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PilotLPTM [1.2K]
3 years ago
10

1. Which of the following statements is true about the numbers 4.5,-6,12,-1.1? * BRAINLIEST PRIZE!

Mathematics
1 answer:
seropon [69]3 years ago
6 0

Answer:

4.5 and -1.1 are rational numbers, -6 is an integer, and 12 is a whole number.

Step-by-step explanation:

<u>Numbers:</u>

  • 4.5,-6,12,-1.1

<u>Let's see which option is correct:</u>

-1.1 is a rational number, 4.5 and -6 are integers, and 12 is a whole number.

  • 4.5 in not an integer, it is incorrect

-1.1 and -6 are rational numbers, 12 is an integer, and 4.5 is a whole number.

  • 4.5 is not a whole number, this is incorrect

4.5 and -1.1 are rational numbers, -6 is an integer, and 12 is a whole number.

  • Correct

12 is a rational number, -1.1 and -6 are integers, and 4.5 is a whole number.

  • -1.1 is not and integer, 4.5 is not a whole number, this is incorrect
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For which value of b can the expression x2 + bx + 18 be factored?
Dmitry_Shevchenko [17]

Answers:

  • b = -19
  • b = -11
  • b = -9
  • b = 19
  • b = 11
  • b = 9

====================================================

Explanation:

Here are all the ways to multiply to 18 when using integers only:

  • -1*(-18) = 18
  • -2*(-9) = 18
  • -3*(-6) = 18
  • 1*18 = 18
  • 2*9 = 18
  • 3*6 = 18

Sum each pair of factors to find out a possible value of b.

  • -1 + (-18) = -19
  • -2 + (-9) = -11
  • -3 + (-6) = -9
  • 1 + 18 = 19
  • 2 + 9 = 11
  • 3 + 6 = 9

Therefore, the possible values of b are

  • b = -19
  • b = -11
  • b = -9
  • b = 19
  • b = 11
  • b = 9

which are the final answers.

----------------------

An example:

Let's say b = 11. This would mean x^2+bx+18 becomes x^2+11x+18

It would factor to (x+2)(x+9) since it was stated earlier that:

2+9 = 11

2 * 9 = 18

You can use the FOIL rule, distributive property, or the box method to confirm that x^2+11x+18 = (x+2)(x+9) is a true equation for all real numbers x.

This same idea applies for the other values of b.

----------------------

If you're curious why this works, consider multiplying the two factors (x+p) and (x+q)

Use the FOIL rule to get (x+p)(x+q) = x^2+qx+px+pq = x^2+(p+q)x + pq

The middle term (p+q)x has the components add to the coefficient, while those same two components multiply to get the last term. This is why when factoring we're looking for two numbers that multiply to 18, and also add to the value of b (which in the case of the last example was 11).

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