If [tex]f(x)[/tex] has a removable discontinuity at [tex]x=a[/tex], then the limit
[tex]\displaystyle \lim_{x\to a} \frac{f(x)}{x-a}[/tex]
exists and is finite.
A non-removable discontinuity at [tex]x=b[/tex] would entail a non-finite limit,
[tex]\displaystyle \lim_{x\to b} \frac{f(x)}{x-b} = \pm\infty[/tex]
or the limit does not exist (which could be due to the limits from either side of [tex]x=b[/tex] not matching or existing).
For a rational function, we want
[tex]f(x) = \dfrac{p(x)}{q(x)}[/tex]
where [tex]p[/tex] and [tex]q[/tex] are polynomials in [tex]x[/tex]. To get a removable discontinuity at [tex]x=a[/tex], both [tex]p[/tex] and [tex]q[/tex] must be divisible by [tex]x-a[/tex], and the limit of their quotient after removing these factors still exists. That is,
[tex]\displaystyle \lim_{x\to a} f(x) = \lim_{x\to a} \frac{p(x)}{q(x)} = \lim_{x\to a} \frac{(x-a)p^*(x)}{(x-a)q^*(x)} = \lim_{x\to a} \frac{p^*(x)}{q^*(x)} = \frac{p^*(a)}{q^*(a)}[/tex]
On the flip side, we get a non-removable discontinuity [tex]x=b[/tex] if [tex]p[/tex] is not divisible by [tex]x-b[/tex], in which case
[tex]\displaystyle \lim_{x\to b} f(x) = \lim_{x\to b} \frac{p(x)}{q(x)} = \lim_{x\to b} \frac{p(x)}{(x-b)q^*(x)} = \frac{p(b)}{0\times q^*(b)}[/tex]
and this is undefined.
Suppose [tex]f(x)[/tex] has a non-removable discontinuity at [tex]x=-5[/tex] and a removable one at [tex]x=4[/tex]. Then one such function could be
[tex]f(x) = \dfrac{x-4}{(x-4)(x+5)} = \dfrac{x-4}{x^2+x-20}[/tex]
Which statement explains how you could use coordinate geometry to prove that quadrilateral ABCD is a square?
Shape ABCD is shown. Point A is at negative 3, 5. Point B is at 1, 7. Point C is at 3, 3. Point D is at negative 1, 1.
If c = 16, solve for b
Answer:
Step-by-step explanation:
given
cos(30°) = [tex]\frac{adjacent}{hypotenuse} \\[/tex]
cos(30°) = [tex]\frac{b}{c} \\[/tex]
cos(30°)=[tex]\frac{b}{16}[/tex]
b = 16cos(30°)
b [tex]16(\frac{\sqrt{3} }{2})\\ = 8\sqrt{3}[/tex]
What is the value of x when Rq=3x+2 ,QN =2x and SM=3x?
The value of x is 2 because the centroid of the triangle divides each median in the ratio of 2:1 option (C) is correct.
What is the triangle?The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have:
RQ = 3x+2 ,QN = 2x and SM=3x
In the figure, the TM, Rn, and SL are medians of the triangle SRT and Q is the centroid.
The centroid of the triangle divides each median in the ratio 2:1
RQ/QN = 2/1
(3x+2)/2x = 2/1
After solving:
3x + 2 = 4x
x = 2
Thus, the value of x is 2 because the centroid of the triangle divides each median in the ratio of 2:1 option (C) is correct.
Learn more about the triangle here:
brainly.com/question/25813512
#SPJ1
1. Use the given conditions to write an equation for the line in point-slope form and general form. Passing through (−4,4) and parallel to the line whose equation is 7x−9y−8=0 Question content area bottom Part 1 The equation of the line in point-slope form is enter your response here. (Type an equation. Use integers or fractions for any numbers in the equation.) Part 2 The equation of the line in general form is enter your response here=0. (Type an expression using x and y as the variables. Simplify your answer. Use integers or fractions for any numbers in the expression.)
1) The equation of the line passing through (−4, 4) and parallel to the line whose equation is 7x − 9y − 8 = 0 is; y - 4 = ⁷/₉(x + 4)
How to find the equation of a line?
