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sasho [114]
3 years ago
14

Solve five and six eighths plus four and four fifths.

Mathematics
1 answer:
pickupchik [31]3 years ago
7 0

Answer:

Two and three fourtieths.

Step-by-step explanation:

5 6/8 + 4 4/5

= 46/8 + 24/5

= 83/40

= 2 3/40

Two and three fourtieths(2 3/40) is the answer.

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Leonhard wants to place a triangular-based cabinet in the corner of his rectangle-shaped living room. The triangular base has a
almond37 [142]

Answer:

A. x=\frac{-7+\sqrt{193}}{4}

Step-by-step explanation:

We have, the dimensions of the living room are 30 ft and 20 ft.

Thus, area of the living room = length × width = 30 × 20 = 600 ft².

Now, it is given that the cabinet takes 6% of the living room i.e. 6% of 600 ft² = 0.06 × 600 = 36 ft².

As, the triangle has dimensions (2x+3) ft and (3x+6) ft.

So, the area of the triangle = \frac{1}{2}\times base\times height

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i.e. Area of cabinet = \frac{3}{2}\times (2x^2+7x+6)

Since, the cabinet takes 6% of the living room, we have,

\frac{3}{2}\times (2x^2+7x+6) = 36

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Further, as the solution of a quadratic equation ax^{2}+bx+c=0 is given by x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}

On comparing we have, a=2, b=7, c= -18.

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i.e. x=\frac{-7\pm \sqrt{193}}{4}

i.e. x=\frac{-7+\sqrt{193}}{4} and x=\frac{-7-\sqrt{193}}{4}

So, according to the options, we have,

A. x=\frac{-7+\sqrt{193}}{4} is the correct value of x.

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