Firstly, let's factorise each equation individually - to do this, find 2 numbers that when summed add to the value of the second term, and when multiplied give the value of the third term.
7 and 12 give us 4 and 3 (4+3=7, 4*3=12) -- 8 and 15 give us 5 and 3 (5+3=8, 5*3=15)
Now we can rewrite these equations as (y+4)(y+3) and (y+5)(y+3) respectively.
Putting this in a fraction: (y+4)(y+3)/(y+5)(y+3) -- We can clearly see that there is a y+3 on both sides of the fraction, and given there are no terms outside of the brackets being multiplied, we can directly cancel.
This gives us our final answer:
(y+4)/(y+5)
Given:
The slope of a line is 
.
To find:
The lines in the options are parallel, perpendicular or neither parallel nor perpendicular to the given line.
Solution:
We know that the slopes of parallel lines are equal.
The slope of line Q and the slope of given line are same, i.e., . So, the line Q is parallel to the given line.
The slope of a perpendicular line is the opposite reciprocal of the slope of the line because the product of slopes of two perpendicular lines is -1.
The slope of a line is . It means the slope of the perpendicular line must be 
. So, the line N is perpendicular to the given line.
The slopes of line M and P are neither equal to the slope of the given line nor opposite reciprocal of the slope of the line.
Therefore, the lines M and P are neither parallel nor perpendicular.
Answer: 200 bulbs will not be defective.
Step-by-step explanation:
The ratio of defective bulbs to good bulbs produced each day is 2 to 10. This ratio can also be expressed as 1 to 5 by reducing to lowest terms.
The total ratio is the sum of the proportions.
Total ratio = 1 + 5 = 6
This means that if n bulbs is produced, the number of defective bulbs would be
1/6 × n
The number of non defective would be
5/6 × n
Since n = 240, then the number of bulbs that will not be defective is
5/6 × 240 = 200 bulbs
Answer:
A
Step-by-step explanation:
