Answers
A real-valued univariate function f=f(x) has a jump discontinuity at a point [tex]x_0[/tex] in its domain provided that
[tex]\lim \limits_{x\to x_0^-}f(x)=A_1[/tex]
and
[tex]\lim \limits_{x\to x_0^+}f(x)=A_2[/tex]
both exist and that [tex]A_1\neq A_2.[/tex]
As you can see at x=-3,
[tex]\lim \limits_{x\to -3^-}f(x)=6,[/tex] [tex]\lim \limits_{x\to -3^+}f(x)=9[/tex] and [tex]6\neq 9.[/tex]
Therefore, there is a jump discontinuity at x=-3.
Answer: correct choice is A.
Related Questions
In 2015 there were approximately 33,500 firearm fatalities. How many deaths per hour
Answers
A cafeteria uses 556 kg of rice each week. The rice comes in bags that hold 13 kg each.
How many bags of rice does the cafeteria use each week?
A. 42
B.42 1/3
C.42 10/13
or
D.43 1/3
Answers
A grocer is going to sort 13.5 pounds of candy weighing 0.75 each. How much candy will be left over? 0 pounds, 0.38 pounds, 0.50pounds, 10.13 pounds
Answers
0 pounds
divide 13.5 by 0.75
[tex]\frac{13.5}{0.75}[/tex] = 18 with no remainder
Aiden is a taxi driver. M(n) models Aiden's fee (in dollars) for his n^th drive on a certain day.What does the statement M(8)<M(4)M, mean
Answers
M(n) denotes Aiden's fee (in dollars) for his n^th drive on a certain day.
Then:
M(8) is Aiden's fee for his 8th drive;M(4) is Aiden's fee for his 4th drive.M(8)<M(4) means that 8th drive was less expensive than 4th drive.
Alicia is making cupcakes for a party she is having and wants to make sure everyone gets at least one cupcake. The recipe calls for 1 of a teaspoon of salt for every batch and each batch makes 21 cupcakes. If 2 alicia is having a party with 84 people attending, how many teaspoons of salt will alicia use?
Answers
[tex]\frac{84}{21}=4[/tex]
Therefore you need 4 batches of cupcakes if you want every person to get one cupcake.
This means you multiply the amount of salt per batch by the number of batches, to get the total amount of salt you need.Each batch contains 1 teaspoon of salt for 21 cupcakes. Multiply: [tex]4\text{ batches of cupcakes}\times1\text{ teaspoon of salt}=4\text{ teaspoons salt}[/tex] for the whole thing.Fill in the blank. Given O below, you can conclude that AC is congruent to _____.
A. DF
B. OB
C. AB
D. O
Answers
Answer:
A. DF
Step-by-step explanation:
The length of OB is the same as OE, and the angle that AC makes with OB is the same as the angle DF makes with OE. This means the length of both chords, AC and DF, must be the same.
We can conclude that [tex]\boxed{\overline {{\text{OD}}} {\text{ is congruent to }}\overline {{\text{OB}}} }[/tex]. Option (A) is correct.
Further Explanation:
Given:
The options are as follows,
A. [tex]\overline {{\text{AC}}} {\text{ is congruent to }}\overline {{\text{DF}}}.[/tex]
B. [tex]\overline {{\text{AC}}} {\text{ is congruent to }}\overline {{\text{OB}}}.[/tex]
C. [tex]\overline {{\text{AC}}} {\text{ is congruent to }}\overline {{\text{AB}}}.[/tex]
D. [tex]\overline {{\text{AC}}} {\text{ is congruent to }}\overline {{\text{O}}}.[/tex]
Explanation:
The length of OE is [tex]{\text{OE}} = 7.12{\text{ units}}.[/tex]
The length of OB is [tex]{\text{OB}} = 7.12{\text{ units}}.[/tex]
The length of OB and OE is [tex]7.12{\text{ units}}.[/tex]
AC and FD are the chords of the circle.
OE and OB are the perpendicular bisector of the chords AC and FD respectively.
The length of the perpendicular bisectors of chords is [tex]7.12{\text{ units}.[/tex]
The given chords of the circle are equidistant from the center of the circle.
We can conclude that [tex]\boxed{\overline {{\text{OD}}} {\text{ is congruent to }}\overline {{\text{OB}}} }[/tex]. Option (A) is correct.
Learn more:
Learn more about inverse of the function https://brainly.com/question/1632445. Learn more about equation of circle brainly.com/question/1506955. Learn more about range and domain of the function https://brainly.com/question/3412497.
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Circles
Keywords: congruent, fill, blank, conclude, DF, OB, AB, AC, chord, tangent, displacement, two chords, radius, center, circle, equidistant,
The height, in feet, of an arrow shot from a bow in an upwards direction, is modeled by the function h(t) = -16t2 + 96t + 5, where t represents the time in minutes.
Answers
Given function: h(t) = -16t^2 + 96t + 5, where t represents the time in minutes.
We need to find the interval for which the arrow is going up.
The arrow is going up would be the values of time t =0 when it start and when it went to highest point.
Given function is a quadratic function and it represents a parabolic shape.
The highest point on the parabola is a vertex point.
Therefore, we need to find the x-coordinate of the vertex.
We know, formula for x-coordinate of the vertex is
[tex]\frac{-b}{2a}[/tex]
For the given quadratic a= -16 and b=96.
Plugging values of a and b in formula, we get
[tex]\frac{-96}{2(-16)}=\frac{-96}{-32} = 3.[/tex]
Therefore, after 3 seconds arrow would be at maximum height.
Therefore, the interval for which the arrow is going up is [0,3].
F the quadratic formula is used to solve 2x 2 = 8x - 3, what are the solutions?
Answers
x = 2 ± [tex]\frac{1}{2}[/tex]√10
express the equation in standard form : ax² + bx + c = 0 ( a ≠ 0 )
then x = ( - b ±√( b² - 4ac) ) / 2a
given 2x² = 8x - 3, then
2x² - 8x + 3 = 0 ( in standard form )
with a = 2, b = - 8, c = 3
x = (8 ±√(64 - 24) )/4 = (8 ±√40) / 4 = (8 ± 2√10) / 4
x = 2 ± [tex]\frac{1}{2}[/tex]√10
@pinkfloyd @taskmasters PLEASE HELP IM STUCK ONE QUESTION??/
Use the figure to answer the question that follows:
Segments UV and WZ are parallel with line ST intersecting both at points Q and R respectively
When written in the correct order, the two-column proof below describes the statements and reasons for proving that corresponding angles are congruent:
Statements Reasons
segment UV is parallel to segment WZ Given
Points S, Q, R, and T all lie on the same line. Given
I m∠SQT = 180° Definition of a Straight Angle
II m∠SQV + m∠VQT = 180° Substitution Property of Equality
III m∠SQV + m∠VQT = m∠SQT Angle Addition Postulate
m∠VQT + m∠ZRS = 180° Same-Side Interior Angles Theorem
m∠SQV + m∠VQT = m∠VQT + m∠ZRS Substitution Property of Equality
m∠SQV + m∠VQT − m∠VQT = m∠VQT + m∠ZRS − m∠VQT
m∠SQV = m∠ZRS Subtraction Property of Equality
∠SQV ≅ ∠ZRS Definition of Congruency
Which is the most logical order of statements and reasons I, II, and III to complete the proof?
Answers
The correct logical order for the statements I, II, and III in the proof is: I. Definition of a Straight Angle, III. Angle Addition Postulate, and II. Substitution Property of Equality. This order supports the conclusion that corresponding angles, created by the transversal intersecting parallel lines, are congruent.
To complete the two-column proof that demonstrates the congruence of the corresponding angles when segments UV and WZ are parallel and line ST intersects both at points Q and R respectively, we need to place statements and reasons I, II, and III in the most logical order. This should allow us to show
corresponding angles are congruent, which is the ultimate aim of the proof.
The correct order of statements and reasons to complete the proof is:
Definition of a Straight Angle (I): We know that the angle measure of a straight line is 180°, hence m∠SQT = 180°.
Angle Addition Postulate (III): Based on the postulate, we can express m∠SQV + m∠VQT as equal to the measure of angle SQT because the two angles combine to form the straight angle, therefore m∠SQV + m∠VQT = m∠SQT.
