List a pair of numbers that both have 1,2,7 and 14 as a common factor explain how you got your answer

ANSWER:  

A pair of numbers that have 1, 2, 7 and 14 as a common factors are 296 and 592.

SOLUTION:

We need to find a pair of numbers that both have 1, 2, 7 and 14 as a common factor.

Let, both the numbers be x and y.

According to the given information,  

“x” has factors 1, 2, 7 and 14.

So, x = 1 × 2 × 7 × 14 × m

Here, m is any integer. Because, x can also have factors other than 1, 2, 7 and 14.

And, y also has factors 1, 2, 7 and 14.

So, y = 1 × 2 × 7 × 14 × n

Here, m is any integer. I used n, but not m as for x, because y can have other factors unlike m.

Now, x = 296m and y = 296n.

From above, we can say that multiples of 296 will have 1, 2, 7 and 14 as factors.

Let us put m = 1 and n = 2

x = 296 and y = 592

Hence, a pair of numbers that have 1, 2, 7 and 14 as a common factors are 296 and 592.

step-by-step explanation:

∆abc has the points a(1, 7), b(-2, 2), and c(4, 2) as its vertices. formed with the point d(1, 2) as its third vertex, then ∆abd is triangle.

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .