The denominator of the first term is a difference of squares, such that
4<em>a</em> ² - <em>b</em> ² = (2<em>a</em>)² - <em>b</em> ² = (2<em>a</em> - <em>b</em>) (2<em>a</em> + <em>b</em>)
So you can write the fractions as
(4<em>a</em> ² + <em>b</em> ²)/((2<em>a</em> - <em>b</em>) (2<em>a</em> + <em>b</em>)) - (2<em>a</em> - <em>b</em>)/(2<em>a</em> + <em>b</em>)
Multiply through the second fraction by 2<em>a</em> - <em>b</em> to get a common denominator:
(4<em>a</em> ² + <em>b</em> ²)/((2<em>a</em> - <em>b</em>) (2<em>a</em> + <em>b</em>)) - (2<em>a</em> - <em>b</em>)²/((2<em>a</em> + <em>b</em>) (2<em>a</em> - <em>b</em>))
((4<em>a</em> ² + <em>b</em> ²) - (2<em>a</em> - <em>b</em>)²) / ((2<em>a</em> - <em>b</em>) (2<em>a</em> + <em>b</em>))
Expand the numerator:
(4<em>a</em> ² + <em>b</em> ²) - (2<em>a</em> - <em>b</em>)²
(4<em>a</em> ² + <em>b</em> ²) - (4<em>a</em> ² - 4<em>ab</em> + <em>b</em> ²)
4<em>ab</em>
<em />
So the original expression reduces to
4<em>ab</em> / ((2<em>a</em> - <em>b</em>) (2<em>a</em> + <em>b</em>))
or
4<em>ab</em> / (4<em>a</em> ² - <em>b</em> ²)
upon condensing the denominator again.
Based on the above, the Triangle XYZ and ACB are known to be similar triangles since tanX = tanA = 5 over 2 and 5 tenths;
Hence:
<h3>What is the triangle about?</h3>
From the question given; Triangle XYZ is known to have been dilated by a scale factor of 2 to form a type of triangle known as triangle ACB, So therefore, XYZ and ACB are known to be the same or similar triangles.
Since Angles Y and C are known to both measure 90 degrees, and angles A and X are said to be congruent. Therefore:
tanX = tanA = 5 over 2 and 5 tenths
AC = 2 x XY
CB = 2 x YZ
For part B:
cosX=Base/Hypotenuse
cos A=AC/AB
AC = 2.05
AB = 5.59
Therefore, Based on the above, the Triangle XYZ and ACB are known to be similar triangles since tanX = tanA = 5 over 2 and 5 tenths;
Hence:
Learn more about triangles from
brainly.com/question/27517432
#SPJ1
Answer:
9) A
10) B
11) A
12) D
13) C
14) A
15) C
16) D
17) E (not sure, can't see full choice)
18) B
19) C
Explanation:
Hope this is what you're looking for friend :)
Answer:
102.5 g
Step-by-step explanation:
The mass is the sum of the values indicated by the sliders:
100 g + 0 g + 2.5 g = 102.5 g
The answer is Strong Positive
