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babymother [125]
3 years ago
13

Question 9. True or false? Provide a simple counter-example if it is false. (9.a) The sum of two rational numbers x, y EQ is alw

ays a rational number, x+y EQ. (9.b) The sum of two irrational numbers x, y ER - Q is always an irrational number, x +y ER-Q. (9.c) The sum of the squares of two distinct real numbers x,y ER, with x #y, is always a positive real number, x2 + y2 ER and x2 + y2 > 0. (9.d) If a, b ER, then ab E R.
Mathematics
1 answer:
eimsori [14]3 years ago
8 0

Answer:

a. True. Rational numbers are closed under the sum operation, therefore, the sum of two rational numbers is always a rational number.

b. True. irrational numbers are closed under the sum operation, therefore, the sum of two irrationals numbers is always a irrational number.

c. True. The square of a real number is always a number greater than zero, and the sum of two numbers greater than zero is greater than zero.

d. True. The real numbers are closed under the product operation, then if a and b are reals numbers, the product ab is also a real number.

Step-by-step explanation:

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Building and solving an equation to model the situation, it is found that it takes 4 min for the prairie dog to reach 13 feet underground.

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Taseem’s loose change consists of dimes and quarters. When you ask her how many of each type of coin she has, she gives you the
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The statement first, and the statement second are correct because the number of dimes is 34, and the number of quarters is 66

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If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have:

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Given :-

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To find :-

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Solution :-

<u>Taking</u><u> </u><u>second</u><u> </u><u>equation</u><u>:</u><u>-</u>

  • 2b + 2ab = 0
  • 2b ( 1 + a ) = 0
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<u>Substitute</u><u> </u><u>in </u><u>first </u><u>equation</u><u> </u><u>:</u><u>-</u><u> </u>

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<u>When </u><u>b </u><u>=</u><u> </u><u>0</u><u> </u><u>,</u>

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  • a² - a = 0
  • a( a -1) =0
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<u>When </u><u>a </u><u>=</u><u> </u><u>-</u><u>1</u><u> </u><u>,</u>

  • (-1)² - 2*(-1) - b² = 0
  • 1 + 2 - b² = 0
  • b² = 3
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<u>Answer </u><u>:</u><u>-</u><u> </u>

  • a = 0,1 ; b = 0
  • a = -1 , b = ±√3
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