What ordered pair is in the solution set of 2x

Help me with #4

Sladkaya [172]

Step-by-step explanation:

a. lim(x→2) [g(x) + h(x)]

Use additive property of limits.

= lim(x→2) g(x) + lim(x→2) h(x)

= 0 + 5

= 5

b. lim(x→2) [3 h(x)]

Use multiplication property of limits.

= [lim(x→2) 3] [lim(x→2) h(x)]

= 3 lim(x→2) h(x)

= 3 (5)

= 15

c. lim(x→2) [g(x) h(x)]

Use multiplication property of limits.

= [lim(x→2) g(x)] [lim(x→2) h(x)]

= (0) (5)

= 0

6 0

3 years ago

Find the equation of the lines parallel and perpendicular to the line 5x+2y=12 through the point (-2,3)

muminat

Answer:

The equation of line parallel to given line and passing through points ( - 2 , 3 ) is 5 x + 2 y + 4 = 0

The equation of line perpendicular to given line and passing through points ( - 2 , 3 ) is 2 x - 5 y + 19 = 0

Step-by-step explanation:

Given equation of line as :

5 x + 2 y = 12

or, 2 y = - 5 x + 12

or , y = $\frac{-5}{2}$ x + $\frac{12}{2}$

Or, y = $\frac{-5}{2}$ x + 6

∵ Standard equation of line is give as

y = m x + c

Where m is the slope of line and c is the y-intercept

Now, comparing given line equation with standard eq

So, The slope of the given line = m = $\frac{-5}{2}$

Again,

The other line if passing through the points (- 2 , 3 ) And is parallel to given line

So, for parallel lines condition , the slope of both lines are equal

Let The slope of other line = M

So, M = m = $\frac{-5}{2}$

∴ The equation of line with slope M and passing through points ( -2 , 3) is

y = M x + c

Now , satisfying the points

So, 3 = $\frac{-5}{2}$ × ( - 2 ) + c

or, 3 = $\frac{10}{2}$ + c

Or, 3 = 5 + c

∴ c = 3 - 5 = - 2

c = - 2

So, The equation of line with slope $\frac{-5}{2}$ and passing through points ( -2 , 3)

y = $\frac{-5}{2}$ x - 2

or, 2 y = - 5 x - 4

I.e 5 x + 2 y + 4 = 0

<u>Similarly</u>

The other line if passing through the points (- 2 , 3 ) And is perpendicular to given line

So, for perpendicular lines condition,the products of slope of both lines = - 1

Let The slope of other line = M'

So, M' × m = - 1

Or, M' × $\frac{-5}{2}$ = - 1

Or, M' = $\frac{-1}{\frac{-5}{2}}$

Or, M' = $\frac{2}{5}$

∴ The equation of line with slope M and passing through points ( -2 , 3) is

y = M' x + c'

Now , satisfying the points

So, 3 = $\frac{2}{5}$ × ( - 2 ) + c'

or, 3 = $\frac{- 4}{5}$ + c'

Or, 3 × 5 = - 4 + 5× c'

∴ 5 c' = 15 + 4

or, 5 c' = 19

Or, c' = $\frac{19}{5}$

So, The equation of line with slope $\frac{2}{5}$ and passing through points ( -2 , 3)

y = $\frac{2}{5}$ x + $\frac{19}{5}$

y = $\frac{2 x + 19}{5}$

Or, 5 y = 2 x + 19

Or, 2 x - 5 y + 19 = 0

Hence The equation of line parallel to given line and passing through points ( - 2 , 3 ) is 5 x + 2 y + 4 = 0

And The equation of line perpendicular to given line and passing through points ( - 2 , 3 ) is 2 x - 5 y + 19 = 0

Answer

4 0

3 years ago

The ratio of athletes to non-athletes at bayside high school is 2 to 6. If there are 1200 non-athletes at school, how many athle

N76 [4]

Answer:

400

Step-by-step explanation:

4 0

3 years ago

I need help with - The product of two integers is -21. The difference between the integers is -10. The sum of the two integers i

Soloha48 [4]

The two integers are +7 and -3.

We didn't need all three hints.
The answer can be found with
any two of them.

4 0

3 years ago

Every other weekend, Bronwyn’s brother Daniel mows the lawn. He can mow ,2 in 3/4 hour. Who mows the lawn in less time? Explain.

True [87]

Answer:

Who the other person?

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

What ordered pair is in the solution set of 2x - 3y > 8?