if you know that limx→6f(x)x=5 and limx→6g(x)=2, then evaluate the following limit: limx→6f(x)g(x)=2 , then evaluate the following limit: Multiply numerator and denominator byx.x→6limg(x)f(x)=?
Answers
The limit as x approaches 6 of f(x)g(x) is equal to 60 and the limit as x approaches 6 of g(x)f(x)/x is equal to 10.
Using the limit laws, we can evaluate the limit of f(x)g(x) as follows:
limx→6 f(x)g(x) = limx→6 f(x) ⋅ limx→6 g(x)
Now, we are given that limx→6 f(x)/x = 5, so we can rewrite f(x) as:
f(x) = 5x + h(x)
where h(x) is a function that approaches zero as x approaches 6. Then, we have:
limx→6 f(x)g(x) = limx→6 (5x + h(x))g(x)
= limx→6 5xg(x) + h(x)g(x)
Now, we are also given that limx→6 g(x) = 2, so we can substitute this in to get:
limx→6 f(x)g(x) = limx→6 5xg(x) + h(x)g(x)
= limx→6 5xg(x) + limx→6 h(x) ⋅ limx→6 g(x)
= 5(6)(2) + 0 ⋅ 2
= 60
Therefore, limx→6 f(x)g(x) = 60.
For the second part of the question, we can use the same approach and multiply the numerator and denominator by x to get:
limx→6 g(x)f(x)/x = limx→6 g(x)(5x + h(x))/x
= limx→6 5g(x) + h(x)/1
= 5(2) + 0/1
= 10
Therefore, limx→6 g(x)f(x)/x = 10.
Hence, the limits are determined to be f(x)g(x) = 60 and g(x)f(x)/x = 10.
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Related Questions
\frac{\left(2a^{2}b\right)^{3}}{8a^{6}b^{3}}
Answers
Answer: I need an image
Step-by-step explanation: ...
30+h=64 what is h equal?????????
Answers
Answer:
h=34
Step-by-step explanation:
Compare the rates to find which is greater
15 laps in 12 seconds or 12 laps in 10 seconds
Answers
Answer: 15 laps in 12 seconds
Step-by-step explanation:
15 divided by 12 is 5/4 which is also 1.25
12 divided by 10 is 6/5 which is also 1.2
1.25 is greater then 1.2
To celebrate answering over 100 questions in math on Brainly, I'm giving away 15 points!
To get brainliest, answer this question as well as receive your points w/ math shown:
If I have answered 112 questions on brainly total, but have 127 thanks total and have an average of 1 thank on each of my answers, about how many thanks have I received on my profile?
Answers
Step-by-step explanation:
127? I hope this is right!
Answer:
Thank you <3
about 15 thanks on your profile
Step-by-step explanation:
112 questions
127 thanks total
Average of 1 thank on each questions
that means 112 questions have 1 thank each
So 112 thanks
subtract the total thanks from the question thanks
127 - 112
15
You have received around 15 thanks on your profile, as its an average of 1 thank on each question which means it could always be more or less.
Please find the volume worth 50 points.
Answers
The volume of the half-sphere is V = 5744.1 cubic units.
How to find the volume?The volume of a sphere of radius R is:
V = (4/3)*pi*R³
Where pi = 3.14
Here we have half a sphere, so the volume will be 1/2 of the above expression, and the radius is, so R = 14 units, then the volume of the half-sphere will be:
V = (1/2)*(4/3)*3.14*(14)³ = 5744.1 cubic units.
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Look at Project TX55: \[ E S(D)=35, E S(E)=47, \text { and } E S(F)=34 \text {. } \] The duration of activities \( \mathrm{D}, \mathrm{E} \), and \( \mathrm{F} \) are 12,13 , and 15 days, respectively
Answers
The project's early start date is 34 (since it is the latest early finish of all the activities' predecessors). In project management, "ES" refers to the early start date. To determine the project's early start, the following formula is used: Early Start (ES) = Latest Early Finish (LEF) of all the predecessors.
