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3 years ago

The value of m in the following system of equations is:

1 answer:

7 0

N=m-2

m-2n=8, using n from above in this equation yields:

m-2(m-2)=8 perform indicated multiplication

m-2m+4=8 combine like terms on left side

-m+4=8 subtract 4 from both sides

-m=4 divide both sides by -1

m=-4

So the correct answer is A) m=-4

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Find the limit (enter 'DNE' if the limit does not exist)

vaieri [72.5K]

Answer:

$\lim\limits_{(x,y)\rightarrow(0,0)}\left(\sqrt{-2x^2-6y^2+1}+1\right)=2$

Step-by-step explanation:

We need to first simplify the expression using rationalization(i.e. if a square root term exists in the denominator, then multiply and divide the whole expression by the denominator(but the change the sign of its middle term))

here, we need to find:

$\lim\limits_{(x,y)\rightarrow(0,0)}\left(\dfrac{-2x^2-6y^2}{\sqrt{-2x^2-6y^2+1}-1}\right)$

first we'll rationalize our expression:

$\dfrac{-2x^2-6y^2}{\sqrt{-2x^2-6y^2+1}-1}\left(\dfrac{\sqrt{-2x^2-6y^2+1}+1}{\sqrt{-2x^2-6y^2+1}+1}\right)$

$\dfrac{-(2x^2+6y^2)(\sqrt{-2x^2-6y^2+1}+1)}{(\sqrt{-2x^2-6y^2+1}+1)^2-(1)^2}$

$\dfrac{-(2x^2+6y^2)(\sqrt{-2x^2-6y^2+1}+1)}{-2x^2-6y^2+1-1}$

$\dfrac{-(2x^2+6y^2)(\sqrt{-2x^2-6y^2+1}+1)}{-(2x^2+6y^2)}$

$\sqrt{-2x^2-6y^2+1}+1$

this is our simplified expression, now we can apply our limits:

$\lim\limits_{(x,y)\rightarrow(0,0)}\left(\sqrt{-2x^2-6y^2+1}+1\right)$

$\sqrt{-2(0)^2-6(0)^2+1}+1$

$1+1$

$2$

the limit does exists and it is 2.

5 0

3 years ago

Adrian made the cakes shown below for a 3 cakes at the party Adrian will serve each guest 1/8 of a cake what is the greatest num

nikdorinn [45]

Answer:

24 Guests

Step-by-step explanation:

3 x 8 = 24.

4 0

3 years ago

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barxatty [35]

Answer:

Step-by-step explanation:

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3 years ago

In how many ways can a teacher arrange 5 students in the front row of a classroom with a total of 20 students?

aksik [14]

Slot method
5 slots

1st slot: 20
2nd slot: 19 (1 went to first slot)
3rd slot: 18
4th slot: 17
5th slot: 16

20*19*18*17*16=186,040 ways

5 0

3 years ago

Read 2 more answers

The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in sec

pashok25 [27]

Answer:

Step-by-step explanation:

in interval ( 0 ; 2)

in interval (2; 4)

in interval (4 ; 6 )

The graph shows that at first the ball rises up ; and then it is seen that it goes down and loses height to zero , from which it can be concluded that the height after 10 seconds remains unchanged and therefore the height of the ball after 16 seconds will be zero

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2 years ago