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lora16 [44]
3 years ago
9

Solve the following system of equations by substitution.

Mathematics
2 answers:
jasenka [17]3 years ago
5 0

Answer:

The answer is B.(5,10)

Step-by-step explanation:

1. y = 2(5)

  y = 10

2.y = -2(5)+20

  y = -10+20

  y = 10

nlexa [21]3 years ago
3 0

The answer is b (5,10)

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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}

is a solution to this system, i.e. x=149+252n for any integer n, the smallest and positive of which is 149.

3 0
3 years ago
Hi, I need some help with the last question of the first problem and the answer to the second page.
bulgar [2K]

Answer:

46.9 for the first one

Step-by-step explanation:

So sorry if i'm wrong <3

6 0
2 years ago
A cyclist rides his bike at a rate of 10 kilometers per hour. What is this rate in miles per hour. How many miles will the cycli
poizon [28]

Answer:

10 km/ hour = 6.25 miles/ hour

Step-by-step explanation:

cyclist travel in 5 hours = 6.25 x 5 = 31.25 miles

8 0
3 years ago
What the correct answer now fast
netineya [11]

Answer:

112.065

Step-by-step explanation:

so divide the triangle in two from x to wy

and you get to triangles

then using the first right angled triangle you can apply tan=opposite/adjacent

to get height as 7.56 then apply 1/2bh to get first area as 58.59

first add all angles and subtract from 180=24

then use tan to get the height as 6.9

then apply 1/2bh to get second area as 53.48

then add the two areas to get total

(after getting first one don't multiply by two)

6 0
3 years ago
The diameter of a circle is 2 centimeters. What is the circle's circumference?
leonid [27]
C=6.28cm
because C=2pi•r
so in this case C=2•3.14•1
which is C=2•3.14
and that leads to C=6.28cm

hope this helped
4 0
3 years ago
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