Project TX55's early start date will be determined using this formula.
Let us first determine the early finish (EF) for the given activities.
For activity D, we have:
EF(D) = ES(D) + Duration(D)
= 35 + 12
= 47
For activity E, we have:
EF(E) = ES(E) + Duration(E)
= 47 + 13
= 60
For activity F, we have:
EF(F) = ES(F) + Duration(F)
= 34 + 15
= 49
Since none of these activities have any predecessors, their early start dates will be equal to their early finish dates. Therefore, the early start for Activity D is ES(D) = 35
The early start for Activity E is ES(E) = 47
The early start for Activity F is ES(F) = 34
Therefore, the project's early start date is 34 (since it is the latest early finish of all the activities' predecessors).
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find the area of the polygon
Answers
Answer:
Area=78m^2
Step-by-step explanation:
4*12=48m^2 <-- The area of a rectangle LxW
12*5=60 60/2=30 <-- The area of a triangle (HxB)/2
30+48=78m^2 Add them together to get the total area
Write an expression for which subtracting 5 from an expression would isolate the variable
Answers
An expression for which subtracting 5 from an expression would isolate the variable is -9x + 5 = x + 2
What are algebraic expressions?Algebraic expressions are described as expressions that consists of coefficients, terms, variables, factors and constants.
These expressions are also known to consist of arithmetic operators, which includes;
Floor divisionDivisionExponentiationAdditionMultiplicationSubtraction, etcFrom the information given, we have to subtract five from an expression to isolate the variable
Now, let's us the algebraic expression;
-9x + 5 = x + 2
Let's subtract 5 from both sides of the equation, we get;
-9x + 5 - 5 = x + 2 - 5
add and subtract the like terms
-9x + x = -3
-8x = -3
x = 3/8
Hence, the expression is -9x + 5 = x + 2
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6x + 4y > 12
What’s the x and y intercepts
Answers
Answer:
x interprets: 2,0
y interprets: 0,3
Step-by-step explanation:
a die is rolled twice. what is the probability of showing a 5 on the first roll and an even number on the second roll? write your answer as a simplified fraction
Answers
The likelihood of showing a 5 on the principal roll and a significantly number on the second roll when a kick the bucket is moved two times is 1/12, which is an improved on part.
Define the term fraction?A division is a numerical articulation that addresses a piece of an entirety. It is made up of two numbers that are separated by a horizontal or diagonal line. The number below the line is referred to as the denominator, and the number above the line is referred to as the numerator.
When a fair die is rolled, there are six equally likely outcomes: 1, 2, 3, 4, 5, or 6.
The probability of rolling a 5 on the first roll is 1/6, since there is only one way to roll a 5 out of six possible outcomes.
The probability of rolling an even number on the second roll is 3/6, since there are three even numbers (2, 4, and 6) out of six possible outcomes.
We multiply the probabilities of each event to determine the probability that both will occur:
P(rolling a 5 on the first roll and an even number on the second roll) = P(rolling a 5 on the first roll) × P(rolling an even number on the second roll)
= (1/6) x (3/6)
= 1/12
Subsequently, the likelihood of showing a 5 on the main roll and a significantly number on the second roll when a bite the dust is moved two times is 1/12, which is an improved on division.
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What is the domain of the step function f(x) = [2x]- 1?
O {x|x2-1}
O {x|x ≥ 1}
O x x is an integer}
O {x|x is a real number}
Answers
Domain: {x | x is a real number}
Option D, "{x | x is a real number}" accurately represents the domain of the function.
The domain of the step function f(x) = [2x] - 1, where [2x] represents the greatest integer less than or equal to 2x, can be determined by considering the restrictions on the input values.
In this case, the step function is defined for all real numbers. However, the greatest integer function imposes a restriction. Since the greatest integer function only outputs integers, the input values (2x) must be such that they produce integer outputs.
