Given the function g(x)=7-x^2, evaluate g(x+h)-g(x)/h , h=0
Answers
The result is g'(x) = -2x.
Given g(x) =[tex]7 - x^2.[/tex]
Evaluate g(x+h)
=[tex]7 - (x+h)^2[/tex]
= [tex]7 - x^2 - 2xh - h^2.[/tex]
Compute g(x+h) - g(x)
=[tex][7 - x^2 - 2xh - h^2] - [7 - x^2][/tex]
= [tex]-2xh - h^2.[/tex]
Divide by h:
(g(x+h) - g(x)) / h
= [tex](-2xh - h^2) / h[/tex]
= -2x - h.
Take the Limit as h Approaches 0: As h approaches 0, the expression -2x - h approaches -2x.
Therefore, g'(x) = -2x.
So, the derivative of g(x) when h = 0 is -2x.
Related Questions
I can't seem to figure it out can someone please help me??
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We know that line DC = 16, that means line AD also 16
Line AE = ED = 8
Line EF = FD = 4
Line FG = GD = 2
Line DB = 16+32 = 48
Line DH = 48/2 = 24
Line GH = 2+24 = 26
Find the quotient of the quantity [tex]
\frac{4x^3y+12x^2y^3-20xy}{4xy} [/tex].
A.[tex]
x^2+3xy^2+5[/tex]
B. [tex]
x^2+3xy-5[/tex]
C. [tex]
4x^3y+12x^2y^3-5[/tex]
D. [tex]
x^2+3xy^2-5[/tex]
Please tell me how to get the correct answer! Thank you!
Answers
remember ab+ac=a(b+c)
so
[tex]\frac{4x^3y+12x^2y^3-20xy}{4xy}=[/tex]
[tex]\frac{(4xy)(x^2)+(4xy)(3xy)+(4xy)(-5)}{4xy}=[/tex]
[tex]\frac{(4xy)(x^2+3xy-5)}{4xy}=[/tex]
[tex]x^2+3xy-5[/tex]
answer is B
Answer:
answer:b
Step-by-step explanation:
we need to factor out the things like in distributive
remember ab+ac=a(b+c)
so
By definition, a rational number is a number q that can be written as a fraction in the form q=a/b where a and b are integers and b≠0. So, 1/3 is rational because it is exactly what you get when you divide one integer by another.Sep 22, 2015
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Simplify 8(x + 6) - 10. 8x - 4 8x + 28 8x + 38
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8x + 48 - 10
8x + 38 <------------- answer
8x + 38 should be the answer...not sure.
solve
18x^2 -3x -10
What is the smallest solution
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x^2-3x-180
(x-15)(x+12)
(6x-5)(3x+2)
Using ZPP
6x-5=0
6x=5
x=5/6 <=== one of the roots
3x+2=0
3x=-2
x=-2/3 <==== another root
Final answer: -2/3
1/12 as a decimal. Long division.
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simplify (4x-4)-3 , pleas help
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unless it asks you to factorise again
12(x+1)
hope this helps! Dont forget to put it as the brainliest answer to help me out too xD
[tex](4x-4)-3[/tex]
Add like terms
[tex]4x-7[/tex]
This is the furthest you can simplify this expression.
Hope this helps.
-Benjamin
Complete the equation and tell what property you used 16+31=31+16
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how do you solve for the variable ?? help
Answers
2(3x - 4) + 10 = 5(x + 4)
First, let's distribute 2 to 3x and -4, then 5 to x and 4.
2(3x) + 2(-4) + 10
6x - 8 + 10
6x + 2 is our first half of the equation simplified. Now let's do the other.
5(x + 4)
5(x) + 5(4)
5x + 20 is our second half of the equation simplified. Now let's put them back in their original spots.
6x + 2 = 5x + 20
Get x on one side - subtract 5x from both sides.
x + 2 = 20
Isolate x by adding 8 to both sides.
x = 18 is our answer.
I hope this helps!
If F(x)=8x, which of the following is the inverse of F(x)
Answers
[tex]f(x) = 8x[/tex]
let : [tex]y=8x[/tex]
so : [tex]x= \frac{1}{8} y[/tex]
the inverse of [tex]f(x)[/tex] is : [tex]g(x) = \frac{1}{8} x[/tex]
Answer: answer is F^1(x) = x/8
Step-by-step explanation:
Find the Solution to the system of equations.
A. (1, 4)
B. (4, 1)
C. (0, 3)
D. (4, -1)
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The solution to the system of equations represented by the graph is (b) (4,1)
How to determine the solution?The solution to the system of equations is the point of intesection of the equations.
From the graph, the lines intersect at the point
(x,y) = (4,1)
Hence, the solution to the system of equations is (4,1)
Read more about system of equations at:
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Please answer correct for brainliest
Answers
So area = (12 + (2*2 + 12) ) *13 / 2 = 182
If 10% of a group ate sandwiches two days in a row, and 40% of the group had a sandwich on the first day, this means that 25% of the group that ate a first sandwich had a second. A. True B. False
Answers
We have P(Day 1 ∩ Day 2) = 0.1 and P(Day 1) = 0.4
We can deduce that 30% of the group ONLY had sandwiches on Day 1 and there's 60% of the group ONLY had sandwiches on Day 2.
