9514 1404 393
Answer:
53/99
Step-by-step explanation:
When an n-digit repeat begins at the decimal point, the repeating digits can be placed over an equal number of 9s to make a fraction. Sometimes, that fraction can be reduced to lower terms.
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If the repeat does not start at the decimal point, the conversion can be done as follows.
For a number x with a decimal fraction that has n digits repeating, multiply by 10^n, subtract x and then divide by (10^n -1).
The fraction will be ...
(x·10^n -x)/(10^n -1) . . . where x has n repeating digits in the decimal fraction
Here, that looks like ...
Answer: (-2, 8)
Explanation:
Plug x = -2 into the second equation. Isolate y.
5x+3y = 14
5(-2)+3y = 14
-10+3y = 14
3y = 14+10
3y = 24
y = 24/3
y = 8
We have x = -2 lead to y = 8.
Therefore, the ordered pair (x,y) = (-2,8) is the solution to this system.
Answer:
- 1. First blank: <u>∠ACB ≅ ∠E'C'D'</u>
- 2. Second blank: <u>translate point E' to point A</u>
Therefore, the answer is the third <em>option:∠ACB ≅ ∠E'C'D'; translate point D' to point B</em>
Explanation:
<u>1. First blank: ∠ACB ≅ ∠E'C'D'</u>
Since segment AC is perpendicular to segment BD (given) and the point C is their intersection point, when you reflect triangle ECD over the segment AC, you get:
- the image of segment CD will be the segment C'D'
- the segment C'D' overlaps the segment BC
- the angle ACB is the same angle E'C'D' (the right angle)
Hence: ∠ACB ≅ ∠E'C'D'
So far, you have established one pair of congruent angles.
<u>2. Second blank: translate point D' to point B</u>
You need to establish that other pair of angles are congruent.
Then, translate the triangle D'C'E' moving point D' to point B, which will show that angles ABC and E'D'C' are congruents.
Hence, you have proved a second pair of angles are congruent.
The AA (angle-angle) similarity postulate assures that two angles are similar if two pair of angles are congruent (because the third pair has to be congruent necessarily).
Answer:
You can use cymath for that
Step-by-step explanation:
