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3 years ago

What is the length X?

Mathematics

2 answers:

dolphi86 [110]3 years ago

5 0

X = 2 cm

You need to use the Pythagorean theorem starting with the triangle on the far left and progressively moving to the right. (Comment if you want further explanation)

jenyasd209 [6]3 years ago

5 0

Answer:

2 cm

Step-by-step explanation:

First you use Pythagorean theorem in solving the triangle closest to the bottom. You would get the square root of two. Then you use Pythagorean theorem again on the second triangle and receive the answer of the square root of three you do the Pythagorean theorem again and receive the answer of the square root of four. Simplify that and get 2 cm.

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Last question please

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Let's try an make a formula to make things easy.

_________________________________________________

Look at Andrew's pattern, it goes up 6 every time. Lets look at the 6 times table

6 times table: 6, 12, 18, 24, ...

____________________________________

First think, how would you work out the 7th term in the 6th times table?

You would do 6 times 7.

So the formula for the 6th times table is:

6n (where n is the term you want to find out)

_______________________________________

So to get the 9th term in the 6 times table, you would replace the n with 9, like so:

9th term in 6 times table = 6 x 9 = 54

______________________________________

Now lets compare the 6 times table to Andrew's pattern:

6 times table: 6, 12, 18, 24,

Andrew's pattern: 3, 9, 15, 21,

_____________________________________

If you look, you can see that Andrew's pattern is the 6 times table minus 3!

So what would be the formula for Andrew pattern?

---> it would be: 6n - 3 (since it's the 6 times table but minus 3)

_____________________________________

We can use this formula to easily work out the 20th term in Andrew's pattern!:

20th term = 6 x 20 - 3 = 120 - 3 = 117 (remember, replace the n with 20)

______________________________________

Now let's make a formula for Ben's pattern!

Ben's pattern goes up in 5s, so lets compare it to the 5 times table:

5 times table: 5, 10, 15, 20

Ben's pattern: 3, 8, 13, 18,

The formula for the 5 times table is 5n, and Ben's pattern is the 5 times table but minus 2.

So the formula for Ben's pattern is: 5n - 2

__________________________________

Now swap out the n for 20 (to get the 20th term):

20th term = 5 x 20 - 2 = 100 - 2 = 98

_________________________________________

So Andrew's 20th term is 117, and Ben's 20th term is 98.

All we do now is subtract them to find the difference:

117 - 98 = 19

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Answer:

Ben's 20th term is smaller by 19!

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3 years ago