This is a classic example of a 45-45-90 triangle: it's a right triangle (one angle of 90) & two other sides of the same length, which means two angles of the same length (and 45 is the only number that will work). With a 45-45-90 triangle, the lengths of the legs are easy to determine:
45-45-90
1-1-sqrt2
Where the hypotenuse corresponds to sqrt2.
Now, your hypotenuse is 10.
To figure out what each leg is, divide 10/sqrt2 (because sqrt2/sqrt2 = 1, which is a leg length in the explanation above).
Problem: you can't divide by radicals. So, we'll have to rationalize the denominator:
(10•sqrt2)/(sqrt2•sqrt2)
This can be rewritten:
10sqrt2/sqrt(2•2)
=10sqrt2/sqrt4
=10sqrt2/2
=5sqrt2
Hope this helps!!
When it says to estimate, I always think of doing it by hand to show work. So set it up like this:
96
<u>x 34</u>
So follow it out multiplying across 4*6 and 4*9 carrying over as needed to get it to look like this:
96
<u>x 34</u>
384
Do the same for the 3 to get this:
96
<u>x 34</u>
384
2880
Add 384+2880=3264
Your final answer is 3,264
The appropriate choice is ...
... On Line 3, Brianna should have divided by 0.1 instead of subtracting 0.1.
_____
Had Brianna simplified her effort properly on line 4, she would have
... -0.1 +0.1x = -1.4
putting her essentially back where she started—with a 2-step equation.
Probability=blue marbles/total marbles
Probability=5/10=1/2
If you draw from the bag twice...
Probability = 1/2 x 1/2 = 1/4
answer: 1/4
41/3/5
Purple.
Maybe this will help:
calculate the mass of the sun
and then divide this. maybe you will get it next time.
