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Alika
18 days ago
9

Andre is setting up rectangle tables for a party. He can fit 6 chairs around a single table. Andre lined up 10 tables end to end

and tries to fit 60 chairs around them, but he is surprised when he cannot fit them all. 1. write an equation for the relationship between the number of chairs c and the number of tables t a. the tables are apart from each other: b. the tables are placed end to end????? plz help I so stuck plzzzz

Mathematics
1 answer:
Zina [9.1K]18 days ago
5 0
When there is one table (t=1), you can place 6 chairs (c=6) around it: 2 along the length of each side and 1 at each end.
With t=2, where the tables are positioned end to end (joined at the width), c=10, that means 4 chairs along each side of the joined tables and 1 chair at each end. Each additional table increases the number of chairs by 4, thus we can express this as c=4t+2, with the constant 2 representing the individual chair at each end. If the tables are spread apart, then c=6t.
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Answer:

c

Step-by-step explanation:

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The number of tropical fish that an aquarium can hold depends on the volume of the fish tank. the interior dimensions of the fis
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<span>To determine the quantity of tropical fish a tank can accommodate, calculate the volume by multiplying length, height, and width to obtain cubic centimeters of the aquarium, then divide that result by 10,000. Hence, 60*50*30 results in 90,000 cubic centimeters. Dividing 90,000 by 10,000 yields 9. Therefore, a tank with these measurements can hold 9 tropical fish.</span>
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Arrange the entries of matrix A in increasing order of their cofactors values
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To ascertain the cofactor of

A=\left[\begin{array}{ccc}7&5&3\\-7&4&-1\\-8&2&1\end{array}\right]

First, eliminate the relevant row and column linked to the specified entries and calculate the determinant of the leftover 2\times 2 matrix while applying alternating signs.


Ac_{11}=\left|\begin{array}{ccc}4&-1\\2&1\end{array}\right|


Ac_{11}=4\times 1- -1\times 2


Ac_{11}=4+ 2

Ac_{11}=6




Ac_{12}=-\left|\begin{array}{ccc}-7&-1\\-8&1\end{array}\right|


Ac_{12}=-(-7\times 1- -1\times -8)


Ac_{12}=-(-7- 8)

Ac_{12}=15




Ac_{21}=-\left|\begin{array}{ccc}5&3\\2&1\end{array}\right|


Ac_{21}=-(5\times 1- 3\times 2)


Ac_{21}=-(5-6)


Ac_{21}=1







A_c{23}=-\left|\begin{array}{ccc}7&5\\-8&2\end{array}\right|


Ac_{23}=-(7\times 2 -8\times 5)


Ac_{23}=-(14-40)


Ac_{23}=26




A_c{31}=\left|\begin{array}{ccc}5&3\\4&-1\end{array}\right|


Ac_{31}=5\times -1 -4\times 3


Ac_{31}=-5-12


Ac_{31}=-17


A_c{33}=\left|\begin{array}{ccc}7&5\\-7&4\end{array}\right|


Ac_{33}=7\times 4- -7\times 5


Ac_{33}=28+35


Ac_{33}=63


Therefore, the entries arranged in increasing order of their cofactors values are;

Ac_{31}=-17,Ac_{21}=1,Ac_{11}=6,Ac_{23}=26,Ac_{12}=15, Ac_{33}=63



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4 days ago
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Question: 2. Musah Stands At The Centre Of A Rectangular Field. He First Takes 50 Steps North, Then 25 Steps West And Finally 50
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Answer:

60.36 steps West from center

85.36 steps North from center

Step-by-step explanation:

Refer to the attached

Musah's starting point and movement are depicted in the image.

  • 1. He moves 50 steps towards the North,
  • 2. Next, he moves 25 steps towards the West,
  • 3. Then he proceeds 50 steps on a bearing of 315°. We now recognize that North is measured at 0°
or 360°, so a bearing of 315° corresponds to North-West 45°.

Note: According to the Pythagorean theorem, a right triangle at 45° with hypotenuse 'a' will have legs equal to a/√2.

What is the distance West of Musah's final position from the center?

25 + 50/√2 ≈ 60.36 steps

What is the distance North of Musah's final position from the center?

  • 50 + 50/√2 ≈ 85.36 steps

7 0
11 days ago
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Response: a) \frac{175}{100}xy\\\\=1.75xy\\\\

b)  The area has grown by 0.75 square meters.

Detailed breakdown:

Let the room's length be l

Let the room's breadth be 'b'

The area of a rectangle is calculated using the formula:

Area=Length\times breadth\\\\Area=l\times b

Per the problem, the room's new area equals 175% of its old area.

Thus, a) The new area of the room is determined as

\frac{175}{100}xy\\\\=1.75xy\\\\

This indicates a 175% increase in the room's length, resulting in a 175% increase in area.

b) The increase in square meters for Megan's room area is

1.75xy-1xy=0.75\\\\\text{So, by 0.75 square meters the new area is increased.}


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