Answer:
11,12
Step-by-step explanation:
when calculated, the square root is 11.7473401245, which is between the two integers, 11 and 12!
Hope this helps!
Answer:
Step-by-step explanation:
Yes, you are correct.
From the image, we can see 3 triangles, the large triangle and the two triangles that make the larger triangle.
All 3 of these triangles are similar since they're angle measurements are the same (can be proven by geometry).
We can gather the following information from the given information.
- The largest triangle (the one made up of two triangles) has a hypotenuse of 3+9=12, and a leg length of x. The hypotenuse to leg ratio is 12/x
- The second largest triangle has a hypotenuse length x and leg length 9. The hypotenuse to leg ratio is x/9
We know the hypotenuse to corresponding leg ratio must be equal since these two triangles are similar. Thus, we have the equation:
12/x = x/9
Using the cross product property gives us:
x² = 9 × 12
x² = 108
Taking the square root of both sides gives us:
x = √108
= 6 √3
Thus, your answer is correct. Great job!
Let me know if you need any clarifications, thanks!
Since the order matters Person A and B can be chosen as AB (A pres B vice pres) or BA (B president A Vice president)
When the order matters we are talking about permutations. How many permutations of 11 taken 2 at a time are there.
It can be written like this 11nPr 2
It means start at 11 and multiply by the next lower number
11 x 10 = 110 ways they can choose.
Extension of the concept:
If there had been three positions President, Vice President, and Treasurer
then it would be 11nPr3 or 11 x 10 x 9
Once again the answer to your problem is 110.
