What is Limit of StartFraction x squared minus 4 Over x + 2 EndFraction as x approaches negative 2?

–4
0
4
DNE

Answers

Answer 1

Using perfect squares simplification, it is found that the value of the desired limit is of -4.

When is a limit?

It is the value of a function as x approach

In this problem, the limit we want to find is given by:

[tex]\lim_{x \rightarrow -2} \frac{x^2 - 4}{x + 2}[/tex]

If we just replace x by -2, we end with an undetermined limit, as we have 0/0.

However, the perfect square simplification states that:

a² - b² = (a - b)(a + b).

Hence:

x² - 4 = (x + 2)(x - 2).

Then:

[tex]\lim_{x \rightarrow -2} \frac{x^2 - 4}{x + 2} = \lim_{x \rightarrow -2} \frac{(x + 2)(x - 2)}{x + 2} = \lim_{x \rightarrow -2} x - 2 = -2 - 2 = -4[/tex]

Hence, the value of the desired limit is of -4.

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Related Questions

which expressions is equivalent to 4^3 x 4^x

Answers

Answer:

Step-by-step explanation:

256x

What is the volume of a sphere with a radius of 15
inches?
235.5
113040.0
14130.0
1766.25

Answers

Answer:

C) V = 14130 in³

Step-by-step explanation:

Volue of a sphere: 4/3πr³

π = 3.14r = 15 in.

Substitute the values from above into the formula to find the volume of the sphere:

V = 4/3πr³

V = 4/3*3.14*15³

V = 4/3*3.14*3375

V = 4/3*10597.5

V = 14130 in³

Hope this helps!

how do i Solve the inequality:

n/3>1

Answers

Answer:

n>3

Step-by-step explanation:

n/3>1

3(n/3)>1(3)

n>3

DO GIVE CORRECT ANSWER other ways I will report you

1.You roll a standard, six-sided number cube. What is the probability of rolling a prime number or a number greater than 4?

2. Garrett throws a dart at a circular dart board. The dart board has a radius of 16 inches, and the bull’s eye in the center of the dart board has a radius of 6 inches. What is the probability that a dart thrown at random within the dartboard will hit the bull’s eye? Round your answer to the nearest tenth, if necessary.

Answers

Step-by-step explanation:

for the prime number it's 1/2

someome help me plsssssssssssssssssss

Answers

Volume formula is WxHxL so 3/2 times 4 times 1/2 is 3, the answer is 3 cm^3

Where does the line with the equation y=4x-7 cross the y axis?

Answers

Answer:

-7

Step-by-step explanation: an easy way to find the y-intercept (the point at which the line crosses the y axis) is by identifying what part of the equation does not have an x value. in this problem, it would be -7. if it were to not have a number that is followed by an x the y-intercept is 0.

hope that helps!

Please! Help

John is collecting data on the number of spots on ladybugs. He records it in this table.

2 7
5 4
3 3
5 5
6 5
The mean of the data is , and the median is .

Answers

Answer:

the mean is 4.5

the median is 5

Step-by-step explanation:

Two numbers have a sum of 23 and a difference of 5. What is the smaller of the two numbers.

Answers

Answer:

9

Step-by-step explanation:

Two numbers have a sum of 23 and a difference of 5. What is the smaller of the two numbers.

x + y = 23

x - y = 5

(23 - 5) : 2 = 9

9 + 5 = 14

check

14 + 9 = 23

14 - 9 = 5

Answer: 14, 9

Step-by-Step Explanation:

Let larger no. be ‘x’
Let smaller no. be ‘y’

Sum (x + y) = 23
Difference (x - y) = 5

Therefore,
x + y = 23 => Eq. 1
x - y = 5 => Eq. 2

On Adding Eq. 1 and 2, we get :-
=> 2x + 0 = 28
=> 2x = 28
=> x = 28/2 = 14

Substitute x = 14 in Eq. 1 :-
=> x + y = 23
=> 14 + y = 23
=> y = 23 - 14 = 9

Therefore, x = 14 ; y = 9

Hence,
Larger number = 14
Smaller number = 9

Here a brainliest if you get it right

Answers

Answer:

D.(2, 2)

Step-by-step explanation:

Staring point = (2, -4)Since he moved 6 units up, so, there will be change in only y-coordinate of the starting point and x-coordinate will remain unchanged.End point of the segment = (2, - 4 + 6) = (2, 2)

Find the value of x.
148°
Гу
х
x = [? ]°
=

Answers

I think it’s 32 but I’m not sure. Because 180-148=32

A basketball player shoots the ball with an initial velocity of 15.8 ft./sec. at an angle of 43.8° with the horizontal. To the nearest tenth, find the initial horizontal component of the vector that represents the velocity of the ball.

A) 4.4 ft./sec.
B) 10.9 ft./sec.
C) 11.4 ft./sec.
D) 15.2 ft./sec.

Answers

The initial horizontal component of the vector which represents the velocity of the ball is; Choice C; 11.4 ft./sec.

What is the horizontal component of the ball's velocity?

It follows from the task content that the velocity vector of the ball has magnitude 15.8 ft./sec. and is at an angle of 43.8° with the horizontal.

On this note, it follows from vector resolution that the horizontal component of the ball's velocity is;

V(x) = V cos 43.8⁰

V(x) = 11.4 ft./sec.

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Hey could someone help me with this question?

Answers

Answer:

u = 5 m/s

Step-by-step explanation:

Given

s = 20 mt = 2 sa = 5 m/s²

Required Formula

s = ut + 1/2at²

Solving

20 = 2u + 1/2(5)(2)²20 = 2u + 102u = 10u = 5 m/s

How many differnt flags with 3 stripes are possible, using the colours red (R), blue (B) and yellow (Y)? Each colour can be used obly once in each flag.

Answers

Answer:

6

Step-by-step explanation:

3 x 2 x 1

first strip you can have 3 options

second only 2 options left

last one, only 1 choice

RBY

RYB

BRY

BYR

YRB

YBR

Answer:

6 flags

Step-by-step explanation:

The flag must have stripes of 3 different colors.

Ways to arrange each stripe :

Stripe 1 = 3Stripe 2 = 3 - 1 = 2Stripe 3 = 1

Stripe 1 x Stripe 2 x Stripe 3

3 x 2 x 16 flags

The density of copper is 8960 /3. What is tmass of a solid cube of copper with side lengths of 4 meters?

Answers

Answer:

573440 Kg

Step-by-step explanation:

       Mass of copper:

[tex]\boxed{\bf Mass = density * volume}[/tex]

Find the volume of the solid cube

          Volume of solid cube = side³

                                              = 4 * 4 * 4

                                              = 64 m³

[tex]\sf Mass = 8960* 64\\[/tex]

        = 573440 Kg

A cylindrical can of cocoa has the dimensions shown at the right.
What is the approximate area available for the label?
9 2

Answers

Answer:

What are the dementions? 9 and 2?

That would be 9*3.14*4 = 133.04

~ 133.04 units cubed

Step-by-step explanation:

i need helpppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp again.

Answers

Answer:

C - 35 gallons per minute

Step-by-step explanation:

350 / 10

Answer:

350/10 = 35 gallons per minute

Step-by-step explanation:


the heights of a group of
people are normally distributed
with a mean of 62 inches and a
standard deviation of 1.5. what
percent of the group is between
62 and 65 inches tall?

Answers

The percentage of the group that is between 62 and 65 inches tall is 47.725%

How to determine the probability?

The given parameters are:

Mean, μ = 62Standard deviation, σ = 1.5

Calculate the z-scores for x = 62 and x = 65 using:

z = (x - μ)/σ

So, we have:

z = (62 - 62)/1.5 = 0

z = (65 - 62)/1.5 = 2

The percentage is then represented as:

P(62 < x < 65) = P(0 < z < 2)

Rewrite as:

P(62 < x < 65) = P(z < 2) - P(z < 0)

Evaluate

P(62 < x < 65) = 0.47725

Express as percentage

P(62 < x < 65) = 47.725%

Hence, the percentage of the group that is between 62 and 65 inches tall is 47.725%

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someone help me please help please please help me asap

Answers

Answer:

50%

Step-by-step explanation:

The given word :

E A C H

There are 2 vowels.