Substitution Property of Equality (II): By substituting the equal values established in statements I and III, we get m∠SQV + m∠VQT = 180°.
After arranging the statements and their corresponding reasons, the proof logically demonstrates that the congruent angle pairs are a result of transversal ST intersecting parallel lines UV and WZ.
How is the divisibility rule for 7 more complicated then the rules for 2,3,5 and 10?
Answers
Final answer:
The divisibility rule for 7 is more complex than the rules for 2, 3, 5, and 10 due to the lack of a simple pattern or quick digit check, requiring multiple steps and manipulations of the number.
Explanation:
The divisibility rule for 7 is more complicated than the rules for 2, 3, 5, and 10 because it does not follow a simple pattern or involve a quick check of a number's last digit or sum. The rules for divisibility by 2, 3, 5, and 10 are straightforward: a number is divisible by 2 if its last digit is even, by 3 if the sum of its digits is divisible by 3, by 5 if its last digit is 0 or 5, and by 10 if it ends in 0.
The rule for divisibility by 7 requires more steps and cannot be easily performed in one's head. The process typically involves subtracting or adding multiples of 7 from different segments of the number, which often makes it more difficult for students to use effectively without practice or further understanding of the method. Complicated rules for divisibility by 7 prove the point that while mathematical rules are universally valid, some rules are inherently more complex than others.
Four times the difference of a number and 5 is the same as 5 increased by four times the number plus five times the number
Answers
The value of expression is,
x = - 5
Here;
The written expression is;
''Four times the difference of a number and 5 is the same as 5 increased by four times the number plus five times the number.''
We have to solve this expression.
What is Mathematical expression?
The combination of numbers and variables by using operations addition, subtraction, multiplication and division is called Mathematical expression.
Now,
Let a number is 'x'.
Then, The mathematical expression is written as;
4* ( x - 5 ) = 5 + (4*x) + (5*x)
We can solve as;
4* ( x - 5 ) = 5 + (4*x) + (5*x)
4x - 20 = 5 + 4x + 5x
- 20 - 5 = 4x + 5x - 4x
- 25 = 5x
x = -5
Hence, The value of expression is,
x = - 5
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Which of the following is equal to the expression below?
[tex](160*243)^{\frac{1}{5} }[/tex]
A. 80
B. 96
C. [tex]5\sqrt[5]{5}[/tex]
D. [tex]6\sqrt[5]{5}[/tex]
Answers
160 = 2 x 2 x 2 x 2 x 2 x 5 = 2^5 x 5
243 = 3 x 3 x 3 x 3 x 3 = 3^5
So
(160 * 243)^1/5
= 5th root of (160 * 243)
= 5th root of (2^5 * 5 * 3^5)
= 2 * 3 * (5th root of 5)
= 6 * (5th root of 5)
Answer is D. 6 * (5th root of 5)
The resultant expression, equivalent to [tex](160*243)^{1/5}[/tex] is Option (D) [tex]6\sqrt[5]{5}[/tex]
Exponents and its properties -An exponent refers to the number of times a number is multiplied by itself. It is represented as a number or letter written above and to the right of a mathematical expression called the base. It indicates that the base is to be raised to a certain power. x is the base and n is the exponent or power.
Represented as [tex]x^{n}[/tex]
What are some of the properties of exponents ?[tex]x*x*x[/tex] ........ upto n times = [tex]x^{n}[/tex][tex](x^{n})^{1/n} = x[/tex][tex](x^{n}*y^{n} )^{1/n} = xy[/tex]How to solve the given exponent problem to get the equivalent expression ?Given expression is [tex](160*243)^{1/5}[/tex].
Now we are separating the expression,
160 = 2*2*2*2*2*5 = [tex]2^{5}*5[/tex]
243 = 3*3*3*3*3 = [tex]3^{5}[/tex]
∴ [tex](160*243)^{1/5}[/tex] = [tex](2^{5}*5*3^{5})^{1/5}[/tex] = [tex]2*3*5^{1/5}[/tex] = [tex]6\sqrt[5]{5}[/tex]
Thus the equivalent expression is Option (C) [tex]6\sqrt[5]{5}[/tex]
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Sal has a small bag of candy containing three green candies and two red candies. While waiting for the bus, he ate two candies out of the bag, one after the other, without looking. What is the probability that both candies were the same color?
