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dimulka [17.4K]
3 years ago
8

If x=5^a, find the value of 5x. How?

Mathematics
1 answer:
Yakvenalex [24]3 years ago
7 0

Answer:

5x = 5^{(a+1)}

Step-by-step explanation:

Here is a problem with the concept of properties of the exponent.

We are given x = 5^{a} and we have to find the value of 5x.

Now, 5x = 5 \times 5^{a} {Since we are given that x = 5^{a}}

⇒ 5x = 5^{1} \times 5^{a} {Since we can write x = x^{1}}

⇒ 5x = 5^{(a+1)} {Since we know the formula of exponent as x^{m} \times x^{n} = x^{(m + n)}}

(Answer)

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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)

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2 years ago
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