step explanation:
it is 10 cause 634+10=644
Answer:
10
Step-by-step explanation:
What is the missing addend?
We can fill in the blank with x
634+x=644
Now we need to get x to the other side
The rule to do this is what we do on one side we have to do the same thing to the other side
so if we subtract 634 on one side we also have to do that on the other side as well:
634-634+x=644-634
634-634 is 0
So it is
x=644-634
644-634 is 10
x=10
So the missing addend is 10
Hope this helps!
Jackie runs and dances for 75 minutes every day.
She dances 25 minutes more than she runs.
What is the greatest amount of time she could spend dancing every day,
given she will take a run.
Answer:
I think it is 50 because 75-25=50
04.03 HC)
Given the function f(x) = 2(3)x, Section A is from x = 0 to x = 1 and Section B is from x = 2 to x = 3.
Part A: Find the average rate of change of each section. (4 points)
Part B: How many times greater is the average rate of change of Section B than Section A? Explain why one rate of change is greater than the other. (6 points)
(10 points)
Part A:
To find the average rate of change, let us first write out the equation to find it.
Δy/Δx = average rate of change.
Finding average rate of change for Section A
Δy = f(1) - f(0) = 2(3)^1 - 2(3)^0 = 6 - 1 = 5
Δx = 1- 0 = 1
Plug the numbers in: Δy/Δx = 5/1 = 5
Therefore, the average rate of change for Section A is 5.
Finding average rate of change for Section B
Δy = f(3) - f(2) = 2(3)^3 - 2(3)^2 = 2(27) - 2(9) = 54 - 18 = 36
Δx = 3 - 2 = 1
Plug the numbers in: Δy/Δx = 36/1 = 36
Therefore, the average rate of change for Section B is 36.
Part B:
(a) How many times greater is the average rate of change of Section B than Section A?
If Section B is on the interval [2,3] and Section A is on the interval [0,1].
For the function f(x) = 2(3)^x, the average rate of change of Section B is 7.2 times greater than the average rate of change of Section A.
(b) Explain why one rate of change is greater than the other.
Since f(x) = 2(3)^x is an exponential function the y values do not increase linearly, instead increase exponentially. In an interval with smaller x values the rate of change is lower than an interval with larger x values.
