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)
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
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
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 is 18.6% of 11,400
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:
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
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)
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:
a + 3 ≥ 2
a. a ≤ -1
b. a ≥ -1
c. a ≥ 1
d. a ≥ 5
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
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:
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:
What is the answer? And why does brainly want me have at least 20 characters for my question?
simplify
0.75 (0.25f-1.5)
Answer:
3 * (f - 6) / 16
Step-by-step explanation:
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
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
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
Can anyone help me in this please?
-2y-5x=2
-5x=2y-4
( I need help solving both equations in y=mx+b form)
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
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
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
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.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:
:)
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)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.
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
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.
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
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