Answer:
1. 48
2. 152.1 ❤️❤️
Use the limit definition of the derivative to find the slope of the tangent line to the curve
f(x)= 7x^2 + 7x + 3 at x= 4
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)
Write the quadratic equation in standard form:
x^2- 1 = -7x
Answer:
standard form: ax² + bx + c = 0
x² - 1 = -7x
x² + 7x - 1 = 0
la pirámide tiene una base cuadrada, por tanto, tiene 4 caras laterales triangulares. hallar el área y el volumen sabiendo que tiene de base 8cm y de altura 13 cm
Answer:
i think i know th problem but i do not understand your language i sorry
Step-by-step explanation:
what is true about the line x-4y=8
I will give brainliest. Help Me, please
Leandro wants to estimate the proportion of light bulbs that arrive broken upon shipment to his store. He
takes a random sample of 500 bulbs and finds that 25 arrived broken. He's willing to assume independence
between bulbs in the sample.
Answer:0.05+1.645v0.05(0.95)/500
Step-by-step explanation:
Help ASAP please Ahhhhh
Answer:its A
Step-by-step explanation:
Answer:
Your answer would be A. Your welcome
Show that (1+i)^2 = 2i
PLEASE HELP WILL GIVE BRAINLIEST ANSWER!!! Thanks
Answer:
please check explanations
Step-by-step explanation:
As we all know, i is same as root of -1
let us expand what we have;
(1 + i)^2
= 1(1 + i) + i(1 + i)
= 1 + i + i + i^2
as i is square root of -1, the square of the square root of -1 is -1
Thus, we have
1 + 2i - 1
= 2i
Triangle ABC has angle measures as shown.
(a) What is the value of x? Show your work.
(b) What is the measure of angle C? Show your work.
Answer:
Step-by-step explanation:
Answer:
12°Step-by-step explanation:
Sum of interior angles of the triangle is 180°:
m∠A + m∠B + m∠C = 180°3x + 28° + 5x + 52° + 2x - 10° = 180°10x + 70° = 180°10x = 110°x = 11°Find the measure of angle C:
m∠C = 2x - 10° = 2(11°) - 10° = 22° - 10° = 12°The owner of a garden center pays $25 for each birdbath . She sells them for 15% more than she paid. Decide whether each expression represents the selling price for b birdbaths.
Answer:
The selling price is $28.75b.
Step-by-step explanation:
There are no options given but I will represent the word problem mathematically.
Let b stand for all the birdbath. If the owner pays $25 for each, then he pays $25b.
Selling them for 15% more means, 15% of the cost price was added to the original price. Finding 15% of cost price we have:
15% x $25b = 0.15 x $25b = $3.75b.
Therefore, the selling price is given as
$25b + $3.75b = $28.75b.
Question 6
4 pts
You flip a coin three times. What is the probability you will have at least 2 heads?
67%
50%
33%
25%
Answer: 33%
Step-by-step explanation:
x^3=1/8 I'm so confused plz help
Answer: 1/3
Step-by-step explanation:
x^3= 1/8
Therefore x= cube root of 1/8= 1/3
What is the constant in the expression 7x + 3
Answer:
3
Step-by-step explanation:
In expressions, there are 4 items to look at :
1. Terms
2. Coefficients
3. Like Terms
4. Constant Terms
Since 4. is the topic at hand, let's focus on that, constant terms are terms that cannot be changed value.
This would mean numbers without a variable, look at the expression below :
7x + 3
Since 3 doesn't have a variable, therefore 3 is a constant term.
what are the measures of angle a,b,c? show your work and explain
Answer: A= 40. Vertical angles are congruent; B=50. 40+90=130 180-130=50; c=115 bc 180-65=115
Step-by-step explanation:
Amos scored 100 points while playing 3 rounds of a game.
Points
Round 1 - 30
Round 2 - 25
Round 3 - ?
Total - 100
How many points did he score in round 3?
Complete the steps to solve the problem.
1. What do you need to solve for this problem? Choose a variable to represent this unknown value.
2. Using the variable you chose, write an equation to represent this situation. (Hint: You may want to put the number of points in each round on one side and the total number of points on the other.)
3. Solve this equation to find how many points Amos scored in round 3. Show your work.
1. We can subtract the scores of the first and second rounds from the total score to obtain the score in the third round.
2. An equation including a variable to solve would be x + 30 + 25 = 100.
3. By solving the equation we obtain Amos scored 45 points in the third game.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
From the given information the score for her third round would be,
= (100 - 30 - 25).
= 100 - 55.
= 45.
Another way to solve this problem is assuming Amos scored 'x' in the third game.
Therefore, (30 + 25 + x) = 100.
