For the element to be congruent only rotations, reflections or translations are allowed to be applied
1)
(x, y) → (x, –y)=reflection
(x, y) → (x + 5, y)=translation
(x, y) → (–x, y)=reflection
->is congruent
2)
(x, y) → (x + 1, y)=translation
(x, y) → (–x, –y)=reflection
(x, y) → (2x, y)=scaling->can't be congruent
3)
(x, y) → (0.5x, 0.5y)=scaling->can't be congruent
(x, y) → (x, –y)
(x, y) → (x, y + 8)
4)
(x, y) → (x – 4, y)=translation
(x, y) → (x, y + 3)=translation
(x, y) → (3x, 3y)=scaling->can't be congruent
so 1) is the only series of transformations with a congruent solution
Answer:
113
Step-by-step explanation:
127 - 2(3+4)
127 - 2(7)
127-14
113
Answer:
The probability that a freshman prefer cheese toppings is 0.241
Step-by-step explanation:
Probability of any event E = 
Here, let E : Event of choosing cheese toppings
So, the number of favorable outcomes = 14
Total number of outcomes = 58
So, 
or, P(E) = 
So,the probability that a freshman prefer cheese toppings is 0.241379
Rounding of 0.241379 to the <u>nearest thousandth</u>, we get
Here , in 0.241379 thousandth digit is 3, and 3 < 5,
so the value of P(E) = 0.241
Answer:
x = 2
Step-by-step explanation:
The sum of the 3 angles in the triangle = 180°
Sum the 3 angles and equate to 180
6x + 15 + 90 + 63 = 180
6x + 168 = 180 ( subtract 168 from both sides )
6x = 12 ( divide both sides by 6 )
x = 2
36 because in total there are 46, 20 playing football, 16 playing hockey and 10 who plays both so if you add 20+16+10 you get 46, but then you take away the 10 who play both to get an answer or 36 students
