Answer:
[tex]\displaystyle f'(4) = 63[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Algebra I
Expand by FOIL (First Outside Inside Last)FactoringFunction NotationTerms/CoefficientsCalculus
Derivatives
The definition of a derivative is the slope of the tangent line.
Limit Definition of a Derivative: [tex]\displaystyle f'(x)= \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}[/tex]
Step-by-step explanation:
Step 1: Define
f(x) = 7x² + 7x + 3
Slope of tangent line at x = 4
Step 2: Differentiate
Substitute in function [Limit Definition of a Derivative]: [tex]\displaystyle f'(x)= \lim_{h \to 0} \frac{[7(x + h)^2 + 7(x + h) + 3]-(7x^2 + 7x + 3)}{h}[/tex][Limit - Fraction] Expand [FOIL]: [tex]\displaystyle f'(x)= \lim_{h \to 0} \frac{[7(x^2 + 2xh + h^2) + 7(x + h) + 3]-(7x^2 + 7x + 3)}{h}[/tex][Limit - Fraction] Distribute: [tex]\displaystyle f'(x)= \lim_{h \to 0} \frac{[7x^2 + 14xh + 7h^2 + 7x + 7h + 3] - 7x^2 - 7x - 3}{h}[/tex][Limit - Fraction] Combine like terms (x²): [tex]\displaystyle f'(x)= \lim_{h \to 0} \frac{14xh + 7h^2 + 7x + 7h + 3 - 7x - 3}{h}[/tex][Limit - Fraction] Combine like terms (x): [tex]\displaystyle f'(x)= \lim_{h \to 0} \frac{14xh + 7h^2 + 7h + 3 - 3}{h}[/tex][Limit - Fraction] Combine like terms: [tex]\displaystyle f'(x)= \lim_{h \to 0} \frac{14xh + 7h^2 + 7h}{h}[/tex][Limit - Fraction] Factor: [tex]\displaystyle f'(x)= \lim_{h \to 0} \frac{h(14x + 7h + 7)}{h}[/tex][Limit - Fraction] Simplify: [tex]\displaystyle f'(x)= \lim_{h \to 0} 14x + 7h + 7[/tex][Limit] Evaluate: [tex]\displaystyle f'(x) = 14x + 7[/tex]Step 3: Find Slope
Substitute in x: [tex]\displaystyle f'(4) = 14(4) + 7[/tex]Multiply: [tex]\displaystyle f'(4) = 56 + 7[/tex]Add: [tex]\displaystyle f'(4) = 63[/tex]This means that the slope of the tangent line at x = 4 is equal to 63.
Hope this helps!
Topic: Calculus AB/1
Unit: Chapter 2 - Definition of a Derivative
(College Calculus 10e)
Find midpoint of PQ with endpoints P (0,2) and Q (6,-2)
Answer:
(3, 0)
Step-by-step explanation:
The easiest way to do this problem is to average the x-coordinates and y-coordinates.
So, (0 + 6) / 2 = 6/2 = 3 = x and (2 - 2)/2 = 0/2 = 0 = y
Therefore, the midpoint is (3,0)
simplify
0.75 (0.25f-1.5)
Answer:
3 * (f - 6) / 16
Step-by-step explanation:
Level 1
Question
1
T is inversely proportional to N.
When T = 30, N = 5.
(a) Find an equation connecting T and N.
(b) Work out the value of T when N = 10
(C) Work out the value of N when T = 25
*
Answer:
a)T=k/N
b)T=15
c)N=6
Step-by-step explanation:
kindly see attached
Which arithmetic sequence has a common difference of 5?
Answer:
5,10,15,20,25,30
Step-by-step explanation:
their common difference is 5
Anthony is buying a new skateboard. for $295. The sales tax is 4.75%, what will he pay in tax?
Answer:
$4.75
Step-by-step explanation:
multiply 4.75% by 100 and then add/ move the decimal place 2 times
1. 11f + 15f
2. 18h + 13h
3. 55m + 11
Will give Brainliest Answer
Answer:
1. 2 6f
2. 31h
3. 1 1 ( 5 + 1 )
hope this helps
Step-by-step explanation:
Answer:
Distributive property:
ab + ac = (a + b)cApplied to the given expressions:
11f + 15f = (11 + 15)f = 26f 18h + 13h = (18 + 13)h = 31h 55m + 11 = 11(5m + 1)A single card is drawn from a deck. Find the probability of selecting a 4 or diamond
Answer:
I believe 16/52
Step-by-step explanation:
There are 13 diamonds and 4 fours. Add those together then you get 17/52. It is not that since there is a four of diamonds card, so you would need to subtract one. Then that reduces to 4/13
A movie theater has a seating capacity of 385. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 2794, How many children, students, and adults attended?
