Answer:
The answer is cosx cot²x ⇒ the first answer
Step-by-step explanation:
∵ cot²x = cos²x/sin²x
∵ secx = 1/cosx
∴ cot²x secx - cosx = (cos²x/sin²x)(1/cosx) - cosx
= (cosx/sin²x) - cosx
Take cosx as a common factor
∴ cosx[(1/sin²x) - 1] ⇒ use L.C.M
∴ cosx[1-sin²x/sin²x]
∵ 1 - sin²x = cos²x
∴ cosx(cos²x/sin²x) = cosx cot²x
They hiked 2.02 kilometers in all because 1.08 + 0.94 = 2.02
In 12 days, Wendy will do the both again.
Step-by-step explanation:
Given,
Wendy goes to gym every 4 days
Wendy swims every 6 days
We will find the least common multiple of both the numbers in order to determine the number of days in which she will do both.
4 = 4,8,12,16,20,....
6 = 6,12,18,24,.....
Therefore;
The least common multiple of 4 and 6 is 12.
Thus,
In 12 days, Wendy will do the both again.
Keywords: multiples, LCM
Learn more about multiples at:
#LearnwithBrainly
Call the notebooks x, and the pencils y.
<span>3x + 4y = $8.50 and 5x + 8y = $14.50 </span>
<span>Then just solve as simultaneous equations: </span>
<span>3x + 4y = $8.50 </span>
<span>5x + 8y = $14.50 </span>
<span>5(3x + 4y = 8.5) </span>
<span>3(5x + 8y = 14.5) </span>
<span>15x + 20y = 42.5 </span>
<span>15x + 24y = 43.5 </span>
<span>Think: DASS (Different Add, Similar Subtract). 15x appears in both equations so subtract one equation from the other. Eassier to subtract (15x + 20y = 42.5) from (15x + 24y = 43.5) </span>
<span>(15x + 24y = 43.5) - (15x + 20y = 42.5) = (4y = 1) which means y = 0.25. </span>
<span>Then substitue into equation : </span>
<span>15x + 20y = 42.5 </span>
<span>15x + 5 + 42.5 </span>
<span>15x = 42.5 - 5 = 37.5 </span>
<span>15x = 37.5 </span>
<span>x = 2.5 </span>
<span>15x + 24y = 43.5 </span>
<span>15(2.5) + 24(0.25) </span>
<span>37.5 + 6 = 43.5 </span>
<span>So x (notebooks) are 2.5 ($2.50) each and y (pencils) are 0.25 ($0.25) each.</span>
Answer:
M=5
Step-by-step explanation:
2 ( 2m ) + 4 ( 4m + 2 ) = 108
step 1. do distributive property
4m + 16m + 8 = 108
step 2. add 4m and 16m and subtract 8 from 108
20m = 100
step 3. divide 100 by 20
m = 5
