How many solutions does the system have?Explain

Find the horizontal asymptote of of the graph of y=(-3x^6+5x+3)/9x^6+6x+4

NNADVOKAT [17]

Answer:

y = -1/3

Step-by-step explanation:

As x gets large, the value of the expression approaches the ratio of the highest-degree terms in numerator and denominator:

y = -3x^6/(9x^6) = -3/9

y = -1/3

5 0

3 years ago

-x + 2y = 3 2x – 3y = -6

s2008m [1.1K]

Answer:

x = -3

y = 0

Step-by-step explanation:

Given equations :- 

-x + 2y = 3 ....... ( i )

2x - 3y = -6 ....... ( ii )

From ( i ) 

-x + 2y = 3

-x = 3 - 2y

x = 2y - 3 ........ ( iii )

From ( ii ) 

2x - 3y = -6

2x = -6 + 3y

$x = \frac{ - 6 + 3y}{2}$

........ ( iv )

Equating ( iii ) and ( iv )

x = x

$2y - 3 = \frac{ - 6 + 3y}{2}$

4y - 6 = -6 + 3y

4y - 3y = -6 + 6

y = 0

Putting value of y in ( iii )

x = 2y - 3

x = 2 ( 0 ) - 3

x = -3

4 0

2 years ago

The cosine of 23° is equivalent to the sine of what angle

Archy [21]

Answer:

So 67 degrees is one value that we can take the sine of such that is equal to cos(23 degrees).

(There are more values since we can go around the circle from 67 degrees numerous times.)

Step-by-step explanation:

You can use a co-function identity.

The co-function of sine is cosine just like the co-function of cosine is sine.

Notice that cosine is co-(sine).

Anyways co-functions have this identity:

$\cos(90^\circ-x)=\sin(x)$

or

$\sin(90^\circ-x)=\cos(x)$

You can prove those drawing a right triangle.

I drew a triangle in my picture just so I can have something to reference proving both of the identities I just wrote:

The sum of the angles is 180.

So 90+x+(missing angle)=180.

Let's solve for the missing angle.

Subtract 90 on both sides:

x+(missing angle)=90

Subtract x on both sides:

(missing angle)=90-x.

So the missing angle has measurement (90-x).

So cos(90-x)=a/c

and sin(x)=a/c.

Since cos(90-x) and sin(x) have the same value of a/c, then one can conclude that cos(90-x)=sin(x).

We can do this also for cos(x) and sin(90-x).

cos(x)=b/c

sin(90-x)=b/c

This means sin(90-x)=cos(x).

So back to the problem:

cos(23)=sin(90-23)

cos(23)=sin(67)

So 67 degrees is one value that we can take the sine of such that is equal to cos(23 degrees).

6 0

2 years ago

Kim and Sam went to Mexico Restaurant for lunch. The total bill was $21.58. They decide to leave an 18% tip. How much will the t

GrogVix [38]

Answer:

$3.88

Step-by-step explanation:

You want to leave a 18% tip on a meal that cost $21.58.

First, convert the 18% to an actual number that can be used in a calculation. For percents,this is always done by simply dividing the percent (in this case 18%) by 100%.So, the conversational term "18%" becomes 18% / 100% = 0.18 in terms of a real mathematical number.

Second, you need to find out what 18% of your $21.58 meal cost is.This is always done by multiplying 0.18 by $21.58, or 0.18 x $21.58=$3.88.

So, the amount of tip you are going to leave is $3.88.

7 0

3 years ago

9=-7x+7x^2 Helppp please

8_murik_8 [283]

Answer:

x= 0.21428571428 or x=0.2

Step-by-step explanation:

-7x+7x^2=9 1. simplify 7x^2

-7x+ 7x(7x)=9 2. combine like terms

-7x+49x=9 3. combine like terms

42x=9 4. /42 on both sides

x= 0.21428571428 or x=0.2

8 0

2 years ago