Answer:
The answer is:
![\frac{6r-5q}{r^2-q^2}](https://tex.z-dn.net/?f=%5Cfrac%7B6r-5q%7D%7Br%5E2-q%5E2%7D)
which agrees with the last answer option (D) in the list.
Step-by-step explanation:
In order to add rational expressions, we need to express them with the same denominator. Therefore we examine what factors there are in the first denominator, which happens to be a difference of squares which is readily factored out as:
![r^2-q^2=(r+q)\,(r-q)](https://tex.z-dn.net/?f=r%5E2-q%5E2%3D%28r%2Bq%29%5C%2C%28r-q%29)
the second denominator consists of only one of these factors:
, then in order to express both rational expressions with the same common denominator, we multiply numerator and denominator of the second fraction by the factor: ![(r-q)](https://tex.z-dn.net/?f=%28r-q%29)
Then we get two expressions that can be easily added as shown below:
![\frac{r}{(r+q)\,(r-q)} +\frac{5\,(r-q)}{(r+q)\,(r-q)} =\frac{r+5(r-q)}{(r+q)(r-q)} =\frac{r+5r-5q}{(r+q)\,(r-q)} =\frac{6r-5q}{r^2-q^2}](https://tex.z-dn.net/?f=%5Cfrac%7Br%7D%7B%28r%2Bq%29%5C%2C%28r-q%29%7D%20%2B%5Cfrac%7B5%5C%2C%28r-q%29%7D%7B%28r%2Bq%29%5C%2C%28r-q%29%7D%20%3D%5Cfrac%7Br%2B5%28r-q%29%7D%7B%28r%2Bq%29%28r-q%29%7D%20%3D%5Cfrac%7Br%2B5r-5q%7D%7B%28r%2Bq%29%5C%2C%28r-q%29%7D%20%3D%5Cfrac%7B6r-5q%7D%7Br%5E2-q%5E2%7D)
Answer:
B. 1 / 4
Step-by-step explanation:
Step 1: We can turn 2 yards into 6 feet.
Step 2: Then we can turn 6 feet into 72 inches.
Step 3: We plug it into the ratio, getting 18 / 72.
Step 4: Simplify. We get 1 / 4 as the answer. Therefore, we choose B.
Answer:
Base at the top should be the same length, thus 20ft.
right triangle thus 90 degrees angle.
180 - 90 - 40 = 50
20ft/sin50 = Height/sin40
Height of the traffic light = 16.78
16.78 + the height of Andrew eyes ( 5ft) = 21.78
Answer:
5 1/8
Step-by-step explanation: