Answer:
[tex]x->-2^{-}, p(x)->-\infty[/tex] and as [tex]x->-2^{+}, p(x)->-\infty[/tex]
Step-by-step explanation:
Given
[tex]p(x) = \frac{x^2-2x-3}{x+2}[/tex] -- Missing from the question
Required
The behavior of the function around its vertical asymptote at [tex]x = -2[/tex]
[tex]p(x) = \frac{x^2-2x-3}{x+2}[/tex]
Expand the numerator
[tex]p(x) = \frac{x^2 + x -3x - 3}{x+2}[/tex]
Factorize
[tex]p(x) = \frac{x(x + 1) -3(x + 1)}{x+2}[/tex]
Factor out x + 1
[tex]p(x) = \frac{(x -3)(x + 1)}{x+2}[/tex]
We test the function using values close to -2 (one value will be less than -2 while the other will be greater than -2)
We are only interested in the sign of the result
----------------------------------------------------------------------------------------------------------
As x approaches -2 implies that:
[tex]x -> -2^{-}[/tex] Say x = -3
[tex]p(x) = \frac{(x -3)(x + 1)}{x+2}[/tex]
[tex]p(-3) = \frac{(-3-3)(-3+1)}{-3+2} = \frac{-6 * -2}{-1} = \frac{+12}{-1} = -12[/tex]
We have a negative value (-12); This will be called negative infinity
This implies that as x approaches -2, p(x) approaches negative infinity
[tex]x->-2^{-}, p(x)->-\infty[/tex]
Take note of the superscript of 2 (this implies that, we approach 2 from a value less than 2)
As x leaves -2 implies that: [tex]x>-2[/tex]
Say x = -2.1
[tex]p(-2.1) = \frac{(-2.1-3)(-2.1+1)}{-2.1+2} = \frac{-5.1 * -1.1}{-0.1} = \frac{+5.61}{-0.1} = -56.1[/tex]
We have a negative value (-56.1); This will be called negative infinity
This implies that as x leaves -2, p(x) approaches negative infinity
[tex]x->-2^{+}, p(x)->-\infty[/tex]
So, the behavior is:
[tex]x->-2^{-}, p(x)->-\infty[/tex] and as [tex]x->-2^{+}, p(x)->-\infty[/tex]
find the HCF and LCM of 150 and 225
Answer:
The LCM of 150 and 225 is 450.Steps to find LCM
Find the prime factorization of 150
150 = 2 × 3 × 5 × 5
Find the prime factorization of 225
225 = 3 × 3 × 5 × 5
Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the LCM:
LCM = 2 × 3 × 3 × 5 × 5
LCM = 450
Look at the methods to find the HCF (150, 225)HCF of 150 and 225 by Prime Factorization
HCF of 150 and 225 by Listing the Common Factors
Method 1: Find HCF of 150 and 225 by Prime Factorization
Represent 8 and 14 as a product of its prime factors.
Prime factorization of 150 is 2 × 3 × 5 × 5
Prime factorization of 225 is 3 × 3 × 5 × 5
The common factor in the prime factorization of 150 and 225 are 3, 5, and 5.
HCF is the product of the factors that are common to each of the given numbers.
So, HCF of 150 and 225 is 3 × 5 × 5 = 75
Method 2: Find HCF of 150 and 225 by Listing the Common Factors
The factors of 150 and 225 are shown below.
Step-by-step explanation:
Hope it is helpful.....
4--9w^2
Can Someone help PLS
Answer:
Step-by-step explanation:
Use the identity: a² - b² = (a + b)(a- b)
4 - 9w² = 2² - (3w²)
= (2 + 3w)(2 - 3w)
What do you call an alligator in a vest?
Answer:
An InVESTtigator
Step-by-step explanation:
I've heard this before
Answer:
An Investigator.
how many 2/5's are in 3
Answer:
7.5
Step-by-step explanation:
Divide 3 by 2/5
3 divided by 2/5 = 7.5
Answer:
7.5
Step-by-step explanation:
when you do 2/5 it = 0.4 then you do 3/0.4 and you get 7.5
g(x)=-(x+1)(r-1)(-4)
In standard form?? Please help!
Answer:
g(x) = 4rx + 4r - 4x - 4
Step-by-step explanation:
g(x)= -(x+1)(r-1)(-4)
please tell me answers I am given you brainliest
Answer:
what is the question or whatever
Please Help!! Brainliest Answer! Thank you!
Answer:
D. 157.5
Step-by-step explanation:
Formual for sum of interior angles
(n-2)*180
so 14*180=2520
but that is the sum
divide that by 16 (2520/16) = 157.5
please help me with this it is practice and I'm confused
Answer:
D
Step-by-step explanation:
A function is any line that does not repeat in x-value (doesn't repeat on the x-axis).
Can y’all recount a story where you were proud of yourself for making a good decision when it was really difficult? Thanks!
Answer:
i was proud of myself when I finally figured out a difficult math problem. I didn't even ask for help. it was a hard time for me but I eventually came through.
The scores on a mathematics exam have a mean of 70 and a stadard deviation of 7. Find the x-value that corresponds to the z-score -1.45.
Answer:
59.85
Step-by-step explanation:
The scores on a mathematics exam have a mean of 70 and a stadard deviation of 7. Find the x-value that corresponds to the z-score -1.45.
We solve the above question using z score formula
z = (x-μ)/σ, where
x is the raw score
μ is the population mean = 70
σ is the population standard deviation = 7
z = -1.45
Hence:
-1.45 = x - 70/7
Cross Multiply
-1.45 × 7 = x - 70
-10.15 = x - 70
x = -10.15 + 70
x = 59.85
Write 200 as a product of primes.
Use index notation when giving your answer.
Answer:
Step-by-step explanation:
The prime factorization of 200 is as follows: 200 = 2 × 2 × 2 × 5 × 5.
The prime factorization of 200 will be equal to 2 × 2 × 2 × 5 × 5 or 2³ × 5².
It is given that a number is 200.
We have to find out the prime factorization of 200.
What do you mean by prime factorization ?
Prime factorization is a way to find the prime factors of a number, such that the original number is evenly divisible by the prime numbers.
As per the question ;
The given number is 200.
We have to find the prime factors of 200.
This meant to find out the prime numbers we should multiply together to make the original number which is 200.
So ;
200
= 2 × 100
= 2 × 2 × 50
= 2 × 2 × 5 × 10
= 2 × 2 × 2 × 5 × 5
or
= 2³ × 5²
Thus , the prime factorization of 200 will be equal to 2 × 2 × 2 × 5 × 5 or 2³ × 5².
To learn more about prime factorization click here ;
https://brainly.com/question/1081523
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people in here again and again. I think this is the last question
Answer:
2.4 cm
Step-by-step explanation:
We know the length of segment AB and the length of segment BC. To find their midpoints, we can divide their length by 2.
Let's find the midpoint of AB.
Segment AB: 10 cm Midpoint of AB: 10/2 = 5 cmNext let's find the midpoint of BC.
Segment BC: 5.2 cmMidpoint of BC: 5.2/2 = 2.6 cmIn order to find the difference between these midpoints, we can subtract the midpoint of AB by the midpoint of BC.
5 cm - 2.6 cm = 2.4 cmTherefore, the difference between the midpoints of AB and BC is 2.4 cm.
Is the following expression greater than, less than, or equal to zero? (a^2+b^2)/(a^2+b^2+1)
so I think it's equal to but can someone verify it for me?
Answer:
is equal cuz a will be cut and be will be cut so what is left 1 is left so it is equal plz Mark me as the brainliest and thank me
Find all numbers whose absolute value is -7. If there is more than one, separate them with commas.
Write ways to represent the fraction 10/9.
Answer:
mixed number form 1 1/9
decimal form 1.11111111111111 it goes on forever
percent form 111.111111111111% it goes on forever (again)
Step-by-step explanation:
i hope that helps!
Answer:
1 1/9
Step-by-step explanation:
10/9, you get 1 as the whole number.
You have a 1 left over when dividing 10 and 9. the 1 will be over 9.
Giving you 1 as the whole number and 1/9 next to it.
need to pass this class!
A roller coaster is at the top of a 72 m hill and weighs 134 kg. The coaster (at this moment) has____________ energy. Calculate it.
A. Kinetic Energy and 347,328J
B. Kinetic Energy and 9,648J
C. Potential Energy and 9,648J
D. Potential Energy and 94,550.4J
Answer:C
Step-by-step explenation: m=134kg,h=72m,g=10m/s
PE=mgh
PE=(134kg)(10m/s^2)(72m)
PE=964800J
A restaurant small salt shakers contains 0.6 ounces of salt. The shakers are filled from a container that has 18.6 ounces of salt. If 8 shakers are filled, how much salt will be remaining in the salt container?
Answer:
13.8 ounces of salt
Step-by-step explanation:
A restaurant small salt shakers contains 0.6 ounces of salt. The shakers are filled from a container that has 18.6 ounces of salt. If 8 shakers are filled, how much salt will be remaining in the salt container?
Step 1
Note that:
1 shaker = 0.6 ounces of salt
8 shakers = x
Cross Multiply
x = 8 × 0.6 ounces of salt
x = 4.8 ounces of salt
Step 2
The shakers are filled from a container that has 18.6 ounces of salt. If 8 shakers are filled, how much salt will be remaining in the salt container?
This is calculated as:
18.6 ounces of salt - 4.8 ounces of salt
= 13.8 ounces of salt
y/3 + 2 = 14 I need help
Answer:
y = 36
Step-by-step explanation:
[tex]\frac{y}{3}+2 = 14\\\\\frac{y}{3}=14-2\\\\\frac{y}{3}=12\\\\y = 12*3\\\\y = 36[/tex]
Find the excluded value of the function Y= - 10/6x-5. The excluded value is x =??
Answer:
The excluded value is x = 5/6
Step-by-step explanation:
Here, we want to calculate the excluded value
The excluded value is simply the value of x that will make the denominator of the fraction equals zero
We have this as;
6x -5 = 0
6x = 5
x = 5/6
100% of what number is 27? Provide an exact fraction answer
Answer:
Your answer is 27
I hope I helped, would appreciate brainliest! ;)
Step-by-step explanation:
'Percent (%)' means 'out of one hundred':
27% = 27 'out of one hundred',
p% is read p 'percent',
27% = 27/100 = 27 ÷ 100
Calculate percentage:
'Percentage' is obtained by multiplying 100 by 27%
27% of 100 is equivalent to multiplying them:
27% × 100 = ?
27% × 100 =
(27 ÷ 100) × 100 =
(27 × 100) ÷ 100 =
2,700 ÷ 100 =
27
Proof.
How do we check the result?
If 27% × 100 = 27 =>
Divide 27 by 100...
... And see if we get as a result: 27%
Note:
100/100 = 100 ÷ 100 = 100% = 1
Multiply a number by the fraction 100/100,
... and its value doesn't change.
n/100 = n%, any number.
Calculate the percent value:
27 ÷ 100 =
0.27 =
0.27 × 100/100 =
(0.27 × 100)/100 =
27/100 =
27%
So we have proved that the calculations are correct.
Answer:
Percentage of
27% of 100 = 27
Answer:
27%
Convert fraction (ratio) 27 / 100 Answer: 27%
Find the amount and compound interest on 5000 at 6% per annum for 3 years annual
Answer:
The amount is 5,955.08
Step-by-step explanation:
Here, we want to calculate compound interest
We can find this by using the compound interest formula
A = P( 1 + r/n)^nt
A is amount
P
is the principal = 5,000
r is the interest rate = 6% = 6/100 = 0.06
n is the number of times per year in which the interest is compounded = 1
t is the number of years = 3
Substituting these values;
A = 5,000(1 + 0.06/1)^3(1)
A = 5000(1.06)^3
A = 5,955.08
Please when answering show your full work. Step-by-step process.
Which is larger, 9 kilograms or 8,500 grams?
Answer: 9 kilograms
Step-by-step explanation:
9 kilograms is larger because the kilogram, or kilogramme, is the base unit of weight in the Metric system. It is the approximate weight of a cube of water 10 centimeters on a side. While a gram is a unit of weight equal to 1/1000th of a kilogram. A gram is the approximate weight of a cubic centimeter of water.
A tip for great service is 20% of the bill. If the bill for dinner is $32, what is the total cost of dinner?
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What is the equation of a line .........
Answer:
y = -x + 2, B is the answer
Step-by-step explanation:
If slope is -1, the equation is y = -x+b
Plug in (3,-1) into that equation.
-1 = -3 + b
b = 2
Marty has a driveway that is 200 feet long. The tires on her car have a diameter of 18 inches. What is the fewest number of tire rotations a tire will make tot travel the entire distance of the driveway?
The the fewest number of tire rotations is 42 to travel the entire distance of the driveway.
It is given that the driveway that is 200 feet long and the tire diameter is 18 inches.
It is required to find the fewest number of tire rotations a tire will make to travel the entire distance of the driveway.
What is a circle?It is defined as the combination of points that and every point has an equal distance from a fixed point ( called the center of a circle).
Driveway length = 200 feet
Diameter of the tire = 10 inches
For converting it to feet divide by 12.
Now the diameter of tire = 18/12 = 1.5 feet
Radius of the tire = 0.75 feet
We know the perimeter of the circle:
[tex]\rm P = 2\pi r[/tex]
P = 2(π)(0.75)
P = 4.71 feet ( π =3.14 and P = 0.75)
[tex]\rm number \ of \ tire \ rotations = \frac{Driveway \ length}{Perimeter \ of tire}[/tex]
[tex]= \frac{200}{4.71}[/tex]
Number of tire rotation = 42.462 ≈ 42
Thus, the the fewest number of tire rotations is 42 to travel the entire distance of the driveway.
Learn more about circle here:
brainly.com/question/11833983
What is the slope of the line?
What is the y-intercept?
Write the equation of the line
Answer:
slope is 2
y-intercept is 3
equation y=2x+3
Step-by-step explanation:
Answer:
slope=4/2 or 2
y-intercept=3
equation=y=2x+3
the slope would be 4/2 because if you do the triangle method you see that the vertical distance of y is 4 and the horizontal distance of x is 2 so that gives you 4/2 the y intercept is where the line starts at 0 which you can see is 3. if the equation is y=mx+b you plug in the slope which is 4/2 or 2 and plug in the y-intercept which is 3 which gives you y=2x+3
Glenn needs to cut pieces of ribbon that are each 1 meter long to make ribbon key chains. If he has 6 pieces of ribbon that are each 1 dekameter long, how many 1−meter pieces of ribbon can he cut?
Answer:
2/3
Step-by-step explanation:
Glenn needs to cut pieces of ribbon that are each 1 meter long to make ribbon key chains. If he has 6 pieces of ribbon that are each 1 dekameter long, how many 1−meter pieces of ribbon can he cut?
1 decametre = 10 metres
Hence,
10 meters = 6 pieces of ribbon
1 meter = x pieces
Cross Multiply
10x = 6
x = 6/10
x = 2/3 (1 meter pieces of ribbon)
One of the flags in front of the United Nations sits on a pole 80 feet tall and casts
a shadow 16 feet long. At the same time of the day, another flag casts a shadow
18 feet long. How high is the other flag?
HELPPPPP
Answer:
90 feet
Step-by-step explanation: