What is 10 2/5 times 15 5/6!<br><br> Thanks

What is the equation of the line that passes through (6, 1) and is perpendicular to the line y 3x+2? CI) At what angle do the li

Andrews [41]

Answer with explanation:

The equation of any line with slope 'm' and passing through any point $(x_1,y_1)$ is given by

$y=mx+(y_1-mx_1)$

As we know that the general equation of a line with slope 'm' is $y=mx+c$

Comparing with the given equation $y=3x+2$ we can conclude slope of the given line is $m_1=3$

Now we know that the product of slopes of perpendicular lines is -1

Mathematically we can write for perpendicular lines

$m_1\times m_2=-1$

Thus the slope of the required line is obtained from the above relation since it is given that they are perpendicular

$3\times m_{2}=-1\\\\\therefore m_{2}=\frac{-1}{3}$

Hence using the given and the obtained values the equation of the required line is

$y=-\frac{1}{3}x+(1-\frac{-1}{3}\times 6)}\\\\y=\frac{-x}{3}+3$

Part b)

The angle of intersection between 2 lines with slopes $m_{1},m_2$ is given by

$\theta =tan^{-1}(\frac{m_2-m_1}{1+m_1m_2})$

Comparing the equations of given lines

$y=6x+3\\\\y=2x+3$

with the standard equation we get

$m_{1}=6\\\\m_{2}=2$

Thus the angle of intersection becomes

$\theta =tan^{-1}(\frac{2-6}{1+2\times6})=17.10$

8 0

3 years ago

Write 0.003 as the product of a whole number and a power of 10

Arte-miy333 [17]

3 × $10^{-3}$

expressing as a whole number, using the digits available, we obtain

3

Now consider the position of the decimal point in the original 0.003

To get it back to where it should be we require to move the decimal point 3 places to the left , denoted by a negative exponent

0.003 = 3 × $10^{-3}$

8 0

3 years ago

(-5x2 – 43 – 1) +(-4x2 – 4x)

emmainna [20.7K]

Answer:

−9x 2 -44-4x

Step-by-step explanation:

1 Simplifica -5{x}^{2}-43-1−5x

2

−43−1 a -5{x}^{2}-44−5x

2

−44.

-5{x}^{2}-44-4{x}^{2}-4x

−5x

2

−44−4x

2

−4x

2 Colecciona los términos semejantes.

(-5{x}^{2}-4{x}^{2})-44-4x

(−5x

2

−4x

2

)−44−4x

3 Simplifica.

-9{x}^{2}-44-4x

−9x

2

−44−4x

listo espero te halla ayudado

4 0

2 years ago

(7 + X) x 8 - 4 x X = 56

devlian [24]

Answer:

12 1/4

Step-by-step explanation:

(7 + X) × 8 - 4 × X = 56

7 + X × 8 - 4 × X = 56

7 + 8X - 4 × X = 56

7 + 8X - 4X = 56

7 + 4X = 56

4X = 56 - 7

X = 49/4

X = 12 1/4

7 0

3 years ago

How do I set up the equation for this word problem? A takes 1/2 of the diamonds plus 1 from the table. B takes 2/3 of what remai

nalin [4]

The first thief takes (1/2 x + 1) . What remains ? x - (1/2x + 1)

So the 2nd thief takes 2/3 of [ x - (1/2x + 1) ]

What remains ? x - 2/3 [ x - (1/2x + 1) ]

So the 3rd thief takes 2/3 of { x - 2/3 [ x - (1/2x + 1) ] } and he takes 1 more .

What remains ? x - ( 2/3 { x - 2/3 [ x - (1/2x + 1) ] } + 1 )

And that whole ugly thing is equal to ' 1 ', so you can solve it for 'x'..

The whole problem from here on is an exercise in simplifying
an expression with a bunch of 'nested' parentheses in it.
===============================================
This is a lot harder than just solving the problem with logic and
waving your hands in the air. Here's how you would do that:

Start from the end and work backwards:

-- One diamond is left.
-- Before the 3rd thief took 1 more, there were 2.
-- That was 1/3 of what was there before the 3rd man took 2/3.
So he found 6 when he arrived.
-- 6 was 1/3 of what was there before the second thief helped himself.
So there were 18 when the 2nd man arrived.
-- 18 was 1 less than what was there before the first thief took 1 extra.
So he took his 1 extra from 19.
-- 19 was the remaining after the first man took 1/2 of all on the table.
So there were 38 on the table when he arrived.

Thank you for your generous 5 points.

3 0

3 years ago

What is 10 2/5 times 15 5/6! Thanks