The population P(t) of a species satisfies the logistic differential equation dP/dt= P(2-(P/5000)) where the initial population 3,000 and t is the time in years. What is the lim t>infinity P(t)?

The correct answer is Roger

The Bible, a book that is considered the perfect word of a perfect god tells us what the value of Pi is. Let's see verse 1 Kings 7:23
 He also melted a sea of ​​ten cubits from one side to the other, perfectly round; Its height was five cubits, and a cord of thirty cubits encircled it.

 These are a list of specifications for the great temple of King Solomon, built about 950 BCE, and his interest here is that it gives a value of π = 3. If we divide 30 cubits between 10 cubits (which are the measures mentioned in written radical) gives us exactly 3.

 We know that the length of the circumference is calculated l = 2 · π · r; Since 2 · r is the diameter, it can also be said that

 circumference = diameter × π

 If we go back to what the Bible says, the diameter is 5 meters and the circumference of 15:

 circumference = diameter × π -> 15 = 5 × π

 with which the value of π is 3.

 This calculation of Pi is a bad approximation to the real value. The figure of 3 in the Bible compared with the real one which is 3.1416 ... indicates an error of about 6%.

Luis is the one that performed an incorrect first step. When you add or subtract from either side, this does not affect the inequality symbol.

What will affect the symbol is when you divide or multiply by a negative because this means the opposite.

Answer:

B

Luis’s, because he flipped the inequality sign when he subtracted

Step-by-step explanation:

got it right on Edge

please mark as Brainliest

(P.S. Luis is my first name)

the answer is c the degree of the trinomial

The answer is {B}. You obtain the c value is the quadratic when you multiply m and n. This is also known at the y intercept. y intercepts are a constant.

To find the number of moles we start by calculating the molar mass:
M(C2H5OH) = 2*M(C) + 6*M(H) + M(O)
M(C2H5OH) = 2* 12.01 + 6* 1.008 + 16
M(C2H5OH) = 46.068g

This is mass of one mole of ethanol. Total mass of ethanol can be calculated by using formula:
m = N * M
Where:
m = total mass
N = number of moles
M = molar mass

We rearrange formula for N:
N = m / M
N = 508 / 46.068
N = 11.03

508g of ethanol contains 11.03 moles.

The correct answers are a) given; b) substitution property; c) subtraction property of equality; d) division property of equality; and e) reflexive property of equality.

Explanation:
The first line of your proof just restates what was given to us; therefore the reason is "given."

Between the first step and the second step, 11x was changed to 88; this is because x=8, and we substitute that in for x. That would give us 11*8=88, with the justification being substitution.

Between the second line and third line, 88 is cancelled from the left side and the -1 becomes -89; this happens because in order to cancel a positive 88, you must subtract it from both sides. This is the subtraction property of equality.

Between the third line and fourth line, -6 is cancelled from the left side and on the right side, -89 is changed to 89/6. This happens because in order to cancel the -6 that is beside the y (which means multiplication), we must divide both sides; this is the division property of equality.

The last step is to rewrite the equation with y on the left and the answer on the right; the reflexive property allows us to do that.

Final answer:

The correct properties of equality used to solve the equation given x = 8 are Given, Substitution Property, Subtraction Property of Equality, Division Property of Equality, and Symmetric Property of Equality.

Explanation:

The student has shared the steps of solving an equation and is asking for the correct sequence of properties used to solve it:

Given: 11x - 6y = -1; x = 8Substitute x: 88 - 6y = -1Subtract 88 from both sides: -6y = -89Divide by -6: y = 89/6State that 89/6 = y

The correct properties of equality should be applied as follows:

Given: Both the equation and x = 8 are provided information.Substitution Property: x = 8 is substituted into the equation for x.Subtraction Property of Equality: 88 is subtracted from both sides of the equation.Division Property of Equality: Both sides of the equation are divided by -6 to solve for y.Symmetric Property of Equality: Rearranges the equation to y = 89/6 for clarity.

The correct answer is (d). If d represents the number of dimes and q the number of quarters, the total number of coins would be d+q, which is given as 40 in the prompt: d+q=40

Since each dime is worth ten cents and each quarter worth twenty-five cents, their total value would be 0.10d+0.25q which would total 5.80.: 0.10d+0.25q=5.80        I HOPE THIS HELPS YOU

D) d + q =40
0.10d+0.25q=5.80

To find all possible values for θ if 0° < θ < 360° and tanθ = -1, we need to determine in which quadrants the tangent function is negative and then find the specific angles in those quadrants where the tangent equals -1.

The tangent function is negative in the second and fourth quadrants. Since tan(45°) = 1, we are looking for angles where the reference angle is 45° and the tangent is negative.

In the second quadrant, the angle that meets these criteria is 180° - 45° = 135°.

In the fourth quadrant, the angle that meets these criteria is 360° - 45° = 315°.

Therefore, the correct values for θ are:

c. 135°

e. 315°

The correct answer is [tex]135^{0}[/tex], [tex]225^{0}[/tex]

To find all possible values of θ if 0° < θ < 360° and tan θ = -1, we need to consider the values of θ in the different quadrants where the tangent function is negative.

In the first quadrant (0° < θ < 90°), the tangent function is positive, so there are no solutions in this range.

In the second quadrant (90° < θ < 180°), the tangent function is negative, and tan(135°) = -1.

In the third quadrant (180° < θ < 270°), the tangent function is also negative, and tan(225°) = -1.

In the fourth quadrant (270° < θ < 360°), the tangent function is positive, so there are no solutions in this range.

Therefore, the possible values of θ satisfying the given conditions are:

[tex]\theta = 135^\circ and \theta = 225^\circ[/tex]

Analyzing the given options:

a. [tex]-225^\circ[/tex] is not a solution, as it lies outside the given range of 0° < θ < 360°.

b. [tex]-45^\circ[/tex] is not a solution, as the tangent function is positive in the fourth quadrant.

c. [tex]135^\circ[/tex] is a solution, as tan(135°) = -1.

d. [tex]225^\circ[/tex] is a solution, as tan(225°) = -1.

e. [tex]315^\circ[/tex] is not a solution, as the tangent function is positive in the fourth quadrant.

Therefore, the correct options are c. 135° and d. 225°.

The equation you have provided is correct:

A(t)=P(1+r/n)^nt

Where P = principal amount

              r = interest rate

              n = number of times the amount is compounded in a year

              t = time in years

The value of n is 12 since it is compounded monthly.

Substituting the amount to the formula:

A(t) = $300 ( 1 + 4%/12)^(12)(8)

A(t) = $300 (1 + 0.003333)^96

A(t) = $300 (1.376351)

A(t) = $412.91

Begin by adding 4.9x to both sides.
1.3> 11.1 + 4.9x This way you never have to remember to turn the > into < when dividing by a minus.

Subtract 11.1 from both sides
-9.8 < 4.9x Divide by 4.9
-9.8 / 4.9 < x
-2 < x

To solve the inequality -4.9x + 1.3 > 11.1, subtract 1.3 from both sides and then divide by -4.9, flipping the inequality sign to get x < -2. The solution set is x < -2.

To solve the inequality -4.9x + 1.3 > 11.1, follow these steps:

Subtract 1.3 from both sides to isolate the term with x:
-4.9x > 11.1 - 1.3
-4.9x > 9.8Divide both sides by -4.9 and remember to flip the inequality sign because you are dividing by a negative number:
x < -9.8 / -4.9
x < -2

The solution set for the inequality is x < -2.

The answer is 6.  It is the second option.
y = kx^2 
Use any coordinate in the set.
The missing is k, to find it, use the equation
24 = k(2^)
= 4k 
k = 6 

48 - 3 = 45.
45 divided by 6 = 7.5
That means that the width is 7.5 and the length is 18. Hope it helps! :)

The missing length can be found using the Pythagorean theorem since it is a right triangle.

a²+b²=c²
(2.7)²+b²=(6.5)²
7.29+b²=42.25
b²=34.96
b=√34.96
b=5.91

Answer:

Option B. 4

Step-by-step explanation:

By the table mentioned by you in the comments that the correct table is

x(miles)   2        5        8     12

y(cost)   8.5   15.25    22    31

As we know that the standard equation of a linear function is represented as

y = mx + c

For the points (2, 8.5) and (5, 15.25)

[tex]Slope(m)=\frac{15.25-8.5}{5-2}=\frac{6.75}{3}=2.25[/tex]

y = 2.25x + c

This function passes through (2, 8.5)

8.5 = 2.25×2 + c

c = 8.5 - 4.5 = 4

Therefore, y- intercept of the function will be option B. 4.

The y-intercept of this line is (4). Therefore, the estimated y-intercept of the function represented by the given data is 4.

To find the y-intercept of the function from the provided table, we look for the point where (x = 0), which represents the cost when no miles are traveled.

However, in the given table, there is no entry for \(x = 0\), which means we don't have a direct value for the y-intercept from the given data.

To estimate the y-intercept, we can use the concept of linear interpolation.

We can assume that the relationship between miles traveled and cost is linear, so we can find the slope of the line passing through two consecutive points and use it to estimate the cost when (x = 0).

Using the points (2, 8.5) and (5, 15.25) from the table:

[tex]\[ \text{Slope} = \frac{{15.25 - 8.5}}{{5 - 2}} = \frac{6.75}{3} = 2.25 \][/tex]

Now, we can use the slope and one of the points to find the y-intercept using the point-slope form of the equation of a line: [tex]\(y - y_1 = m(x - x_1)\).[/tex] Let's use the point (2, 8.5):

y - 8.5 = 2.25(x - 2)

y - 8.5 = 2.25x - 4.5

y = 2.25x + 4

The y-intercept of this line is (4). Therefore, the estimated y-intercept of the function represented by the given data is [tex]\(\boxed{4.00}\)[/tex].

Complete question:

By the table mentioned by you in the comments that the correct table is

x(miles)   2        5        8     12

y(cost)   8.5   15.25    22    31
In the table below, x represents miles traveled and y represents the cost to travel by train.

What is the y-intercept of this function?

2.25

4.00

6.50

17.13

The answer for the blank is 0.003

This is the slope value, which is the number in front of the x in the least squares regression line. Each time x increases by 1, y increases by 0.003

This is the predicted y value of course. 

(x^15)(x^-3) = x^(15 + (-3)) = x^12
n = 12

E) 2 
 Remember that the first derivative of a function is the slope of the function at any specified point. We've been told that f(0) = -5 and that f'(x) is always less than or equal to 3. So let's look at the available options and see what the average slope would have to be in order to get the specified value of f(2).
 A) -10: (-10 - -5)/(2 - 0) = -5/2 = -2.5
 B) -5: (-5 - -5)/(2 - 0) = 0/2 = 0
 C) 0: (0 - -5)/(2 - 0) = 5/2 = 2.5
 D) 1: (1 - -5)/(2 - 0) = 6/2 = 3
 E) 2: (2 - -5)/(2 - 0) = 7/2 = 3.5 
 Now taking into consideration the mean value theorem, the value of the function f'(x) has to have the value equal to the average slope between the two points at at least one point between the two given values. For options A, B, C, and D it's possible for f'(x) to return values that make that slope possible. However, for option E, the mean value theorem indicates that f'(x) has to have the value of 3.5 for at least 1 point between x=0 and x=2. And since we've been told that f'(x) is less than or equal to 3 for all possible values of x, that is in conflict and f(2) can not have the value of 2.

Final answer:

Using the Mean Value Theorem, we can determine the possible values for f(2) which is D) 1

Explanation:

To find the possible values for f(2), we can use the Mean Value Theorem. Taking into consideration the mean value theorem, the value of the function f'(x) has to have the value equal to the average slope between the two points at at least one point between the two given values.

Since f(0) = -5 and f'(x) is less than or equal to 3 for all x, we know that f(2) must lie between -5 and -5 + 3(2) = 1.

Therefore, 1 is not a possible value for f(2), making the correct answer choice D) 1.

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The firts thing we are going to do here is use the simple interest formula: [tex]A=P(1+rt)[/tex]
where 
[tex]A[/tex] is the final amount after [tex]t[/tex] years
[tex]P[/tex] is the initial investment  
[tex]r[/tex] is the interest rate in decimal form 
[tex]t[/tex] is the number of years 
With this formula we will find the final amount Azhar's investment after 7 years. We know from our problem that [tex]P=10000[/tex], [tex]r= \frac{2}{100}=0.02 [/tex], and [tex]t=7[/tex]. Lets replace those values in our formula to find [tex]A[/tex]:
[tex]A=10000(1+(0.02)(7))[/tex]
[tex]A=10000(1.14)[/tex]
[tex]A=11400[/tex]

Now, since Sarah is investing in a compound interest account, we are going to use the compound interest formula: [tex]A=P(1+ \frac{r}{n})^{nt} [/tex]
where
[tex]A[/tex] is the final amount after [tex]t[/tex] years
[tex]P[/tex] is the initial investment 
[tex]r[/tex] is the interest rate in decimal form
[tex]n[/tex] is the number of times the interest is compounded per year
[tex]t[/tex] is the number of years
Notice that we know from our problem that after 7 years their investments are worth the same amount, so [tex]A=11400[/tex]. We also know that [tex]P=10000[/tex], [tex]r= \frac{x}{100} =0.01x[/tex], and [tex]t=7[/tex]. Since the interest are compounded per year, [tex]n=1[/tex]. Lets replace all the vales in our compound interest formula and solve for [tex]x[/tex] to find our rate:
[tex]11400=10000(1+ \frac{0.01x}{1} )^{(1)(7)} [/tex]
[tex] \frac{11400}{10000} =(1+0.01x) ^{7} [/tex]
[tex](1+0.01x) ^{7} =1.14[/tex]
[tex]1+0.01x= \sqrt[7]{1.14} [/tex]
[tex]0.01x= \sqrt[7]{1.14} -1[/tex]
[tex]x= \frac{ \sqrt[7]{1.14}-1 }{0.01} [/tex]
[tex]x=1.89[/tex]

We can conclude that the interest rate of Sarah's investment is approximately 1.89%, so x=1.89%.

10(cos(4pi/3) + i sin(4pi/3)) To multiply complex numbers in trigonometric form, you simply multiply the radii and add the thetas. We have: z1=5(cos(pi/2)+i sin(pi/2)) z2=2(cos(5pi/6)+i sin(5pi/6)) The radii for the above 2 numbers are 5 and 2. So the result will have a radius of 5*2 = 10. The thetas are pi/2 and 5pi/6, so the new theta will be pi/2 + 5pi/6 = 3pi/6 + 5pi/6 = 8pi/6 = 4pi/3. So the answer is: 10(cos(4pi/3) + i sin(4pi/3))

The reflection across the y -axis is that it would be the x -axis. Your welcome!

Answer:

G (-6,-8) H(-2,-2) F(0,-4)

Step-by-step explanation:

So really you add an negitive symbol to each number then its reflected acroos the x axis

1)
the letters in the sequence are in the order of first letter of numbers.
the sequence thats in the numerical order - one, two , three...
each number is taken and the first letter of the word is taken for the sequence,
one - first letter of one is O
O(one), T(two), T (three), F (four), F(five), S(six), S(seven),(eight)
first letter of eight is E, so next letter in the sequence is E

2)
a- whole number 
whole numbers are integers that don't have any decimal places and are not fractions either.
b- digit
digit is a single number that can hold a position in a numerical value. for example 7 in 7000 is holding the thousands digit. And in number 7000 we can call it a 4 digit number as there are 4 digits in it.
c - place value
this is when a number holds a certain value depending on its position/ place in the numerical value. for example in 200, number 2 is in the hundreds place therefore its having a value of 2 counts of hundred , therefore has a place value of 200. place value means that each place has a value 10 times of that of the value to its right. so 2 is in the hundreds place, right of that is tens place, hundreds place value is 10 times of tens value = 10*10 = 100 therefore when number 2 is in the hundreds places its 2*100 = 200
d - rounded number 
rounded number is when a number is made to a simpler form. rounding off can be done to any place of the number. Its to bring it to a simpler number by dropping off the unnecessary digits to make it easier to work with
e - equals
equals is when a number is equal in value to another number. By equalling it means that the value on the right side of the equals sign is equal to the value on the left side of the equals sign

3)
we are asked to insert commas in the following numbers. Commas are inserted for convenience to add breaks to the number so that its easy to read out the number and to see if the number is a thousand, million or billion by looking at the number of commas.
Commas are inserted in numbers with 4 or more digits, after every three digits from right to left.
a. 13,886
b. 365
c. 719,463
d.40,047,209
e. 2,145,739,180
f.  1,783,457

4)
when writing word names, the numbers are read out for every three digits for the right to left. first 3 digits are written as it is, next 3 digits are written as thousand, next 3 digits as million and 3 digits after that as billion
we are asked to write the word names for the following numerals;
(a) two million four hundred thousand 
(b) forty billion
(c)four hundred seventy three thousand five hundred
(d)one thousand two hundred

5) when writing numerals from thousands same rules apply. first three digits as it is, next three digits are thousands and 3 digits to the left of that are millions
(a)2,155,120
(b)225,060,000
(c)251,720,000

6)
depending on where number 5 is in the number, it will hold different values. 
for example in 5234, 5 holds the thousands place, 2 holds the hundreds place, 3 in tens place and 4 in ones place.         
a. tens 
b. thousands
c. ones
d. ten thousands
e. hundred thousands
f. millions

7)
this shows the value of each position
                           7,          8            9       0    ,          4         3       2
hundred   ten  ones      hundred   ten   ones      hundred   ten   ones                  
 --------million-------       ----------thousand---        ---------ones-----------
7,890,432, name the digit located in each of these positions.
a. Hundreds - 4
b. Millions - 7
c. Ten thousands - 9
d. Tens - 3
e. Hundred thousands - 8
f. Thousands - 0

8)
in the number line the lesser number to the left of the number line and the greater number is to the right of the number line
Which of the numbers in each pair is farther to the left on the number line?
a.17  -17 is smaller than 305 therefore its farther to the left than 305
b. 187 
c. 16 
d. 149 984

Q9)symbol > is when the number on the left is greater than the number on the right
symbol < is when the number on the right is greater than the number on the left 
= is when both the numbers on either side of the symbol are equal to each other
a.39 > 38
b. 16 = 16
c. 11 < 315
d. 5 > 4

10)
In rounding off, the digit which you're rounding off, the digit to the right of that digit should be considered. If the digit to the right is 5 or greater than 5, then the digit which you're rounding off increases by a value of 1. If the digit to the right is less than 5 then the digit which you're to round off stays as it is. All the digits too the right of the digit being rounded off becomes zeroes.
 1,360,760,100. Round off 
a. thousands place digit is 0,digit to the right is 1, since 1<5 then, 0 stays as it is and all the digits to the right of 0 are dropped off and becomes zeroes - 1,360,760,000
b. millions digit is 0, digit to the right is 7, then its greater than 5, 0 then increases by 1 and becomes 1, all the digits to the right of 1 become dropped off and turns into zeroes. 
- 1,361,000,000
c. hundred million is 3 right of that is 6, 6>5 therefore 3 increases by 1 
- 1,400,000,000
d. hundred thousand is 7 and digit to the right is 6, then 7 increases by 1
- 1,360,800,000

Answer:

a. A whole number is a counting number that represents a quantity of whole things.

b. A digit is any one of the numerals in the group 0 through 9.

c. Place value is the value that a digit has within a number. Place value is determined by the digit’s position in the number.

d. A rounded number is a close approximate for an exact whole number.

e. “Equals” means “exactly the same.”

a. 13,886

b. No commas are needed.

c. 719,463

d. 40,047,209

e. 2,145,739,180

f. 1,783,457

a. Two million, four hundred thousand

b. Forty billion

c. Four hundred seventy-three thousand, five hundred

d. One thousand, two hundred

a. 2,155,120

b. 225,060,000

c. 251,720,000

a. Tens

b. Thousands

c. Ones

d. Ten thousands

e. Hundreds

f. Millions

a. 4

b. 7

c. 9

d. 3

e. 8

f. 0

a.17

b. 184

c. 16

d. 149,984

a. >

b. =

c. <

d. >

a. 1,360,760,000

b. 1,361,000,000

c. 1,400,000,000

d. 1,360,800,000

Step-by-step explanation:

Finding the lengths of the legs of the right triangle, we have 6 and 3. (6*3)/2 = 9. Finding the area of the semi-circle we obtain [tex]\frac{1.5^2\pi}{2} [/tex] which rounding to 3.14 as pi, we obtain 3.5325. Adding up the area of the triangle and the semi-circle and the triangle we get 9+3.5325 which equals 12.5325

The area of the figure that is made up of a triangle and a semicircle is 23.137 units².

What is the area of a triangle?

The area of a triangle is half the product of its base and its height.

[tex]Area \triangle = \dfrac{1}{2}\times base \times height[/tex]

In order to solve the problem, we will divide the given figure into two parts such that the first one will be a right-angled triangle while the second one is a semi-circle as shown below.

As we can see in the ΔABC, the height of the triangle is 3 units, while the length of the base of the triangle is 6 units. therefore, the area of the triangle can be written as,

[tex]\begin{aligned}\triangle ABC &= \dfrac{1}{2} \times height \times base\\\\&= \dfrac{1}{2} \times BC \times AB\\\\& = 0.5 \times 3 \times 6\\\\& = 9\rm\ unit^2 \end{aligned}[/tex]

Now, if we look at the semi-circle we will find that the diameter(BC) of the semi-circle is 3 units, therefore, the area of the semi-circle can be written as,

[tex]\begin{aligned}\text{Area of Semi-circle} &= \dfrac{\pi}{2}d^2\\\\ &= \dfrac{\pi}{2}(3)^2\\\\&= 14.137\rm\ units^2 \end{aligned}[/tex]

Further, in order to get the total area of the figure, simply add the two areas, therefore,

The area of the figure = Area of triangle + Area of the semi-circle

                                     = 9 + 14.137

                                     = 23.137 units²

Hence, the area of the figure that is made up of a triangle and a semicircle is 23.137 units².

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the complete question in the attached figure

we know that
[the ratio of the hypotenuse to the given side]=(6√2)/(6)-----> √2/1

therefore

the answer is the option A) √2/1

A ratio shows us the number of times a number contains another number. The correct option is C.

What is a Ratio?

A ratio shows us the number of times a number contains another number.

The complete answer is mentioned in the below image.

The ratio of the hypotenuse to the given side is,

Ratio = (6√2)/ 6 = √2 : 1

Hence, the correct option is C.

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It would just be 4a² as the LCD, because the first fraction can have the denominator easily multiplied by 4a to make 4a²

The period of sine is 2π.
Look at the picture.

Correct Answer:
First Option

Let the first integer be n.
Since the integers are consecutive, the integer next to n will be n+1
and so the third integer will be n+2

Therefore, the three integers are:
n , n +1, n+2

Their sum is 75. So we can write the equation as:

n + (n+1) + (n+2) = 75

This equation can be used to find n. After finding n, we can find the next two integers by finding (n+1) and (n+2)

The greatest common factor is what both terms have in common. 
7 and 8 have nothing in common.
ab and b^3 have b in common.
The greatest common factor is b.

Sure!

1) 5.1*10^-4
2) 5.5*10^-2 LEAST TO
3) 2.2*10^-2 GREATEST
4) 4.4*10^-2
5) 6*10^2
6) 3.5*10^4

If the exponent is negative go left, if it is positive, go right.

Example:

<------ (-4) (4) ------>

If you need anymore help, just ask... <3

Hope this helps! Good luck on Scientific Notation! :-)

The numbers ordered from least to greatest are: 5.1 × 10⁻⁴ ,2.2 × 10⁻²,5.5 × 10⁻²,4.4 × 10², 6 × 10², 3.5 × 10⁴. This ordering is based on comparing the exponents of 10 first and then the coefficients where the exponents are equal.

To order the numbers 5.5 × 10⁻², 6 × 10², 4.4 × 10², 3.5 × 10⁴, 2.2 × 10⁻², and 5.1 × 10⁻⁴ from least to greatest, you must understand scientific notation. Scientific notation expresses numbers as a product of a number between 1 and 10 and a power of 10. It's commonly used for very large or very small numbers.

5.1 × 10⁻⁴ : The smallest exponent of 10 and a small coefficient.

2.2 × 10⁻² : Next smallest exponent with a small coefficient.

5.5 × 10⁻² : Slightly larger coefficient but same exponent as the previous.

4.4 × 10² : Positive exponent and the smaller coefficient of the positive exponents group.

6 × 10² : Larger coefficient than the previous, but same exponent.

3.5 × 10⁴ : The largest exponent and a large coefficient, makes it the largest number.

Final answer:

To find the range of a rational function with a slant asymptote, you first find the asymptote by long division. Then by examining the behavior of the function near the vertical asymptotes by plugging in values, you determine the limits of the range. Generally, the range is all real numbers except where interrupted by the asymptotes.

Explanation:

To find the range of a rational function with a slant asymptote, you need to first find the slant asymptote by dividing the numerator by the denominator using long division. When you perform the division, if the degree of the numerator is one more than the degree of the denominator, then the quotient (excluding the remainder) will be the equation for the slant asymptote.

Next, you need to explore the behavior of the function on the left and right of the vertical asymptotes, this is done by substituting values just to the left and right of each vertical asymptote into the function and observing the outputs.

If the function approaches negative infinity, the lower limit of the range will be negative infinity. If the function approaches positive infinity, the upper limit of the range will be positive infinity.

So, the range of the function is typically all real numbers except for the values that are 'cut out' by the asymptotes.

Learn more about Rational Functions here:

https://brainly.com/question/18953904

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Final answer:

To determine the range of a rational function with a slant asymptote, graph the function, analyze for vertical and horizontal asymptotes, discontinuities, and observe its long-term behavior relative to the slant asymptote. The range typically includes all real numbers except for values excluded due to vertical asymptotes or holes.

Explanation:

To find the range of a rational function with a slant asymptote, follow these steps:

Graph the rational function to observe its behavior and identify the slant asymptote.Analyze the graph to see where the function's output values (y-values) lie as the input (x-values) become very large or very small.Identify any horizontal or vertical asymptotes, as these will also affect the range.Look for any discontinuities such as holes or vertical asymptotes that might create gaps in the range.Combine all this information to determine the set of all possible y-values the function can attain, remembering that the function will approach but not touch the slant asymptote.

Considering the slant asymptote, the function will continue to increase or decrease without bound in at least one direction, unless there is another horizontal asymptote. Therefore, the range can often be all real numbers, except possibly excluding specific values or intervals due to vertical asymptotes or holes.

I believe the answer would be Whole Numbers