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3 years ago

The line x+ 2y = 9 intersects the curve xy + 18 = 0 at the points A and B. Find the coordinates of A and B.

Mathematics

1 answer:

victus00 [196]3 years ago

6 0

Subtracting the second equation by 18 on both sides, we have xy=-18. Next, we divide both sides by x to get y=-18/x Plugging that into the first equation, we have x+2(-18/x)=9. Multiplying both sides by x, we get x^2-36=9x. After that, we subtract both sides by 9x to get x^2-9x-36=0. Finding 2 numbers that add up to -9 but multiply to -36, we do a bit of guess and check to find the answers to be -12 and 3. Factoring it, we get
x^2-12x+3x-36=x(x-12)+3(x-12)=(x+3)(x-12). To find the x values, we have to find out when 0=(x+3)(x-12). This is simple as when you multiply 0 with anything, it is 0. Therefore, x=-3 and 12. Plugging those into x=-18/y, we get x=-18/y and by multiplying y to both sides, we get xy=-18 and then we can divide both sides by x to get -18/x=y. Plugging -3 in, we get -18/-3=6 and by plugging 12 in we get -18/12=-1.5. Therefore, our points are (-3,6) and (12, -1.5)

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andy is wrapping gifts for his family. he ties 25 inches of ribbon around each gift. which function gives the relationship betwe

Vaselesa [24]

The total length of the ribbon used is expressed as r and is a product of the number of gifts (g) and the length of ribbon tied in each gift. This relationship may be expressed by the equation,
r = (25) x (g)

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2 years ago

Ashley bought 4 packages of juice boxs in each package. She. gave 2 juice boxs to each of her friends. How many juice boxes does

Harlamova29_29 [7]

I am assuming there are more than one juice box in a package so if the amount of juice boxes in each package is X and there are four packages 4X.
So 4X - 2= Answer

If we make it so that there are 6 juice boxes in each package and use the same method this is what we'll get:
24 - 2= 22

22 would be the juice boxes left over.

I hope this answers your question, if it doesn't use the same method with the number of juice boxes in a package.

8 0

2 years ago

Can someone help me ?

lozanna [386]

Answer:

10 > v (if you don't trust me, check it yourself. Subsitute v for 10 in the first equation.

Step-by-step explanation:

1) 7 > v - 3

2) add 3 to both sides

3) so 7 plus 3 equals 10

So you basically do this

7 > v - 3 (ad 3 to both sides)

You get 10 > v (which is as simplified as possible)

Hope this helps! :)

8 0

2 years ago

A jar holds no more than 500 buttons. If 5 people bring 330 buttons each, how many jars are necessary to hold all of the buttons

Strike441 [17]

Answer:

We know

1 jar = 500 buttons

5 people bring 330 buttons EACH

We can find/solve by...

people x buttons = total buttons

total buttons / 500 = number of jars needed

So..

5 x 330 = 1650

1650 / 500 = 3.3

Your answer:

4 jars

Explanation

It's impossible to have 3.3 jars, so you must round up.

Step-by-step explanation:

8 0

2 years ago

3. Consider the sequence,-8, -5, -2, 1, ...

Naddik [55]

Answer:

a) $a_n=3\,n-11$

b) $a_{20}=49$

c) term number 17 is the one that gives a value of 40

Step-by-step explanation:

The sequence seems to be arithmetic, and with common difference d = 3.

Notice that when you add 3 units to the first term (-80, you get :

-8 + 3 = -5

and then -5 + 3 = -2 which is the third term.

Then, we can use the general form for the nth term of an arithmetic sequence to find its simplified form:

$a_n=a_1+(n-1)\,d$

That in our case would give:

$a_n=-8+(n-1)\,(3)\\a_n=-8+3\,n-3\\a_n=3n-11$

Therefore, the term number 20 can be calculated from it:

$a_{20}=3\,(20)-11=60-11=49$

c) in order to find which term renders 20, we use the general form we found in step a):

$a_n=3\,n-11\\40=3\,n-11\\40+11=3\,n\\51=3\,n\\n=\frac{51}{3} =17$

so term number 17 is the one that renders a value of 40

5 0

2 years ago