The absolute value function is defined as
[tex]|x| = \begin{cases}x & \text{for }x \ge 0 \\ -x & \text{for }x < 0\end{cases}[/tex]
If x is strictly positive (x > 0), then |x| = x, and d|x|/dx = dx/dx = 1.
If x is strictly negative (x < 0), then |x| = -x, and d|x|/dx = d(-x)/dx = -1.
But if x = 0, the derivative doesn't exist!
In order for the derivative of a function f(x) to exist at x = c, the limit
[tex]\displaystyle \lim_{x\to c}\frac{f(x) - f(c)}{x-c}[/tex]
must exist. This limit does not exist for f(x) = |x| and c = 0 because the value of the limit depends on which way x approaches 0.
If x approaches 0 from below (so x < 0), we have
[tex]\displaystyle \lim_{x\to 0^-}\frac{|x|}x = \lim_{x\to0^-}-\frac xx = -1[/tex]
whereas if x approaches 0 from above (so x > 0), we have
[tex]\displaystyle \lim_{x\to 0^+}\frac{|x|}x = \lim_{x\to0^+}\frac xx = 1[/tex]
But 1 ≠ -1, so the limit and hence derivative doesn't exist at x = 0.
Putting everything together, you can define the derivative of |x| as
[tex]\dfrac{d|x|}{dx} = \begin{cases}1 & \text{for } x > 0 \\ \text{unde fined} & \text{for }x = 0 \\ -1 & \text{for }x < 0 \end{cases}[/tex]
What coordinates do I plot at
Answer:
Step-by-step explanation:
y - 10 = -2(x - 10)
y - 10 = -2x + 20
y = -2x + 20 + 10
y = -2x + 30
When x = 0 ; y = 0 + 30 = 30 ; (0,30)
When x = 10 ; y = -2*10 + 30 = -20 +30 = 10 ; (10 , 10)
When x = 5 ; y = -2*5 + 30 = -10 + 30 = 20 ; (5 , 20)
Plot ( 0 ,30) ; (10,10) & (5,20)
A path is made of red tiles and blue tiles.
1/5of the tiles are red.
a) Write down the ratio of red tiles to blue tiles in its simplest form.
There is a total of 85 tiles.
b) Work out the number of blue tiles.
(2)
Total marks: 3
Answer: 17 red , 68 blue
Step-by-step explanation:
85 divided by 5=17
1/5 of 85=17
17x4=68
4/5 of 85=68
(1). The ratio of red tiles to blue tiles is [tex]\frac{1}{4}[/tex]
(2). The number of blue tiles are 68.
Fraction:It is given that,
A path is made by red and blue tiles and [tex]\frac{1}{5}[/tex] part of tiles are red.
So that,
Blue tiles[tex]=1-\frac{1}{5} =\frac{4}{5}[/tex] parts.
The ratio of red tiles to blue tiles in its simplest form,
[tex]\frac{Red}{Blue}=\frac{1}{5}*\frac{5}{4} \\\\\frac{Red}{Blue}=\frac{1}{4}[/tex]
Since, total number of tiles are 85.
Number of blue tiles[tex]=\frac{4}{5} *85=68[/tex]
Learn more about the fraction here:
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Answer:
C. (2,7)
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
In order to find which ordered pair makes the equation true, we have to understand that the format of a coordinate pair is (x, y)
Knowing that, we can plug in the numbers from each coordinate pair that correspond to the x and y values of the equation
For instance, for A (-1, 5) we would plug in 5 for x and -1 for y
Now we have -1 = 3(5) + 1
Multiply 3 and 5
-1 = 15 +1
Add
-1 = 16
The numbers on each side are not equal so this is not the answer
Now for B (10,3)
We do the same thing, plug in the numbers
3 = 3(10) + 1
Multiply
3 = 30+1
3 = 31
This choice is false as well
Option C (2, 7)
Plug in the numbers
7 = 3(2) + 1
Multiply
7 = 6+1
Add
7 = 7
Thus C is the answer as it is the same number on both sides~!