Probability (vowel) = No. of vowels / Total lettersP (vowel) = 2 / 4P (vowel) = 1/2 = 0.5P (vowel) = 50%

Given m n, find the value of x and y.

Answers

Answer:

X= 38°

Y = 142°

Step-by-step explanation:

let the angle vertically opposite to 142° = w

therefore, w= 142° ( vertically opposite angles are equal)

hence,x+ w =180° ( two interior angles sum up to 180°)

x+ 142° = 180°

x= 180 - 142 = 48°

X = 38°

then calculating for Y

X + Y = 180° ( angles on a straight line sum up to 180°)

38+Y = 180

Y = 180- 38

Y = 142°

we're done here...please don't forget to rate and mark brainliest!!!

A represents Mr. Mole's altitude relative to the ground (in meters) after t
minutes.
A=-2.3t-7A=−2.3t−7A, equals, minus, 2, point, 3, t, minus, 7
How fast did Mr. Mole descend

Answers

Using the slope of the linear function, it is found that Mr. Mole descends 2.3 meters per minute.

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

In this problem, Mr. Mole's altitude in meters after t minutes is given by:

A = -2.3t - 7.

The rate of change is the slope of m = -2.3, hence, Mr. Mole descends 2.3 meters per minute.

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Please help with math questions.​

Answers

[tex]\bold{ANSWER:}[/tex]
x = 2

[tex]\bold{EXPLANATIONS:}[/tex]

factor 2x^3 + 5x^2y - 2xy^2 - 5

Answers

Answer:

The expression is not factorable with rational numbers.

Hope this helps.

This is not a factorable with rational numbers . have a good day

Need help plsss is 3/100 equal to 0.300 ???

Answers

Answer:

Yes. 3/100 = 0.3

Step-by-step explanation:

3/100 converted to decimal form equals 0.3.

Answer:

No

Step-by-step explanation:

If you divide 100 by 3 you will end up with 0.03, not 0.3.

Hope this helps!

PLEASE HELP!! What is the probability that the top three finishers in the contest will all be seniors?

Answers

Using the hypergeometric distribution, it is found that there is a 0.1538 = 15.38% probability that the top three finishers in the contest will all be seniors.

What is the hypergeometric distribution formula?

The formula is:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.

In this problem:

There are 14 players in total, hence N = 14.Eight are seniors, hence k = 8.Three will be taken from the sample, hence n = 3.

The probability that all of them are seniors is P(X = 3), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 3) = h(3,14,3,8) = \frac{C_{8,3}C_{6,0}}{C_{14,3}} = 0.1538[/tex]

0.1538 = 15.38% probability that the top three finishers in the contest will all be seniors.

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Grogg typed the following $1000$ expressions into his calculator, one by one: \[\sqrt{1}, \sqrt{2}, \sqrt{3}, \sqrt{4}, \dots, \sqrt{999}, \sqrt{1000}. \]how many times will grogg's result be an integer?

Answers

Since 30² = 900 and 40² = 1600, between 30 and 40 of the numbers Grogg enters will reduce to integers. Now just find which count is correct. We don't have to look far:

31² = 961

32² = 1024

so there 31 of the outputs of √1, √2, √3, ..., √1000 are integers.

Grogg will result to integers  with  31  outputs from √1, √2, √3, ..., √1000 .

What are integers?

An integer serves as the whole number which can be a positive or negative numbers , such as 6, 9, but it cannot be a fraction.

since, she is starting from √1, √2, √3, up to √1000 , then we know that

31² = 961, then we can find the correct count which is 31. so if she is to input those number into square root one after the other , she will have 31 count.

Therefore, Grogg will result to integers  with  31  outputs from √1, √2, √3, ..., √1000 .

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PLEASE ASAP this is due in 10 minutes

Answers

Answer: 10•12 = 120

I won’t explain it since you are in a hurry

In a bag are 100 marbles: 10 red, 20 white, 30 blue, and 40 green. If one marble is drawn from the bag, what is the probability that the marble will not be red, white, or blue?

