Every weekday, mr. jones bikes from his home to his job. sometimes he rides along two roads, the long route that is shown by the solid lines. other times, he takes the shortcut shown by the dashed line.

how many fewer kilometers does mr. jones bike when he takes the shortcut instead of the long route?
6 kilometers
8 kilometers
23 kilometers
32 kilometers

Mr. Jones take 6 km less when he goes by shortcut instead of the long route.

Step-by-step explanation:

We shall use the pythagoras theorem here to solve.

a^2 + 15^2 =17^2

a^2+225=289

a^2=64

a=8

Since a =8, the long route distance is 8+15=23

The short route distance is 17 km

So, (23-17)=6 km.. So Mr. Jones take 6 km less when he goes by shortcut instead of the long route.

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.

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