In math, an isometry is a congruent transformation in which the distance (or length) and the angle is preserved or remains the same even after the transformation.
The transformation can be translation, rotation, reflection, etc.
Let us not use this definition of isometry to answer our question, one at a time.
(I) In here, as we can see the distances 10 and 5 and the angle 43 degrees has been preserved. So, <u>this is an isometry.</u>
(II) In here, distances have been halved, so this is<u> not an isometry</u>, even though the angles have been preserved.
(III) In here, the corresponding distances and the angles have been preserved. So, <u>this is an isometry.</u>
The probability of the uppermost faces is 34
Answer:
Here c represents the total number of children in choir.
As per the statement:
Total number of boys in choir = 12
It is also given that: Three sevenths of a children's choir are boys.
⇒ Total number of boys = 
or
By cross multiply we have;
84 = 3c
Divide both sides by 3 we have;
c = 28
Therefore, the total number of children in choir is 28 children
5x + 2y = 7....multiply by -3
-2x + 6y = 9
----------------
-15x - 6y = -21 (result of multiplying by -3)
-2x + 6y = 9
---------------add
-17x = - 12
x = 12/17 or 0.7
5x + 2y = 7
5(12/17) + 2y = 7
60/17 + 2y = 7
2y = 7 - 60/17
2y = 119/17 - 60/17
2y = 59/17
y = 59/17 * 1/2
y = 59/34 or 1.7 when rounded <====
