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WITCHER [35]
4 years ago
14

At a garage sale, all of the prices of the items sold were different. If the price of a radio sold at the garage sale was both t

he 15th highest price and the 20th lowest price among the prices of the items sold, how many items were sold at the garage sale?
Mathematics
1 answer:
NISA [10]4 years ago
4 0

Answer:34

Step-by-step explanation:

Given

radio Price is 15 th highest i.e. there are 14 other items ahead of it

It is also given that it is 20 th lowest Price among the prices

i.e. there 19 other items below it therefore there are total

14+19+1=34 items in the garage sale

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The expression cube root of 54x^8y^12 can be written in simplest radical form as
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Answer:

The simplest radical form of the cubic root is 3x^2y^4\sqrt[3]{2x}

Step-by-step explanation:

Cube root of 54x^8y^12

That is:

\sqrt[3]{54x^8y^12}

Can be simplified as:

\sqrt[3]{54x^8y^12} = \sqrt[3]{54}\sqrt[3]{x^8}\sqrt[3]{y^12}

We find each separate simplification, and multiply them:

Cubic root of 54:

54 = 2*3^3

So

\sqrt[3]{54} = \sqrt[3]{2*3^3} = 3\sqrt[3]{2}

Cubic root of x^8

\sqrt[3]{x^8} = \sqrt[3]{x^6*x^2} = x^2\sqrt[3]{x^2}

Cubic root of y^12

\sqrt[3]{y^{12}} = y^4

Multiplying all these terms:

\sqrt[3]{54}\sqrt[3]{x^8}\sqrt[3]{y^12} = 3\sqrt[3]{2}(x^2\sqrt[3]{x^2})(y^4) = 3x^2y^4\sqrt[3]{2x}

The simplest radical form of the cubic root is 3x^2y^4\sqrt[3]{2x}

4 0
3 years ago
Robert is lying on the ground, looking at the top of a flagpole. The angle of elevation to the top of the flagpole is 25°. What
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hope this helps you

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3 years ago
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Line g passes through points (5, 9) and (3, 2). Line h passes through points (9, 10) and (2, 12). Are line g and line h parallel
icang [17]

For this case we find the slopes of each of the lines:

The g line passes through the following points:

(x_ {1}, y_ {1}) :( 3,2)\\(x_ {2}, y_ {2}) :( 5,9)

So, the slope is:

m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {9-2} {5-3} = \frac {7} {2}

Line h passes through the following points:

(x_ {1}, y_ {1}) :( 9,10)\\(x_ {2}, y_ {2}) :( 2,12)

So, the slope is:

m = \frac {y_ {2} -y_ {1}}{x_ {2} -x_ {1}} = \frac {12-10} {2-9} = \frac {2} {- 7} = - \frac {2} {7}

By definition, if two lines are parallel then their slopes are equal. If the lines are perpendicular then the product of their slopes is -1.

It is observed that lines g and h are not parallel. We verify if they are perpendicular:

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Answer:

The lines are perpendicular.

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3 years ago
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