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2 years ago

5^11 times 5^3 = 5^?

Mathematics

1 answer:

postnew [5]2 years ago

7 0

Answer:

$5^{13}$

Step-by-step explanation:

$5^{11}\times \:5^2$

Apply exponent rule : $a^b\times \:a^c=a^{b+c}$

$5^{11}\times \:5^2=5^{11+2}$

$5^{11+2}$

Add 11 +2 = 13

$=5^{13}$

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7. Use the quadratic formula to find the solution(s). x² + 2x - 8 = 0

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Hey there!

Use the quadratic formula to find the solution(s). x² + 2x - 8 = 0

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x = -4 or x = 2 ✅

Explanation :

Quadratic formula : ax² + bx + c = 0 where a ≠ 0

The number of real-number solutions (roots) is determined by the discriminant (b² - 4ac) :

If b² - 4ac > 0 , There are 2 real-number solutions

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If b² - 4ac < 0 , There is no real-number solution.

The roots of the equation are determined by the following calculation:

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1) Calculate the discriminant :

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b² - 4ac = 36 > 0 ; The equation admits two real-number solutions

2) Calculate the roots of the equation:

▪️ (1)

$x_1 = \frac{ - b - \sqrt{ {b}^{2} - 4ac} }{2a} \\ \\ x_1 = \frac{ - 2 - \sqrt{36} }{2(1) } \\ \\ x_1 = \frac{ - 2 - 6}{2} \\ \\ x_1 = \frac{ - 8}{2} \\ \\ \blue{\boxed{\red{x_1 = -4}}}$

▪️ (2)

$x_2 = \frac{ - b + \sqrt{ {b}^{2} - 4ac } }{2a} \\ \\ x_2 = \frac{ - 2 + \sqrt{36} }{2(1)} \\ \\ x_2 = \frac{ - 2 + 6}{2} \\ \\ x_2 = \frac{4}{2} \\ \\ \red{\boxed{\blue{x_2 = 2}}}$

>> Therefore, your answers are x = -4 or x = 2.

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