Answer:
Step-by-step explanation:
The number of children is 198, adults are 99 and students are 88.
What is word problem?A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
Given that, the theatre sitting capacity is 385 and the theatre charges are $5.00 for children $7.00 for students, and $12.00 for adults.
Let the number of children be c, since, there are half as many adults as there are children therefore, number of adults = c/2
The number of students = 385 - c - c/2 = 385 - 3c/2
The total cost = $2794
Therefore,
2794 = 5c+c/2×12+(385-3c/2)×7
2794 = 5c+6c+2695 - 21c/2
c = 198
Therefore, number of adults = 198/2 = 99
The number of students = 385-3/2×198 = 88
Hence, The number of children is 198, adults are 99 and students are 88.
For more references on word problems, click;
https://brainly.com/question/29203255
#SPJ2
ILL GIVE BRAINLIESAT FOR FIRST ANSWER!
Divide
3÷1/12
Step-by-step explanation:
is 36 hello my name is santiago i am fron Colombia
Express as integer: a deposit of $100
Answer:
Well if you deposit something you won't have it so negative. If you earn something then it is positive. So it is negative
Step-by-step explanation:
:)
A
B
C
D
PLZ HELP ASAP
Answer:
B. 4, 4, 4√2
Step-by-step explanation:
45° - 45° - 90° is the measure of special right triangle
the side lengths that sees these angles can be shown as a, a, and a√2 the values that meets these conditions are shown in option b
Can anyone help me in this please?
The diagram shows a regular octagon.
Not drawn
accurately
The base line of the octagon is extended.
Work out the size of angle y.
Answer:
15 b
Step-by-step explanation:
a + 3 ≥ 2
a. a ≤ -1
b. a ≥ -1
c. a ≥ 1
d. a ≥ 5
Write an inequality to match the graph below.
lets use x as the variable in this situation
x > -2 or x is greater than negative two.
hope this helps
A fish is 12 feet below the sea level. A bird is 28 feet above sea level. If the bird is directly
above the fish, how far apart are they?
Answer:
they are 40 feet apart!
Step-by-step explanation:
hopes this helps!!>_<
Answer:
40 Feet Apart
Step-by-step explanation:
Since the fish is 12 below sea level and the bird is 28 above sea level you just add both their distances together.
what does it mean to name the parts of an expression?
Answer:
Each expression is made up of terms. A term can be a signed number, a variable, or a constant multiplied by a variable or variables.
Step-by-step explanation:
Answer:
name the expression with terms like variable and constants. variable usually uses a letter like x and variables are just a number.
Step-by-step explanation:
What is the answer? And why does brainly want me have at least 20 characters for my question?
Which graph represents the function f(x) = 4x
Answer:
[tex]\boxed{\textsf{ The required graph of y = 4x will be a straight line passing through the origin . }}[/tex]
Step-by-step explanation:
Here we need to plot the graph for the function given to us . The function is ,
[tex]\sf \implies f(x)= 4x [/tex]
In order to plot a graph let us assume that ,
[tex]\sf\implies y = f(x) [/tex]
Hence we now get , that ,
[tex]\sf\implies y = 4x [/tex]
Now let's find out some values of x and y taking which we will plot the graph .
• So , firstly let , x = 0 then y will be equal to 4*0 = 0 . Hence we got one coordinates as (0,0) .
• Secondly let x = 1 , then y will be equal to 4*1 = 4 . Hence we get the third coordinate as (4,0) .
• Thirdly let us take that x = 0.5 then y will be equal to 4*0.5 = 2 . Hence we got the third coordinate as ( 0.5 , 2 )
• Fourthly let x = -0.5 then y will be equal to 4*-0.5 = -2 . Hence the fourth coordinate will be (-0.5 , -2)
Now when we plot it's graph taking suitable scale then it will look something like that as shown in attachment .
For the graph of y = 4x kindly refer to the attachment :) .
★Hence the graph of y = 4x will be a straight line passing through the origin.An ice cream shop uses 4 pints of ice cream to make 10 sundaes. How many pints of ice cream are used for each sundae?
Answer:
10/4 or 5/2 = 2.5
Step-by-step explanation:
Question 4 0
A two-sample t-test for a difference in means was conducted to investigate whether defensive players on a football team can bench-press more weight, on average, than
offensive players. The conditions for inference were met, and the test produced a test statistic of t = 1.083 and a p-value of 0.15.
Based on the p-value and a significance level of a = 0.05, which of the following is the correct conclusion?
