Answer and Step-by-step explanation:
Suppose x = 0.2355555... .
Multiply x by 100 and 1000:
100x = 23.5555....
1000x = 235.5555....
Let's subtract the first equation from the second:
1000x - 100x = 235.5555.... - 23.555.....
Because the decimal part for each goes on forever, we can simply cancel them out in our subtraction statement:
900x = 235 - 23 = 212
Divide both sides by 900:
x = 212/900 = 53/225
Thus, since x = 0.235555..., we know that:
0.23555.... = 53/225
Since p = 53 and q = 225 are integers, we have proven that this repeating decimal can be written as a fraction.
<em>~ an aesthetics lover</em>
Answer:
Apple- 14 Maple- 154
Step-by-step explanation
Since 11 x n - n is equal to a number that ends in 10, 20 etc. and the number has to be a multiple of 11 for the maple tree, and the difference has to stay the same throughout two all we need to find is 15 x n = a number that is divisable by 10. 15 x 10 = 150 so that's the age of the trees this year, and the difference between the trees is 140 so it corresponds with our rule. and the multiple of 11 that the difference is 140 is 11 x 14 = 154 and 154 - 11 = 140. Therefore the apple tree is 14 years old and the maple tree is 154 years old.
Answer:
Step-by-step explanation:
Solving for x. Want to solve for f instead?
Step 1 move all terms to one side
fx - 4x² + 100 =0
Step 2 Use the Quadratic Formula
x = -f + √f² + 1600 ÷ -8, -f-√f²+1600 ÷ -8
Done.
A cube has all sides the same length, check the picture below.
since the cube is just 6 squares stacked up to each other at the edges, we can simply get the area of each square and sum them up, and that's the surface area of the cube.
(3.5 · 3.5) + (3.5 · 3.5) + (3.5 · 3.5) + (3.5 · 3.5) + (3.5 · 3.5) + (3.5 · 3.5) .
4 x 7 = 28
49 x 13 = 637
28/637
=4/91
