What is the smallest integer that can be divided by the product of a prime number and 7 while yielding a prime number?
(a) 7
(b) 14
(c) 24
(d) 28
(e) 35

(D). 28

Step-by-step explanation:

We have been given that the smallest integer that can be divided by the product of a prime number and 7 while yielding a prime number.  

We know that smallest prime is 2. The product of 2 and 7 is 14.

Let us divide our given numbers by 14.

(A) 7.

The quotient is not a integer or prime number.

(B). 14

We know that 1 is not a prime number.

(C) 24.

The quotient is not a integer or prime number.

(D). 28

Since 2 is a prime number, therefore, 28 is the smallest integer that can be divided by the product of a prime number and 7 and yield a prime number.

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

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