The vol. of a cube of side length s is V=s^3.
So, if the side length is 5a+4b, then the volume of the cube is
V(a, b) = (5a+4b)^3. This could, of course, be expanded, using the binomial theorem, but there's no point in doing so.
When we multiply a whole number with a fraction, we can think of the whole numbers as "over one"...
5 3 5 15
3 * --- = --- * ---- = ----
6 1 6 6
We can further simplify the fraction, by dividing numerator and denominator by 3...
15 15 / 3 5
--- = ------- = ----
6 6 / 3 2
Since this is an improper fraction, we need to turn it into a mixed number...
5 2 + 2 + 1 2 2 1 1 1
---- = -------------- = --- + ---- + --- = 1 + 1 + ---- = 2 --- or 2.5
2 2 2 2 2 2 2
Answer:
m∠LTE = 110
Step-by-step explanation:
1. add up all of the arcs.
2x+3x+4x-8+x-12
2. all of the arcs equal 360
2x+3x+4x-8+x-12=360
3. Find x
10x-20=360, x=38
4. angle LTE is equal to half of the sum of the intercepted arcs.
0.5(arc LE +GF)
5. plug in LE +GF with x
.5(76+144)
Unit price is the price for 1.
9.20/8 = 1.15
Unit price = $1.15
Answer:
(3x + 1) • (3x - 1)
Step-by-step explanation:
Step by Step Solution
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STEP
1
:
Equation at the end of step 1
3
x - 1
STEP
2
:
Trying to factor as a Difference of Squares:
2.1 Factoring: 9x-1
Theory : A difference of two perfect squares, A - B can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A - AB + BA - B2 =
A
- AB + AB - B2 =
A - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 9 is the square of 3
Check : 1 is the square of 1
Check : x is the square of x1
Factorization is : (3x + 1) • (3x - 1)
Final result :
(3x + 1) • (3x - 1)
