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3 years ago

Find the equation of the line perpendicular to y=−2 that passes through the point (4, −2).

Mathematics

1 answer:

vfiekz [6]3 years ago

5 0

Answer:

x = 4

Step-by-step explanation:

y = - 2 is the equation of a horizontal line parallel to the x- axis.

A perpendicular line is therefore a vertical line parallel to the y- axis with equation

x = c

where c is the value of the x- coordinates the line passes through.

The line passes through (4, - 2 ) with x- coordinate 4 , thus

x = 4 ← equation of perpendicular line

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2 years ago

What is the measure of ZBAC?

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1 year ago

4, Find a number x such that x = 1 mod 4, x 2 mod 7, and x 5 mod 9.

olchik [2.2K]

4, 7 and 9 are mutually coprime, so you can use the Chinese remainder theorem.

Start with

$x=7\cdot9+4\cdot2\cdot9+4\cdot7\cdot5$

Taken mod 4, the last two terms vanish and we're left with

$x\equiv63\equiv64-1\equiv-1\equiv3\pmod4$

We have $3^2\equiv9\equiv1\pmod4$ , so we can multiply the first term by 3 to guarantee that we end up with 1 mod 4.

$x=7\cdot9\cdot3+4\cdot2\cdot9+4\cdot7\cdot5$

Taken mod 7, the first and last terms vanish and we're left with

$x\equiv72\equiv2\pmod7$

which is what we want, so no adjustments needed here.

$x=7\cdot9\cdot3+4\cdot2\cdot9+4\cdot7\cdot5$

Taken mod 9, the first two terms vanish and we're left with

$x\equiv140\equiv5\pmod9$

so we don't need to make any adjustments here, and we end up with $x=401$ .

By the Chinese remainder theorem, we find that any $x$ such that

$x\equiv401\pmod{4\cdot7\cdot9}\implies x\equiv149\pmod{252}$

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2 years ago

2<br>Decrease R420 in the ratio 4:7

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Step-by-step explanation:

Let the numbers are 4x and 7x. According to the question if each number is increased by 20, the ratio becomes 7 : 9.

Then,

( 4x + 20 ) : ( 7x + 20 ) = 7 : 9

9( 4x + 20 ) = 7( 7x + 20 )

9( 4x ) + 9( 20 ) = 7( 7x ) + 7( 20 )

9( 20 ) - 7( 20 ) = 7( 7x ) - 9( 4x )

2( 20 ) = 49x - 36x

40 = 13 x

40 / 13 = x

Therefore, number are :–

4 x = 4( 40 / 13 ) = 160 / 13

7 x = 7( 40 / 13 ) = 280 / 13

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3 years ago

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2 years ago