[tex]f(x) = x^2 +x (2a+2b) +4ab-x\\\\f'(x) = 2x+x \cdot 0 + 2a+2b + 0 -1\\\\~~~~~~~~=2x+0+2a+2b-1\\\\~~~~~~~~=2x+2a+2b-1[/tex]
From the definition of the derivative,
[tex]f'(x) = \displaystyle \lim_{h\to0} \frac{f(x+h) - f(x)}h[/tex]
We have
[tex]f(x) = x^2 + x(2a+2b) + 4ab - x = x^2 + (2a+2b-1)x + 4ab[/tex]
and so
[tex]\displaystyle f'(x) = \lim_{h\to0} \frac{\left((x+h)^2 + (2a+2b-1)(x+h) + 4ab\right) - \left(x^2 + (2a+2b-1)x + 4ab\right)}h[/tex]
[tex]\displaystyle f'(x) = \lim_{h\to0} \frac{x^2 + 2xh + h^2 + (2a+2b-1)x + (2a+2b-1)h + 4ab - x^2 - (2a+2b-1)x - 4ab}h[/tex]
[tex]\displaystyle f'(x) = \lim_{h\to0} \frac{2xh + h^2 + (2a+2b-1)h}h[/tex]
[tex]\displaystyle f'(x) = \lim_{h\to0} (2x + h + 2a+2b-1)[/tex]
[tex]\displaystyle f'(x) = \boxed{2x + 2a + 2b - 1}[/tex]
Anybody want to help with math? Pls hurry, I’ll give brainiest and everything.
Find the missing number in the ratio table below.
11 22 33 44
9 18 27 ?
A: 38
B: 36
C: 35
D: 37
Answer:
B
Step-by-step explanation:
You are going to add 9 to 27 because you are counting by nines on the bottom.
Simplify: √645³
O 872
O 84
O 3272
O 324
Answer:
√645^3=16,380.9. Mathematically correct
A diner is serving a special lunch combo meal that includes a drink, a main dish, and a side. Customers can choose among 5 drinks, 4 main dishes, and 5 sides. How many different combo meals are possible? Select from the drop-down menu to correctly complete the statement Customers can create Choose... different lunch combo meals. 4 A 1 2 3 4 5. oc 9
Since the customers can choose among 5 drinks, 4 main dishes, and 5 sides. there 100 different combo meals are possible.
Since order is not important we use combination to solve the problem
What is combination?This is the number of ways in which x objects can be selected out of n objects. It is given mathematically as ⁿCₓ = n!/x!(n - x)!
The number of different combo mealsNow, given that the customer can choose among 5 drinks, 4 main dishes, and 5 sides.
There are ⁵C₁ ways of choosing the drinks.
So, ⁵C₁ = 5!/1!(5 - 1)!
= 5!/1!/4!
= 5
There are ⁴C₁ ways of choosing the main dishes.
So, ⁴C₁ = 4!/1!(4 - 1)!
= 4!/1!/3!
= 4
There are ⁵C₁ ways of choosing the sides.
So, ⁵C₁ = 5!/1!(5 - 1)!
= 5!/1!/4!
= 5
So, total number of ways of choosing the combo meals is
⁵C₁ × ⁴C₁ × ⁵C₁ = 5 × 4 × 5
= 100 ways.
So, there 100 different combo meals are possible.
Learn more about combination here:
https://brainly.com/question/26852614
#SPJ1
Answer: The answer is 100
Step-by-step explanation:
kyle runs 5 days a week. On Sunday he runs half of his weekly distance. On monday he runs 1/4 of the remaining distance for the week. What fraction of the weekly distance remains to be run?
A. 1/8
B. 1/4
C. 3/8
D. 3/4
Answer:
B. 1/4
Step-by-step explanation:
We can use the distance = rate ⋅ time formula to find the distance Lee traveled. The formula d = rt looks like this when we plug in the numbers from the problem. The unknown distance is represented with the variable d. To find d, all we have to do is multiply 65 and 2.5.
4 people are going to a dinner party. Each person at the party will eat 5/6 pound of salad but you can only buy in pounds.If you can only buy whole pounds of salad, how many pounds should you buy?
(please help will give brainlyest)
enter the lowest whole number in the numerator to make the comparison ?/7 > 1/2 true.
14/7 is greater than 1/2
Sure hope this helps you
#7 HELP ME IM STUCK ON THIS
Answer:
30 ft
Step-by-step explanation:
since they're both feet no conversion is needed
multiply the model to scale (5) to find actual
6 * 5 = 30
your answer is 30 ft.
hope this helps:)
The elements magnesium (mg) and calcium (ca) play vital roles in maintaining human health, including processes like bone building. the majority of americans have lower levels of magnesium than health experts recommend. do some research in order to propose a possible hypothesis that could explain this phenomenon.
The reason why Americans have lower levels of magnesium than health experts recommend is because of the prevalence of processed food.
What are nutrients?The nutrients in food are those components of food that serve the purpose of nourishing our body. The nutrients present in processed food are different from those present in natural food.
Since many Americans eat a lot of processed instead of natural food, they often lack magnesium which is often absent in processed food.
Learn more about processed food:https://brainly.com/question/27044001
#SPJ4
how know ????????????
Answer:
0.16
Step-by-step explanation:
AND = Probability(of 1)*Probability(of 2)
OR = Probability(of 1)+Probability(of 2)
probability of spinning red = 0.2 or 20%
probability of NOT spinning red = 0.8 or 80%
The question says "AND" so 0.2 * 0.8 = 0.16 or 16%
Hope this helps!!!
Please mark as brainliest!!!
Last month, Korey’s Comics had $4,350 in net sales with a gross profit of $3,320 and a net income of $1,850. Calculate Korey’s net profit margin. a. 42.5% b. 55.7% c. 76.3% d. 179.5%
b. 55.722
Step-by-step explanation:
1850/3320
I assume that you know what the question is asking to solve for.
The net profit margin for Korey's Comics is 42.5%.
Option A is the correct answer.
What is a profit?Profit is the difference between the selling price and the cost price.
We have,
Net profit margin is calculated by dividing net income by net sales and multiplying the result by 100 to get a percentage.
Net Profit Margin = (Net Income / Net Sales) x 100%
Substituting the given values.
Net Profit Margin = (1,850 / 4,350) x 100%
Net Profit Margin = 0.425 x 100%
Net Profit Margin = 42.5%
Therefore,
The net profit margin for Korey's Comics is 42.5%.
Learn mroe about profit here:
https://brainly.com/question/15699405
#SPJ5
Find the mean of the data: 125, 15, 30, 110, 70
Answer:
The mean of the data is 70
Step-by-step explanation:
Hope this helps you! :D
Answer:
70
Step-by-step explanation:
Mean-
Add all the numbers to the total = 350
Divide by the amount of numbers (125, 15, 30, 110,70 = 5 numbers)
350/5 = 70
What is the greatest common factor
Of the monomials shown below?
6x^4 y^3 z^4 22xy^3 z^3
A. 66x^4 y^3 z^4
B. 2x^4 y^3 z^4
C. 66x^5 y^6 z^7
D. 2xy^3 z^3
Answer:
Your answer given is that a great common factor of the monomials shown below 6x^4 y^3 z^4 22xy^3
A said Given 66x^4 y^3 z^4
B said Given 2x^4 y^3 z^4
C said Given 66x^5 y^6 z^7
D said Given 2xy^3 z^3
my answer is that C. 66x^5 y^6 z^7
because it greatest common factor
If h = 3.5u, what is the value of h when u = 17?
Give any decimal answers to 1 d.p.
Put u=17
h=3.5(17)h=51+8.5h=59.5Answer:
59.5.
Step-by-step explanation:
h = 3.5u
When u = 17,
h = 3.5*17
= 59.5
Ruth ann wants to research two different careers, medical doctor and astronaut. what is a good first step ruth ann could take? if she went to a bookstore to research her careers, which section would she search?
Ruth can visit US Bureau of Labor Statistics website so that she could know more about those careers.
What is a career?career can be regarded as a profession that individuals choose to follow in his lifetime and this his occupation.
Therefore, in choosing a career , one needs to equip himself with information about it, he can visit Bureau of Labor Statistics.