We obtain the value 60% = 0.6 from 100%-(10%+30%)=60%
We also can deduce that there 70% of the group that had sandwiches on Day 2
The proportion of people who ate sandwiches on Day 2 GIVEN that they ate sandwiches on Day 1 is given by
P(Day 1 ∩ Day 2)÷P(Day 2) = 0.1÷0.4 = 0.25 = 25%
The statement is TRUE
Which of these is the algebraic expression for "some number to the power of 4?"
x4
4x
4x
x + 4
Answers
Answer:
They deserve brainliest!
Step-by-step explanation:
In this exercise we have to identify the formula that is being treated in a written way, so correlating correctly we have:
Letter A
What is power number?The power is a simplified notation of representing the multiplication of a number, which we call the base, repeatedly by the value of a power that determines how many times we must multiply this number.
So the only one that corresponds to "some number to the power of 4" is:
[tex]x^4[/tex]
See more about power at brainly.com/question/1618040
Which statement is true about the circumference of a circle?
It is about three times the diameter.
It is about three times the radius.
It is about twice the radius.
It is about half the diameter.
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C = pi*d
where
C = circumference
pi = 3.14 approximately
d = diameter
So saying "the circumference is roughly 3 times the diameter" is appropriate because pi = 3.14 is roughly 3 if you round to the nearest whole number.
Answer: Choice A) three times the diameter
What is the 24% of 40?
Answers
40 times 0.24 = 9.6
Therefore 24% of 40 = 9.6
Anyhow, lets start working out this problem, shall we? 24(40) = ? 24 ÷ 100 = 0.24 0.24 (40) = 9.6 Your answer would be: 9.6
In order for the data in the table to represent a linear function with a rate of change of –8, what must be the value of m?
A. m = 2
B. m = 3
C. m = 19
D. m = 35
Which is the correct answer???
Answers
Answer: The correct option is (C) 19.
Step-by-step explanation: We are given to find the value of m so that the data the table to represent a linear function with a rate of change of –8.
We know that
the rate of change for a linear function with two points (a, b) and (c, d) is given by
[tex]R=\dfrac{d-b}{c-a}.[/tex]
From the table, we note that the points (10, 27) and (11, m) satisfy the given linear function.
So, the rate of change of the linear function will be
[tex]R=\dfrac{m-27}{11-10}\\\\\\\Rightarrow -8=\dfrac{m-27}{1}\\\\\Rightarrow -8=m-27\\\\\Rightarrow m=27-8\\\\\Rightarrow m=19.[/tex]
Thus, the required value of m is 19.
Option (C) is CORRECT.
One side of a triangle is 15 inches, and the area of the triangle is 90 sq. inches. Find the area of a similar triangle in which the corresponding side is 9 inches.
Answers
(9/15) ratio of sides
(9/15)^2 ratio of areas
81/225
Multiply for the known area
90*(81/225) = 162/5 = 32,4 sq. inches (area of corresponding triangle)
find the value of x below if necessary round to the nearest tenth.
NEED ANSWER PLEASE HELP
Answers
x = 20 x sin(27)
= 9.0798
rounded to nearest tenth = 9.1
Polygons EFHG and E′F′H′G′ are shown on the following coordinate grid: A coordinate grid is shown from positive 6 to negative 6 on the x-axis and from positive 6 to negative 6 on the y-axis. A polygon EFHG is shown with vertex E on ordered pair 2, 2, vertex F on ordered pair 2, 4, vertex H on ordered pair 3, 5 and vertex G on ordered pair 3, 1. A polygon E prime F prime H prime G prime is shown with vertex E prime on ordered pair negative 1, 2, vertex F prime on ordered pair negative 3, 2, vertex H prime on ordered pair negative 4, 3, and vertex G prime on ordered pair 0, 3. What set of transformations is performed on EFHG to form E′F′H′G′?
Answers
All choices involve a rotation by 90° or 270° counterclockwise about the origin.
consider a rotation by 90° counterclockwise. Each point P(a, b) can be rotated 90° cwise about the origin to form P"(a",b") :
by drawing the right angle POP", such that |PO|=|OP"|.
or by plotting each P"(a",b") so that (a",b")=(-b, a)
for example if G(3, 1) is mapped to G(-1, 3) by either of the procedures described.
check picture 2.
EFHG is mapped to E′'F'′H'′G′'.
In order to map E′'F'′H'′G′' to E'F′H'G′, we need to translate the figure 1 unit right.
Answer:
"A 90-degree counterclockwise rotation about the origin followed by a translation 1 unit to the right"
Answer:
A 90-degree counterclockwise rotation about the origin followed by a translation 1 unit to the right
Step-by-step explanation:
i took the test
The range is the set of
A. first coordinates
B. ordered pairs
C. second coordinates
Answers
Feel free to ask me more questions on my profile. I am more than happy to help. Don't forget Brainliest! :)
:)
A theater company charges $4.50 per ticket for people of all age groups. If c represents the total number of children who bought tickets and a represents the total number of adults who bought tickets, which expression best represents the total money earned by the company from the sale of tickets? 4.5(c + a) 4.5c + a c + 4.5a 9(c + a)
Answers
Answer:
4.5 c+a)
Step-by-step explanation:
Brenda needs $40 to buy a large box of chocolate. She has saved $12 and plans to work as a babysitter to earn $7 per hour. Which inequality shows the minimum number of hours, n, that Brenda should work as a babysitter to earn enough to buy the large box of chocolate?
