(a-b) X (a+b)
= aXa - bXa +aXb -bXb (distributing)
Now, cross product of a vector with itself = 0
so, aXa = 0, bXb = 0
Also, aXb = - bXa
so,
(a-b) X (a+b) = 0 + aXb + aXb + 0
= 2aXb
hence, proved :)
common ratio = a4/a3 = a3/a2
8/a3 = a3/18
(a3)^2 = 8 * 18
(a3)^2 = 144
a3 = 12 or a3 = -12
common ratio = 8/12 or common ratio = 8/(-12)
common ratio = 2/3 or common ratio = -2/3
Answer: 12 or -12
Answer:
No, h = (-23)/5
Step-by-step explanation:
Solve for h:
3 (4 - 6 h) - 7 h = 127
3 (4 - 6 h) = 12 - 18 h:
12 - 18 h - 7 h = 127
-18 h - 7 h = -25 h:
-25 h + 12 = 127
Subtract 12 from both sides:
(12 - 12) - 25 h = 127 - 12
12 - 12 = 0:
-25 h = 127 - 12
127 - 12 = 115:
-25 h = 115
Divide both sides of -25 h = 115 by -25:
(-25 h)/(-25) = 115/(-25)
(-25)/(-25) = 1:
h = 115/(-25)
The gcd of 115 and -25 is 5, so 115/(-25) = (5×23)/(5 (-5)) = 5/5×23/(-5) = 23/(-5):
h = 23/(-5)
Multiply numerator and denominator of 23/(-5) by -1:
Answer: h = (-23)/5
Answer:
x = - 5
Step-by-step explanation:
3x - 3 - 6x = 12
group like terms
3x - 6x - 3 = 12
add similar elements
- 3x - 3 = 12
add 3 to both sides
- 3x - 3 + 3 = 12 + 3
simplify
- 3x = 15
divide both sides by 3
- 3x / 5 = 15 / - 3
simplify
x = - 5
Dilation is a transformation of scaling that requires a center of scaling and a factor of scaling.
Similarity is a relationship between two figures when there is a special transformation that transforms one figure into another.
This transformation can include any combination of rotation, shift and dilation.
That's why a pair of a source and its image after dilation are similar, but not all similar figures can be connected by dilation. For instance, rotation and/or shift transform a figure into another, similar one to the original, but not related through dilation..
