From his house, Manuel could drive due north to get to his parents' house or he could drive due east to get to his grandparents' house. It is 6 miles from Manuel's house to his parents' house and a straight-line distance of 10 miles from his parents' house to his grandparents' house. How far is Manuel from his grandparents' house?

The distance is 8 miles.

Step-by-step explanation:

Manuel's house, his parents house, and grandparents house can be expressed as the three vertices of a right angled triangle. Thus, Pythagoras theorem can be applied to determine the distance from Manual's house to that of his grandparents.

Let the distance from Manuel's house to that of his grandparents be represented by x, so that;

= +

= +

100 = + 36

= 100 - 36

   = 64

⇒ x =

      = 8

x = 8 miles

Thus, Manuel's house is 8 miles from his grandparents house.

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

1696 hundred thousand

step-by-step explanation: