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S_A_V [24]
3 years ago
6

The area of a triangular block is 64 square inches. If the base of the triangle is twice the height, how long are the base and h

eight of the triangle?
Mathematics
1 answer:
serious [3.7K]3 years ago
3 0

If the base of the triangle is twice the height, then the base would be 42 2/3 and the height would be 21 1/3. You have to divide 64 by 3 to get the height and 64/1.5 to get the base length.

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faust18 [17]

The solutions for ‘x’ are 2 and -5

<u>Step-by-step explanation:</u>

Given equation:

                    12^{x^{2}+5 x-4}=12^{2 x+6}

Since the base on both sides as ‘12’ are the same, we can write it as

                     x^{2}+5 x-4=2 x+6

                     x^{2}+5 x-2 x-4-6=0

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Often, the value of x is easiest to solve by a x^{2}+b x+c=0 by factoring a square factor, setting each factor to zero, and then isolating each factor. Whereas sometimes the equation is too awkward or doesn't matter at all, or you just don't feel like factoring.

<u>The Quadratic Formula:</u> For a x^{2}+b x+c=0, the values of x which are the solutions of the equation are given by:

                       x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}

Where, a = 1, b = 3 and c = -10

                       x=\frac{-3 \pm \sqrt{(-3)^{2}-4(1)(-10)}}{2(1)}

                       x=\frac{-3 \pm \sqrt{9+40}}{2}

                       x=\frac{-3 \pm \sqrt{49}}{2}=\frac{-3 \pm 7}{2}

So, the solutions for ‘x’ are

                       x=\frac{-3+7}{2}=\frac{4}{2}=2

                       x=\frac{-3-7}{2}=\frac{-10}{2}=-5

The solutions for ‘x’ are 2 and -5

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