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If n = number of hours Brenda works then her baby sitter earning = 7n
12 + 7n ≥ 40 , so n≥4
So answer is c
Help me with the first question
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Part B) The discount here is 10%. So far, discount A is better
Part C) The discount here is 15%. Discount A is also better because 15.798% is larger than 15%
Part D) Convert 1/4 to decimal form to get 0.25 and then move the decimal point 2 spots to the right to get 25%. So 1/4 = 25%. The discount here is 25%. This discount (of 25%) is much better than discount A.
Store 5 has the best discount since 25% is the largest among all the percentages.
Answer: Choice D)
Tim Duncan is shooting free throws. Making or missing free throws doesn't change the probability that he will make his next one, and he makes his free throws 72% of the time. What is the probability of Tim Duncan making all of his next 8 free throw attempts?
Answers
Answer:
Hence, the probability of Tim Duncan making all of his next 8 free throw attempts is:
[tex](\dfrac{18}{25})^8=0.0722204136[/tex]
Step-by-step explanation:
As the probability of one free throw does not depend on the any other i.e. the probability of each throw is independent.
Hence, the probability of making all of his next 8 free throw is calculated as:
Probability of next 8 free throw=Probability of first free throw×probability o f second free throw×··················× Probability of 8th free throw.
i.e. it is given by:
[tex]Probability=\dfrac{72}{100}\times \dfrac{72}{100}\times \dfrac{72}{100}\times \dfrac{72}{100}\times \dfrac{72}{100}\times \dfrac{72}{100}\times \dfrac{72}{100}\times \dfrac{72}{100}\\\\\\Probability=(\dfrac{72}{100})^8\\\\Probability=(\dfrac{18}{25})^8[/tex]
Hence, the probability is:
[tex](\dfrac{18}{25})^8=0.0722204136[/tex]
We have that the he probability of Tim Duncan making all of his next 8 free throw attempts is mathematically given as
[tex]P=0.72^8[/tex]
From the question we are told
Tim Duncan is shooting free throws. Making or missing free throws doesn't change the probability that he will make his next one, and he makes his free throws 72% of the time. What is the probability of Tim Duncan making all of his next 8 free throw attempts?ArithmeticGenerally the equation for the binomial probability is mathematically given as
[tex]P=\frac{n!}{X!(n-X)!}*p^X*(1-p)^{n-X}\\\\Therefore\\\\ P=\frac{8!}{8!(8-8)!}*0.72^8*(1-0.72)^{0}[/tex]
[tex]P=0.72^8[/tex]
For more information on Arithmetic visit
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Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = 4 cos 3θ. PLEASE HELP ME SOLVE RN I NEED THIS, ALSO INCLUDE THE PROVING PART.
Answers
If
f(r, θ) = f(r,-θ), symmetric to the polar axis or the x-axis
f(r, θ) = f(-r,θ), symmetric to the y-axis
f(r, θ) = f(-r,-θ), symmetric to the pole or the origin
Test for symmetry about the x-axis
f(r,θ): r=4 cos3θ
f(r,-θ): r = 4 cos3(-θ) ⇒ r = 4 cos3θ
∴The graph is symmetric about the x-axis.
Test for symmetry about the y-axis
f(r,θ): r=4 cos3θ
f(-r,θ): -r = 4 cos3θ
∴The graph is not symmetric about the y-axis.
Test for symmetry about the origin
f(r,θ): r=4 cos3θ
f(-r,-θ): -r = 4 cos3(-θ) ⇒ r = -4 cos3θ
∴The graph is not symmetric about the origin.
In your day-to-day routines, you use math when you go to the grocery store, bank, mall and when cooking. How do you imagine that you will use math in your healthcare career?
Answers
How many quarts in a gallon
Answers
The population of a type of local dragonfly can be found using an infinite geometric series where a1 = 65 and the common ratio is 1/6. Find the sum of this infinite series that will be the upper limit of this population.
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The common ratio is denoted as r. For values of r<1, the sum of the infinite series is equal to
S∞ = A₁/(1-r), where A1 is the first term of the sequence. Substituting A₁=65 and r=1/6:
S∞ = A₁/(1-r) = 65/(1-1/6)
S∞ = 78
The basement of a large department store features discounted merchandise. Their policy is to reduce the previous month's price of the item by 5 % each month for 6 months, and then give the unsold items to charity. Let Upper S Subscript 6 be the sale price for the sixth month and Upper P the original price. Express Upper S Subscript 6 as a function of Upper P Baseline Number .
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S = P(1-0.05t)
Simplifying,
S = 0.95Pt
So, after 6 months, the sales price would be:
S₆ = 0.95P(6)
S₆ = 5.7P