6 3/4=6*4+3/4=24+3/4=27/4
z/12=27/4
4z=27*12
4z=324
z=81
Answer:
Jimmy has a ratio of 1:20, or 1 page:20 seconds. Carlo has a ratio of 1:30, or 1 page:30 seconds. Jimmy reads at a faster pace than Carlo, as he is able to read a page in 2/3 of the time it takes Carlo.
Step-by-step explanation:
Jimmy reads a page, on average, every 20 seconds.
5 × 60 = 300
300/15 = 20
therefore, one page every 20 seconds
1:20
Carlo reads a page, on average, every 30 seconds.
6 × 60 = 360
360/12 = 30
therefore, one page every 30 seconds
1:30
The solution for the given equations x + 3y = 5 and x - 3y = -1 are x=2 and y=1.
Step-by-step explanation:
The given is,
......................................(1)
....................................(2)
Step:1
By elimination method,
Subtracting Equations (1) and (2),


( - )
(
) + (
) = (
)
= 6
= 1
Step:2
Substitute the value of y in equation (1),

+ ( 3 × 1 ) = 5
= 5-3
= 2
Step:3
Check for Solution,
Substitute the values of x and y in Eqn (1),

2 + ( 3 × 1 ) = 5
5 = 5
Result:
The solution for the given equations x + 3y = 5 and x - 3y = -1 are x=2 and y=1, by elimination method.
Answer:
First, let's recall some usefull information:
- cot(x) = 1/tg(x) = cos(x)/sin(x)
- tan(x) = sin(x)/cos(x)
We also know that:
- cos(x - pi/2) = sin(x)
- sin(x - pi/2) = -cos(x)
Now we can use those relationships and get:
cot(x - pi/2) = cos(x - pi/2)/sin(x -pi/2) = sin(x)/-cos(x) = -tan(x)
So we have verified the identity, and explained step by step why the identity is true.