Answer:
True
Step-by-step explanation:
**plug it in using the Pythagorean Theorem**
6^2+8^2= 10^2
36+64=100
100=100 (true)
Answer:
It is linear since it is a straight line.
Answer:
x = 16
Step-by-step explanation:
The equation shown can be solved this way.
x^2 +(x -4)^2 = 20^2
x^2 +x^2 -8x +16 = 400
2x^2 -8x -384 = 0
x^2 -4x -192 = 0
(x -16)(x +12) = 0
The positive solution is ...
x = 16
_____
Since this makes use of the Pythagorean theorem, you've probably run across the 3-4-5 triangle. You often find scaled versions of it in algebra and geometry problems. Here, it is scaled by a factor of 4 to give a 12-16-20 triangle as half of the display screen.
The 3-4-5 triple is the only Pythagorean triple that is an arithmetic sequence. So, if the difference in side lengths is 4 and the diagonal is 5×4, you can be pretty certain that x = 4×4 and x-4 = 4×3.
Answer:
3.16
Step-by-step explanation:
Let us find the length of rope Jules will need using the pythagoras theorem .
Width of the moat ( let the moat be the base of this triangle ) = 14 foot
Distance from Roma's window to the boat ( let this be the side of the triangle where the right angle is present ) =20 feet
Then the length of rope needed ( hypotenuse ) =
= Let us name the triangle that is formed as △ ABC . Then ;
In △ ABC :
AB = the width of moat ( leg of triangle ) = 14 foot
BC = The distance from the window to the moat ( base ) = 20 feet
AC = Length of rope needed ( hypotenuse ) =
= AB ² + BC² = AC² ( according to the pythagoras theorem the square on the hypotenuse will be equal to the sum of the squares on the other two legs )
= 14² + 20² = AC²
= 196 + 400 = AC²
= 596 = AC²
= 24 × 24 = AC × AC
= 24 foot = AC = length of rope needed by jules .
Therefore , Jules will need a 24 foot rope so that his girlfriend can slide down and escape from her apartment .
