How do you compare and order fractions?
1 answer:
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Try this:
Given:
![\left \{ {{x-y=1} \ [1] \atop {x+y=3} \ [2]} \right.](https://tex.z-dn.net/?f=%20%5Cleft%20%5C%7B%20%7B%7Bx-y%3D1%7D%20%5C%20%5B1%5D%20%5Catop%20%7Bx%2By%3D3%7D%20%5C%20%5B2%5D%7D%20%5Cright.%20)
1) [1]+[2]: 2x=2 ⇒ x=2
2) [2]-[1]: 2y=1 ⇒ y=1.
3) answer: (2;1)
Given:
1) [1]+[2]: 2x=2 ⇒ x=2
2) [2]-[1]: 2y=1 ⇒ y=1.
3) answer: (2;1)
Answer:
- AH = 3.2
- CH = 1.8
- BH = 2.4
Step-by-step explanation:
It can be convenient to compute the length of the hypotenuse of this triangle (AC). The Pythagorean theorem tells you ...
AC^2 = AB^2 + CB^2
AC^2 = 4^2 + 3^2 = 16 + 9 = 25
AC = √25 = 5
The altitude divides ∆ABC into similar triangles ∆AHB and ∆BHC. The scale factor for ∆AHB is ...
scale factor ∆ABC to ∆AHB = AB/AC = 4/5 = 0.8
And the scale factor to ∆BHC is ...
scale factor ∆ABC to ∆BHC = BC/AC = 3/5 = 0.6
Then the side AH is 0.8·AB = 0.8·4 = 3.2
And the side CH is 0.6·BC = 0.6·3 = 1.8
These two side lengths should add to the length AC = 5, and they do.
The remaining side BH can be found from either scale factor:
BH = AB·0.6 = BC·0.8 = 4·0.6 = 3·0.8 = 2.4
_____
The sides of interest are ...
AH = 3.2
CH = 1.8
BH = 2.4