1) We are told that the line passes through (−4, 4) and is parallel to the line whose equation is 7x − 9y − 8 = 0
Thus, let us rearrange to find the slope.
7x − 9y − 8 = 0
⇒ 9y = 7x - 8
⇒ y = ⁷/₉x - ⁸/₉
Slope; m = ⁷/₉
Now, the point slope formula is;
y − y₁ = m(x − x₁)
where;
y₁ is the y-coordinate
x₁ is the x-coordinate
m is the slope
Thus the line Passing through (−4,4) is;
y - 4 = ⁷/₉(x + 4)
2) The equation in general form is;
y = 4 + ⁷/₉x + ²⁸/₉
y = ⁷/₉x + ⁶⁴/₉
Read more about equation of a line at; https://brainly.com/question/13763238
#SPJ1
If a person who is 5 feet tall throws a ball into the air, the path can be modeled using the table of values, where x represents the time in seconds and y is the height of the ball in feet. x y 0 5 1 6.75 2 8 3 8.75 4 9 5 8.75 which quadratic equation models the data in the table?
The quadratic equation is y = -0.15x² + 2x + 5.5 , Option D is the correct answer.
The complete question is
If a person who is 5.5 feet tall throws a baseball into the air, the path can be modelled using the table of values, where x represents the time in seconds and y is the height of the ball in feet.
(table is in the photo below)
Which quadratic equation models the data in the table?
y= −0.25x2 + 2x + 5.5
y= −0.35x2 + 2x + 5.5
y= −0.27x2 + 3x + 5.5
y= −0.15x2 + 2x + 5.5
The quadratic equation represented by the table is y = -0.15x² + 2x + 5.5
What is an Equation ?When two algebraic expressions are linked with an equal sign , the expression formed is called an Equation.
The standard form of the Quadratic equation is
y = ax² + bx + c
here a, b and c are constants.
From the given data in the table
at point (0, 5.5)
5.5 = a(0)² + b(0) + c
at point (1, 7.35)
7.35 = a(1)² + b(1) + c
at point (2, 8.9)
8.9 = a(2)² + b(2) + c
The system of equations will be solved to determine the value of a,b and c
a= -0.15, b = 2, c = 5.5
Therefore , The quadratic equation is y = -0.15x² + 2x + 5.5 .
To known more about Equation
https://brainly.com/question/10413253
#SPJ1
Answer:
B) y= -0.25x^2 + 2x + 5
Step-by-step explanation:
I got it correct on test
PS: Can I have brainiest?
(Giving 40 points and brainly if correct!)
If OP=17 and QP=6, what is OQ? First, complete the Segment Addition Postulate for this problem.
OQ+QP= ?
In the given diagram, the length of OQ is 11
Calculating the length of a line segmentFrom the question, we are to determine the length of OQ
From the given information,
OP = 17
QP = 6
In the diagram, we can observe that
OQ + QP = OP
∴ OQ + 6 = 17
Subtract 6 from both sides
OQ + 6 - 6 = 17 - 6
OQ = 11
Hence, the length of OQ is 11
Learn more on Calculating the length of a line here: https://brainly.com/question/11795570
#SPJ1
[tex]\huge \boxed{\sf 11}\\\\\\\displaystyle \sf OP=OQ+QP\\\\OQ=OP-QP\\\\OQ=17-6\\\\OQ=11[/tex]
When the outlier are removed, how does the mean change?
A.
The mean decreases by 3.
B.
The mean increased by 2.
C.
The mean increased by 3.
D.
There are no outliers.
Step-by-step explanation:
hope you can understand
Toby has five coins. Three of the coins add up to 30p. Three of the coins add up to 40p. All the coins add up to 50p. List Tony's coins in ascending order of value.
Tony's coins in ascending order of value will be 5p, 10p, and 15p.
Definition of in Ascending order
Arranged in a series that begins with the smallest or least and ends with the largest or greatest The children were lined up in ascending order of height. Test score are listed in ascending order from lowest to highest.
How do depict the information?
Based on the information given, the values of the coins will be 5p, 5p, 10p, 15p, and 15p.