For any real number x, the greatest integer less than or equal to 2x will always be an integer. Therefore, the domain of the function f(x) = [2x] - 1 is:
Domain: {x | x is a real number}
Option D, "{x | x is a real number}" accurately represents the domain of the function.
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2. Two angles are called?_ if they are not adjacent and their sides are formed by two intersecting lines.
Answers
Answer:
Vertical angles — two non-adjacent angles formed by two intersecting lines.
Step-by-step explanation:
State if the triangles are congruent by SAS or SSS or Not Congruent.
SAS
SSS
Not Congruent
Answers
Answer:
SAS
Step-by-step explanation:
they are congruent by SAS since the angle is between the two equal sides
can someone solve all of these?
Answers
Answer:
M, P, O, K------------------------
Solve each system by subtraction.
System 1x + 6y = 10x + 2y = 2After subtraction we get:
6y - 2y = 10 - 24y = 8y = 2Find x by substitution:
x + 2*2 = 2x + 4 = 2x = - 2Solution is (-2, 2), choice M.
-------------
System 23x + y = 7-2x + y = - 8After subtraction we get:
3x - (-2x) = 7 - (-8)5x = 15x = 3Find y by substitution:
3*3 + y = 79 + y = 7y = - 2Solution is (3, - 2), choice P.
------------
System 33x + 2y = 18x + 2y = 14After subtraction we get:
3x - x = 18 - 142x = 4x = 2Find y by substitution:
2 + 2y = 142y = 12y = 6Solution is (2, 6), choice O.
--------------
System 4x + 3y = 62x + 3y = 9After subtraction we get:
x - 2x = 6 - 9- x = - 3x = 3Find y by substitution:
3 + 3y = 63y = 3y = 1Solution is (3, 1), choice K.
Which of the following sets of numbers could repersent the three sides of a triangle?
a: 15,27,42
b:15,18,33
c:8,20,25
d:12,23,35
Answers
Answer:
c: 8,20,25
Step-by-step explanation:
You want to know which set of side lengths can form a triangle from the sets ...
a: 15,27,42b: 15,18,33c: 8,20,25d: 12,23,35Triangle inequalityA set of lengths can form a triangle if and only if the sum of the shorter two exceeds the longest.
In sets a, b, d, the sum of the shorter two is equal to the longest. These lengths will form a line segment, not a triangle.
A triangle can be formed by ...
c: 8,20,25 . . . . . . 8+20=28 > 25
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RIGHT ANSWER GETS 15 POINTS
In the figure below, angle y and angle x form vertical angles. Angle y forms a straight line with the 60° angle and the 70° angle.
A straight line is shown and is marked with three angles. The first angle measures 60 degrees. The second angle measures 60 degrees. The third angle is labeled y. The line between the 70 degree angle and angle y extends below the straight line. The angle formed is labeled angle x.
Write and solve an equation to determine the measure of angle x. (5 points)
Your answer:
Answers
Since angle y and angle x form vertical angles, the measure of angle x is equal to 50°.
What is the vertical angles theorem?In Geometry, the vertical angles theorem is also referred to as vertically opposite angles theorem and it states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other.
Furthermore, the sum of the angles on a straight line is equal to 180. Therefore, we would sum up all of the angles as follows;
60° + 70° + y = 180°
130° + y = 180°
y = 180° - 130°
y = 50°
Since both angle x and angle y are vertical angles, we can logically deduce that they are congruent and as such the magnitude of angle x is equal to 50°.
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Is -2 a solution to 4x^(3)-x^(2)+16x-4
Answers
Answer:
Not a solution
Step-by-step explanation:
In order for \(x=-2\) to be a solution, the result after substituting must be 0:
\(4(-2)^3-(-2)^2+16(-2)-4\stackrel{?}{=}0\)
\(4(-8)-4-32-4\stackrel{?}{=}0\)
\(-32-40\stackrel{?}{=}0\)
\(-72\neq0\)
Therefore, \(x=-2\) is not a solution to \(4x^3-x^2+16x-4\)
Need help ASAP !!! Am I correct? Just checking….
