Answer:
Anika is correct
Step-by-step explanation:
* Lets revise the rules of reflection and rotation
- If point (x , y) reflected across the x-axis then its image is (x , -y)
- If point (x , y) rotated about the origin by angle 270° clock wise then
its image is (-y , x)
* Lets check the vertices of the two triangles
- The vertices of Δ ABC are:
# A (-7 , 2)
# B (-3 , 6)
# C (-2 , 1)
- The vertices of Δ PRQ
# P (-7 , -2)
# R (-3 , -6)
# Q (-2 , -1)
* By comparing between the vertices of the two triangles
∵ Each y-coordinates of Δ PRQ has opposite sign of each
y-coordinates of Δ ABC
∵ All x-coordinates of Δ PRQ are the same with x-coordinates of
Δ ABC
- That means Δ PRQ is the image of Δ ABC after reflection across
the x-axis
∵ Reflection doesn't change the shape and the size of the figure
∴ Δ ABC and Δ PRQ have same size (equal sides and equal angles)
∴ Δ ABC is congruent to Δ PRQ
* Anika is correct
Answer:
BC = 144 units
Step-by-step explanation:
BC = BD + DC , substitute values
8x = 4x + 10 + 3x + 8 = 7x + 18 ( subtract 7x from both sides )
x = 18
Thus
BC = 8x = 8 × 18 = 144 units
Answer:
x(x-3) ( x+4)
Step-by-step explanation:
2 5
---------- + ------------
x^2 -3x x^2 + x - 12
Factor the denominator
2 5
---------- + ------------
x(x -3) (x-3) (x+4)
The common denominator is
x(x-3) ( x+4)
So, 11 = 7 + 2^2;
19 = 11 + 2^3;
35 = 19 + 2^4;
35 + 2^5 = 35 + 32 = 67 is the next number in the series 7, 11, 19, 35, ...