Answer:
no
Step-by-step explanation:
30 cents < 10 cents/dime × d dimes < 1 dollar × 100 cents/dollar
if d = 10
30 cents < 10 cents/dime × 10 dime < 1 dollar × 100 cents/dollar
30 cents < 10 cents/dime × 10 dime < 1 dollar × 100 cents/dollar
notice how the units bolded all cancel out, just leaving cents
30 cents < 100 cents is NOT < 100 cents
Answer:
The proof is given below.
Step-by-step explanation:
Given the two triangles which are similar we have to prove that the ratio of their angle bisectors and the side or we can say that the ratio of their altitude are proportional.
In ΔABP and ΔDEQ
∠1=∠2 (Given)
∠3=∠4 (each 90°)
By AA similarity rule ΔABP≅ΔDEQ
As if the two triangles are similar then their corresponding sides are proportional
⇒ 
Hence, Corresponding angle bisectors of similar triangles are proportional and their ratio is equal to the ratio of altitude.
Answer:
6.5
Step-by-step explanation:
We can assume that 2 is the smallest integer in the set. That means we would have a minimum of 2 2s. Then the largest integer in the set is 9. Since we can't have more than one 9 (due to the mode of 2), the next largest number we can have is 8. After that would be 7. Then the last digit would be 6. So now the set contains { 2, 2, 6, 7, 8, 9}. To find the median in an even set, we need to take the middle numbers and find the average. In this case, the two numbers are 6 and 7. The average of 6 and 7 is 6.5.
We are given the following functions:
![\begin{gathered} f(x)=7\sqrt[]{x}+6 \\ g(x)=x+6 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20f%28x%29%3D7%5Csqrt%5B%5D%7Bx%7D%2B6%20%5C%5C%20g%28x%29%3Dx%2B6%20%5Cend%7Bgathered%7D)
We are asked to determine the composite function:

The composition of functions is equivalent to:

Therefore, we replace the value of "x" in function "f" for the function "g", therefore, we get:
![(f\circ g)(x)=f(g(x))=7\sqrt[]{x+6}+6](https://tex.z-dn.net/?f=%28f%5Ccirc%20g%29%28x%29%3Df%28g%28x%29%29%3D7%5Csqrt%5B%5D%7Bx%2B6%7D%2B6)
Since we can't simplify any further this is the composition.
Now we are asked to determine the domain of this function. Since we have a square root, the domain must be the values of "x" where the term inside the radical is greater or equal to zero, therefore, we have:

Now we solve for "x" by subtracting 6 from both sides:

Therefore, the domain is:
Answer:

Step-by-step explanation:
Given

Required
Find 

In trigonometry:
If sin(A) = cos(B), then

So, we have:

Collect Like Terms


