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dybincka [34]
3 years ago
7

the driving distance from the sports arena to Kristina's house in 10 9/10 miles. the distance from the sports arena to Luke's ho

use is 2 7/10 miles. how much greater is the driving distance between the sports arena and Kristina's house than between the sports arena and Luke's house?
Mathematics
1 answer:
nydimaria [60]3 years ago
3 0

Answer:

  8.2 miles

Step-by-step explanation:

  (arena to Kristina's house) - (arena to Luke's house) = 10.9 - 2.7

  = 8.2 . . . miles

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When 8 is subtracted from the square of a number, the result is 7 times the number.
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Step-by-step explanation:

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x - 8= 0   x + 1=0

x=8           x= -1

8 is the positive solution

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5x3 + 14x2 + 9x <br> help
Cerrena [4.2K]
<h3>Answer:    x(x+1)(5x+9) </h3>

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

Work Shown:

5x^3 + 14x^2 + 9x

x( 5x^2 + 14x + 9 )

To factor 5x^2 + 14x + 9, we could use the AC method and guess and check our way to getting the correct result.

A better way in my opinion is to solve 5x^2 + 14x + 9 = 0 through the quadratic formula

x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(14)\pm\sqrt{(14)^2-4(5)(9)}}{2(5)}\\\\x = \frac{-14\pm\sqrt{16}}{10}\\\\x = \frac{-14\pm4}{10}\\\\x = \frac{-14+4}{10} \ \text{ or } \ x = \frac{-14-4}{10}\\\\x = \frac{-10}{10} \ \text{ or } \ x = \frac{-18}{10}\\\\x = -1 \ \text{ or } \ x = \frac{-9}{5}\\\\

Then use those two solutions to find the factorization

x = -1  or  x = -9/5

x+1 = 0  or  5x = -9

x+1 = 0  or  5x+9 = 0

(x+1)(5x+9) = 0

So we have shown that 5x^2 + 14x + 9 factors to (x+1)(5x+9)

-----------

Overall,

5x^3 + 14x^2 + 9x

factors to

x(x+1)(5x+9)

6 0
3 years ago
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