Solve for x 2/3 + x / 3 = 4

Mathematics

1 answer:

Stolb23 [73]3 years ago

8 0

You said . . . . . 2/3 + x/3 = 4

Subtract 2/3 from each side: x/3 = 3-1/3

Multiply each side by 3: 3 · (x/3) = 3 · (3-1/3)

Simplify that mess : x = 10

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Problem:

Consider a rectangle such that the length of the rectangle is 12 more than thrice its width. Find a formula for the length in terms of its width. Take width as 'x'.

Step-by-step explanation:

Consider a rectangle such that the length of the rectangle is 12 more than thrice its width. Find a formula for the length in terms of its width.

Let the width be 'x'.

Therefore, as per question, length is 12 more than thrice the width.

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square: 9 square units
triangle: 24 square units

Step-by-step explanation:

Using a suitable formula the area of a polygon can be computed from the coordinates of its vertices. You want the areas of the given square and triangle.

<h3>Square</h3>

The spreadsheet in the first attachment uses a formula for the area based on the given vertices. It computes half the absolute value of the sum of products of the x-coordinate and the difference of y-coordinates of the next and previous points going around the figure.

For this figure, going to that trouble isn't needed, as a graph quickly reveals the figure to be a 3×3 square.

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<h3>Triangle</h3>

The same formula can be applied to the coordinates of the vertices of a triangle. The spreadsheet in the second attachment calculates the area of the 8×6 triangle.

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<em>Additional comment</em>

We have called the triangle an "8×6 triangle." The intention here is to note that it has a base of 8 units and a height of 6 units. Its area is half that of a rectangle with the same dimensions. These dimensions are readily observed in the graph of the vertices.