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3 years ago

prove that the line whose intercepts on the axes of x and y. are respectively -2and3 pass Through the point 2 and 6

Mathematics

1 answer:

Irina18 [472]3 years ago

6 0

Answer:

see explanation

Step-by-step explanation:

Using the intercept form of the equation of a straight line

$\frac{x}{a}$ + $\frac{y}{b}$ = 1

where a is the x- intercept and b the y- intercept

here a = - 2 and b = 3, hence

$\frac{x}{-2}$ + $\frac{y}{3}$ = 1

Multiply through by - 6

3x - 2y = - 6 ← equation in standard form

Substitute x = 2 and y = 6 into the left side of the equation and if equal to the right side then (2, 6) lies on the line

left side = (3 × 2) - 2(6) = 6 - 12 = - 6

Hence line passes through (2, 6)

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A line passes through the point (1,4) and is perpendicular to the line with equations y=-1/5x+2. what's the equation of the line

jekas [21]

To find the slope of the perpendicular line, you can take the negative reciprocal of the slope of the line it is perpendicular to.

Taking the negative reciprocal of -1/5 gives 5.

Now we have y=5x+b, where b is the y-intercept. Since we know that the perpendicular line passes through the point (1,4), we can substitute those values into the equation we have to find b.

y=5x+b

4=5(1)+b

4=5+b

b=-1

Therefore, the equation of the perpendicular line is y=5x-1.

4 0

2 years ago

Eli invested $ 330 $330 in an account in the year 1999, and the value has been growing exponentially at a constant rate. The val

Cloud [144]

Answer:

The value of the account in the year 2009 will be $682.

Step-by-step explanation:

The acount's balance, in t years after 1999, can be modeled by the following equation.

$A(t) = Pe^{rt}$

In which A(t) is the amount after t years, P is the initial money deposited, and r is the rate of interest.

$330 in an account in the year 1999

This means that $P = 330$

$590 in the year 2007

2007 is 8 years after 1999, so P(8) = 590.

We use this to find r.

$A(t) = Pe^{rt}$

$590 = 330e^{8r}$

$e^{8r} = \frac{590}{330}$

$e^{8r} = 1.79$

Applying ln to both sides:

$\ln{e^{8r}} = \ln{1.79}$

$8r = \ln{1.79}$

$r = \frac{\ln{1.79}}{8}$

$r = 0.0726$

Determine the value of the account, to the nearest dollar, in the year 2009.

2009 is 10 years after 1999, so this is A(10).

$A(t) = 330e^{0.0726t}$

$A(10) = 330e^{0.0726*10} = 682$

The value of the account in the year 2009 will be $682.

4 0

3 years ago

Solve the equation 2sin x cos x = cos x, for 0° < x≤ 90°

lilavasa [31]

Answer:

2sinx.Cosx=cosx

2sin90°.cos90°=cos90°

2×1.0=0

0=0

4 0

2 years ago

Dean needs $150 for a miming class. He already has $85 and he can earn the rest by working 13 hours at his job. If h represents

AnnyKZ [126]

Answer:

h=$65/13

Step-by-step explanation:

So he has $85

Now the remaining amount he needs is $65

And in every 13h he produces the $65

So to find his hourly earning is h=$65/13

So the equation is

h = $65/13

3 0

3 years ago

Bharat and ingrid leave their building at the same time on their bikes and travel in opposite directions. If bharat's speed is 1

yanalaym [24]

Answer:

3 hours

Step-by-step explanation:

speed of Bharat = 12kilometers / hour

speed of Ingrid=14 kilometers / hour

For this problem we'll be using formula relating time, distance and speed.i.e

Distance = speed x time

Suppose Bharat is riding at a distance of 'b' kilometers, therefore time taken by him will be:

Time = distance/ speed

Time= b/12 hours.

Also, Ingrid can ride the distance at this time with speed of 14km/hr

The distance would be,

Distance = speed x time

Distance = 14 x (b/12) => 14b/12

Distance= 7b/6

Let ' $d_{b}$ ' be the distance that Bharat have covered after time 't'

therefore, $d_{b}$ = 12 x t

Let ' $d_{i}$ ' be the distance that Ingrid have covered after time 't'

therefore, $d_{i}$ = 14 x t

In order to find the time when they are 78 kilometers apart, we will add $d_{i}$ and $d_{b}$ , because they are travelling in opposite direction creating distance between them.

So,

$d_{i}$ + $d_{b}$ = 78

( 14 x t) + (12 x t) =78

14t + 12t =78

26t= 78

t= 78/26

t= 3hours.

thus, it will take 3 hours until they are 78 kilometers apart

6 0

3 years ago

prove that the line whose intercepts on the axes of x and y. are respectively -2and3 pass Through the point 2 and 6​

prove that the line whose intercepts on the axes of x and y. are respectively -2and3 pass Through the point 2 and 6