Kepler believed in the Copernican system and sought the key to reconciling Tycho’s observations with a heliocentric model for the solar system. In addition to his mathematical genius, his philosophical contribution was huge - as described by Einstein: "[Kepler] had to realize clearly that logical-mathematical theorizing, no matter how lucid, could not guarantee truth by itself; that the most beautiful logical theory means nothing in natural science without comparison with the exactest experience. Without this philosophical attitude, his work would not have been possible." (from the introduction Einstein wrote for Baumgard & Callan's 'Johannes Kepler: Life and Letters' (1953)). Kepler's focus on fitting the exact observations from Tycho led him to abandon the idea that the planets had to move on combinations of circles, a bit of logical-mathematical theorizing that had held sway for 1800 years!
Since you do not have a picture, i will give you the steps, and you can see where the differences are at.
6x - 1 = -2x + 9
Note the equal sign. What you do to one side, you do to the other. Isolate the x.
First, add 1 to both sides
6x - 1 (+1) = -2x + 9 (+1)
6x = -2x + 10
Next, add 2x to both sides to isolate the x
6x (+2x) = -2x (+2x) + 10
6x + 2x = 10
8x = 10
Finally, isolate the x by dividing 8 from both sides
8x/8 = 10/8
x = 10/8 (may be where they stopped at, but you can go further)
Simplify. Divide 2 from top and bottom
(10/8)/(2/2) = 5/4
x = 5/4 should be final answer
hope this helps
Start with the slope formula.
m = y₂ - y₁ / x₂ - x₁
m = -6 - 3 / 5 - -2
m = -9 / 7
So the slope is -9/7.
Answer:
1. x=74
2. x=86
Step-by-step explanation:
1. the sum of interior angles in a triangle is 180 degrees
81 + 25 + x = 180
106 + x = 180
x = 74
2. once again the sum of interior angles in a triangle is 180 degrees so add up the terms and set them equal to 180
x + x-35 + 43 = 180
add up like terms (x and x, -35 and 43)
2x +8 = 180
2x = 172
x = 86