Answers

Answer: 60/100 or 6/10 or 3/5

Step-by-step explanation:

We get 10+20+30=60.

We Covert to a fraction, 60/100

Reduce Down. 6/10

Reduce again, 3/5

Final answer is 3/5, the chance of it not being Red, White, or Blue is 3/5.

See your levels
Deb started doing yard work at 9:52 A.M. After working for 1 hour and 48 minutes, she
stopped to have lunch. It took her 36 minutes to eat lunch.
When did Deb finish eating lunch?
12:16 P.M.
12:32 P.M.
1:16 P.M.
1:32 P.M.
Submit
Id
Conany
Rina
Hein center
ser des
Toll

Answers

You add 1 hour and 46 min to 9:52am and then add another 36min
So deb finished eating her lunch at 12:16pm

The correct answer is 12:16 P.M.

How to find when did Deb finish eating lunch ?

According to the problem,

Deb started doing yard work at 9:52 A.M.After working for 1 hour and 48 minutes, she stopped to have lunch.It took her 36 minutes to eat lunch.

Time at which Dev finishes her lunch =

                  9:52 A.M.  + ( 1 hour and 48 minutes +  36 minutes )

                =   11:40 A.M. +  36 minutes = 12 : 16 P.M.

∴ Deb finish eating lunch at 12:16 P.M.

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QUICK PLEASE HELP!FOR 30 POINTS TY Marisol drives 14 miles to a movie theater. She stops after 6.5 miles to pick up
at her house. Then she continues to drive to the movie theater. Marisol wants to know the
distance she and Alicia travel together.
Let y be the distance in miles from Alicia's house to the movie theater.
»Which equations can you solve to find the value of y?
Choose ALL that apply.
y=14-6.5 y +6.5 = 14
O What is the distance from Alicia's house to the movie theater?
? miles

Answers

Answer:

equation 1, y = 14 - 6.5

From Alicia's house, the movie theater is 7.5 miles away

Step-by-step explanation:

the total miles is 14

Marisol already drove 6.5 so the remaining amount of miles to the movie theater is 14 - 6.45

PLEASE tell me I'm dead with this question

There were 27 children in a class.
There were twice as many boys as girls.
How many boys were there?
A 21 boys B 18 boys C 16 boys D 14 boys E 9 boys

Answers

Answer:

b 18 boys

Step-by-step explanation:

In order to solve this problem we must create a system of equations.

Creating a system of equations

Let x = number of boys and y = # of girls

We are given that in total there are 27 children which means # of boys + # of girls = 27 so we can say x + y = 27

We are also given that there are twice as many boys as girls so we can also say x = 2y ( as # of boys = twice the number of girls )

Solving the system

Now to find the # of boys and girls we must solve the system. To do so we are going to use the substitution method.

What is the substitution method?

The substitution method is where one of your variables ( x in this case ) is defined by an expression in which you can plug in or " substitute " it into the other equation ( we can substitute x = 2y into the other equation and solve for y )

Substitute equation 2 into equation 1

Equation 1 : x + y = 27

==> plug in x = 2y

y + 2y = 27

==> combine like terms

3y = 27

==> divide both sides by 3

y = 9

So there are 9 girls in the classroom

Solving for # of boys

To solve for the number of girls we plug in the # of girls (y=9) into one of the equations and solve for x

equation : x + y = 27

==> plug in y = 9

x + 9 = 27

==> subtract 9 from both sides

x = 18

There are 18 boys in the classroom

Checking our work:

Now that we have found the possible answers we can check our work. To do so we are going to want to plug in the values of x and y into both equations and if both are true our answer is correct

Equation 1 x + y = 27

==> plug in x = 18 and y = 9

18 + 9 = 27

==> simplify

27 = 27 ✓

equation 2 x = 2y

==> plug in x = 18 and y = 9

18 = 2(9)

==> multiply 2 and 9

18 = 18 ✓

Both are correct therefore we can conclude that there are 18 boys and 9 girls.

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