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Komok [63]
3 years ago
11

What is ​ BC ​ ? Enter your answer in the box. units

Mathematics
1 answer:
Vladimir79 [104]3 years ago
6 0

Answer:

BC = 25

Step-by-step explanation:

AB = AC since it is an isosceles triangle

4x+1 = 2x+23

subtract 2x from each side

4x-2x+1 = 2x-2x+23

2x +1 = 23

subtract 1 from each side

2x+1 -1 = 23-1

2x = 22

divide by 2

2x/2 =22/2

x =11

BC = 3x-8

BC = 3(11) -8

BC =33-8

BC = 25


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Answer:

\frac{140}{3}, \frac{140}{3}, \frac{140}{3}

Step-by-step explanation:

Let the numbers be x, y\ and\ z.

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z = 140 -x - y

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f(x,y,z) = xyz

Substitute z = 140 -x - y in f(x,y,z) = xyz

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f_x=140y - 2xy - y^2

f_y=140x - x^2 - 2xy

Since the products are maximum, then f_x = f_y = 0

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y(140 - 2x - y) = 0

Split

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140x - x^2 - 2xy = 0

---------------------------------------------------

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---------------------------------------------------

Substitute y = 140 - 2x

140x - x^2 - 2xy = 0

140x - x^2 - 2x(140 - 2x) = 0

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Re-arrange

4x^2 -x^2 +140x - 280x = 0

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Factor x out

x(3x - 140) = 0

Divide through by x

3x - 140 = 0

3x = 140

x = \frac{140}{3}

Recall that: y = 140 - 2x

y = 140 - 2 * \frac{140}{3}

y = 140 - \frac{280}{3}

Take LCM

y = \frac{140*3-280}{3}

y = \frac{140}{3}

Recall that:

z = 140 -x - y

z = 140 - \frac{140}{3} - \frac{140}{3}

Take LCM

z =  \frac{3 * 140- 140 - 140}{3}

z =  \frac{140}{3}

Hence, the numbers are:

\frac{140}{3}, \frac{140}{3}, \frac{140}{3}

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