Given f(x) = x²+x-6, find f(0).

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

Which sign makes the statement true?<br> 5.01 x 10-3 ? 0.00105

attashe74 [19]

Answer:

47.1 > .00105

Step-by-step explanation:

Given :

5.01×10-3 ? 0.00105

Now,

5.01×10-3 ? 0.00105

50.1-3?0.00105

47.1?0.00105

From the above equation, we can say that 47.1 is greater than 0.00105

Therefore, 47.1 > .00105

8 0

3 years ago

Which property is best to use when determining the strength of an ionic bond in a solid?

Shtirlitz [24]

I think the best property to use is electronegativity since that is how much it attracts/wants electrons. The larger the difference in electronegativity is between two atoms, the stronger the ionic bond will be. This is also why two atoms need to have a minimum difference between the electronegativity to be considered ionic and not covalent.

6 0

3 years ago

Due to fire laws, no more than 720 people may attend a performance at Metro Auditorium. The balcony holds 120 people. There are

deff fn [24]

p=people
s=seats
r=rows

There are 32 rows with x amount of seats but only p amount of people can be in the auditorium due to fire laws.
32r=x>p

3 0

3 years ago

Write these numbers in order of size. start with the smallest number: 1/2, 2/3, 2/5, 3/4

qaws [65]

First make the fractions into decimals so it's easier to compare them.

1/2 ⇒ 0.5
2/3 ⇒ 0.66
2/5 ⇒ 0.4
3/4 ⇒ 0.75

Now it's easy to order the numbers from least to greatest.

First order the decimals.

0.4, 0.5, 0.66, 0.75

Now order them with their corresponding fractions.

2/5, 1/2, 2/3, 3/4 is your answer.

3 0

4 years ago

Read 2 more answers