Abook shelf is 2 feet long. each book on the shelf is 5/8 inches wide. how many books will fit on the shelf?

we will need four cases and a bookend

Step-by-step explanation:

STEP 1 - How many books fit on 1 shelf?

We divide 2%263%2F4 feet by 1%2F4 feet.

We could use fractions, or decimals.

We could even transform both measurements to inches.

The result is that 2%263%2F4 feet divided by 1%2F4 is 11 exactly.

It divides evenly, so we can fit 11 books per shelf, tightly packed, with no room to spare.

Calculation using fractions:

2%263%2F4=2%2B3%2F4=8%2F4%2B3%2F4=11%2F4 (transforming mixed number into improper fraction)

11%2F4�1%2F4=11%2F4�4%2F1=11

Calculation using decimals:

If we know that 2%263%2F4=2.75

and we know that 1%2F4=0.25

and we can use a calculator, it is to divide

2.75%2F0.25=11

If we prefer to measure in inches we would think that

the shelf width is 33 inches

and each book is 3 inches wide,

so we divide 33%2F3=11 to find that 11 books fit on each shelf.

STEP 2 -How many shelves will be used?

We divide the 35 books into piles of 11 books.

We find that we can make 3 piles of 11 books, and we will have 2 books left over.

We will need highlight%284%29 shelves (and a bookend).

Three (3) shelves could have 11 books (full shelves),

but you need at least one more shelf, for a total of 4 shelves.

If the first 3 shelves are filled with 11 books each,

the fourth shelf could hold the remaining 2 books.

Or you could arrange the books differently, but you need at least 4 shelves.

The calculation:

1 pile = 1 x 11 books = 11 books

2 piles = 2 x 11 books = 22 books

3 piles = 3 x 11 books = 33 books

4 piles = 4 x 11 books = 44 books

Obviously, we can make 3 piles of 11 books, and we will have 2 books left over.

35 - 33 = 2

The teacher would say that 35 divided by 11 is 3 with a remainder of 2.

When we do long division, we do exactly the calculations above.

THE WRONG WAY:

Someone could figure that 35 books at 1%2F4 foot per book require

35%281%2F4%29=35%2F4 feet of shelf space.

Then, dividing the space needed by the space per shelf,

35/4 feet divided by 2%263%2F4 feet,

that person could find that 3&2/11 shelves are needed,

and round up to 4 shelves.

The result is the same in this case, but the approach is wrong,

because if the measures of book and shelf width were different,

you might find a number of shelves that could not hold the books,

unless we cut some of the books in pieces.

New! FREE algebra solver that shows work:

3x-x+2=4

the value of x is 9 ⇒ answer b

step-by-step explanation:

* we can solve this problem using cosine and sine rule

- in δ abc

∵ ab = 36 , bc = 28 , ac = 16

- lets find the measure of angle b using the cosine rule

∵ cos b = [ab² + bc² - ac²]/2(ab)(bc)

∴ cos b = [36² + 28² - 16²]/2(36)(28)

∴ cos b = 19/21

∴ m∠b = cos^-1(19/21) ≅ 25°

- lets find the measure of angle a using the sine rule

∵ sina/bc = sinb/ac = sinc/ab

∴ sina/28 = sin25°/16 ⇒ by using cross multiplication

∴ sina = 28 × sin25°/16

∴ sina = 0.7396

∴ m∠a = sin^-1(0.7396) ≅ 48°

- from the figure m∠abd = m∠dbc

∵ m∠abc = 25°

∴ m∠abd = 25°/2 = 12.5°

- in δabd

∵ m∠a = 48° , m∠abd = 12.5°

∵ the sum of the measures of the interior angles of any δ is 180°

∴ m∠adb = 180° - (48° + 12.5°) = 119.5°

∵ ab = 36

∵ ad = x

- use the sine rule to find x

∵ sin∠adb/ab = sin∠abd/x

∴ sin119.5°/36 = sin12.5°/x ⇒ by using cross multiplication

∴ x = 36 × sin12.5°/sin119.5° = 8.95 ≅ 9

* the value of x is 9

the ratios are reciprocals im positive

step-by-step explanation:

they are all positive numbers so it wouldn't be the other ones