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!
-3/5 = -6/10
9/10 - 6/10 = 3/10
Let “t” represent the number of minutes Martha exercises each day. If she needs to exercise *at least* 30 minutes, t has to be equal to or greater than 30, so our inequality would be
t ≥ 30
Answer:
D
Step-by-step explanation:
So we are given the limit:

To figure out this limit, we can use direct substitution. Simply substitute 0 for x and then simplify. Therefore:

Therefore, the limit equals 10.