The volume of a rectangular prism is its length times width times height, or algebraically,

. You may be used to computing volume with numbers, but remember, a variable is a stand-in for a number. So you can solve this in the same way. Substitute

into the formula for volume. You get

, and you multiply these factors together. As you would with ordinary fractions, multiply the numerators and denominators across. You get

. It seems that the book wants you to simplify by bringing the 6 up to the denominator. Recall the rule

, if n is non-negative. The opposite applies so that

. For your final answer, you write

. This corresponds to
answer choice B.
Answer:
f(x) = 1.5x - 0.5x
Step-by-step explanation:
The function of the pattern represented by the pentagonal numbers is the sum of three triangular numbers.
The triangular number general formula
x (x + 1) / 2
For example,
The sequence
1, 3, 6, 10
*
* * *
* * * * * *
* , * *, * * *, * * * *
_____________________________
The pentagonal numbers
The sequence:
1, 5, 12, 22, 35
As shown in the picture can be divided into three triangles
Triangle 2
x (x + 1) / 2
Triangle 1 and 3 (they are triangles one unit smaller than 2)
n (n + 1) / 2
n= x-1
Replacing n
(x-1) ((x-1) + 1) / 2
(x-1) (x) / 2
(x-1) x / 2
______________
Function represents the pattern
Triangle 2 + (Triangle 1 + Triangle 3)
Triangle 1 = Triangle 3
So then,
Triangle 2 + 2* Triangle 1
x (x +1) /2 + 2* (x -1) x/2
Rearranging
0.5 x (x +1) + x(x -1)
0.5x^2 + 0.5x + x^2 -x
(0.5 x^2 + x^2) + (0.5x -x )
1.5 x^2 - 0.5 x
______
Answer:
3
Step-by-step explanation:
Standard form is written in the order of the exponent <em>on</em><em> </em><em>a</em><em> </em><em>variable</em> from highest to lowest.
#1 exponents go 2, 1 , then zero. So, this is standard form.
#2 exponents go 2 then zero, so this is standard form.
#3 exponents go 1 then 2 then zero, so this is <em><u>not</u></em> in standard form.
#4 exponents go 3 to 2 to 1, so this is still in standard form.
hope this helps!
The width of a room can be from around 15 cm to about 40 cm.
meaning 1 m
and about less than 1/6 of a km
Hope it helped!
We have that
x²<span>-20x
</span><span>Group
terms that contain the same variable
</span>(x²-20x)
Complete
the square
(x²-20x+10²)------> (x-10)²
the answer is
the number must be 100