55 + x = 100.
x = 100 - 55.
x = 45.
learn more about numerical expressions here :
https://brainly.com/question/29199574
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Three different, positive integers have a
mean of 8 and a median of 11. Find the
three numbers.
Answer: mean is 8, median is 11
Step-by-step explanation:
15. x2 + 11x + 10 = 0
can yall do me a favor, i know this random but i got played by someone so can u spaam his ig, acc name is sturdyyyyy_ just spam his comments called him a cheater and tell him he weird. please. females help a person out.
Answer:
okkkkk
Step-by-step explanation:
Please help me in this
The answer is A. 2 and 4
Reason:
To formula for circumference is 2 x r x pi
2 x 2 = 4, 2 x 4 = 8and 4 + 8 = 12
Area is r ^2 x pi
2 ^2 = 4, 4^2 = 16 and 4 + 16 = 20
FINDING SLOPE given GRAPHS, TABLES, POINTS and EQUATIONS!! Thank youu
The formula for slope is vertical change ÷ horizontal change, which means choose two points, (x1,y1) and (x2,y2), then do (y2-y1) ÷ (x2-x1).
For the graph, just pick two random points that you like. For the table, pick two sets of numbers (for example -10,-47 and 4,9). For the equation, create two sets of coordinates. For example, if you have f(x) = x + 3, then if x = 1, y = 4 and if x = 2, y = 5.
help pls ill mark as brainliest if correct
Step-by-step explanation:
5 miles =8 km
? miles=74 km
[tex] x \: miles = \frac{74 \times 5}{8} \\ = 46.25 \\ \frac{5 \: miles}{8 \: km} = \frac{46.25 \: miles}{74 \: km} \\ [/tex]
Write the slope-intercept form of the equation for the line given the slope and y-intercept (equation: y=mx+b) Slope = 5, y-intercept = 2
Answer:
y=5x+2
Step-by-step explanation:
Slope formula:
y=mx+b
- m stands for slope
- b stands for y intercept.
Plug the information in:
y=5x+2
Please can someone helpppp
20. Q(-1, 4), R(-1, -9), S(11, -2), T(11, 6)
Parallel
Perpendicular
Neither
Please help fast must be turned in in 3 hours!
Answer:
Parallel
Step-by-step explanation:
QR and ST both parallel to y axis.
The lines are parallel each other. Therefore, option A is the correct answer.
The given coordinate points are Q(-1, 4), R(-1, -9), S(11, -2), T(11, 6).
What is the graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.
After plotting the given points on the graph, we can see that the lines are parallel to each other.
The lines are parallel each other. Therefore, option A is the correct answer.
To learn more about the graph visit:
brainly.com/question/14375099.
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Solve for xxx. Your answer must be simplified. -4+x≤9
Answer:
x≤13
Step-by-step explanation:
-4+x≤9
Add 4 to each side
-4+4+x≤9+4
x≤13
Answer:
x≤13
Step-by-step explanation:
khan
BRAINLIEST+50 POINTS
Hey! I really need help figuring this problem out. I have a test in a few hours and I don't know how to find the answer to questions like these, I would really appreciate it if you show your work so I can figure out how to solve these myself. Thank you!
Answer:
(2, -1)Step-by-step explanation:
Given system:
-3x - 2y = -49x + 3y = 15Solving by elimination
Multiply the first equation by 3 and add up equations, then solve for y:
3(-3x) - 3(2y) + 9x + 3y = 3(-4) + 15-9x - 6y + 9x + 3y = -12 + 15-3y = 3y = 3/(-3)y = -1Find the value of x:
-3x - 2(-1) = -4-3x + 2 = -4-3x = - 4 - 2-3x = -6x = -6/(-3)x = 2The answer is: (2, -1)
A recipe calls for 3/2 cups of sugar to make 24 cookies. How many cups of sugar are needed to make 60 cookies?
Answer:
3.75 or 3 and 3/4
Step-by-step explanation:
3/2 Cups = 24 Cookies
?Cups 60=Cookies
Divide 60 by 24, which is 2.5
2.5x3/2 is 3.75 or, in fraction, 3 and 3/4
3 and 3/4 cups of sugar and needed to make 60 cookies
A farmer needs to box 740 apples. A box holds 9 apples. If every box is full except for the last, how many apples are in the last box?
An airplane ticket to new york is priced at $1232.10 inclusive of 11% sales tax what amount would the airline ticket cost exclusive of sales tax
Answer:
net is before tax
gross is after tax
N a survey, a group of students were asked their favorite sport. Eighteen students chose "other" sports. baseball: 40% football: 37.5 other:?
Answer:
22.5%
Step-by-step explanation:
The total number of students in percentage terms is 100%
Students that chose others = 100% - 40% - 37.5% = 22.5%