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3 years ago

Which of the following points lie in the solution set to the following system of inequalities?

Mathematics

1 answer:

emmasim [6.3K]3 years ago

6 0

<h3>Answer:</h3>

B. (5, -2)

<h3>Step-by-step explanation:</h3>

Try the points in the inequalities and see what works. Here, we evaluate the point in the first inequality, and if that works, then the second inequality.

A. 2 ≤ -(-5) -5 . . . ⇒ . . . 2 ≤ 0 . . . false

B. -2 ≤ 5 -5 . . . true

... -2 ≥ -(5) -4 . . . true . . . . . . selection B is a viable choice

C. we know from A that the first inequality will be satisfied

... -2 ≥ -(-5) -4 . . . ⇒ . . . -2 ≥ 1 . . . false

D. 2 ≤ 5 -5 . . . . false

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Read 2 more answers

8. Is the following statement true or false? Justify your conclusion. If a and b are nonnegative real numbers and a + b =0, then

atroni [7]

Answer:

If $a + b = 0$ then $a = 0$ and $b =0$

a | b | a + b (answer)

0 | 0 | 0

0 | 1 | 1

0 | 2 | 2

1 | 0 | 1

2 | 0 | 2

1 | 1 | 2

2 | 1 | 3

Step-by-step explanation:

Considering the following conditions for the real numbers:

$a\geq 0\\b\geq 0$

Following the rules of these in-equations, it is possible to deduce:

$a + b \geq 0$

Then, if the proposed statement is:

$a + b = 0$

The conditions above shall comply the requirements established, but first, analyzing the statement:

If $a \geq 0$ and $b \geq 0$ then $a + b \geq a$ , $a + b \geq b$ and $a + b \geq 0$ .

If $a = 0$ and b a non negative real number, then $a + b \geq b$ , but because to $a = 0$ , then $a + b = b$ . Due to the commutative property of sums, the same behavior will be presented if $b = 0$ and a a non negative real number.