help plz its worth 100 points

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

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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]

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

Answer:

y = 2

Step-by-step explanation:

Given

y = x² + 2x + 3 ← substitute x = - 1

y = (- 1)² + 2(- 1) + 3 = 1 - 2 + 3 = 2

Answer:

Notice that the side length of the square is  38 m.

area of square  =  (side length)2  =  (38 m)2   =   1444 m2

Notice that the diameter of the circle is  38 m .

And its radius  =  diameter / 2   =   38m / 2   =   19 m

area of circle  =  pi * radius2  =  pi * (19m)2  =  pi * 361 m2   ≈   1133.54 m2

So......

area of shaded region  =  area of square - area of circle

area of shaded region  ≈       1444 m2     -  1133.54 m2

area of shaded region  ≈    310.46 m2

Step-by-step explanation:

Notice that the side length of the square is  38 m.

area of square  =  (side length)2  =  (38 m)2   =   1444 m2

Notice that the diameter of the circle is  38 m .

And its radius  =  diameter / 2   =   38m / 2   =   19 m

area of circle  =  pi * radius2  =  pi * (19m)2  =  pi * 361 m2   ≈   1133.54 m2

So......

area of shaded region  =  area of square - area of circle

area of shaded region  ≈       1444 m2     -  1133.54 m2

area of shaded region  ≈    310.46 m2

Answer:

$9,151.38

Hopefully that is correct!!

Answer:

C find ur x value by solving the simultaneous equations

Answer:

-2

Step-by-step explanation:

6x+4y=-14. X=-2y+7

—————

3

Answer:

do math

Step-by-step explanation:

Answer:

Lesser returns > T bills

Higher risks > A-rated bonds

Costly and time consuming > Property

No steady cash flow > stocks

Step-by-step explanation:

I just took the test

Answer:

3

Step-by-step explanation:

15*1/5= 3

Answer:

13000m

Step-by-step explanation:

Given data

Total distance travelled=  65,000

Number of days= 5 days

Hence the distance covered per day is

= 65,000/5

=13000m

Therefore the distance covered per day is 13000m

Answer:

6.75cm

Step-by-step explanation:

The straw fits diagonally inside the can so it makes a right angled triangle with height and base of the can ( which is the diameter of the can)

So, hypotenuse = length of straw = 22.5cm

perpendicular = 18cm

base = diameter of can(d)

Using pythagoras theorem

h² = p² + b²

(22.5)² = 18² + d²

506.25 = 324 + d²

d² = 506.25 - 324

d² = 182.25

d = 13.5cm

Now radius = d/2 = 13.5/2 = 6.75cm

Answer: a parallelogram

Answer:

D) The very last one

Step-by-step explanation:

n + 6 < 4

n < -2

< means it's an open circle and goes in the LEFT direction

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.

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:

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Answer:

Five less than the number than....... 8/n - 5 +7

Eight more than the product........ 8 +7n - 2

Five times the sum..... 5(n+7)

Twice the difference.... 2 (8-n)

Answer:

Blue:

[tex] \frac{8}{n} - 5 + 7[/tex]

Green:

[tex]8 + 7n - 2[/tex]

Orange:

[tex]5(n + 7)[/tex]

Purple:

[tex]2(8 - n)[/tex]

Answer:

i think is is 64a

Step-by-step explanation:

Answer:

[tex](8 - 3a)(8 - 3a) \\ 8(8 - 3a) - 3a(8 - 3a) \\ 64 - 24a - 24a + 6a {}^{2} \\ 64 - 48a + 6a {}^{2} \\ 6a {}^{2} - 48a + 64[/tex]

Answer:

the answer is 150

Step-by-step explanation:

Answer: 10 miles

Step-by-step explanation:

You can set this up as an equation where x will represent the number of miles charged. So if we know how much the pick up fee is, how much it is per mile and the total charge we can set up the equation as follows:

3.20 + 3x = 33.20

If we solve for x we will find out how many miles she traveled. So to do so we need to get x on one side and the other numbers on the other side of the equal sign. So to begin we'll subtract 3.20 from both sides:

3x = 30.00

and then divide both sides by 3:

x = 10

So she traveled 10 miles.

The Taxi ride was 10 miles.

An equation is an expression that shows the relationship between two or more numbers and variables.

We can set an equation where x will represent the number of miles charged. So, the total charge we can set up the equation as follows:

3.20 + 3x = 33.20

If we solve for x we will find out the miles she traveled.

Then subtract 3.20 from both sides:

3x = 30.00

then divide both sides by 3;

x = 10

Therefore, she traveled 10 miles.

Learn more about equations here;

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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 ;

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Answer:

about 62%

Step-by-step explanation:

add all of the numbers

subtract the number of purple skittles

do 16÷26

multiply your answer by 100

get 61.5

round up

Answer:

78.54 m

Step-by-step explanation:

To obtain how much circular fence, we obtain the Circumference of the circular playground.

The Circumference of a circle, C = 2*pi*r

pi = 3.14 ; r = diameter / 2 = 25 /2 = 12.5 m

C = 2 * 3.14 * 12.5

C = 78.539816

Hence, the fencing which need to go up is ;

78.54 m

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%

Answer:

10

Step-by-step explanation:

4(1)+2(3)=10

Nora would score 10 and for  x free throws and y three point shots x + 3y.

When graphed, a linear equation always produces a straight line because it is an algebraic equation with each term having an exponent of 1. It is referred to as a "linear equation" for this reason.

One-variable linear equations and two-variable linear equations exist.

Given

points on free throws = 1

points on 4 free throws = 4x1 = 4

and  points on 2 three point shot = 2x3 = 6

total points are 4 + 6 = 10

and if she made x free throws then points are = 1x

and for y three point shots = 3y

total points for x free and y three point shots

x + 3y

Hence the points are 10 and x + 3y.

Learn more about linear Equation;

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Answer:

The answer is below

Step-by-step explanation:

Two triangles are congruent if they have the same shape and their corresponding sides are equal to each other.

1) AB = DC, BE = CE     (given)

2) ∠AEB≅∠DEC  (vertical angles are congruent)

3) ΔABE ≅ ΔACE (side angle side congruence theorem)

If the two sides and an included angle of one triangle is equal to two sides and one included angle of another triangle, then the two triangles are congruent by SAS congruence theorem.

Answer:

An InVESTtigator

Step-by-step explanation:

I've heard this before

Answer:

An Investigator.

Answer:

12

Step-by-step explanation:

Answer:

there are 12 men

Step-by-step explanation:

men:3×4=12

woman:8×4=32