Answers
Answer: 2,1 & 2
Step-by-step explanation:
[tex]\lim_{x \to c}[3g(x)][/tex] = 2, [tex]\lim_{x \to c}[f(x)+g(x)] = \frac{-1}{3}[/tex], [tex]\lim_{x \to c}[\frac{f(x)}{g(x)} ] = \frac{1}{2}[/tex]
What is Limit?"A limit is the value that a function (or sequence) "approaches" as the input (or index) "approaches" some value."
We have Limit functions
[tex]\lim_{x \to c} f(x)[/tex] [tex]= \frac{1}{3}[/tex]
[tex]\lim_{x \to c} g(x)[/tex] = [tex]\frac{2}{3}[/tex]
(i) [tex]\lim_{x \to c} [3g(x)] = 3 \lim_{x \to c} [g(x)][/tex]
= [tex]3[/tex] × [tex]\frac{2}{3}[/tex]
= 2
(ii) [tex]\lim_{x \to c}[f(x)+g(x)][/tex]
= [tex]\lim_{x \to c} f(x)+ \lim_{x \to c} g(x)[/tex]
= [tex]\frac{1}{3}-\frac{2}{3}[/tex]
= [tex]\frac{1-2}{3}[/tex]
= [tex]\frac{-1}{3}[/tex]
(iii) [tex]\lim_{x \to c}[\frac{f(x)}{g(x)} ][/tex]
= [tex]\frac{\lim_{x \to c} f(x)}{\lim_{x \to c} g(x)}[/tex]
= [tex]\frac{\frac{1}{3} }{\frac{2}{3} }[/tex]
= [tex]\frac{1}{2}[/tex]
∴ [tex]\lim_{x \to c}[3g(x)][/tex] = 2, [tex]\lim_{x \to c}[f(x)+g(x)][/tex] = [tex]\frac{-1}{3}[/tex] , [tex]\lim_{x \to c}[\frac{f(x)}{g(x)} ] = \frac{1}{2}[/tex]
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Related Questions
Look at the two patterns below: Pattern A: Starts from 4 and follows the rule "add 9" Pattern B: Starts from 4 and follows the rule "add 5" Select the statement that is true. (4 points) Group of answer choices The first five terms in Pattern A are 4, 13, 22, 31, 40. The first five terms in Pattern B are 0, 4, 9, 14, 19. The terms in Pattern A are 2 times the corresponding terms in Pattern B. The terms in Pattern B are one fifth the corresponding terms in Pattern A.
Answers
Answer:b
Step-by-step explanation:
The terms in Pattern B are one third the corresponding terms in Pattern A.
A circus acrobat is shot out of a cannon with an initial upward speed of 50 . The equation for the acrobat's pathway can be modeled by the equation h = - 16t ^ 2 + 50t + 4 .
a.Find the maximum height of the acrobat.
b.How long will it take to reach the ground?
Answers
Answer:
Step-by-step explanation:
h = - 16t ^ 2 + 50t + 4
maximum height take the first derivative of h (calculus if you are taking it)
h' = -32t + 50 set this equal to zero
0 = -32t +50
t = 50/32
t = 1.5625 now plug t = 1.5625 into the height equation
h = - 16(1.5625) ^ 2 + 50(1.5623) + 4
h = 43.0625 ft
you can also find the maximum height by graphing the function and locating the peak value (much easier)
how long to reach the ground h = zero
0 = - 16(t) ^ 2 + 50(t) + 4
use the quadratic equation to solve this or graph the function h(t) and find the roots (much easier) and you will find that
t = -0.078 and 3.203 seconds
obviously the negative root makes no sense unless he time travelled so
t = 3.203 seconds
The area of a circle is pi square centimeters. What is the diameter? Please help!!!!
Answers
Answer:
Radius of the circle = 1 centimeter.
Step-by-step explanation:
Expression that represents the area of a circle,
Area = πr²
Here, r = Radius of the circle
Area of the circle given = π square centimeters
πr² = π
r² = 1
r = 1
Therefore, radius of the circle is 1 centimeter.
Write the fraction that represents the amount of candy bar each person would get when sharing three candy bars equally among seven
people.
Answers
Answer:
I think the answer is 1 2
5
Two bonds are available on the market as follows: Bond 1: Face value $250, 5 years to maturity at a simple interest rate of 5%. Bond 2: Face value $350, 3 years to maturity at a simple interest rate of r. Given that both bonds yield the same interest at maturity, calculate r. Round your answer to the nearest hundredth of a percent. Do NOT round until you have calculated your final answer.
Answers
Answer:
5.95%
Step-by-step explanation:
Bond 1:
I = 250(.05)5
I = $62.50
Bond 2:
62.5 = 350(3)r
62.5 = 1050r
r = 62.5/1050
r = 5.95%
Answer:
5.95%
Step-by-step explanation:
A large corporation sent out four groups of people to conduct observational studies on the average wait time at four different restaurants in its restaurant group. The restaurants have approximately the same ratings in terms of quality and popularity.
In their reports to the company board, each of the four groups described different methods used to conduct their studies, as shown in the table. Which group’s method will give the most accurate, unbiased results?
Answers
Answer:
It's midwest
Step-by-step explanation:
Midwest's groups will give the most accurate, unbiased results, and the correct option is B.
To solve this question, we analyze each sample, and find which of them will give the most accurate results.
Northeast: Only 3 hours a day, which can either have a very low or very high wait time, not being a correct representation, so there are bias factors.West Coast: One full day, which also can be a day with a lot of demand, leading to high wait time, or a day with low demand leading do low demand time, so there are also bias factors.South: Phone survey is not very accurate, people may not remember, for example.Midwest: Consider lots of periods over the course of the week, thus surveying both periods of low and of high demand, to get a good estimate for the average time, not having bias factors.Thus, the Midwest's groups will give the most accurate, unbiased results, and the correct option is B.
A similar example is given here: https://brainly.com/question/16609573
pleaseehehhehe bellopppp
Answers
Answer:
A is right
Step-by-step explanation:
#11. The space occupied by a wooden block is 4cm × 2cm × 2cm=_____cm 3 Which is equivalent to_______mililiters
Answers
Answer:
Solution given;
The space occupied by a wooden block is 4cm × 2cm × 2cm=_16__cm 3 Which is equivalent to____16___mililiters
Step-by-step explanation:
we have
1cm³=1millilitre.
The Stem-and-Leaf plot and the Box-and-Whisker Plot here display the number of shoes sold daily in a 12-day sale. What is the median number of this data set?
A. 80
B. 89
C. 84
D. 86
Answers
What is the data set?
Post it in the comments... PLZ
The right triangle on the right is a scaled copy of the right triangle on the left. Identify
the scale factor. Express your answer in simplest form
Answers
Answer:
scale factor = [tex]\frac{34}{39}[/tex]
Step-by-step explanation:
The scale factor is the ratio of corresponding sides, image to original.
scale factor = [tex]\frac{34}{39}[/tex]
How many solutions does the equation 6z − 3z − 7 = −2 + 3 have?
Two
None
Infinitely many
One
Answers
There could only be one aolition
An angle measures 10° more than the measure of its complementary angle. What is the
measure of each angle?
Answers
Answer:
50 and 40
Step-by-step explanation:
Complimentary angles must add up to equal 90 degrees. Therefore, you must find two numbers that add to 90 and have a difference of 10. Try different number values until this is true. One must be 50 and the other 40 degrees.
Gift wrappers tend to have competitions on who can wrap more presents in a day. If Benjamin wrapped 9 less presents than Christopher, who wrapped x presents, choose the expression that shows how many presents Benjamin wrapped.
Answers
Answer:
x-9.
the expression that shows how many presents benjamin wrapped would be x-9
Find the missing number in this function table.
Answers
Answer:
25
Step-by-step explanation:
2(13)-1=25
Answer:
25
Step-by-step explanation:
Using the equation given, 2x-1, you can plug in x, which is given in the table, and solve.
13 is given for x so you plug 13 into 2x-1;
2(13)-126-125you can then check your answer to make sure you did it correctly by plugging in another x number (such as 4) and checking to see if you get the same number as the one given.
40 PTS ! The length of the rectangle is 2 ft more than its width. The area of the rectangle is 80 square feet. Find the width of the rectangle.
Answers
Answer:
The length of a rectangle is 2 feet more than it's width. How do you find the dimensions of the rectangle if its area is 63 square feet?