A.
2/5
B.
3/100
C.
8/25
D.
3/5
Answers
Answer:
A. 2/5
Step-by-step explanation:
3/5*2/4+2/5*1/4
6/20+2/20
8/20 = 2/5
Answer:
Option A
Step-by-step explanation:
Given that Sal has a small bag of candy containing three green candies and two red candies.
He ate two candies one after the other.
The probability that both candies were the same color has to be calculated.
The probability that both candies were the same color = P(both are red or both are green)
= P(both are red)+P(both are green)
Total no of ways to draw 2 candies out of 5 = 5C2 = 5(4)/2 = 10
No of ways of drawing 2 red candies = 2C2 =1
No of ways of drawing 2 green candies = 3C2 =3
Hence required prob =(1+3)/10 = 2/5
Meg cycles 6.2 km every morning. How many feet are in 6.2 km, given that 1 mile= 1.609 km and 1 mile= 5280ft
Answers
Answer:
There are 20345.556... feet in 6.2 km.
Step-by-step explanation:
Given that, 1 mile = 1.609 km and 1 mile = 5280 ft.
That means we can say, 1.609 km = 5280 ft.
So, 1 km = [tex](\frac{5280}{1.609})ft = 3281.541... ft[/tex]
Now, for converting 6.2 km into feet, we will just multiply 6.2 by 3281.541... ft.
Thus, 6.2 km = [tex](6.2 \times 3281.541...)ft = 20345.556... ft[/tex]
So, there are 20345.556... feet in 6.2 km.
Tobias dropped a tennis ball from a height of 60 meters. The time in seconds it takes for the ball to fall is 60 feet is 0.25 √60. Find three sets of approximations for the amount of time it will take. Then determine how long it will take for the ball to hit the ground.
Answers
Answer:-1)The three sets of approximation of time will be
Time taken to fall tennis ball from height of 60 m =35.41014 s ≈35.410 s (to the nearest thousandth)
≈35.41s (to the nearest hundredth)
≈35.5 seconds(to the nearest tenth)
2)Time by the ball to hit the ground =35.5 seconds
Step-by-step explanation:
Time taken to fall tennis ball from height of 60 feet = 0.25 √60 s
So,time taken to fall tennis ball from height of 1 foot =0.25√60 divided by 60=[tex]\frac{0.25\sqrt{60} }{60}s[/tex]
We know that 1 m = 0.3048 foot
⇒60 m =60×0.3048=18.288 feet
therefore, Time taken to fall tennis ball from height of 60 m = 18.288 ×time taken to fall tennis ball from height of 1 foot=[tex]\frac{0.25\sqrt{60} }{60}\cdot18.288=35.41014\ s[/tex]
∴Time taken to fall tennis ball from height of 60 m =35.41014 s ≈35.410 s (to the nearest thousandth)
≈35.41s (to the nearest hundredth)
≈35.5 seconds(to the nearest tenth)
The time it will take for a tennis ball dropped from a height of 60 meters to reach the ground can be calculated using the equation t = 0.25 √h. Three sets of approximations were determined for heights of 30m, 45m and 60m, with the final time for the 60m drop being approximately 1.94 seconds.
Explanation:
The time it takes for the tennis ball to hit the ground can be calculated using the equation t = 0.25 √h, with 't' being time and 'h' being height. Inserting the given height of 60 meters into this equation will reveal how long it takes for the tennis ball to hit the ground.
Approximation set 1: If h = 30 m, t = 0.25 √30 = 1.37 sec Approximation set 2: If h = 45 m, t = 0.25 √45 = 1.68 sec Approximation set 3: If h = 60 m, t = 0.25 √60 = 1.94 sec
From these calculations, it can be determined that the time it will take for the tennis ball dropped from a height of 60 meters to hit the ground is "approximately 1.94 seconds".
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It costs $100 to be a member of a music club. A member of the club pays $20 per music lesson. A nonmember pay $30 per music lesson. How many music lessons must a member and a nonmember take so the cost for each is the same?
