What is the vertical asymptote of the function f(x) = (x - 5)/(x ^ 2 - 2x - 15)

If x is an integer, and

x + (x + 1) + … + 2020 + 2021 = 2021

then of course

x + (x + 1) + … + 2020 = 0

and we can write the left side as a sum,

[tex]\displaystyle \sum_{k=0}^n (x+k) = 0[/tex]

with n such that x + n = 2020. (Notice that there are n + 1 terms in the sum.) Then x = 2020 - n, so that

[tex]\displaystyle \sum_{k=0}^n (2020 - n + k) = (2020 - n) \sum_{k=0}^n 1 + \sum_{k=0}^n k= 0[/tex]

Recall that

[tex]\displaystyle \sum_{k=1}^n 1 = 1 + 1 + 1 + \cdots + 1 = n[/tex]

[tex]\displaystyle \sum_{k=1}^n 1 = 1 + 2 + 3 +  \cdots + n = \frac{n(n+1)}2[/tex]

Then

[tex]\displaystyle (2020 - n) (n + 1) + \frac{n(n+1)}2= 0[/tex]

Solve for n :

(2020 - n) (n + 1) + n (n + 1) / 2 = 0

4040 + 4039 n - n² = 0

(n - 4040) (n + 1) = 0

⇒   n = 4040   or   n = -1

But we are taking the sum of a positive number of terms, so n = 4040.

Then since x + n = 2020, it follows that x = 2020 - 4040 = -2020.

Answer:

you are correct

Step-by-step explanation:

Answer:

Hello again! Fellow Connexus user? Because I just had this on my Honors Algebra 1 test today. Anyways the answer is: A. x + y = 126 and 2.25x + 1.50y = 225.75; 49 Hot Dogs and 77 Sodas.

Step By Step Explanation:

To verify just use the substitution method to solve the equations x+y=126 and 2.25x + 1.50y = 225.75 then you'll get your x (Number of Hotdogs) and y (Number of Sodas)

Hope this helps!

The required equations are use to solve this problem;

[tex]x + y =126[/tex]

[tex]2.25x + 1.50y = 223.75[/tex]

There are x = 49 hot dogs, and y = 77 sodas were sold.

Given that,

Each hot dog costs $2.25 and each soda costs $1.50.

At the end of the night, you made a total of $225.75.

You sold a total of 126 hot dogs and sodas combined.

We have to determine,

What equations did you use to solve this.

And How many hot dogs were sold and how many sodas were sold.

According to the question,

Let, The x represent the number of hot dogs,

And y represent the number of sodas.

Then,

You sold a total of 126 hot dogs and sodas combined.

Number of sell hot dogs + number of sell sodas = Total of hot dogs and sodas combined.

[tex]x + y =126[/tex]

And Each hot dog costs $2.25 and each soda costs $1.50.

At the end of the night, you made a total of $225.75.

Then,

Cost of each hot dogs + cost of each soda = total earning end of the night

[tex]2.25x + 1.50y = 223.75[/tex]

On solving both the equation,

[tex]x + y = 126\\\\x = 126-y[/tex]

Substitute the value of x in the equation 2,

[tex]=2.25(126-y) + 1.50y = 225.75\\\\= 283.5 -2.25y + 1.50y = 225.75\\\\= - 0.75 y = 225.75 - 283.5\\\\= - 0.75y = -57.75\\\\= y = \dfrac{-57.75}{-0.75}\\\\= y = 77[/tex]

Then,

Substitute the value of y in the equation 1,

[tex]x + y = 126\\\\x + 77 = 126\\\\x = 126-77\\\\x = 49[/tex]

Hence, There are x = 49 hot dogs, and y = 77 sodas were sold.

To know more about the Equation click the link given below.

https://brainly.com/question/24070713

[tex]6x+34x -6 = 8(5x+10)\\\\\implies 40x -6 = 40x +10\\\\\implies 40x -40x = 10+6 \\\\\implies 0 =16\\\\\text{Which is not true. So no solution.}[/tex]

Answer: £4,164

Step-by-step explanation: multiply 896 by 4 to get £3,584 next add 580 to 3,584 to get £4,164

Answer: 4,164

Step-by-step explanation: I am confused if the 896 is a percent or the money she owes every year, now here is the explanation.

Emily took the £580 and after the 4 years she owes 896*4 = £3,584 plus the original £580 which is £4,164

If it it without the original £580 then the answer is 896*4 = £3,584

If that is not correct then i am sorry

Answer:

6. 47

7. –25

8. 15

9. –33

10. –9

Step-by-step explanation:

Substitute.

6. x=-7

y = -8x - 9

= -8(-7)-9

= 56-9

y=47

7. x=2

y= -8x-9

= -8(2)-9

= -16-9

y= -25

8. x=-3

y= -8x-9

= -8(-3)-9

=24-9

y= 15

9. x=3

y= -8x-9

= -8(3)-9

= -24-9

y= -33

10. x=0

y= -8x-9

= -8(0)-9

= 0-9

y= -9

Using the normal approximation to the binomial, it is found that there is a 0.9319 = 93.19% probability that fewer than 260 are women.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem:

The mean and the standard deviation for the approximation are given by:

[tex]\mu = np = 300(0.833) = 249.9[/tex]

[tex]\sigma = \sqrt{np(1 - p)} = \sqrt{300(0.833)(0.167)} = 6.46[/tex]

Using continuity correction, as the binomial distribution is discrete and the normal distribution is continuous, the probability that fewer than 260 are women is P(X < 260 - 0.5) = P(X < 259.5), which is the p-value of Z when X = 259.5, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{259.5 - 249.9}{6.46}[/tex]

[tex]Z = 1.49[/tex]

[tex]Z = 1.49[/tex] has a p-value of 0.9319.

0.9319 = 93.19% probability that fewer than 260 are women.

A similar problem is given at https://brainly.com/question/25347055

Answer: I believe it would be 60% tell if I am wrong

Step-by-step explanation:

The probability of getting first bill is greater than $5 is 1/5 or 0.2

Probability:

The probability of any event is the mathematical possibility of that event.

Probability is always lies between 0 to 1

Sure event has probability 1 while impossible event probability 0

The formula for probability is

Probability = [tex]\frac{number of favorable event}{total number of event}[/tex]

Here the total event is

S = {$1, $5, $10, $20, $50}

Total number of events = 5

The probability of find greater than $5 is

Probability = 1/5 = 0.2

Hence the final answer is 0.2

Learn more about probability here-

https://brainly.com/question/251701

#SPJ2

Answer:

$5.84

Step-by-step explanation:

Explanation:

The constant of proportionality is the same as the slope for equations of the form y = kx.

To find the value of k, we divide the y over x values.

k = y/x = 12/8 = 1.5

or

k = y/x = 6/4 = 1.5

Either way the answer is 1.5

This means Ziah ran at a rate of 1.5 city blocks per minute.

Answer:

15

Step-by-step explanation:

15 can go into 90, 6 times. It is neither a multiple of 6 or 9. It is larger than 10 and smaller than 20.

Answer:

13 blue and 20 yellow

urwelcome

Answer: 95,800 - 28,766 = 67,034

Step-by-step explanation: hope this helps :)

Answer: the answer is 8

Step-by-step explanation:

Hope this helped.

hi have a nice day

20

4

+(2)(5)

=15

Marissa wants to know how much she would make using the simple interest calculation.

She will have $4,432.35

Given data

Principal = $3,900

Time = 7 years 6 months = 7.5 years

Rate = 1.82%

I = A - P = $532.35

Equation:

A = P(1 + rt)

Calculation:

First, converting R percent to r a decimal

r = R/100 = 1.82%/100 = 0.0182 per year.

Solving our equation:

A = 3900(1 + (0.0182 × 7.5)) = 4432.35

A = $4,432.35

The total amount accrued, principal plus interest, from simple interest on a principal of $3,900.00 at a rate of 1.82% per year for 7.5 years is $4,432.35.

Learn more about simple interest here:

https://brainly.com/question/20690803

Answer:

n is 0.5

Step-by-step explanation:

Answer:

1:0.5

Step-by-step explanation:

Answer:

y=-x+9

Step-by-step explanation:

The answer above is written in slope-intercept form because it is the easiest form to graph (in my opinion); slope-intercept form is y=mx+b, where m is slope and b is the y-intercept. However, to get the answer, you must first use slope-point. Slope-point is [tex]y-y_{1}=m(x-x_{1})[/tex]. So, plug in the point and slope into the formula. This gives the equation, y-6=-1(x-3). Then, solve the equation for the answer of y=-x+9.

On a graph, the y-intercept will be 9. So, the line will cross the y-axis at a value of 9. Additionally, the slope is -1. So, y will increase by one and x will decrease by one. This means that the line will look like it decrease left to right.

Answer:

correct answer explained above

Answer:

Frequently Asked Questions on LCM of 8 and 9

Find the prime factorization of 8 8 = 2 x 2 x 2

Find the prime factorization of 9 9 = 3 x 3

Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm: LCM = 72 = 2 x 2 x ...

Therefore, the least common multiple of 8 and 9 is 72.

Step-by-step explanation:

Answer:

0 and -81

Step-by-step explanation:

So, we know anything times zero is zero, and anything added or subtracted to zero would give you that number, meaning one of these numbers is zero.

Zero plus -81 will give you the same number, -81, and zero times -81 will give you zero since anything added to or subtracted to zero is that number.

Answer:

Positive

Step-by-step explanation:

Anything below 0 is negative. 0.75 > 0

Answer:

[tex]x^{2} -49[/tex]

Step-by-step explanation:

Answer:

[tex](x-7)(x+7) =x^2 -7^2 = x^2 -49[/tex]

Step-by-step explanation:

Answer:

45.05 seconds

Step-by-step explanation:

Use the formula: d = v[tex]i[/tex] t + [tex]\frac{1}{2}[/tex] a[tex]t^{2}[/tex]

d = distance      v[tex]i[/tex] = initial velocity (m/s)    

t = time (s)     a = acceleration (m/[tex]s^{2}[/tex])

m is meters and s is seconds. They are units of measurement so leave them be.

Assuming the object is simply dropped, the initial velocity is 0 since the object was not moving before it was dropped.

The distance is 725 feet, which is 220.98 meters.

The acceleration is 9.81m/[tex]s^{2}[/tex] since that is the acceleration of Earth's gravity, aka free fall.

Time is what we are trying to find so just leave it as the variable t.

So plug the values into the equation:

220.98m = (0)(t) + [tex]\frac{1}{2}[/tex] (9.81m/[tex]s^{2}[/tex])(t)

220.98m = (4.905m/[tex]s^{2}[/tex])(t)

45.0519877676s = t

t = 45.05s

Remember to pay attention to units because your answer will be wrong otherwise

Answer:

50%

Step-by-step explanation:

Cuz 75 is 1/2 of 150, so 1/2 is equal to 50%.

Answer:

0.4n = 8

n = 20

Step-by-step explanation:

0.4n = 8

n = 8 / 0.4

n = 20

[tex]-2(x+1) = -2+5\\\\\implies -2x -2 = 3\\\\\implies -2x = 3 +2 =5\\\\\implies x = - \dfrac 52[/tex]

Add the numbers, then add 2 to both sides of the equation. The solution would be x = - 5/2

Answer:

D

Step-by-step explanation:

The first equation would have to have a y-intercept of 4, and the second equation would have to have a y-intercept of -1.

-hope it helps

Answer: what the actual fudge is this?? i am a former harvard professer for math and I have never seen such a monstrocity of a math question, but the answer is the first one.

Step-by-step explanation:

[tex]e^y +19-e^2 = 3x^2 +4y^2\\\\\implies \dfrac{d}{dx}(e^y +19-e^2) = \dfrac{d}{dx}(3x^2 +4y^2)\\\\\implies e^y \dfrac{dy}{dx}+0 = 3\dfrac{d}{dx} x^2 +4\dfrac{d}{dx} y^2\\\\\implies e^y y' = 6x + 8y y'\\\\\implies e^y y' -8yy' = 6x\\\\\implies y'(e^y -8y) = 6x\\\\\implies y' = \dfrac{6x}{e^y -8y}\\\\\text{At point (-1,2)}\\\\y' = \dfrac{6(-1)}{e^2 -8(2)} = - \left(\dfrac{6}{e^2 -16}\right) =-0.25[/tex]