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vlabodo [156]
3 years ago
11

A 20-foot ladder is leaning against a tree. The bottom of the ladder is 12 feet away from the bottom of the tree. Approximately

how high up the tree does the top of the ladder reach? /2.4 feet/ /6 feet/ /9.2 feet/ /16 feet/
Mathematics
1 answer:
arsen [322]3 years ago
3 0
Pythagorean theorem is a^2 + b^2 = c^2. the hypotenuse is always the longest, so lets plug in the values.

a^2 + 12^2 = 20^2
if we simplify, we get a^2 + 144 = 400

then subtract 400-144 = 256
then find the sq. root of 256 = 16.

the answer is 16 feet
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The parabola is translated down 2 units.

Step-by-step explanation:

You have the parabola f(x) = 2x² – 5x + 3

To change this parabola to f(x) = 2x² - 5x + 1, you must have performed the following calculation:

f(x) = 2x² – 5x + 3 -2= 2x² - 5x + 1  <u><em>Expresion A</em></u>

The algebraic expression of the parabola that results from translating the parabola f (x) = ax² horizontally and vertically is g (x) = a(x - p)² + q, translating in the same way as the function.

  • If p> 0 and q> 0, the parabola shifts p units to the right and q units up.
  • If p> 0 and q <0, the parabola shifts p units to the right and q units down.
  • If p <0 and q> 0, the parabola shifts p units to the left and q units up.
  • If p <0 and q <0, the parabola shifts p units to the left and q units down.

In the expression A it can be observed then that q = -2 and is less than 0. So the displacement is down 2 units.

This can also be seen graphically, in the attached image, where the red parabola corresponds to the function f(x) = 2x² – 5x + 3 and the blue one to the parabola f(x) = 2x² – 5x + 1.

In conclusion, <u><em>the parabola is translated down 2 units.</em></u>

3 0
3 years ago
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