Step-by-step explanation:
x(x+2) = 63
x^2 + 2x = 63
x^2 + 2x - 63 = 0
Quadratic formula with numbers plugged in: (-2 +or- sqrt(4 - 4* 1 * -63))/2 becomes
-2 +or- sqrt(256)/2 so (-2 +or- 16)/2 therefore -18/2 or 14/2. Discard negative result.
x = 7. 63/7=9. Sides are 7ft and 9ft.
Answer:
8 ftStep-by-step explanation:
Given
The length l = w + 2The area lw = 80Substitute l and solve the following for w:
w(w + 2) = 80w² + 2w = 81w² + 2w + 1 = 81(w + 1)² = 9²w + 1 = 9w = 8The width is 8 ft
How to do y=5x+2 and 3x=-y+ 10
Answers
y = 5x + 2
5 is the slope 2 is the y-intercept
3x = -y + 10 turns into y = -3x + 10
-3 is the slope 10 is the y-intercept
they intersect at (1, 7)
step-by-step explanation:
I’m not sure what you are wanting me to do with these but i will give you all the information about them
y = 5x + 2 is already in slope-intercept form
5 being the slope and 2 being the y-intercept
to solve for 3x = -y + 10
-3x+y +y-3x
y = -3x + 10
the slope is -3
the y-intercept is 10
they intersect at (1, 7)
Can anyone help? I’ll give Brainly.. thank you
Answers
Explanation;
NEED HELP ASAP! brainlist... A rectangular feild has a perimeter of 100 feet. Its length is 20 feet longers than its width. What are the dimensions of the feild?
answers:
15 ft by 35 ft
20ft by 30ft
35ft by 55ft
40ft by 60ft
Answers
Answer:
15 ft by 35 ft
Step-by-step explanation:
15 + 15 + 35 +35
=100 ft
Answer:
Perimeter = 2 × (length + width) -------(1)
Let width be w
Given length is 20ft longer than width, L = 20 + w
substitute L and w in (1)
perimeter = 2× ( 20 + w + w)
100 = 2 ×(20 + 2w)
50 = 20 + 2w
30 = 2w
w= 15feet
L = 20 + w = 20 + 15 = 35feet
option 1) 15 ft by 35ft
1. Which point is a solution to this system of equations? 3х - у = 7 and 2x + 3y = 1
Answers
9514 1404 393
Answer:
(x, y) = (2, -1)
Step-by-step explanation:
A graphing calculator can find a solution quickly. (see attached)
__
The first equation can give an expression for y:
y = 3x -7
We can substitute this into the second equation:
2x +3(3x -7) = 1
11x -21 = 1 . . . . . . simplify
11x = 22 . . . . . . . add 21
x = 2 . . . . . . . divide by 2
y = 3(2) -7 = -1 . . . . using our equation for y
The solution is (x, y) = (2, -1).
Olivia's team played 8 games of basketball. During those 8 games her team's score was: 70, 67, 79, 66, 64, 80, 64 and 75. Find the median.
Round to the nearest TENTH.
Answers
Answer:
70
Step-by-step explanation:
First put it to least to greatest- 64, 64, 66, 67, 70, 75, 80
Then find the median which is the number in the middle
Round it so it gives us are answer of 70
x raise to the fourth power three times
Answers
Answer:
If you mean multiply by three when you say “three times”, then 3.
If you mean 1 to the third power when you say “three times”, then 1.
Step-by-step explanation:
1 x 1 x 1 x 1=1 is 1 to the fourth power.
If you mean multiply by three when you say “three times”, then 1x3=3.
If you mean 1 to the third power when you say “three times”, then 1x1x1=1.
What is the exponent for 4.4.4.4=?
Answers
Answer:
the answer is four to the the power of four
Step-by-step explanation:
how, well because the main number there is four and the the amount is four so there's your answer
The exponent for 4.4.4.4 = 4^4
What is exponent?An exponent of a number is the number of times the number is multiplied to itself. For example, 10 is multiplied for n times by itself can be expressed as 10^n.For any number x raised to the power n can be expressed as x^n = x.x.x....x (n times) = x^nIn x^n, x is called base and n is called exponent otherwise index or power of x.In short,Exponentation is the shortest method for repeated multiplication.It is given that 4.4.4.4
Here 4 is multiplied repeatedly by the number itself. So we use exponentation.
Base is 4 and exponent is 4
Therefore, the exponent for 4.4.4.4 is 4^4
Learn more about exponent here:
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Dean ran 2.3 fewer kilometers than Sam. If Dean ran 6.8 km, how far did Sam run?
