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oksano4ka [1.4K]
3 years ago
15

I need help with this math problem

Mathematics
1 answer:
Y_Kistochka [10]3 years ago
3 0
What is the problem?
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Solve this identifying holes, vertical asymptotes, and horizontal asymptotes for
USPshnik [31]

x^2+7x+12=x^2+4x+3x+12=x(x+4)+3(x+4)=(x+4)(x+3)\\\\-x^2-3x+4=-(x^2+3x-4)=-(x^2+4x-x-4)\\\\=-[x(x+4)-1(x+4)]=-(x+4)(x-1)\\\\f(x)=\dfrac{x^2+7x+12}{-x^2-3x+4}=\dfrac{(x+4)(x+3)}{-(x+4)(x-1)}\\\\\text{Vertical asymptotes:}\\\\(x+4)(x-1)=0\iff x+4=0\ \vee\ x-1=0\\\\\boxed{x=-4\ and\ x=1}\\\\\text{Horizontal asymptotes:}

\lim\limits_{x\to\pm\infty}\dfrac{x^2+7x+12}{-x^2-3x+4}=\lim\limits_{x\to\pm\infty}\dfrac{x^2\left(1+\dfrac{7}{x}+\dfrac{12}{x^2}\right)}{x^2\left(-1-\dfrac{3}{x}+\dfrac{4}{x^2}\right)}=\dfrac{1}{-1}=-1\\\\\boxed{y=-1}

6 0
4 years ago
A point lies on AB and is the distance from A to B. Point A is located at (4, 8) and point B is located at (14, 10)
Rzqust [24]

Answer:

(9,9)

Step-by-step explanation:

Assuming the point is exactly halfway between A and B, to find it we just need to find the centre point between (4,8) and (14,10).

To find the midpoint, we just need to find the middle value, by dividing the difference between the x values by 2, and repeating the process with the y values.

This is because the point is in the middle, so it's y value will be in the middle of the given AB y values, and its x value will also be directly in the middle of the AB x values.

The x values are 4 and 14. The midpoint is

14-4=10

10/2=5 (the midpoint is 5 away from each reference point)

4+5=9

The midpoint is 9 for the x values. This means the x-value for the point is 9.

Repeat for y-values:

10-8=2

2/2=1

8+1=9

The midpoint is 9, therefore it has the y coordinate of 9.

Therefore the coordinates for the point are (9,9).

Hope this helped!

6 0
3 years ago
the five members of the traynor family each buy train tickets during the train ride each family member buys a box one for $6.50
NeX [460]

Answer:

  $43.20

Step-by-step explanation:

If each family member buys one ticket and one lunch, then for ticket price t we have the total expenditure as ...

  5(t +6.50) = 248.50

  t +6.50 = 49.70 . . . . . divide by 5

  t = 43.20 . . . . . . . . . . subtract 6.50

The price of each train ticket is $43.20.

8 0
4 years ago
Plz help i will mark brainliest
Alexus [3.1K]
2,3,and4 is 72
1 and 5 is 36
5 0
3 years ago
Ethan sold 2 3 gallon of lemonade. Kayla sold some lemonade too. Together, they sold 1 1 4 gallons. Who sold more lemonade, Etha
zhenek [66]

Step-by-step explanation:

Ethan sold 2/3 gallon of lemonade.

Kayla sold some lemonade too.

Together they sold 1 1/4 gallons.

Subtract 2/3 from 1 1/4 as follows :

S=1\dfrac{1}{4}-\dfrac{2}{3}\\\\=\dfrac{5}{4}-\dfrac{2}{3}\\\\=\dfrac{7}{12}

So, Kayla sold 7/12 gallons of lemonade.

As 2/3 is more than 7/12, it means Ethan sold more lemonade.

\dfrac{2}{3}-\dfrac{7}{12}=\dfrac{1}{12}

It means Eathn sold 1/12 more lemonade.

5 0
3 years ago
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