Answers
Answer:
[tex]\displaystyle \lim_{\Delta x \to 0} \frac{(x+\Delta x)^2-2(x+\Delta x)+1-(x^2-2x+1)}{\Delta x}=2x-2[/tex]
Step-by-step explanation:
We want to find the limit:
[tex]\displaystyle \lim_{\Delta x \to 0} \frac{(x+\Delta x)^2-2(x+\Delta x)+1-(x^2-2x+1)}{\Delta x}[/tex]
We can expand the numerator:
[tex]=\displaystyle \lim_{\Delta x \to 0} \frac{(x^2+2x\Delta x+\Delta x^2)+(-2x-2\Delta x)+1+(-x^2+2x-1)}{\Delta x}[/tex]
Simplify. Combine like terms:
[tex]\displaystyle \lim_{\Delta x\to 0} \frac{(x^2-x^2)+(-2x+2x)+(1-1)+(2x\Delta x+\Delta x^2-2\Delta x)}{y}[/tex]
The first three terms will cancel:
[tex]\displaystyle \lim_{\Delta x\to 0} \frac{2x\Delta x+\Delta x^2-2\Delta x}{\Delta x}[/tex]
Factor:
[tex]\displaystyle \lim_{\Delta x \to 0} \frac{\Delta x(2x+\Delta x-2)}{\Delta x}[/tex]
Cancel:
[tex]\displaystyle \lim_{\Delta x\to 0}2x+\Delta x-2[/tex]
Now, we can use direct substitution:
[tex]\displaystyle \begin{aligned} &\Rightarrow 2x+(0)-2\\ &=2x-2\end{aligned}[/tex]
Therefore:
[tex]\displaystyle \lim_{\Delta x \to 0} \frac{(x+\Delta x)^2-2(x+\Delta x)+1-(x^2-2x+1)}{\Delta x}=2x-2[/tex]
Answer:
2x-2
Step-by-step explanation:
let d = delta x
lim as d goes to 0 ( ( x+d)^2 - 2(x+d) +1 - ( x^2 -2x+1))/d
Expand the term in side the parentheses
( ( x+d)^2 - 2(x+d) +1 - ( x^2 -2x+1))
x^2 +2dx +d^2 -2x-2d+1 - x^2 +2x -1
Combine like terms
2dx +d^2 -2d
Replace
lim as d goes to 0 ( 2dx +d^2 -2d)/d
Factor out a d
lim as d goes to 0 d( 2x +d -2)/d
Cancel the d in the numerator and denominator
lim as d goes to 0 ( 2x +d -2)
Take the limit of each term as d goes to zero
2x +0-2
2x-2
Related Questions
For g(x)= (x+7)^2 + 6x determine the input of x when the output of g(x) =13
Answers
Answer:
x = -2 or -18.
Step-by-step explanation:
(x+7)^2 + 6x = 13
x^2 + 14x + 49 + 6x - 13 = 0
x^2 + 20x + 36 = 0
(x + 2)(x + 18) = 0
x = -2, -18.
Jordan's football team gained 12 yards on their first play. On the second play, the team
lost 8 yards. Which expression could be used to describe the total yards gained by
Jordan's team?
Answers
Answer:
4 yards
Step-by-step explanation:
they gained 12 yards and then lost 8
that can be expressed as 12-8=4
Answer:
12+(−8)
Step-by-step explanation:
How are the properties of segments and angles used to determine their measures
Answers
Answer:
See below
Step-by-step explanation:
Use of following postulates and properties of line segments and angles will help in measuring them.
The Segment Addition Postulate
It states that given 2 points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = ACThe Angle Addition Postulate
It states that if B is in the interior of AOC , then m∠AOB+m∠BOC=m∠AOC. That is, the measure of the larger angle is the sum of the measures of the two smaller ones.Which expression is equivalent to 3(3x + 8) ? A B С C D 9x = 21
Answers
Answer: it would be D.
Step-by-step explanation: you'd multiply the 3 by the 3x then multiply the 3 with the 8.
