Question. 7 Let abc be a three-digit number. Then, abc + bca + cab is not divisible by (a) a + b + c (b) 3 (c) 37 (d) 9

D. 9

Step-by-step explanation:

Let

abc=100a+10b+c

bca=100b+10c+a

cab=100c+10a+b

abc + bca + cab=(100a+10b+c) + (100b+10c+a) + (100c+10a+b)

=100a + 10b + c + 100b + 10c + a + 100c + 10a + b

Collect like terms

=100a + a + 10a + 10b + 100b + b + c + 10c + 100c

=111a + 111b + 111 c

Factorise

=111(a+b+c)

abc + bca + cab = 111(a+b+c)

Factors of 111(a+b+c)= 1, 3, 37, 111, and (a+b+c)

abc + bca + cab is divisible by a+b+c because it is a factor of 111(a+b+c)

abc + bca + cab is divisible by 3 because 3 is a factor of 111(a+b+c)

abc + bca + cab is divisible by 37 because 37 is a factor of 111(a+b+c)

abc + bca + cab is not divisible by 9 because 9 is not a factor of 111(a+b+c)

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.