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jekas [21]
3 years ago
5

What two numbers multiply to -320 and add to 32

Mathematics
1 answer:
iragen [17]3 years ago
8 0
Let a and b be the numbers,then a+b=32,b=32-a
ab=-320
a(32-a)=-320
32a-a^2=-320
a^2-32a-320=0
a^2-40a+8a-320=0
a(a-40)+8(a-40)=0
(a-40)(a+8)=0
a=40 or-8
when a=40,b=32-40=-8
when a=-8,b=32-(-8)=32+8=40
so numbers are 40 and -8
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Answer:

The sum of the internal ángles = 360°

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then:

(3x-70) + (3y+40) + 120 + x = 360     ⇒ first eq.

(3y+40) + (3x-70) = 180      ⇒  second eq

development:

from the first eq.

3x + x + 3y  =  360  + 70 - 40 - 120

4x + 3y = 430 - 160

4x + 3y = 270       ⇒  third eq.

3y = 270 - 4x

y = (270 - 4x) / 3    ⇒  fourth eq.

from the secon eq.:

3y + 3x = 180 + 70 - 40

3y + 3x = 250 - 40

3y + 3x = 210    ⇒  fifth eq.

multiply by -1  the fifth eq and sum with the third eq.

  -3y  - 3x = -210    ⇒   (fifth eq. *-1)

   3y  + 4x = 270

⇒  0   +  x  = 60

x = 60°

from the fourth eq.

y = (270-4x)/3

y = (270-(4*60)) / 3

y = (270 - 240) / 3

y = 30/3

y = 10°

Probe:

from the first eq.

(3x-70) + (3y+40) + 120 + x = 360

3*60 - 70 + 3*10 + 40 + 120 + 60 = 360

180 - 70 + 30 + 40 + 120 + 60 = 360

180 + 30 + 40 + 120 + 60 - 70 = 360

430 - 70 = 360

Answer:

y = 10

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