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2 years ago

How many squares will be in case 100?

Mathematics

1 answer:

Thepotemich [5.8K]2 years ago

5 0

Answer:

a(100) = 298 squares

Step-by-step explanation:

It seems to be an arithmetic sequence problem but I'm not quite sure. Here's how I would have solved it:

The general term for an arithmetic sequence is an = a1 + (n - 1) d

the common difference would be case 2 squares - case 1 squares, or 4 - 1 =3

a1 represents the 1st term, which is case 1 or one square.

Now we can just substitute for variable and place in a value for n:

an = 1 + (n - 1)(3)

an = 1 + 3n -3

an = 3n -2

Now, we just set n = 100, so

a(100) = 3 (100) -2

a(100) = 298 squares

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5 x {3 x [9 - (4 + 1)]} + 20 ÷ 4 x 2 =

adell [148]

To solve a problem like this, we need to start with the innermost parenthesis. Doing that, we get to 4+1, evaluating it giving us 5. This turns our expression into 5 x {3 x [9 - 5]} + 20 ÷ 4 x 2.

Now, the innermost parenthesis is 9-5. Evaluating that gives us 4. Our expression is now 5 x {3 x 4} + 20 ÷ 4 x 2.

Once again, we go to the innermost parenthesis and evaluate whatever is there. This turns our expression into <span>5 x 12 + 20 ÷ 4 x 2.

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7 0

3 years ago

Read 2 more answers

Match the expressions with their equivalent simplified expressions.

Tasya [4]

Answer:

$\sqrt[4]{\frac{16x^6y^4}{81x^2y^8}}\rightarrow\frac{2x}{3y}\\\sqrt[4]{\frac{81x^2y^{10}}{81x^6y^6}} \rightarrow\frac{3y}{2x}\\\sqrt[3]{\frac{64x^8y^7}{125x^2y^{10}}}\rightarrow\frac{4x^2}{5y}\\\sqrt[5]{\frac{243x^{17}y^{16}}{32x^7y^{21}}}\rightarrow\frac{3x^2}{2y}\\\sqrt[5]{\frac{32x^{12}y^{15}}{243x^7y^{10}}} \rightarrow\frac{2xy}{3}\\\sqrt[4]{\frac{16x^{10}y^{9}}{256x^2y^{17}}}\rightarrow\frac{x}{2y}$

Step-by-step explanation:

$\sqrt[4]{\frac{16x^6y^4}{81x^2y^8}} =\sqrt[4]{\frac{(2^4)(x^{6-2})(y^{4-8})}{(3^4)}} =\sqrt[4]{\frac{2^4x^4y^{-4}}{3^4}} =\frac{2xy^{-1}}{3}=\frac{2x}{3y}$

$\sqrt[4]{\frac{81x^2y^{10}}{81x^6y^6}} =\sqrt[4]{\frac{(3^4)(x^{2-6})(y^{10-6})}{(2^4)}} =\sqrt[4]{\frac{3^4x^{-4}y^{4}}{2^4}} =\frac{3x^{-1}y^1}{3}=\frac{3y}{2x}$

$\sqrt[3]{\frac{64x^8y^7}{125x^2y^{10}}} =\sqrt[3]{\frac{(4^3)(x^{8-2})(y^{7-10})}{(5^3)}} =\sqrt[3]{\frac{4^3x^6y^{-3}}{5^3}} =\frac{4x^2y^{-1}}{5}=\frac{4x^2}{5y}$

$\sqrt[5]{\frac{243x^{17}y^{16}}{32x^7y^{21}}} =\sqrt[5]{\frac{(3^5)(x^{17-7})(y^{16-21})}{(2^5)}} =\sqrt[5]{\frac{3^5x^{10}y^{-5}}{2^5}} =\frac{3x^2y^{-1}}{2}=\frac{3x^2}{2y}$

$\sqrt[5]{\frac{32x^{12}y^{15}}{243x^7y^{10}}} =\sqrt[5]{\frac{(2^5)(x^{12-7})(y^{15-10})}{(3^5)}} =\sqrt[5]{\frac{2^5x^{5}y^{5}}{3^5}} =\frac{2x^1y^{1}}{3}=\frac{2xy}{3}$

$\sqrt[4]{\frac{16x^{10}y^{9}}{256x^2y^{17}}} =\sqrt[4]{\frac{(2^4)(x^{10-2})(y^{9-17})}{(4^4)}} =\sqrt[4]{\frac{2^4x^{8}y^{-8}}{4^4}} =\frac{2x^{1}y^{-1}}{4}=\frac{x}{2y}$

Thus,

3 0

3 years ago

A packing crate measures 3 feet by 12 feet by 7 feet. what is the area of its smallest side

8090 [49]

The packing crate measures 3 feet by 12 feet by 7 feet (volume). To find the area of the smallest side, multiply the two smaller numbers

3 x 7 = 21

21 feet² is the area of the smallest side

hope this helps

5 0

3 years ago

If you could show the work or an explanation

DanielleElmas [232]

Brenda’s Bottle

3 1/4 = 13/4 in improper fraction form.

13/4*-0.26 = -0.845. This is the difference in the change.

John’s Bottle

2 5/6 = 17/6 in improper form

17/6*-0.21 = -0.595 in difference.

4 0

3 years ago

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Zanzabum

Answer:

4500 inches, check image below

Step-by-step explanation:

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3 years ago