A 2-column table with 4 rows. Column 1 is labeled Situation with entries increasing, difference, finding part of a total, sharing, or grouping. Column 2 is labeled Operation with entries +, minus, times, divided by.
Select all that apply.
You know the difference in the distances the boys ran, so this is a subtraction problem.
You are finding the total distance the boys ran, so this is an additional problem.
Dean ran part of the distance Sam ran, so this is a multiplication problem.
The correct equation is s + 2.3 = 6.8.
The correct equation is s – 2.3 = 6.8.
The correct equation is 2.3s = 6.8.
HELP MEEEEEEEEEEEEEE
Answers
Answer:
Sam ran 8.1 km
6.8 + 2.3= 8.1
Answer:
A. You know the difference in the distances the boys ran, so this is a subtraction problem.
E. The correct equation is s – 2.3 = 6.8.
The answers are a and e
Plz help me well mark brainliest if correct!!...
Answers
9514 1404 393
Answer:
B) fifth grade boys
Step-by-step explanation:
55 tickets is halfway between the lines marked 50 tickets and 60 tickets. The bar that comes closest to that value is the right-most green bar, representing ...
fifth-grade boys
HELP I NEED TO DO THIS NOW NO LINKS THEY WOULD BE REPORTED JUST TELL ME WHAT I NEED TO PUT
Answers
where does f(x) and the line y=1 intersect?
Answers
What is the value of X HELP PLEASE
Answers
Answer:
x = 25
Step-by-step explanation:
In the image shown you have correctly identified the angles as vertical. Vertical angles are equal. This means that the angle "4x - 25" is the same as the angle "75". we can write this as:
4x - 25 = 75
Add 25 to both sides
4x = 100
This means that 4 x's will make one hundred. If you divide 100 by four you get four equal parts that make 100. Divide both sides by 4.
x = 25
what are the slope and y-intercept of the line described by y = 2x +6?
Slope is m= ________
Y-interept is (0, ________)
Answers
Answer:
Slope is m= 2
Y-interept is (0, 6)
Step-by-step explanation:
y = 2x +6
Equating it with
y = mx + b
We find
m = 2
b = 6
Therefore,
Slope is m= 2
Y-interept is (0, 6)
Answer:
slope is m=2
y intercept is (0,6)
Step-by-step explanation:
questionon on picture
Answers
Answer:
yes this option is correct
PLZZ HELP I WILL GIVE A !)) POINTS Danny attempts the feat of jumping his motorcycle through the Flaming Hoop Jump of Awesome. In order for Daredevil Danny to pass through the hoop, he will need a safe path to travel. Let’s explore the parabolic trajectory that he will need for a safe journey.Step 4: Calculate the equation for the flaming hoop jump.
Using the same method for the practice jump, write the standard form of the equation that will get Daredevil Danny safely through the Flaming Hoop Jump of Awesome!
Determine the values of a, b, and c. Show your work. (10 points)
Using your values of a, b, and c, did Daredevil Danny successfully pass through the Flaming Hoop Jump of Awesome? If not, describe what happened. Then, go back to critique your work and revise it. Write about your revision. (5 points)
Once you have determined the correct values of a, b, and c, verify algebraically that Daredevil Danny will successfully pass through the Flaming Hoop Jump of Awesome. (5 points
Answers
Answer:
par t a:
plug in the root (4,0) to find a
0=a(4-24)^2+50
subtract 50 from both sides
-50=a(4-24)^2
4-24
=-20
-20^2=400
back to the equation
-50=a(400)
-50=400a
-50/400=-0.125
a = -0.125
part b:
-0.125(x-24)^2+50
-0.125(x-24)(x-24)+50
-0.125(x^2-24x-24x+576)+50
-0.125(x^2-48x+576)+50
-0.125x^2+6x-75+50
-0.125x^2+6x-22
a=-0.125
b=6
c=-22
part c: yes he went through
part d:
plug in vertex (4,0) and (44,0)
if x is 4 and y is 0
0=-0.125(4)^2+6(4)-22
0=-2+24-22
0=-2+2
0=0
if x=44 and y=0
0=-0.125(44)^2+6(44)-22
0=-242+264-22
0=-242+242
0=0
Step-by-step explanation:
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