Images of transformation are congruent if they were translated, mirrored/flipped or rotated
1)
(x, y) → (–x, –y) mirrored
(x, y) → (0.8x, 0.8y) scale->not congruent
(x, y) → (x, y + 5)
2)
(x, y) → (x, –y) mirrored
(x, y) → (–x, y) mirrored
(x, y) → (x + 1, y – 1) translation
-> is congruent
3)
(x, y) → (x + 5, y + 5) translation
(x, y) → (x, –y) mirror
(x, y) → (2x, y) scale-> not congruent
4)
(x, y) → (3x, 3y) scale->not congruent
(x, y) → (–x, y)
(x, y) → (x – 4, y)
so the second series of transformations is the only one with a congruent after image
Answer:
ΔBFG
Step-by-step explanation:
Since top face points are
and bottom face points are
The side BF can be a hypotenuse of the triangle BFG only
This triangle is on the top face and all the rest given triangles are formed by the points that are not on the same face, therefore BF can't be a hypotenuse of those, as ether B or F is becoming a right angle of the triangles.
Answer:
5
Step-by-step explanation:
Answer:
see explanation
Step-by-step explanation:
Using the Remainder theorem
If f(x) is divided by (x - h) then f(h) = remainder, thus
f(3) = 3³ + a(3)² + b(3) + 4 = 10, that is
27 + 9a + 3b + 4 = 10
9a + 3b + 31 = 10 ( subtract 31 from both sides )
9a + 3b = - 21 → (1)
f(- 1) = (- 1)³ + a(- 1)² + b(- 1) + 4 = 6, that is
- 1 + a - b + 4 = 6
a - b + 3 = 6 ( subtract 3 from both sides )
a - b = 3 → (2)
Rearrange (2) expressing a in terms of b
a = 3 + b → (3)
Substitute a = 3 + b into (1)
9(3 + b) + 3b = - 21 ← distribute and simplify left side
27 + 9b + 3b = - 21
12b + 27 = - 21 ( subtract 27 from both sides )
12b = - 48 ( divide both sides by 12 )
b = - 4
Substitute b = - 4 into (3)
a = 3 - 4 = - 1
Hence a = - 1 and b = - 4
Answer: X = 1/4 or X = -1
Step-by-step explanation:
4x2+3x−1=0
(4x−1)(x+1)=0
4x−1=0 or x+1=0
4x=1 or x=-1
Now divide 4 from both sides
like this 4x/4=1/4
now cancel out two 4's so the answer will be x=1/4
