Answer:
36.5 inches
Step-by-step explanation:
Given
See attachment for the given data
Required
Which length is closest to 4.2lb
The given data is a linear dataset.
So, we start by calculating the slope (m)
Pick any two corresponding points from the table
So, we have:
So:
The linear equation is then calculated using:
This gives:
Open bracket
To get the length closest to 4.2lb,
we set 
Then solve for x
So, we have:
Collect like terms
Solve for x
The correct answer is C.
Because: 2.9 multiplied by 10 bags equals 29cubic ft and she needs 30 cubic ft. So she would need to buy 11 bags to make sure she has enough sand for the whole thing. 11 x 2.9 = 31.9 which ensures she has enough for the whole thing including extra in case. So you answer would be Answer C.
I'm assuming all of (x^2+9) is in the denominator. If that assumption is correct, then,
One possible answer is 
Another possible answer is 
There are many ways to do this. The idea is that when we have f( g(x) ), we basically replace every x in f(x) with g(x)
So in the first example above, we would have
In that third step, g(x) was replaced with x^2+9 since g(x) = x^2+9.
Similar steps will happen with the second example as well (when g(x) = x^2)
Tan(angle) = opposite leg/ adjacent leg
Tan(30) = x/22
X = 22 * tan(30 )
X = 12.701 feet.
Round as needed
Answer:
12, 13, 14
Step-by-step explanation:
Denote the integers as:
x
x+1
x+2
The sum of their squares, so that would be;
(x^(2)) + (( x + 1 )^(2)) + (( x + 2 )^(2)) = 509
write out the squares
x^2 + x^2 + 2x + 1 + x^2 + 4x + 4 = 509
combine like terms
3x^2 + 6x + 5 = 509
inverse operations
3x^2 + 6x + 5 = 509
-5 -5
3x^2 + 6x = 504
factor
3x^2 + 6x = 504
3 ( x^2 + 2x ) =504
Inverse operations
3 ( x^2 + 2x ) = 504
/3 /3
x^2 + 2x = 168
Factor again
x ( x + 2 ) = 168
At this point, it should be obvious that x is 12 (because 12 * 14 = 168)
So now substitute back into the consecutive numbers
x = 12
x + 1 = 13
x + 2 = 14