Hope this helpsss! :D
What is the missing constant term in the perfect square that starts with x2 + 18x
Answer:
81
Step-by-step explanation:
Take half of the x-term coefficient, and square it.
Half of 18 is 9.
9² = 81
Answer: 81
please help me solve this problem.
Answer:
a=36
Step-by-step explanation:
The given angles are corresponding
2a+3a=180
5a=180
a=180/5=36
What are the sums for both of those?
100 POINTS IF U GET THIS RIGHT!
Answer:
The y-intercept is 4.
Step-by-step explanation:
Our equation: y = mx + b
m = slope
b = y-intercept
=> Now, let's compare:
=> y = mx + b = y = -7x + 4
We can tell that b = 4
Hoped this helped.
[tex]y =-7x +4 \\\\\text{ The above equation is in a form of y=mx+b, where b is the y-intercept}\\\\\\\text{Hence the y-intercept of the given equation is}~ 4.[/tex]
2x-4>-14 or 2x-4\leq10
Answer:
x>0
Step-by-step explanation:
2x−4>−142x−4
Multiplica −14 y 2 para obtener −28.
2x−4>−28x−4
Agrega 28x a ambos lados.
2x−4+28x>−4
Combina 2x y 28x para obtener 30x.
30x−4>−4
Agrega 4 a ambos lados.
30x>−4+4
Suma −4 y 4 para obtener 0.
30x>0
El producto de dos números es >0 si ambos son >0 o <0. Puesto que 30>0, x debe ser >0.
x>0
|3x - 5| = |6x - 1|
Answer:
x = -4/3
Step-by-step explanation:
|3x - 5| = |6x - 1|
=> 3x - 5 = 6x - 1
=> 1 - 5 = 6x - 3x
=> -4 = 3x
=> x = -4/3
Hoped this helped.
Answer:
x = [tex]\frac{-4}{3}[/tex] or x = -1.333333.....
Step-by-step explanation:
3x - 5 = 6x - 1
Move the 3x to the other side by subtracting, because the 3x is positive on the left side.
-5 = 3x - 1
Move -1 to the other side by adding.
-4 = 3x
Divide by 3 to get x
[tex]\frac{-4}{3}[/tex] = x
Hope this helps! <3
3) Find the values of a,b ,c and for y=x^2-9x+18.
Answer:
a = 1
b = -9
c = 18
titan won 9 games last year and average eight this year write equation for the number of wins they can except to have after X year
Step-by-step explanation:
x = how many games won last year
x - 1 = how many games won each year
You can buy a seat cushion at the College Softball World Series for $4. They
paid $2.50 to have them made, and they make a profit of $300 when sold out.
How many seat cushions did they have made?
Answer:
$118.40
2.50x Plus 4 Equal 300
2.50x Equal 296
2.50x/2.50 Equal $118.40
PLEASE TELL ME IF I AM WRONG!What is a logarithm.
Answer:
Logarithms were invented in the 17th century as a calculation tool by Scottish mathematician John Napier (1550 to 1617), who coined the term from the Greek words for ratio (logos) and number (arithmos
Step-by-step explanation:
Express each ratio as a fraction in the simplest form:
8dm to 3.2 m and 0.3k to 500 m
Answer:
1/4, 3/5
Step-by-step explanation:
0.8/3.2=8/32=1/4
0.3/0.5=3/5
IDENTIFY TWO SEGMENTS THAT ARE MARKED PARALLEL TO EACH OTHER.
PLEASE HELP, WILL GIVE BRAINLIEST.
Hey there!
I believe segment ED and AB are parrarel to each other.
Hope this helps! :)
Have a great day!
Answer Quick! No links, please.
Answer:
#1
Slope: 1/2
Y Intercept: -3
#2
Slope: -3
Y Intercept: 2
The slope is -10 and it passes through (2,5)
Answer:
y=-10x+25
Step-by-step explanation:
Help please please help me
Answer:
Hi! I hope this answer helps you.
In mathematics, the vertical line test is a visual way to determine if a curve is a graph of a function or not. A function can only have one output, y, for each unique input, x.
any vertical line in the plane can intersect the graph of a function at most once.
HOW TO DO THIS
take your pencil and place it on your paper vertically (up and down direction)
move the pencil across the paper to the right
if the pencil crosses more than two points on the line it is not a function
the first problem would be a function
the second problem would be a function
the third problem would not be a function
hope this helps !!!!
What are the solutions of y=x^2+5x-7
Answer:
You have two variables, and only one condition. It means you have infinite solutions of the form [tex](t; t^2+5t-7)[/tex]. Technically correct, probably not what you want to know.
If you wanted to know if and where the RHS crosses the x axis, the points are the solution to
[tex]x^2+5x-7= 0 \rightarrow x=\frac12(-5\pm\sqrt{25+28})\\x_1= \frac12(\sqrt{53}-5); x_2=-\frac12(\sqrt{53}+5)[/tex]
If you wanted the graph it's a parabola passing through the two points we just found, (0;-7), and with an axis of equation [tex]x=-\frac52[/tex].
The segments shown below could form a triangle.
A
с
B
4
9
B
15
A
A. True
B. False
Answer: True.
Step-by-step explanation:
do the math and u will see
No, The segments shown below could not form a triangle.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
Three line segment with measure 9 , 4 and 15 are shown.
We know that;
The sum of two sides of a triangle are always greater than the third side,
Here, 9 + 4 = 13 < 15
Hence, The segments shown below could not form a triangle.
Thus, The segments shown below could not form a triangle.
Learn more about the triangle visit;
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I’m not good at stuff like this but I would give my life if someone can help me please
Answer:
I want so much to help u, but I can't right now. I will come back tomorrow and answer it.
What is 45% written as a fraction in lowest terms?
Enter your answer by filling in the boxes.
Answer:
✓ 45% = 9/20
Step-by-step explanation:
What box?
Answer:
9/20.
Step-by-step explanation:
45/100
= 45/5 / 100/5
= 9/20.
two rays that have a common endpoint and form a line
Answer: Overview. An angle is the union of two rays with a common endpoint. The common endpoint of the rays is called the vertex of the angle, and the rays themselves are called the sides of the angle.
Step-by-step explanation: just have done with before! i am really good at it
What is the location of F on the decimal number line below?
Write your answer as a decimal.
6.7
6.8
6.9
II
Х
?
Solve for value of y
(9y - 6) + 51 = 90 (right angle)
9y - 6 + 51 = 90
9y - 6 = 90 - 51
9y - 6 = 39
9y = 39 + 6
9y = 45
y = 45/9
y = 5
_______
Hope it helps!
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Laura is saving to buy a 10-speed bike that costs $189. For four weeks she saved part of her check in the amounts of $15, $39, $18 and $27. How much more does she need?
Answer:
90$
Step-by-step explanation:
Answer:
$90
Step-by-step explanation:
$15 + $39 + $18 + $27 = $99
$189 - $99 = $90
Hope this helps <3
on a map, 1 inch equals 25 miles. If two cites are 4 inches apart on the map, how far are they actually apart?
Answer: They are 100 miles apart
Step-by-step explanation:
1 inch = 25 miles
4x25=100
Answer: 100 miles
Step-by-step explanation:
Since we have 25 miles per inch. and there are 4 inches, you would multiply 25 by 4 to get to your answer of 100 miles.
25x4=100
01:36:08
Which two events are independent?
A
B
С
Total
X
15
5
30
50
Y
5
8
15
28
Z
10
7
5
22
Total
30
20
50
100
A and X
A and Y
Band X
B and y
Sede
Save and Exit
y.com/contentViewers AssessmentViewer Activit
Answer:
check online for more information
Help 10 pts available !!!!!
Answer:
increasing
add
21
those are the answers for the blanks going down
what would be 8/1 x 1/2
Answer:
4.
Step-by-step explanation:
8*1 / 1*2
= 8/2
= 4.
[tex]8\times \dfrac 12 = 4[/tex]
