The digit 9 is in the thousands place
Option 1, 6, 3 are all correct
Answer:
679
Step-by-step explanation:
The goal of this exercise is to find a three digit number given five statements.
1 - We can conclude that two digits out of 964 are correct but in the wrong place.
2 - One digit out of 147 is correct, but in the wrong place
3 - One digit out of 189 is correct and in the right place. Since 1 is on the same place in 147 and 189, 1 is not the correct digit. The correct digit is either 8 or 9.
4 - One digit out of 286 is correct, but in the wrong place. Since 8 is on the same place in 189 and 286, 8 is not the correct digit. We can then conclude that 9 is correct (statement 3) and in the right place (third) and that either 2 or 6 are correct but in the wrong place.
5 - 523 are all wrong. We can then conclude that 6 is correct and that is not in the third or second place, which leaves it in the first place.
If 1 and 4 are incorrect, from the second statement, we infer that 7 is the remaining correct digit at the second place.
Therefore the number is 679
Answer:
x = 28°, ∠ABC = 57°
Step-by-step explanation:
∠ABD = 2x+1
∠BCD = 33°
∠ABD = 90° (right angle)
which means that
∠ABC + <CBD = 90° (In the middle of ∠ABD)
Then, we can substitute to the equation to find x
(2x+1) + 33° = 90°
(2x+1) = 57°
2x = 56°
x = 28°
after finding x, we can find ∠ABC:
∠ABC = 2(28) + 1 = 57°
I hope this helps, have a great day! :)