Answers
Member ＝ 100 + 20x
Non member ＝ 30x
Must be same, so 100 + 20x ＝ 30x
Solve for x:
Group like terms.
100 ＝ 30x － 20x
100 ＝ 10x
100/10 ＝ x
x＝10
10 music lessons for member and non member to have same costs of $300.
Im not very good at maths. But this seems easy :D. I'm still a beginner, but please give me points.
A member and a nonmember must each take 10 music lessons in order for the cost to be the same for both.
Explanation:To find the number of music lessons that must be taken by a member and a nonmember so that the cost for each is the same, we can set up an equation. Let x represent the number of music lessons. For a member, the cost is $100 + $20x, and for a nonmember, the cost is $30x. We can set up the equation:
100 + 20x = 30x
To solve for x, we can subtract 20x from both sides:
100 = 10x
Then, we can divide both sides by 10:
x = 10
Therefore, a member and a nonmember must each take 10 music lessons in order for the cost to be the same for both.
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What is the solution for this inequality?
-4x < 28
A.
x > -7
B.
x < 7
C.
x < -7
D.
x > 7
Answers
EXPLANATION
We have
[tex]-4x<28[/tex].
We want to solve for x so we divide through by
[tex]-4[/tex]
and reverse the sign of the inequality.
[tex]\frac{-4x}{-4}>\frac{28}{-4}[/tex]
This gives us,
[tex]x>\frac{7 \times4}{-4}[/tex]
[tex]x>\frac{7}{-1}[/tex]
[tex]x>-7[/tex]
What type of number cannot be written as a fraction p and q where p and q are interfere and q is not equal to zero?
Answers
The definition of a rational number is that it can be written in form [tex]\frac{p}{q}[/tex]. If it cannot be written in that form then it is not a rational number (which makes it an irrational number)
Answer: irrational number
What is the product of 6+5i and 4+7i?
Enter your answer, in standard form, in the box.
______
Answers
The answer to this question is the product is 12i
Answer: The required product is [tex]-11+62i.[/tex]
Step-by-step explanation: We are given to find the product of the following two complex numbers :
[tex]z_1=6+5i,~~~z_2=4+7i.[/tex]
We will be using the following property :
[tex](a+b)(c+d)=a(c+d)+b(c+d).[/tex]
Also, we will use the fact that [tex]i=\sqrt{-1},~~i^2=-1.[/tex]
The product of the given complex numbers is
[tex]z_1z_2\\\\=(6+5i)(4+7i)\\\\=6(4+7i)+5i(4+7i)\\\\=24+42i+20i+35i^2\\\\=24+62i-35\\\\=-11+62i.[/tex]
Thus, the required product is [tex]-11+62i.[/tex]
The area of a rectangle is 117117117 square meters. The width is 999 meters.
Answers
Area = 117 m² width = 9 m
Area (A) = length (L) x width (w)
117 = L * 9
117 = 9L
[tex]\frac{117}{9} = \frac{9L}{9}[/tex]
13 = L
Answer: length = 9 m
Answer:
117/9=13
13*9=117
So, the length is 13 since L*W=area.
:)
Each section of a race is 2/5 mile.the race has 44 sections.which expression tells how many miles long the entire race is?
Answers
answer is equal to 2X44/5mile=17.6mile
Each section of a race is 25 mile.
The race has 4 sections.
Which expression tells how many miles long the entire race is?
Answer:
4×2/5
Take away 32 from the product of 6 and a number
Answers
Terry sees an offer about a refurbished phone which is 35% off the original price the new price is £78 how much was the phone before the discounted price
Answers
part/whole=0.65
78/whole=0.65
whole =78/0.65 =120 £
Answer:
The price before discount would be $120
Step-by-step explanation:
The actual price of the phone is 100%-35% = 65% of the original price of the phone.
So by rule of three
If 65% of the price is $78, the total price of the phone would be:
[tex]Total price = \frac{74}{0,65} \\\\Total price = 120[/tex]
Use the drop-down menus to complete each equation so the statement about its solution is true.
no solutions:
7-5+3x-1 = __x + __
one solution:
7-5+3x-1 = __x +__
infinitely Many Solutions
7−5+3x−1=__ x +__
FILL IN THE BLANKS PLEASE :)) (will try to make you brainlist if correct!)
