Answer:
The length of one side of the jewelry box is 8 inches
Step-by-step explanation:
we know that
The volume of a cube is equal to
where
b is the length side of the cube
In this problem we have
substitute in the equation and solve for b
so
In the figure p || q...
1 answer:
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To model and solve our situation we are going to use the equation: 
where
is speed
is distance
is time
1. We know that the distance between the cities is 2400 miles, so
. We also know that the speed of the plane is 450 mi/h. Since we don't know the speed of the air, 
. We don't know how much the westward trip takes, so 
, and we also don't know how much the eastward trip takes, so 
.
Going westward. Here the plane is flying against the air, so we need to subtract the speed of the air from the speed of the plane:
Going eastward. Here the plane is flying with the the air, so we need to add the speed of the air to the speed of the plane:
2. We know for our problem that the round trip takes 11 hours; so the total time of the trip is 11,
. Notice that we also know that the total time of the trip equals time of the tip going westward plus time of the trip going eastward, so 
. Since we know that the total trip takes 11 hours, we can replace that value in our total time equation and solve for 
:
Now we can replace in our going westward equation to model our round trip with a system of equations:
equation (1)
equation (2)
3. To solve our system of equations, we are going to solve for
in equations (1) (2):
From equation (1)
equation (3)
From equation (2):
equation (4)
Replacing (4) in (3)
Now, we can solve for
to find the speed of the wind:
Since speed cannot be negative, the solution of our equation is:
We can conclude that the speed of the wind is 78 mph.
where
1. We know that the distance between the cities is 2400 miles, so
Going westward. Here the plane is flying against the air, so we need to subtract the speed of the air from the speed of the plane:
Going eastward. Here the plane is flying with the the air, so we need to add the speed of the air to the speed of the plane:
2. We know for our problem that the round trip takes 11 hours; so the total time of the trip is 11,
Now we can replace
3. To solve our system of equations, we are going to solve for
From equation (1)
From equation (2):
Replacing (4) in (3)
Now, we can solve for
Since speed cannot be negative, the solution of our equation is:
We can conclude that the speed of the wind is 78 mph.
Hey there :)
Let us translate the sentences to mathematics for ease!
A 3-digit number
Ones digit → ( let p represent is )
Hundreds digit is four more than ones digit → ( 4 + p )
Tens digit is twice hundreds digit → 2 ( 4 + p ) = 8 + 2p
Sum of the digits is 12
↓
Hundreds digit + Tens digit + Ones digit = 12
( 4 + p ) + ( 8 + 2p ) + p = 12
Combine like terms
4 + 8 + p + p + 2p = 12
12 + 4p = 12
Take 12 to the opposite side { Do subtraction when you see addition }
12 ( - 12 ) + 4p = 12 - 12
4p = 0
Divide by 4 on either side
p = 0
( 4 + 0 ) + ( 8 + 2 ( 0 ) ) + ( 0 )
The number is 480
Check
Hundreds + Tens + Ones = 12
4 + 8 + 0 = 12
12 = 12
Let us translate the sentences to mathematics for ease!
A 3-digit number
Ones digit → ( let p represent is )
Hundreds digit is four more than ones digit → ( 4 + p )
Tens digit is twice hundreds digit → 2 ( 4 + p ) = 8 + 2p
Sum of the digits is 12
↓
Hundreds digit + Tens digit + Ones digit = 12
( 4 + p ) + ( 8 + 2p ) + p = 12
Combine like terms
4 + 8 + p + p + 2p = 12
12 + 4p = 12
Take 12 to the opposite side { Do subtraction when you see addition }
12 ( - 12 ) + 4p = 12 - 12
4p = 0
Divide by 4 on either side
p = 0
( 4 + 0 ) + ( 8 + 2 ( 0 ) ) + ( 0 )
The number is 480
Check
Hundreds + Tens + Ones = 12
4 + 8 + 0 = 12
12 = 12