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dimulka [17.4K]
3 years ago
9

A piece of paper is in the shape of a rectangle. The piece of paper is 1 5/8 inches (in.) wide and 8 3/4 in. long. A student cut

s the piece of paper in the following order: The student cuts off inch from the width. The student cuts off inch from the length. The student cuts the remaining piece of paper into 12 equally long pieces of paper. What is the area of each of the 12 equally long pieces of paper? Explain your answer completely and show all your work. Include in your explanation an equation you can use to find the area of each of the 12 equally long pieces of paper.
Mathematics
1 answer:
PolarNik [594]3 years ago
7 0

Answer:

.403645833 square inches

Step-by-step explanation:

1 5/8-1 equals 5/8

8.75-1 equals 7.75

7.75/12 equals .6458

.6458 times 5/8 equals .4 square inches

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2(8r+5)-3=4(4r-1)+11 is it an only solution or a no solution or infinite solution
pogonyaev

Answer:

Infinitely many solutions.

Step-by-step explanation:

Let's begin by carrying out the indicated multiplications, which must be done before any addition or subtraction:

2(8r+5)-3=4(4r-1)+11  becomes  16r + 10 - 3 = 16r - 4 + 11.

Subtracting 16r from both sides, we get 10 - 3 = - 4 + 11, or 7 = 7

This is always true, so we can conclude that this equation has infinitely many solutions.

3 0
3 years ago
Factor completely:<br>64 - y^3
madam [21]
From your equation, you can see that you have a difference of two cubes (aka two cubes being subtracted): 64, which is 4^{3}, and y^{3}.

There is rule for the difference of two cubes:
The difference of two cubes is equal to the difference of the cube roots times a binomial, which is the sum of the squares of the roots plus the product of the roots.

That sounds pretty confusing, but it's much easier to understand when put mathematically. Let's say our two cubes are a^{3} and b^{3}. The difference of those two cubes is:
a^{3} - b^{3} = (a - b)( a^{2} + ab + b^{2})

In our problem, a = 4 (since a^{3} = 64) and b = y (since b^{3} = y^{3}. Plug these values into the rule to find the factor of 64 - y^3:
64 - y^3 \\&#10;= (4 - y)( 4^{2} + 4y + y^{2}) \\&#10;=  (4 - y)( 16 + 4y + y^{2})

-----

Answer: (4 - y)( 16 + 4y + y^{2})

8 0
3 years ago
three bags of packing peanuts are used to fill 2 boxes.how many bags of packing peanuts does each box use?between which two whol
igomit [66]
3/2 = 1.5
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6 0
3 years ago
Read 2 more answers
Factoring trinomials<br> Select two for each
JulijaS [17]

Answer:

x² - 3x - 10 = (x - 5) (x + 2)

x² - 3x - 18 = (x + 3) (x - 6)

Step-by-step explanation:

<u>x² - 3x - 10</u>

x² + 2x - 5x - 10

x(x + 2) - 5(x + 2)

(x - 5) (x + 2)

<u>x² - 3x - 18</u>

x² - 6x + 3x - 18

x(x - 6) + 3(x - 6)

(x + 3) (x - 6)

<u>-TheUnknown</u><u>S</u><u>cientist</u>

4 0
2 years ago
A line passes through the point, (−8,7) and has a slope of −5/4. Please help...
o-na [289]

Answer:

5x + 4y + 12 = 0

Step-by-step explanation:

Start with the point-slope equation of a straight line:  y - k = m(x -  h):

Here we are given the point (h, k):  (-8, 7) and the slope m = -5/4.  Inserting this info into the equation give above, we get:        y - 7 = (-5/4)(x + 8).

We must put this equation into "standard form" Ax + By + C = 0.

Multiply all three terms by 4 to remove fractions:  4y - 28 = -5(x + 8), or

4y - 28 + 5x + 40 = 0

Rearranging these terms, we get 5x + 4y + 12 = 0, which is the desired equation in standard form.

8 0
3 years ago
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