Submit
Reject the null hypothesis because 0.15 > 0.05. There is not convincing evidence that defensive players can bench-press more weight, on average, than
offensive players.
B
Reject the null hypothesis because 0.15 > 0.05. There is convincing evidence that defensive players can bench-press more weight, on average, than
offensive players
с
Fail to reject the null hypothesis because 0.15 > 0.05. There is not convincing evidence that defensive players can bench-press more weight, on average,
than offensive players,
D
Fail to reject the null hypothesis because 0.15 > 0.05. There is convincing evidence that defensive players can bench-press more weight, on average,
than offensive players
Fail to reject the null hypothesis because 0.15 > 0.05. There is convincing evidence that defensive players can bench-press the same amount of weight,
on average, as offensive players.
Answer:
Fail to reject the null hypothesis because 0.15>0.05
. There is not convincing evidence that defensive players can bench-press more weight, on average, than offensive players.
Step-by-step explanation:
Since P>a we can not reject the null hypothesis. We cannot conclude the alternative hypothesis in context.
Good Afternoon! please help me with these questions! So Far No one has helped me and I really need help. i found answers but the answers are not any of the multiple-choice answers!
For #1 I had gotten 5078.9 using the formula A=p(1+r/n)^n(t)
For # 2 I had gotten 2464.7 using the formula A=p(1+r/n)^n(t)
But I see no answer choices with these answers.
Please tell me the correct answers and explain what I did wrong!
Answer:
I think the first one is $1288.94 and the second is 3001.99
Step-by-step explanation:
I might be wrong forgive me if so
what is 18.6% of 11,400
-2y-5x=2
-5x=2y-4
( I need help solving both equations in y=mx+b form)
The interior angles formed by the sides of a hexagon have measures that sum to 720°. What is the measure of angle A? Enter your answer in the box. m∠A= °
Answer:
The answer is 100
Step-by-step explanation:
i took the quiz right now
If the points (1, -4) and (-1, r) and lie on a line whose slope is 5, what does r equal?
Answer:
mabe 5
Step-by-step explanation
becuse its probly in the x1,5 becuse it slopes down 5
State the slope of the line 4.0 + 3y = 1.
Answer:
State the slope of the line 4.0 + 3y = 1.
Step-by-step explanation:
How do you stop depression.
Answer:
Slope=0
Step-by-step explanation:
The midpoint of AD is C. The midpoint of AC is B. If A is at (-10,4) and D is at (2,12), find the coordinates of B. Group of answer choices (-5,5) (-4,8) (-2.5,9) (7,6)
Answer:
[tex]B(x,y) =(-7,6)[/tex]
Step-by-step explanation:
Given
[tex]A = (-10,4)[/tex]
[tex]D = (2,12)[/tex]
Required
Determine the coordinates of B
C is the midpoint of AD. So, we calculate the coordinates of C, first.
[tex]C(x,y) = (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
Where:
[tex]A = (-10,4)[/tex] --- [tex](x_1,y_1)[/tex]
[tex]D = (2,12)[/tex] --- [tex](x_2,y_2)[/tex]
So, we have:
[tex]C(x,y) = (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
[tex]C(x,y) = (\frac{-10+2}{2},\frac{4+12}{2})[/tex]
[tex]C(x,y) = (\frac{-8}{2},\frac{16}{2})[/tex]
[tex]C(x,y) = (-4,8)[/tex]
So, the coordinates of C is (-4,8)
The midpoint of AC is B.
So, we calculate the coordinates of B using:
[tex]B(x,y) = (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
Where:
[tex]A = (-10,4)[/tex] --- [tex](x_1,y_1)[/tex]
[tex]C(x,y) = (-4,8)[/tex] --- [tex](x_2,y_2)[/tex]
So, we have:
[tex]B(x,y) = (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
[tex]B(x,y) =(\frac{-10-4}{2},\frac{4+8}{2})[/tex]
[tex]B(x,y) =(\frac{-14}{2},\frac{12}{2})[/tex]
[tex]B(x,y) =(-7,6)[/tex]
Hence, the coordinates of B is (-7,6)
None of the options is correct.
please someone please help me with this problem I’ll thank you forever
Answer:
The answer is about 9.85
Step-by-step explanation:
4 ^ 2 = 16
9 ^ 2 = 81
16 + 81 = 97
97 radical thing is ABOUT 9.85
Find the area of the parallelogram shown below.
9
15
17
square units
Answer:
135
Step-by-step explanation:
its the base (9) times the height (15)
Answer:
135
Step-by-step explanation:
because of the rule base times hight we know it is 135