Answers
Answer:
Yes you are
Step-by-step explanation:
If you multiply the first equation by 3 , y becomes 3y and so you can eliminate from there.
What is closure property of integers with addition example?
Answers
The closure property of integers with addition states that when you add any two integers together, the result will always be an integer.
For example, if you add the integers 3 and 5 together, the result will be 8, which is an integer. Similarly, if you add the integers -4 and 6 together, the result will be 2, which is also an integer. Therefore, the set of integers is closed under addition because it includes all possible results of adding two integers together.
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Convert the DFA shown to its equivalent regular expression using
ardens theorem
Why in example 1, on 2 =, 1 is substituted in but in example 2,
on 2 =, 1 is not substituted.
a,b 1 2 3 1 = 3a + ε 2 = 1(a + b) + 2a + 3b 3 = 2b 2 = 1(a + b) + 2a + 2bb = 1(a + b) + 2(a + bb) = (2ba+=)(a+b) + 2(a+bb) = 2ba(a+b)+(a+b) + 2(a+bb) = 2(a+bb+ba(a+b)) + (a+b) = (a+b)(a+bb+ba(a+b))*
Answers
The equivalent regular expression for the given DFA using Arden's theorem is (a+b)(a+bb+ba(a+b))*.
1. Start with the given DFA and its transition table:
State | Input a | Input b
------|---------|---------
1 | 3 | 2
2 | 1 | 2
3 | 2 | -
2. Apply Arden's theorem, which states that for a DFA with a single final state, the regular expression for that state can be obtained by substituting the regular expressions for the other states into the equation: R = S + RP, where R is the regular expression for the final state, S is the regular expression for the current state, and P is the regular expression for the next state.
3. Begin with state 1:
- Substitute the regular expression for state 3 into the equation:
1 = 3a + ε
- Since state 3 has no outgoing transition for input b, it is represented as ε (empty string).
4. Move to state 2:
- Substitute the regular expression for state 1 into the equation:
2 = 1(a + b) + 2a + 3b
- State 1 is represented as (a + b) from the previous step.
- Note that 1 is substituted because it is the regular expression for the state itself.
5. Move to state 3:
- Substitute the regular expression for state 2 into the equation:
3 = 2b
- State 2 is represented as b from the previous step.
6. Substitute the obtained regular expressions back into the previous equations until no new substitutions are made:
- In this case, there are no new substitutions to be made.
7. The resulting regular expression for state 1 is (a + b)(a + bb + ba(a + b))*.
Therefore, the equivalent regular expression for the given DFA using Arden's theorem is (a + b)(a + bb + ba(a + b))*.
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a developer wants to develop a 16-acre subdivision. he figures that the streets and common area will take up about 30% of this overall area. if the minimum lot size is to be 12,000 sf, how many lots can the developer have on this property?
Answers
The developer can have a maximum of 40 lots on the 16-acre subdivision.
To calculate the number of lots the developer can have on the 16-acre subdivision, we need to subtract the area occupied by streets and common areas from the total area and then divide it by the minimum lot size.
1 acre is equal to 43,560 square feet, so 16 acres is equal to 16 * 43,560 = 696,960 square feet.
The streets and common areas will take up 30% of this overall area:
30% of 696,960 = 0.3 * 696,960 = 209,088 square feet.
Now we subtract the area occupied by streets and common areas from the total area to find the area available for the lots:
696,960 - 209,088 = 487,872 square feet.
Since the minimum lot size is 12,000 square feet, we divide the available area by the minimum lot size to find the number of lots:
487,872 / 12,000 = 40.656.
Since we cannot have a fraction of a lot, the developer can have a maximum of 40 lots on this property.
As a result, the 16-acre subdivision may only accommodate a maximum of 40 lots from the developer.
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Solve for x. Show each step of the solution.
