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Kaylis [27]
3 years ago
6

Define a two column proof

Mathematics
2 answers:
kkurt [141]3 years ago
8 0

Answer:


Step-by-step explanation:


eimsori [14]3 years ago
6 0

Answer: The two-column proof is the method we use to present a logical argument using a table with two columns.



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PLEASE HELP
Tems11 [23]

QUESTION A

The given multiplication problem is

\frac{39}{64} \times \frac{8}{13}

Factor each term to obtain;

\frac{13\times 3}{8\times8} \times \frac{8}{13}

Cancel out the common factors to obtain;

\frac{1\times 3}{8\times1} \times \frac{1}{1}

Simplify to get;

\frac{3}{8}

QUESTION B

The given multiplication problem is

\frac{2}{3}\times \frac{1}{5}\times \frac{4}{7}

This the same as

\frac{2\times 1\times 4}{3\times 5\times 7}

This simplifies to;

\frac{8}{105}

QUESTION C

The given problem is

\frac{3}{5}\times \frac{10}{12} \times \frac{1}{2}

This is the same as

\frac{3}{5}\times \frac{5}{6} \times \frac{1}{2}

=\frac{1}{1}\times \frac{1}{2} \times \frac{1}{2}

This simplifies to

=\frac{1}{4}

QUESTION D.

The given expression is

\frac{4}{9}\times 54

Factor the 54 to obtain;

\frac{4}{9}\times 9\times 6

Cancel the common factors to get;

\frac{4}{1}\times 1\times 6

This simplifies to;

=24

QUESTION E

The given problem is

20\times 3\frac{1}{5}

Convert the mixed numbers to improper fraction to obtain;

=20\times \frac{16}{5}

=4\times5 \times \frac{16}{5}

Cancel the common factors to get;

=4\times1 \times \frac{16}{1}

=64

QUESTION F

The multiplication problem is

11 \times 2 \frac{7}{11}

Convert the mixed numbers to improper fractions to obtain;

11 \times \frac{29}{11}

Cancel out the common factors to get;

=1 \times \frac{29}{1}

Simplify;

=29

QUESTION G

The given problem is

5\frac{1}{3}\times 5\frac{1}{8}

Convert to improper fractions;

=\frac{16}{3}\times \frac{41}{8}

Cancel out the common factors to get;

=\frac{2}{3}\times \frac{41}{1}

=\frac{82}{3}

Convert back to mixed numbers

=27\frac{1}{3}

QUESTION H

The given expression is

10\frac{2}{3} \times 1\frac{3}{8}

Convert to improper fraction to get;

\frac{32}{3} \times \frac{11}{8}

Cancel common factors to get;

=\frac{4}{3} \times \frac{11}{1}

Simplify

=\frac{44}{3}

Convert back to mixed numbers;

=14\frac{2}{3}

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The University of Virginia has an acceptance rate of 24%. Another 20% get waitlisted, and the rest get denied. If you were going
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sStep-by-step explanation:

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This app doesn’t know how to read a picture
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It’s the 3rd one hopefully this helps
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In the first equation in the system of equations, y represents the money collected from selling sweatshirts. In the second equat
NeTakaya

Answer:

The solution x = 229.89 ≅ 230 (since we cannot have a decimal number of sweatshirts)implies that, the money collected from selling sweatshirts equals the money used in producing sweatshirts when 230 sweatshirts have been sold or produced.

Step-by-step explanation:

Here is the complete question

In the first equation in the system of equations, y represents the money collected from selling sweatshirts. in the second equation, y represents the money spent to produce x sweatshirts with team logos on them for a professional sports league.

y=35x; y=-0.05(x-400)²+9,492

what does the solution of the system represent in this context?

Solution

The solution of the system is obtained when both equations are equal. That is y=35x = y=-0.05(x-400)²+9,492 .

So, 35x = -0.05(x-400)² + 9,492.

Expanding the right side, we have

    35x = -0.05(x² - 800x + 160000) + 9492

    35x = -0.05x² -800x × -0.05 + (-0.05) × 160000 + 9492

    35x = -0.05x² +40x - 8000 + 9492

    35x = -0.05x² +40x + 1492

Collecting all the terms to the left side, we have

0.05x² - 40x - 1492 + 35x = 0

0.05x² - 5x -1492 = 0

Using the quadratic formula,

x = \frac{-(-5) +/- \sqrt{(-5)^{2} - 4 X 0.05 X - 1492}  }{2X0.05}   = \frac{5 +/- \sqrt{25 + 298.4}  }{0.1} =  \frac{5 +/- \sqrt{323.4}  }{0.1}\\=  \frac{5 +/- 17.983 }{0.1}\\=  \frac{5 - 17.983 }{0.1}  or  \frac{5 + 17.983 }{0.1}\\= \frac{-12.983 }{0.1} or  \frac{22.983 }{0.1}\\= -129.83 or 229.83

We choose the positive answer x = 229.83. Since we cannot have a decimal number of sweatshirts, we approximate to the nearest whole number. So, x = 229.83 ≅ 230 sweatshirts.

The solution implies that the money collected from selling sweatshirts equals the money used in producing sweatshirts when 230 sweatshirts have been sold or produced.

We confirm that by plugging in x = 229.83 in both equations.

y = 35x = 35(229.83) = 8044.05 ≅ 8044.1

y=-0.05(x-400)²+9,492 = y=-0.05(229.83-400)²+9,492 = y=-0.05(-170.17)²+9,492 = y=-0.05(28,957.8289)+9,492 = -1447.8914 + 9492 = 8044.11 ≅ 8044.1

3 0
3 years ago
Read 2 more answers
How do I explain the steps to the question involving the pie?
jok3333 [9.3K]

Answer:

Area = pi x radius squared

the radius is 2.39 so that's squared  that is 5.7121pi

Step-by-step explanation:

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