Answer:
b = 1
Step-by-step explanation:
Given the equation is:
- 5b + 2b - (-b) + 7 = 5
We separate the terms of b and the constants. To do that we subtract 7 from both the sides. We get:
- 5b + 2b - (-b) + 7 - 7 = 5 - 7
⇒ - 5b + 2b - (-b) = - 2
Now, simplifying the terms with 'b'.
⇒ -5b + 2b + b = - 2
⇒ (-5 + 2 + 1)b = - 2
⇒ -2b = -2
Dividing both the sides by -2, we get:
b = 1 which is the required answer.
Let
be any integer. Then
In other words:
(1) If
is a multiple of 4, then
.
(2) If dividing
by 4 leaves a remainder of 1, then
, since
for some integer
, and from (1) we know that
(because, obviously,
is a multiple of 4).
(3) If instead you get a remainder of 2, then
. This follows from (1) as well.
.
(4) Finally, if you get a remainder of 3, then
.
Answer: 72 minutes
Step-by-step explanation:
Pipe A can empty the water in 180 minutes = (180/60) =3 hours
Pipe A does 1/ 3 of the job in 1 hour.
Pipe B can empty the water in 120 minutes = (120/60) = 2 hours.
Pipe B does 1/ 2 of thejob in 1 hour.
Together they will do:
1/ 3 + 1/ 2 = 5/6
Together, both pipes will do 5/ 6 of the job in one hour.
To get the total time to completely drain the water will be:
= 60 ÷ 5/6
= 60 × 6/5
= 12 × 6
= 72 minutes
It takes 72 minutes to empty the pool.
Make the length x+4 and the width x and then make a formula x(x+4)=21
then u ll get x^2+4x-21=0 and then solve for x ..... the width is 3