In this case, 5p + 10p + 15p = 30p
10p + 15p + 15p = 40p
5p + 5p + 10p + 15p + 15p = 50p
Therefore, Tony's coins in ascending order of value will be 5p, 10p, and 15p.
Learn more about coins on: brainly.com/question/2974216
#SPJ10
Solve for x. Round to the nearest tenth, if necessary
[tex]\tan 61^{\circ}=\frac{59}{x}\\\\x=\frac{59}{\tan 61^{\circ}} \approx \boxed{32.7}[/tex]
PLEASE SOLVE THIS
Also I really don't want a long answer so you don't have to give me an explanation
Answer:
No
Step-by-step explanation:
To determine if a point is a solution to a system of equations, you need to determine if the point is a solution to both equations.
Is ( 2,10) a solution to -3x-4y = 4
Substitute into the equation and see if it is true
-3(2) -4(10) = 4
-6 -40 = 4
-46 =4
This is not true so it is not a solution
Answer:
No
Step-by-step explanation:
The solution(s) of a system is/are the point(s) (x, y) where the lines intersect.
The question asks if (2, 10) is a solution of the system. This means the "x" value is "2" and the "y" value is "10".
We can substitute those values into both of the equations.
[tex]-3x-4y=4\\-3(2)-4(10)=4\\-6-40=4\\-46=6 \Rightarrow Incorrect![/tex]
The "x" and "y" values must be true for both equations, therefore (2, 10) is not a solution of the system.
Part A: Is there any correlation between the number of hours spent practicing and the score in the game? Justify your answer. (4 points) Part B: Write a function that best fits the data. (3 points) Part C: What does the slope and y-intercept of the plot indicate? (3 points)
All the parts are answered , y = 6x + 5 represents the scatter data points given.
The complete question is
A coach is assessing the correlation between the number of hours spent practising and the average number of points scored in a game. The table shows the data:
Number of hours spent practising
(x) 0 0.5 1 1.5 2 2.5 3 3.5 4
Score in the game
(y) 5 8 11 14 17 20 23 26 29
Part A: Is there any correlation between the number of hours spent practising and the score in the game? Justify your answer. (4 points)
Part B: Write a function that best fits the data. (3 points)
Part C: What does the slope and y-intercept of the plot indicate? (3 points)
What is a Function ?A function is a law that connects the y and x variable , i.e. the dependent and independent variable.
Part (A)
There is a positive correlation between the number of hours spent practising and the score in the game , as the time is increasing the scores is also seen to be increasing.
Part (B)
From the online scatter point equation calculator or by using three points which best fits the linear regression the equation can be determined
y = 6x + 5
x represents the timeline spent in practising
Part C:
slope = 6
When the time spent practising increases by 1 hour, the average scores increases by 1 hour, the score in a game is predicted to increase by an average of 6 and
as intercept = 5
When no time is spent on the practice the score obtained is 5.
To know more about Function
https://brainly.com/question/12431044
#SPJ1
Which graph represents the solution set for the compound inequality below? ---x+ 10 ≥7 X-10≥7
x-10≥7
A graph which represents the solution set for the compound inequality is shown in the image attached below.
How to determine the graph?In order to determine the graph which represents the solution set for the compound inequality, we would evaluate the given inequalities as follows.
Given the following inequalities:
⅓x + 10 ≥ 7
x - 10 ≥ 7
For the first inequality, we have:
⅓x + 10 ≥ 7
Multiply all through by 3;
x + 30 ≥ 21
x ≥ 21 - 30
x ≥ -9 ⇒ x < 9.
For the first inequality, we have:
x - 10 ≥ 7
x ≥ 7 + 10
x ≥ 17.
In conclusion, a graph which represents the solution set for the compound inequality is shown by using the number line in the image attached below.
Read more on inequalities here: https://brainly.com/question/24372553
#SPJ1
A 12 foot ladder leans against a wall so that the base of the ladder is 7 feet from the wall. How high up on the wall will the ladder reach? Round to the nearest hundredth of a foot.
Find the surface area of this composite solid.
Answer:
d. 93 [tex]m^{2}[/tex]
Step-by-step explanation:
4×3= 12, 12/2 =6, 6×4 = 24
5×3= 15, 15×4= 60
3×3=9,
24+60+9= 93
simplify -9 2/7-(-10 3/7)
Answer:
8/7
Step-by-step explanation:
-convert the mixed fractions into improper fractions
-find the LCD (least common denominator)
-solve!
-65/7-(-73/7)
8/7
mixed number form: 1 1/7
hope this helps!!
Answer:
8/7
Step-by-step explanation:
On day 1, Perry shipped packages and tracked their weight to the nearest kilogram. The packages weighed 1, 8, 1, 12, 1, 11, 7, and 6 kilograms.
On day 2, Perry shipped 12 kilograms more weight than he did on day 1 while shipping the same number of packages.
What is the increase in the mean kilograms per package for the second day compared to the first?
Enter your answer in the box.
Answer:
1.5kg
Step-by-step explanation:
The mean for the packages on day 1 will be:
= (1 + 8 + 1 + 12 + 1 + 11 + 7 + 6)/8
= 47/8
= 5.875
The mean for day 2 will be:
= (47 + 12)/8
= 59/8
= 7.375
The increase in mean:
= 7.375 - 5.875
= 1.5
(X-3)2 -0
Ajuda, alguém ajuda?
Answer:
(X- 3)² - 0
(X - 3 )( X - 3 )
x² + 9 - 6x
x² - 6x + 9
a = 1
b = -6
c = 9
Find six rational numbers between -2 and 5
Answer:
1/4, 0.5, -4/6, 4.5, 1/3, 7/8
explanation: it is the ratio of two integers
a/b where b is not = to 0
Alex, jas and stef each get a student loan to help with living expenses. they decide to allocate two fifths of their loans for food, and one-sixth for travel. what fraction of their student loan will be left to spend?
The fraction of their student loan will be left to spend is half of their loan.
A number expressed quotient, in which numerator is divided by denominator is called a fraction.
Let the loan amount be $100.
Expenses for food is given that two fifths of their loan
i.e.
= 2/5 × 100
= $40
Now,
Remaining part will be = $100- $40 = $60
So,
Expenses for travel are given that one sixth of their loan,
i.e.
= 1/6 × 60
= $10
So,
Remaining part will be = $60 - $10 = $50
Hence, the fraction of their student loan will be left to spend is half of their loan.
Learn more about fraction here:
https://brainly.com/question/415517
#SPJ10
A robot moves at a constant speed. The distance it moves and the time it spends moving are shown in this table:
10min 7km
15min 10.5km
20min 14km
Write an equation to describe the relationship between t, the time, and d, the distance.
The equation to describe the relationship between t, the time, and d, the distance is t = 1.43d
What is a proportional relationship?It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.
As we know,
time(t) = speed(s)×distance(d)
Speed is constant:
t ∝ d
t = kd
k = t/d = 10/7 = 15/10.5 = 20/14 = 1.428 ≈ 1.43
The equation is:
t = 1.43d
Thus, the equation to describe the relationship between t, the time, and d, the distance is t = 1.43d
Learn more about the proportional here:
brainly.com/question/14263719
#SPJ1
Answer:
d=0.7t
Step-by-step explanation:
the other dude is wrong
If the zeros of a quadratic equation are
7 and 4, what would be the factors?
Answer:
The factors are (x-7) and (x-4)
Step-by-step explanation:
We are finding the factors of a function from the zeros
The zeros are 7 and 4
We can use the zero product property which is
(x-b)(x-c) = 0 where b and c are the zeros
(x-7) (x-4) =0
The factors are (x-7) and (x-4)
Can someone help me with fill the blanks of this pls? It’s about geometry
Answer:
see below
Step-by-step explanation:
2: letter at the vertex, placing a letter or number inside .... , or by using 3 letters
3:
WXY
WXZ
YXZ
4: X
The coordinates of the vertices of △HIJ are H(−2,2), I(8,−2), and J(−4,−3). Identify the perimeter of △HIJ to the nearest tenth
Answer:
28.2
Step-by-step explanation:
The perimeter of a plane figure is the sum of the lengths of its sides. Those lengths and their sum can be found a number of different ways.
__
graphing aidThe values computed by the graphing program in the attachment add up to 28.2 units.
__
using algebraThe length of each side of the triangle can be computed using the distance formula or the Pythagorean theorem. For a given "rise" and "run", the length of a line segment is ...
d = √(rise^2 +run^2)
HI = √((-4)^2 +10^2) = √116 ≈ 10.770
IJ = √(1^2 +12^2) = √145 ≈ 12.042
JH = √(5^2 +2^2) = √29 ≈ 5.385
The perimeter is the total of the lengths of the sides:
P = HI +IJ +JH = 10.770 +12.042 +5.385 = 28.197
To the nearest tenth, the perimeter is 28.2 units.
Which of the following equations demonstrate the multiplication property of equality for the equation x = 2? Check all
that apply.
✔x(3) = 2(4)
x(5) = 10
x(1.5) = 2(2)
x(0.5) = 2(0.5)
x(12) = 12
Intro
Done
3 of 12
Answer: x(5) = 10 has the multiplication property.
Step-by-step explanation:
To verify the multiplication property of equality , We need to put the value of x= 2
1. x(5) = 10
Solution = 2(5) = 10 ✔
2. x(1.5) = 2(2)
Solution = 2 (1.5) = 3 X
3. x(0.5) = 2(0.5)
Solution = 2 (0.5) = 1 X
4. x(12) = 12
Solution = 2 (12) = 24 X
For more multiplication property related question visit here
https://brainly.com/question/14059007
#SPJ1
Answer:
Step-by-step explanation:
answer B and D
I got it right and didnt spell the entire constitution
suppose that average total cost is $36 when q=24. what is the profit-maximizing price and resulting profit?
The profit-maximizing price and resulting profits are $36 and $0 respectively.
What is profit-maximizing price?The profit-maximizing price for the monopoly will be to produce at the quantity where marginal revenue is equal to marginal cost.
Therefore, suppose the average total cost is $36 when q = 24, the profit maximizing price is as follows:
when Q = 24 at average cost = $36,
Then,
profit-maximizing price = p = $36
Hence, the resulting profit is as follows;
resulting profit = 36 - 36 = $0
learn more on profit here:https://brainly.com/question/13376895
#SPJ11
The measure of an angle is 42.1°. What is the measure of its complementary angle?
Answer:
47.9°
Step-by-step explanation:
complementary angles are two angles that add up to 90° [90 degrees]
so, we can find the complementary angle of 42.1 by finding what angle it needs to add up to 90
we can use subtraction to find this value:
90 - 42.1 = 47.9
So, the complementary angle to the angle 42.1° has a measure of 47.9°
hope this helps, have a lovely day!! :)
You need to know that two angles are complementary when they are equal to 90°. If you want to find the complement of an angle, and you have one of the angle measures, you need to subtract it from 90°. You have an angle measure of 42.1°. This will be the number you subtract.
⇢ 90° - 42.1°
⇢ 47.9
Which angle refers to the same angle as \angle DAC∠DACangle, D, A, C?
Answer:
Option
Step-by-step explanation: The way tell what the answer is are the similar lines. The single yellow line helps indicate that it's a similar angle.
Select the correct answer.
Consider the function represented in this table.
X
f(x)
-1
-21
0
-9
1
3
2
15
Which of these tables could represent the inverse of function f? Ahh
State the value of 'x' in this equation, and explain why you know this to be true without doing any calculations. 5X=59
The value of x in the equation is 59/5
How to solve for x?The equation is given as:
5x = 59
Divide both sides by 5
x = 59/5
This means that the value of x in the equation is 59/5
To know if the value is accurate, we simply multiply 5 by 59/5 and we get 59 as in 5x = 59
Read more about equations at:
https://brainly.com/question/2972832
#SPJ1
The nth term of a sequence is -2n-4. Work out the 50th term of the sequence
Answer:
-104
Step-by-step explanation:
Completed by plugging 50 in the equation:
-2(50) - 4 =
-100 - 4 =
-104
