Factor completely x3 + 8x2 − 3x − 24.
1 answer:
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The Pythagorean's Theorem for our situation would look like this:
So let's call the short leg s, the long leg l and the hypotenuse h. It appears that all our measurements are based on the measurement of the short leg. The long leg is 4 more than twice the short leg, so that expression is l=2s+4; the hypotenuse measure is 6 more than twice the short leg, so that expression is h=2s+6. And the short leg is just s. Now we can rewrite our formula accordingly:
And of course we have to expand. Doing that will leave us with
Combining like terms we have
Our job now is to get everything on one side of the equals sign and solve for s
That is now a second degree polynomial, a quadratic to be exact, and it can be factored several different ways. The easiest is to figure what 2 numbers add to be -8 and multiply to be -20. Those numbers would be 10 and -2. Since we are figuring out the length of the sides, AND we know that the two things in math that will never EVER be negative are time and distance/length, -2 is not an option. That means that the short side, s, measures 10. The longer side, 2s+4, measures 2(10)+4 which is 24, and the hypotenuse, 2s+6, measures 2(10)+6 which is 26. So there you go!
<u>Answer-</u>
Set of constraints to model the problem are,
<u>Solution-</u>
<em>x = the number of lawns weeded by Gwen,</em>
<em>y = the number of dogs walked by Fabio.</em>
1.
As, Gwen charges $12 each time she weeds a yard and Fabio charges $9 each time he walks a dog,
They need at least $510 to purchase the new gaming station, means they need $510 or more than $510.
The equation for this is,
2.
The number of dog walks that Fabio has scheduled is no more than twice the number of yards Gwen has scheduled to weed, means
y must be less than or equal to 2x.
The equation for this is,
3.
Fabio will walk at least 25 dogs, means y must be greater than of equal to 25.
The equation for this is,