Answers
First, let's simplify the expression: 7 - 5 + 3x - 1 ⇒ 3x + 1 (slope=3, y-intercept = 1)
Next, let's understand what they are asking for:
no solutions means same slope but different y-intercepts
Answer: 3x + _______ (the blank can be anything except 1)
one solution means different slopes
Answer: ________x + _______ (the first blank can be anything except 3, the second blank can be anything)
infinitely many solutions means same slope and same y-intercept
Answer: 3x + 1
Answer:
1.3x+9
2.1x+4
3.3x+1
Step-by-step explanation:
Andre earns $165 for each digital projector that she sells if she works five days a week for 11 hours each day and sales 12 digital projectors a week on average what is her average hourly wage
Answers
1980/55 = AHW
36 = AHW
$36 is her average hourly wage.
Answer: Hi!
Andre earns $165 for each digital projector that she sells.
We know that she works 11 hours per day, 5 days per week and that she sells 12 digital projectors a week. We want to know the average hourly wage.
First, we need to know how much she wins in the week. This is the number of digital projectors sold multiplied by the profit for each one:
12*$165 = $1980
And now we need to see how the amount of hours that she works each week, this is 11 hours per day and 5 days per week, then she works 11*5 = 55 hours per week.
Now we can divide the earns per week by the number of hours that she works each week, and obtain the average hourly wage:
$1980/55 = $36
So Andre wins an average of $36 per hour.
A recipe includes 6 cups of flour and three fourths cup of butter butter. Write the ratio of the amount of flour to the amount of butter butter as a fraction in simplest form.
Answers
To express the ratio of flour to butter from a recipe as a fraction in simplest form, start by setting it up as a fraction and then multiply by the reciprocal of the denominator. In this case, a recipe with 6 cups of flour and three-fourths cup of butter simplifies to a ratio of 8:1.
Explanation:To find the ratio of the amount of flour to the amount of butter as a fraction in simplest form, we start by writing the amounts given in the recipe as a fraction. There are 6 cups of flour and three-fourths (3/4) cup of butter. The initial ratio is therefore:
6 cups of flour / (3/4) cup of butter
To simplify, we can multiply both the numerator (the top part of the fraction) and the denominator (the bottom part of the fraction) by the reciprocal of the denominator:
6 / (3/4) = 6 × (4/3) = 24/3 = 8
So, the simplest form of the ratio of flour to butter is 8:1.
Tell the numbers that are odd and prime 2,14,23,24,25,31,45
Answers
Odd numbers are those numbers that gives a fraction when divided by 2
Prime numbers are those that can be divided only by 1 and the number itself.
Odd numbers are therefore : 23, 25, 31 and 45
Prime numbers are therefore: 2, 23 and 31
What are the like terms of 10a+4b+3a-15b
Answers
4b-15b are like terms because of the b and this equals to -11b
Expression: 10a-11b
The like terms in the expression are 10a and 3a, as well as 4b and -15b.
We have,
The like terms of the expression 10a + 4b + 3a - 15b are the terms that have the same variable(s) raised to the same power(s).
In this case, the like terms are:
10a and 3a (both have the variable 'a')
4b and -15b (both have the variable 'b')
Thus,
The like terms in the expression are 10a and 3a, as well as 4b and -15b.
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Find the Area and Perimeter!
Answers
Area of a triangle is 1/2 x base x height.
base = 12
Height = x+6
Area = 1/2 * 12 * x+6
Area = 1/2 * 12x * 72
Area = 6x + 36
Perimeter is the sum of the 3 sides:
x-7 + 12 + 2x+5
3x -2 + 12
3x+10
The last choice is the correct answer.
Lenny has $74. He spent $24 on video games, and $21 at the grocery store. How much does lenny have left? $
Answers
If you spend money, you have less money than before. Subtraction is the operation that describes this "taking quantities away".
So, you start with 74$. You spend 24$, so we have to subtract 24:
[tex] 74-24 = 50 [/tex]
Then, you spend 21$. So, we have to subtract again:
[tex] 50-21 = 29 [/tex]
So, you're left with 29$ after you buy the video game and the groceries.