If f(x) = 2x + 7 and g(x)= 3x² -1, what expression represents (f(g(x)) ?
A 6x2 +5
B 6x2 +12
C 3x2 - 2x -8
D 3x2 + 2x + 6
Answers
Answer:
A. 6x^2+5
Step-by-step explanation:
The expression that represents the function (f(g(x))) is 6x² + 5, option A is correct.
Given expressions are f(x) = 2x + 7 and g(x) = 3x² - 1
To find (f(g(x))), we substitute g(x) into f(x):
f(g(x)) = 2(g(x)) + 7
Substituting g(x) = 3x² - 1:
f(g(x)) = 2(3x² - 1) + 7
Distributing the 2:
f(g(x)) = 6x² - 2 + 7
Combining like terms:
f(g(x)) = 6x² + 5
To learn more on Expressions click:
https://brainly.com/question/14083225
#SPJ2
I need help ASAP
integrated math ll
Answers
Answer:
Its most likely A
sorry If I get it wrong
Simplify this expression.
20x - 8 - 15x - 10
[?]x + [?]
Enter the numbers that go in the box.
Answers
Answer:
5x-18
Step-by-step explanation:
Answer:
3x+2y=4
Step-by-step explanation:
bro it says wait till 20 sec to send this brruuhhhhh
Olivia is tracking the growth rate of a population of termites, x, living in a mound. When the population is x = 400, it is the 0th hour. Initially, it takes f(x) = 1 hour for the population to grow by 400 termites. When the population grows by another 400 termites, the total time taken is f(x) = 1.585 hours. The time taken keeps decreasing to model the same incremental growth. Does the equation for f(x) or the graph of g(x) correctly model the situation?
Answers
Answer:
Based on the information in the problem statement, the function must pass through points (400 , 0), (800 , 1), and (1,200 , 1.585). Notice that the graph of function g(x) passes through these points.
Next, check the graph of f(x). Plot the function using the given equation to see which points it passes through.
The equation indeed starts at (400 , 0), but it doesn’t pass through the other two required points. So, the graph of g(x) fits the situation, but the equation for f(x)does not.
-2 3/4 divided by 5/-9 = ? in the simplest form
Answers
Answer:
Read Exp:
Step-by-step explanation:
Exact Form:
- 99/20
Decimal Form:
- 4.95
Mixed Number Form:
- 4 19/20
Answer:
Step-by-step explanation:
[tex]-2\frac{3}{4}[/tex] ÷ [tex]\frac{5}{-9}[/tex] = [tex]\frac{-11}{4}[/tex] ÷ [tex]\frac{5}{-9}[/tex]
[tex]=\frac{-11}{4}*\frac{-9}{5}\\\\\\=\frac{99}{20}\\\\\\= 4\frac{19}{20}[/tex]
Leonel computed the average rate of change in the depth of a pool over a two week interval to be zero. Which statement is true
Answers
A bag contains 7 red marbles and 4 blue marbles.
A marble is taken at random from the bag and replaced.
Another marble is taken from the bag.
Work out the probability that the two marbles
taken from the bag are the same colour.
Answers
Answer:
calculate the probability that the marbles are the same color, then subtract this probability from 1 to find the probability they are different colors. P(2 of the same) = P(2 green) + P(2 yellow) + P(2 red) = 1/26 + 5/26 + 2/26 = 8/26 = 4/13. P(2 different) = 1 - P(2 of the same) = 1 - 4/13 = 9/13.
Step-by-step explanation:
Solve for 20 points, 5stars and brainliest
Answers
Hey there!
Functions are basically like machines you put a number into and they give you a new one as an output. This f represents this machine. f(x) represents whatever the output is because it is the x after it has gone through the function machine.
We want to figure out what x is when f(x)=12. Well, we can simply replace f(x) with 12 in the first equation and solve for x!
12=-16x+8
We flip the equation so x is on the left side.
-16x+8=12
We subtract 8 from both sides.
-16x=4
We divide both sides by -16.
x=-1/4
Have a wonderful day! :D
Answer:
f(x) = -16x + 8
F(x) = 12
=> f(12) = -16x + 8
=> 12-8 = -16x + 8 - 8
=> 4 = 16x
=> 4/16 = 16x/16
=> 1/4 = x
So, the answer is 1/4.
You can just keep 0 as the whole number to answer this question.
NEED HELP ASAP ALGEBRA 1
There are approximately 330,000,000 people that live in the United States. There
are approximately 33,000,000 people that live in California. How many times
bigger is the population of the United States than the population of California?
Answers
Answer:
330,000,000/33,000,000=10
10 times bigger
Step-by-step explanation:
Solve for n
3n-2=2n
N=
Answers
Answer:
Hey there!
3n-2=2n
n-2=0
n=2
Let me know if this helps :)
n =?
3n - 2n = 2
n = 2 ✔️
Which of the following can not be used to express the number -6?
negative six
six below zero
six less than zero
six above zero
Answers
explanation: six is negative meaning it can’t be above zero
how to do splitting method of x square- 2x -8
Answers
Answer:
x^2+2x+1=0
x^2+(1+1)X+1=0
x^2+X+X+1=0
X(X+1)+1(X+1)=0
(X+1)(X+1)=0
X=-1,X=-1
hope it helps :)
please mark it the brainliest!
Answer:
Hey mate
kindly see attached picture:)
hope it helped you ☺️
HELP PLEASE. Solve. 6(x+20)=168
Answers
Answer:
x=8
Step-by-step explanation:
6(x+20)=168
Divide each side by 6
6/6(x+20)=168/6
x+20 =28
Subtract 20 from each side
x+20-20 = 28-20
x =8
Answer: x=8
Step-by-step explanation: 168/6=28. x+20=28. 8+20=28.
6(8+20)=168
Line segment EF has a length of 5 units. It is translated 5 units to the right on a coordinate plane to obtain line segment E'F'. What is the length of E'F?
Answers
Answer:
5 units
Step-by-step explanation:
If both points are translated the same amount, then the length of the line will stay the same.
PLEASEEEEEE Which system of equations does not have a real solution? y = x 2 + 3 x - 5 and 4 x + 5y = 20 y = x 2 + 3 x - 5 and x + y = -10 y = x 2+ 3 x- 5 and x + y = -9
Answers
Answer:
[tex]\Large \boxed{y = x^2 + 3 x - 5 \ \ \mathrm{and} \ \ x + y = -10}[/tex]
Step-by-step explanation:
y = x² + 3 x - 5 and x + y = -10 are the system of equations that do not have a real solution.
When the two equations are graphed and if they do not intersect, then there are no real solutions for the system of equations.
Answer:
Step-by-step explanation:
Complete the conditional statement. If -2a > 6, then _____.
Answers
Answer:
a < -3
Step-by-step explanation:
-2a > 6
Divide each side by -2, remembering to flip the inequality
-2a/-2 < 6/-2
a < -3
Step-by-step explanation:
[tex]-2a > 6 \\ a > \frac{6}{ - 2} \\ a > - 3[/tex]
Hope this helps
How do I do this, im not sure what im supposed to do
Answers
Answer:
Step-by-step explanation:
3<x<7
the set will contain all elements greater than 3 and less than 7
Roster form ={4,5,6}
b) Roster form :{-6,-5,-4,-3......}
set builder form is all numbers greater than -6
I hope it is right
The sum of 43.9 and a number is 49.65, as shown below. What number should go in the box to complete the addition problem? 43.9 plus box _.75 equals 49.65
Answers
43.9 + x = 49.65
Subtract 43.9 from both sides:
49.65 - 43.9 = 5.75
The missing number is 5
Your sock drawer has two white socks, four brown socks, and two black socks. You randomly pick a sock and put it on your left foot and then pick another sock and put it on your right foot. You leave the house with a white sock on your left foot and a brown sock on your right foot. Find the probability of this occuring.
Answers
Answer:
The probability of this occurring is 1/7
Step-by-step explanation:
Okay, here is a probability question.
From the question, we can identify the following;
Total number of socks = 2 + 4 + 2 = 8 socks
Since we are not given the order in which the socks was worn, we can assume any order.
Let’s say the right leg socks was worn first.
From the question, the socks on the right leg is a brown one.
So now let’s calculate the probability of selecting a brown socks out of the mix
That would be ;
number of brown socks/ total number of socks = 4/8 = 1/2
Now, for the left foot, we are having white sock here.
Kindly recall that since we already have a sock on the right foot, we have 7 socks left to pick from.
Now we need the probability of picking a white sock from the total 7. That would be ; 2/7
So the probability of both action occurring is simply the product of both probabilities and that is ;
1/2 * 2/7 = 1/7
Q={(-2,4), (0,2), (-1,3), (4,-2)} Domain and range
Answers
Answer:
Read exp:
Step-by-step explanation:
Domain: {(-2,0), (-1,4)}
Range: {(4,2), (3,-2)}
One morning, the temperature in Oakdale was -4°F. By noon, a strong wind had caused the temperature to drop another 3°F. What was the temperature at noon in Oakdale?
Answers
Answer:
-7°F
Step-by-step explanation:
if -4 was it's original number and the number has dropped means subtraction and by that means subtracting 3 to -4.Answer: -7
Step-by-step explanation: if -4 was it's original number and the number has dropped means subtraction and by that means subtracting 3 to -4.
what is the width?
2w + 2(w+6) = 84
Answers
Answer: w = 18
Step-by-step explanation:
2w + 2(w+6) = 84
Distribute: 2w + 2w + 12 = 84
4w + 12 = 84
4w=72
If he pays $16.80 for one year. He receives one magazine each month for 12 months. Find the dollars he pays for each
magazine
Answers
Answer:
About $1.40 per each monthly magazine.
Step-by-step explanation:
16.80 / 12 = 1.4
PLEASE ANYONE HEEELLLLPP.......I NEED HELP I DONT UNDERSTAND!!!
Answers
Answer:
[tex]\large \boxed{\mathrm{Option \ 4}}[/tex]
Step-by-step explanation:
The area has to be found for the floor.
The whole rectangle = length × width = x × (x-4), has an area of x(x-4).
The area x(x-4) has to be subtracted from the area of the stage and closet.
Area of stage = area of triangle : base × height × 1/2
(x-4) × 8 × 1/2
(0.5) × (8) × (x-4)
Area of closet = area of rectangle : length × width
(3) × (7)
The area of the floor = x(x-4) - 0.5(8)(x-4) - 3(7)
Answer:
i don’t understand it either
Step-by-step explanation:
Point P is located at (-3,5)
Point P' is the image of P after a translation three units to the left, then a reflection using the x-axis.
Find the coordinates of P'
Answers
Answer:
P' (- 7, - 5 )
Step-by-step explanation:
A translation of 3 units to the left means subtractin 3 from the x- coordinate with no change to the y- coordinate, thus
P(- 3, 5 ) → (- 3 - 4, 5 ) → (- 7, 5 )
Under a reflection in the x- axis
a point (x, y ) → (x, - y ), thus
(- 7, 5 ) → P'(- 7, - 5 )
Joseph built a model of a pyramid where the base of the pyramid is a square. If the base has an area of 49 cm2 (squared), what is the side length of the base?
Answers
Answer:
7 cm
Step-by-step explanation:
We are told that the pyramid has a square base of an area of 49 cm².
Therefore, the side length of the base of the pyramid is still the same as the side length of a square having an area of 49 cm².
Area of a square = s², where s is the side length of the square.
The side length of the base can be gotten using the following equation,
[tex] s^2 = 49 [/tex]
Solve for s by looking for the share root of both sides.
[tex] \sqrt{s^2} = \sqrt{49} [/tex]
[tex] s = 7 [/tex]
The side length of the base = 7 cm