Answer:
Personal items=15
Step-by-step explanation:
We are given:
Total number of artifacts = 72.
We are told that 2/3 of total artifacts are shards of pottery.
We are also told that 1/8 of total artifacts are tools.
Now we will find out number of personal items by subtracting combined number of shards of pottery and tools from total number of artifacts.
Therefore, there are 15 personal items.
Answer:
Step-by-step explanation:
The first two steps are for the purpose of eliminating fractions. Doing so results in 4(2x - 5) = 9(x - 2), which is to be solved for x.
Perform the indicated multiplication, obtaining:
8x - 20 = 9x - 18.
Then combine like terms: -2 = x, or
x = -2.
To complete the formal check, substitute -2 for x in the first equation. This results in:
(1/3)(-4 - 5) = (3/4)(-2 -2), or
-3 = -3
... which is obviously true.
Answer:
C.
Step-by-step explanation:
Circumference=PI*diameter
Circumference=3.14*19.5
Circumference=61.23 rounds to 61.2 so the answer is C
Answer:
0
Step-by-step explanation:
Combine like terms, perform the operations with the coefficients of the variable, then write the variable.
10r - 5r + 3r - 8r
= 5r + 3r - 8r
= 8r - 8r
= 0
The volume of a pyramid is V = 1/3 x base length^2 x height
Let X = base length.
We are told the height is 1/2 the length, so height would be 1/2x
Now we have:
972 = 1/3 * x^2 * 1/2x
Simplifying we get:
972 = 1/6x^3
Multiply both sides by 6:
5832 = x^3
Take the cube root of both sides:
x = 18
The length of the base is 18 inches.
The height is 1/2 that, so the height would be 18/2 = 9 inches.
