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2 years ago

The length of a rectangle is six times its width. if the perimeter of the rectangle is 140 in , find its area.

1 answer:

4 0

L = 6W ---- the lenght is 6 times its width
P = 2(L + W) = 140
A =?

P = 2(L+W)
P = 2L + 2W
we know that L = 6W so we plug it into the equation
P = 2(6W) + 2W= 140
12W + 2W = 140
14W = 140
W = 140/14
W = 10

Lets plug 10 into the equation L = 6W
L = 6(10)
L = 60

AREA = LW
= 60 * 10
= 600

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Find the solution set of the following equations: 2y=2x+7 X=y+2

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Answer:

The system of equations has no solution.

Step-by-step explanation:

Given the system of equations

2y = 2x+7

x = y+2

solving the system of equations

$\begin{bmatrix}2y=2x+7\\ x=y+2\end{bmatrix}$

Arrange equation variables for elimination

$\begin{bmatrix}2y-2x=7\\ -y+x=2\end{bmatrix}$

Multiply -y+x=2 by 2: -2y+2x=4

$\begin{bmatrix}2y-2x=7\\ -2y+2x=4\end{bmatrix}$

so adding

$-2y+2x=4$

$+$

$\underline{2y-2x=7}$

$0=11$

so the system of equations becomes

$\begin{bmatrix}2y-2x=7\\ 0=11\end{bmatrix}$

0 = 11 is false, therefore the system of equations has no solution.

Thus,

No Solution!

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Answer:

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Explanation:

The figure attached shows the Venn diagram for the given sets.

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From the whole numbers 1 to 15, the multiples of 3 that are factors of 24 are in the intersection of the two sets: 3, 6, and 12.

There are a total of 7 multiples of 24, from 1 to 15.

Then, there are 3 multiples of 3 out of 7 factors of 24, and the probability that the number chosen is a multiple of 3 given that is a factor of 24 is:

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Then, the probability that the number chosen is a factor of 24 given that is a multiple of 3 is:

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