The definition of similar triangles says that 2 triangles are similar if they have the same shape but different size. There are two criteria to check for this:
1) If all angles in one triangle are equal to the angles in another one, then the 2 are equal.
2) If the sides have the same proportions, then the 2 triangles are similar.
1) We have that all the angles of the 2 triangles have an equal angle in the other triangle. In specific, Q is matched to B, P to A and R to C. Hence, since corresponding angles are congruent, the two triangles are similar.
2) Here we are given information about the sides of the triangles, so we will check the second criterion. We form the ratio of the largest sides of each trangle and the shortest sides. 30/5=6. For the shortest sides, 18/3=6. Finally for the middle sides, 24/4=6. Hence, we have that the triangles are similar since the ratios are equal. (it doesn't matter whether we take the bigger or the smaller side as a numerator, as long as we are consistent).
Step-by-step explanation:
y= 5
x=3
.................
So the -4x is the M and then 6 is the B. So m is the slope and B is the y-intercept. The 6 goes on the y axis and the -4 will be how the line looks. It’ll be rise (-4) over run (1).
1. First, let us define the width of the rectangle as w and the length as l.
2. Now, given that the length of the rectangle is 6 in. more than the width, we can write this out as:
l = w + 6
3. The formula for the perimeter of a rectangle is P = 2w + 2l. We know that the perimeter of the rectangle in the problem is 24 in. so we can rewrite this as:
24 = 2w + 2l
4. Given that we know that l = w + 6, we can substitute this into the formula for the perimeter above so that we will have only one variable to solve for. Thus:
24 = 2w + 2l
if l = w + 6, then: 24 = 2w + 2(w + 6)
24 = 2w + 2w + 12 (Expand 2(w + 6) )
24 = 4w + 12
12 = 4w (Subtract 12 from each side)
w = 12/4 (Divide each side by 4)
w = 3 in.
5. Now that we know that the width is 3 in., we can substitute this into our formula for length that we found in 2. :
l = w + 6
l = 3 + 6
l = 9 in.
6. Therefor the rectangle has a width of 3 in. and a length of 9 in.
Answer: <em>3. The correct option is: A) 3.57 decibels.</em>
<em>6. The correct option is: B)
</em>
Step-by-step explanation:
3. Sound intensity is cut to 44% of its original level. That means, if the original sound intensity was 100, then now sound intensity will be 44.
So,
and 
Using the formula
, we will get.....

<em>(Rounded to the nearest hundredth)</em>
So, the loudness would be reduced by 3.57 decibels.
6. Given expression is: 
First applying the property
, we will get.....

Now using the formula,
, we will get....

Thus, the answer as a single natural logarithm is 