Answer:
The carpenter used 2 7/4 feet of plank for the shelf
Step-by-step explanation:
Total length of plank =10 1/2 foot
He used
For Deck board=4 1/4 feet
Step=3 2/3 feet
Shelf=x feet
Total plank=deck board + step + shelf
10 1/2 = 4 1/4 + 3 2/3 + x
Change the fractions
21/2 = 17/4 + 11/3 + x
Add 17/4 + 11/3
21/2 =51+44/12 + x
21/2= 95/12 + x
Collect like terms
21/2 - 95/12 =x
126-95/12 = x
31/12=x
2 7/12 =x
Therefore, the carpenter used 2 7/4 feet of plank for the shelf
Answer:
Step-by-step explanation:
Total length of plank =10 1/2 foot
He used
For Deck board=4 1/4
Step=3 2/3
Shelf=x
Total plank=deck board + step + shelf
10 1/2 = 4 1/4 + 3 2/3 + x
Answer:
See below
Step-by-step explanation:
If an expression is not dependent on x, it simplified form must not contain x. To show that this is the case for (a) and (b) we need to simplify them and assess:
(a)

Indeed, does not depend on x!
And (b)

Again, does not depend on x.
Answer:
580 seedlings altogether.
Step-by-step explanation:
Given that,
Ali plants 40% of the total number of seedlings, Ben plants 45% of the total number of seedlings, and Cliff plants the rest of the seedlings. Cliff plants 87 seedlings.
The percentage of the seedling planted by Cliff = 100% - 45% - 40% = 15%
<em>Let x = the total number of seedlings</em>
<em />
Hence, three boys plant 580 seedlings altogether.
Answer:
k\.
Step-by-step explanation:
The sequence
1, 3, 7, 13, 21, ...
has first-order differences
2, 4, 6, 8, ...
Let
denote the original sequence, and
the sequence of first-order differences. It's quite clear that

for
. By definition of first-order differences, we have

for
, or

By substitution, we have






and so on, down to

You should know that

and we're given
, so

or

Alternatively, since we already know the sequence is supposed to be quadratic, we can look for coefficients
such that

We have



and we can solve this system for the 3 unknowns to find
.