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Minchanka [31]
4 years ago
14

Allyson has 4.5 pieces of rope to use for a tire swing. If each full piece is 2 2/3 feet long, how much rope does Allyson have i

n all?
Mathematics
1 answer:
Scorpion4ik [409]4 years ago
6 0

Answer:

12 feet

Step-by-step explanation:

4.5 pieces of rope = 9/2 pieces in fractions

Also, 2 2/3 can be rewritten as 8/3 in fractions

So, 9/2 *8/3 = 72/6 = 12 feet

Allyson has 12 feet of rope in all.

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Select the correct answer. Which matrix represents this system of equations? -2y + 7z = 10 9x + 5y = 1 2x + z = -5
Stells [14]

Answer:

In matrix form this can be represented as

\left[\begin{array}{ccc}0&-2&7\\0&5&0\\2&0&1\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}10\\1\\5\end{array}\right]



Step-by-step explanation:

The given equations are

-2y + 7z = 10

9x + 5y = 1

2x + z = -5

Which can be written as

0x+-2y + 7z = 10

9x + 5y+0z = 1

2x +0y+ z = -5

In matrix form this can be represented as

\left[\begin{array}{ccc}0&-2&7\\0&5&0\\2&0&1\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}10\\1\\5\end{array}\right]



When we multiply the above matrices we get the given set of equations.

In multiplying the matrices we check the no of columns of the first matrix and the number of rows of the second matrix. If they are equal ( as in this case they are 3) then the matrices can be multiplied .

The answer has the number of rows equal to the number of rows of the first matrix and the number of columns equal to the number of columns of the second matrix which is true in this case.

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3 years ago
6-8x=7x-9x+12<br><br> x = ??
Snezhnost [94]

Answer:

x = -1

Step-by-step explanation:

<u>Step 1:  Combine like terms on the right side </u>

6 - 8x = 7x - 9x + 12

6 - 8x = -2x + 12

<u>Step 2:  Add 8x to both sides </u>

6 - 8x + 8x = -2x + 12 + 8x

6 = 6x + 12

<u>Step 3:  Subtract 12 from both sides </u>

6 - 12 = 6x + 12 - 12

-6 = 6x

<u>Step 4:  Divide both sides by 6 </u>

-6 / 6 = 6x / 6

-1 = x

Answer:  x = -1

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3 years ago
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How to find the sides of a 45 45 90 triangle when given the hypotenuse?
Vlada [557]
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