Learn more about career at;
https://brainly.com/question/15604938
#SPJ4
Answer:
visit the US. Bureau of Labor Statistics website to find information on both careers and the career section
Step-by-step explanation: well i know it right because i just answered it correct
A) The function f is defined by : f(x) = x2+ax+b
a and b are constants.
It is known that: f(0) = 7 and f(-2) = 17
Find the values of a and b.
B) Use the values of a and b to solve this equation: f(x) = 35
x = __ or x = __?
Answer:
A. a = -3 and b = 7.
B. x = -4 or x = 7.
Step-by-step explanation:
A)
f(0) = 0^2 + a(0) + b = 7
So b = 7.
f(-2) = (-2)^2- 2a + 7 = 17
4 - 2a = 17 - 7
4 - 2a = 10
-2a = 10 - 4 = 6
-2a = 6/-2
a = -3.
B)
Substituting a = -3 and b = 7 we get:-
x^2 - 3x + 7 = 35
x^2 - 3x - 28 = 0
(x - 7)(x + 4) = 0
x - 7 = 0 or x + 4 = 0
x = -4 or x = 7.
help me pls!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
d. 0.771.
Step-by-step explanation:
This probability is equal to the area other than the green triangle divided by the total area of backyard.
Total area = 120^2 = 14400
Area of green triangle = 1/2 * 120 * 55 = 3300
So area of the part of yard not covered by the triangle = 14400 - 3300
and the required probability = (14400 - 3300) / 14400
= 0.771.
Answer:
d. 0.771
Step-by-step explanation:
What is probability?
Probability is the likelihood of the occurrence of something.
In simpler terms we can say probability = # of favorable outcomes / total # of outcomes.
Understanding the question
Here we have a square and a triangle inside of the square and we want to find the probability that a tennis ball thrown inside of the square will not land inside of the triangle.
So we have # of favorable outcomes as the area of the outside of the triangle but inside of the square ( so area of square - area of triangle ) and we have total # of outcomes as the total area of the square including the triangle
Finding the areas
Area of square
Area of square = (side length)²
the square shown has a given side length of 120ft
So area = 120² = 120 × 120 = 14400
Area of triangle
Area of a triangle = (base length × height) / 2
Here the base length is shared with the side length of the square menaing the base length of the triangle = 120 and the given height of the triangle is 55 feet
So area would = ( 120 × 55 ) / 2 = 3300
Finding the probability
Again we want to find the probability that a ball thrown in the square will not land in the triangle
This can be calculated using the probability formula we created earlier
probability = ( area of square - area of triangle ) / area of square
we have area of square = 14400 and area of triangle = 3300
so probability = (14400 - 3300) / 14400
==> subtract 3300 from 14400
probability = 11100 / 14400 = 0.771 ( rounded )
And we are done!
Learn more about shaded area here: https://brainly.com/question/27777552
Learn more about probability here: https://brainly.com/question/27607459
Write 23/4 as a mixed number. give your answer in its simplest form.
Answer:
Here is the ans...Hope it helps :)
Can anyone help me with this quick question please, ASAP, Thank You!
Answer:
15.7 lbs (please mark brainliest)
Step-by-step explanation:
2.6+x+x=34
2x=31.4
x=15.7
Answer: 14.4
Step-by-step explanation: I took 34 and divided it by 2 then subtracted 2.6 from 17 which gave me 14.4. If it's wrong, sorry.
What is the answer??
Answer:
5 given as -1 and 8 positive 8 cross by axis
Use the given scale and determine the actual straight -line distance between East London and Bloemfontein
Answer:
Driving Distance : 569 KM and 398 meters / 353.8 miles.
Straight Line Distance : 467 KM and 700 meters / 290.6 miles.
Travel time : 11 hours and 19 minutes.
Direction and bearing : South side, 159 degree.
Step-by-step explanation:
What is the area of the circle?
(3.14 for pi)
Explanation:
The diameter is 64 yards
Divide it in half to get 64/2 = 32 yards as the radius.
Plug it into the formula below to get the area of the circle.
A = pi*r^2
A = 3.14*32^2
A = 3215.36
The area of the circle is approximately 3215.36 square yards.
The area is approximate since pi = 3.14 is approximate.
In january, desmond begins saving $25 per month for a used car. each month, he is able to save $5 more than the previous month. after how many months will desmond first have enough money to purchase a $3,000 used car? 14 21 31 35
Answer:
After 31 months, Desmond first have enough money to purchase a used car.
Step-by-step explanation:
Since we have given that
Saving per month for a used car = $25
Each month he is able to save = $5 more than the previous month
If we have $3000 to purchase a used car.
So, we need to find the number of months Desmond to have enough money.
Our sequence will be
25,30,35,..............3000
So, it becomes,
Months can't be negative, So,
n = 31 months.
Hence, After 31 months, Desmond first have enough money to purchase a used car.
Answer:
C. 31
Step-by-step explanation:
Write a system of inequalities using the given graph
Take two points
(-2,1)(0,-3)Slope
m=-3-1/0+2=-4/2=-2Parallel lines so slopes are equal
Only y intercept will vary
So both lines have y intercept at -3 and -1 respectively
The equations
y=-2x-3y=-2x-1Put (0,0) on first one
0>-3On second one
0>-1So as lines are dashed symbols remain >
The inequalities are
y>-2x-3y>-2x-1What is the value of x in the image below?
Answer:
a
Step-by-step explanation:
Complete the standard form equation representing the quadratic relationship displayed above, where a, b, and c are constants.
The owner of a sports complex wants to carpet a hallway connecting two buildings. The carpet costs $2.50 per square foot. How much does it cost to carpet the hallway?
If the area of the carpet will be 301 square feet. Then the cost of the carpet will be $ 752.5.
What is a trapezium?It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a trapezium, one pair of opposite sides are parallel.
The owner of a sports complex wants to carpet a hallway connecting two buildings.
The diagram is given below.
The carpet costs $2.50 per square foot.
The area of the carpet will be given by the area of the trapezium.
Area = 1/2 (24 + 28) x 7 + 1/2 (15 + 19) x 7
Area = 0.5 x 52 x 7 + 0.5 x 34 x 7
Area = 182 + 119
Area = 301 square feet
Then the cost of the carpet will be
Cost of carpet = $ 2.5 x 301
Cost of carpet = $752.5
More about the trapezium link is given below.
https://brainly.com/question/22607187
#SPJ1
exponential function question
Answer: [tex]y = 850(0.943)^t[/tex]
Reason:
The exponential of the form [tex]y = a*b^x[/tex] has 'a' as the initial term and b as the growth or decay factor.
a = 850 is the starting amount
b = 1 + r = 1 + (-0.057) = 0.943 is the decay factor
If the sample loses 5.7% of its mass each year, then it keeps the remaining 94.3% of it.
Four types of soda are served at a birthday party. in an icebox containing a large number of cans of soda, 20% are ambrase, 30% are butonic, 15% are colana, and 35% are dynamite. a party guest randomly chooses four cans of soda. calculate the probability that the guest chooses one of each type of soda.
The probability that the guest chooses one of each type of soda will be 8.03%.
What is probability?Its simple notion is that something will most likely occur. The favorable event's proportion to the overall number of occurrences.
Four types of soda are served at a birthday party. in an icebox containing a large number of cans of soda, 20% are Ambrase, 30% are Butonic, 15% are Colana, and 35% are Dynamite.
A party guest randomly chooses four cans of soda.
Then the probability that the guest chooses one of each type of soda will be
Let the total number of the soda can will be 100. Then we have
Ambrase = 20
Butonic = 30
Colana = 15
Dynamite = 35
[tex]\rm P = \dfrac{^{20}C_1 \times ^{30}C_1\times ^{15}C_1\times ^{35}C_1}{^{100}C_4}\\\\\\P =\dfrac{20 \times 30 \times 15 \times 35}{3921225}\\\\\\P = \dfrac{600}{7469}\\\\\\P = 0.08033\\\\\\P = 8.03\%[/tex]
More about the probability link is given below.
https://brainly.com/question/795909
#SPJ1
Given the function f(x) = 8x-1, what is the corresponding value when x = -1?
Which one 3, 4, 6, or 7
Answer:
i think that it is 6
Step-by-step explanation:
hope this helps
Please give me Brainlist