5(2-x)-10=25-2(3x+40)
Answers
Answer:
x=-55Step-by-step explanation:
\(5(2-x)-10=25-2(3x+40)\\\\10-5x-10=25-6x-80\\\\-5x=-6x-55\\\\-5x+6x=-55\\\\x= -55 \)
Answer:
x = -55
Step-by-step explanation:
Hello!
We can solve for x by isolating the variable.
Solve for x5(2 - x) - 10 = 25 - 2(3x + 40)5(2) - 5(x) - 10 = 25 - 2(3x) - 2(40)10 - 5x - 10 = 25 - 6x - 80-5x = -55 - 6xx = -55The value of x is -55.
3) your friend's math test contained 42 questions, some of which were worth two points while the rest were worth three points. your friend tells you that a perfect score is 100 points, but she cannot remember how many of each type (2 point or 3 point) were on the test. help your friend out: how many of each type were on the test? write your answer in a sentence.
Answers
Your friend's math test had 28 two-point questions and 14 three-point questions to achieve a perfect score of 100 points.
Let's solve the problem using algebraic equations. Let's assume the number of questions worth two points is represented by 'x', and the number of questions worth three points is represented by 'y'.
According to the given information, the total number of questions is 42. Therefore, we can write the equation:
x + y = 42
We also know that a perfect score is 100 points. Since the two-point questions are worth 2 points each and the three-point questions are worth 3 points each, we can write the equation for the total score:
2x + 3y = 100
Now we have a system of two equations:
x + y = 42
2x + 3y = 100
By solving this system of equations, we can determine the values of 'x' and 'y', which represent the number of questions worth two points and three points, respectively. Solving the system of equations, we find that there were 16 questions worth two points and 26 questions worth three points on the test.
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Write an equation of the graph shown in terms of cosine:
Answers
Answer:
Step-by-step explanation:
A squiggly line can refer to a variety of different shapes or patterns. To create an equation using cosine that resembles a squiggly line, you can use a combination of sine and cosine functions with different frequencies and amplitudes. Here's an example equation that produces a squiggly pattern:
y = A * cos(B * x) + C * sin(D * x)
In this equation, A, B, C, and D are constants that you can adjust to modify the shape and characteristics of the squiggly line. By experimenting with different values for these constants, you can create various squiggly patterns. Keep in mind that the specific equation may vary depending on the exact shape and features you have in mind for the squiggly line.
Is (0,8) a solution to the following system of inequalities:
y<-3/2x-8
y>2x-1
Yes
No
Answers
Explanations:
Simplify (5x3y) (2xy4)
Answers
Answer: 10x^4y^5
Step-by-step explanation:
5x^3y^1•2x^1y^4
5•2=10
x^3•x^1=x^4
y^1•y^4=y^5
10x^4y^5
Cassie baked 24 cookies with 4 scoops of flour. How many scoops of flour does Cassie need in order to bake 42 cookies?
Answers
Answer:
7
Step-by-step explanation:
24 with four scoops is 6 with one scoop and 6 times 7 is 42 so 1 times 7 is 7 so the answer is 7 scoops
A bag contains 20 coloured marbles. Copy and
complete the table below to show the probability of
picking each colour at random and the number of
each colour marble in the bag. What is the
probability, as a percentage (%), of picking a purple
marble at random? How many purple marbles are in
the bag?
Colour
Yellow
Blue
Green
Purple
Probability
10%
15%
Number of marbles
6
Answers
Blue Probability = 30 %
Green No. of balls = 3
Purple Probability = 45 %
Purple No. of balls = 9
A person is wearing a bracelet with 11 settings around the bracelet. How many different ways can 12 birthstones be
arranged around the bracelet?
O 10!
11!
O 12!
Answers
Answer:
10
Step-by-step explanation:
I think I hope this helps
What is the Slop?????Please give an actual answer. WILL ADD BRAINLIEST FOR BEST ANSWER!!!!!
Answers
Answer:
The Slope Is 2/3
Step-by-step explanation:
Hope This Helps!
Plz Mark Brainliest!
Answer:
The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
Step-by-step explanation: