MATHEMATICS MIDDLE SCHOOL

Determine the equations of the vertical and horizontal asymptotes, if any, for g(x)=x-2/x^2+4x+3 A.x=-1,x=3
B.x=-1,x=-3,y=0
C.x=1,x=-3,y=0
D.x=-1,x=-3

Answers

Answer 1
Answer:

Answer:

B. x = -1, x = -3, y = 0

Step-by-step explanation:

g(x)=(x-2)/(x^2+4x+3)\n\nvertical\ asymptote:\n\nx^2+4x+3=0\nx^2+x+3x+3=0\nx(x+1)+3(x+1)=0\n(x+1)(x+3)=0\iff x+1=0\ \vee\ x+3=0\n\n\boxed{x=-1\ \vee\ x=-3}\n\nhorizontal\ asymptote:\n\n\lim\limits_(x\to\pm\infty)(x-2)/(x^2+4x+3)=\lim\limits_(x\to\pm\infty)(x^2\left((1)/(x)-(2)/(x^2)\right))/(x^2\left(1+(4)/(x)+(3)/(x^2)\right))=\lim\limits_(x\to\pm\infty)((1)/(x)-(2)/(x^2))/(1+(4)/(x)+(3)/(x^2))=(0)/(1)=0\n\n\boxed{y=0}

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Ben drinks tea at an incredible rate. He drinks 3\dfrac123 2
1
​ liters of tea every \dfrac23
3
2
​ of an hour. Ben drinks tea at a constant rate.
How many liters of tea does he drink in one hour?

Answers

Answer:

5(1)/(4) liters of tea does he drink in one hour.

Step-by-step explanation:

Unit rate defined as the rate are expressed as a quantity 1 such as 2 miles per hour or 4 meter per second.

As per the statement:

Ben drink 3(1)/(2) = (7)/(2) liters of tea every (2)/(3) of an hour.

We have to find the liters of tea does he drink in one hour.

\text{Unit rate per hour} = ((7)/(2) )/((2)/(3)) = (7)/(2) * (3)/(2) =(21)/(4) = 5(1)/(4) liters

Therefore, 5(1)/(4) liters of tea does he drink in one hour.

What is 0.04 times 7.6? Using ur work

Answers

Well, you'll multiply regularly, then move da decimals to the left 3 times, because if you add the amount of decimal places in 0.04 and 7.6, (2 + 1), it equals 2, but so 0.04 times 7.6 = 0.304
I hope I helped! =D

Im so lost..
5n + 34 = -2 (1 - 7n )

Answers

first, you can distribute the -2 to 1 - 7n
the new equation is 5n + 34 = -2 + 14n
then, you can add 2 to both sides to cancel the -2 on the right
now you have 5n + 36 = 14n
after this, you add -5n to both sides, again, to cancel the 5n on the left
you are left with 34 = 9n
lastly, divide both sides by 9 to find the value of n, which is 4.
The answer for 
-3 (4x+3) +4 (6x+1) =43
is 

Jonathan is making his favorite pasta dish. He serves his mom 1/12 of the pot of pasta and his brother 1/6 of the pot. How much of the pot is left over?

Answers

Answer: (1)/(4) of the pot is left.


Step-by-step explanation:

Let x be the total amount of pasta in the pot .

Then the amount of pasta her mother got= (1)/(12)x

The amount of pasta her brother got=  (1)/(6)x

The total amount of pasta he serve= (1)/(12)x+(1)/(6)x

First convert them in like fractions,then

The total amount of pasta he serve=(1)/(12)x+(2)/(12)x=(x+2x)/(12)=(3x)/(12)=(1)/(4)x

Hence, (1)/(4) of the pot is left over.
1/6 also is 2/12. So, there is 9/12 of the pasta left.

if five potatoes together have a mass of one kilogram and eight pears together have a mass of 1200 grams,which has the greater mass a potato or a pear?explain

Answers

Solutions 

We know that five potatoes together have a mass of one kilogram and eight pears together have a mass of 1200 grams. 

5 potatoes = one kilogram 

eight pears = 1200 grams 

To solve the problem we have to convert 1 kilogram into grams. 

1 kilogram  = 1000 grams 

Now we have 

5 potatoes = 1000 grams 

eight pears = 1200 grams  

The next step is to use division:

1000 ÷ 5 = 200 -> 1 potato weighs 200 grams.

1200 ÷ 8 = 150 -> 1 pear weighs 150 grams

Therefore a potato has a greater mass than a pear. 
1kg = 1000 grams
Use division:

1000 / 5 = 200 -> 1 potato weighs 200 grams.

1200 / 8 = 150 -> 1 pear weighs 150 grams

Thus a potato has a greater mass than a pear. 

is there a 9's trick in multiplication? if so please tell me! i would love to know since i am so terrible with my 9.

Answers

There is a nine trick
First, you hold up all of your fingers
So if you're doing 6x9, you would hold up your 10 fingers, and count to six, while each number, hold a finger down. When you're done, you should have the thumb of your right hand down. So since your left hand has 5 fingers down, that's 50. Next, you skip your thumb and count 4. That's 54
6x9 is 54
There is a nines trick Ex. 9 x 8 You put your hands in front of you and would put the eighth finger down. The eight finger is like an imaginary line. The fingers that are up on the left side are the tens. And the fingers up on the right are the ones. Then when you add them together they make the anwser of 72. And it works for any number. I hope i helped
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