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blagie [28]
3 years ago
12

Which system of equations has the same solution as the system below?

Mathematics
1 answer:
zepelin [54]3 years ago
6 0
2x + 2y = 16 ⇒ 2x + 2y = 16
3x -  1y =   4 ⇒ 6x -  2y =   8
                                 8x = 24
                                  8      8
                                   x = 3
                         2x + 2y = 16
                       2(3) + 2y = 16
                           6 + 2y = 16
                         - 6           - 6
                                 2y = 10
                                  2      2
                                   y = 5
                             (x, y) = (3, 5)
The systems of equations that has the same solution as the system is one common solution.
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Arisa [49]

Answer:

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Step-by-step explanation:

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Suppose that f : [a, b] → [a, b] is continuous. Prove that f has a fixed point. That is, prove that there exists c ∈ [a, b] such
nikklg [1K]

Answer:

Step-by-step explanation:

define the function:

g(x) = f(x) -x

As both f(x) and x are continuous functions, g(x) will also be continuous.

Now, what can we say about g(a) = f(a) -a?

we know that a\leq f(a) \leq b, thus:

a-a\leq f(a)-a \leq b-a\\0 \leq g(a) \leq b-a

thus  g(a) is non-negative.

What about g(b) ? Again we have:

a\leq f(b) \leq b\\a-b \leq f(b) -b \leq  0\\a-b \leq g(b) \leq  0

That means that g(b) is not positive.

Now, we can imagine two cases, either one of g(a) or g(b) is equal to zero, or none of them is. If either of them is equal to zero, we have found a fixed point! In fact, any point c for which g(c)=0 is a fixed point, because:

g(c) = 0 \implies f(c) -c = 0 \implies f(c) = c

Now, if g(a) \neq  0 and g(b) \neq 0, then we have that

g(a) >0 and g(b) < 0. And by Bolzano's theorem we can assert that there must exist a point c between a and b for which g(c)=0. And as we have shown before that point would be a fixed point. This completes the proof.

6 0
3 years ago
PLEASE HELP
UkoKoshka [18]

Answer:

really easy its 180

Step-by-step explanation:

because you multiply 30 times 6 u get 180

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