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postnew [5]
2 years ago
15

Find all values of x that make the triangles congruent. Explain your reasoning.

Mathematics
1 answer:
RSB [31]2 years ago
3 0

Answer:

x = \frac{4}{5},5

Step-by-step explanation:

If both the triangles ΔABC and ΔBCD are congruent,

Corresponding sides of both the triangles will be proportional.

\frac{AB}{BD}=\frac{AC}{CD}

\frac{5x}{3x+10}=\frac{5x-2}{4x+3}

5x(4x + 3) = (5x - 2)(3x + 10)

20x² + 15x = 15x² + 50x - 6x - 20

20x² + 15x = 15x² + 44x - 20

20x² - 15x² = 44x - 15x - 20

5x² = 29x - 20

5x² - 29x + 20 = 0

5x² - 25x - 4x + 20 = 0

5x(x - 5) - 4(x - 5) = 0

(5x - 4)(x - 5) = 0

x=\frac{4}{5},5

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Find the percent of the area under the density curve where x is more than 3. <br>​
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Answer:

The percent of the area under the density curve where x is more that 3 is 25 %.

Step-by-step explanation:

Since the density curve is a linear function, the area under the curve can be calculated by the geometric formula for a triangle, defined by the following expression:

A = \frac{1}{2}\cdot (x_{f} - x_{o})\cdot  (y_{f}-y_{o}) (1)

Where:

A - Area, in square units.

x_{f} - x_{o} - Base of the triangle, in units.

y_{f} - y_{o} - Height of the triangle, in units.

The percent of the area is the ratio of triangle areas under the density curve multiplied by 100 per cent, that is:

x = \frac{\frac{1}{2}\cdot (5-3)\cdot (0.25) }{\frac{1}{2}\cdot (5-1)\cdot (0.5) }\times 100\,\%

x = 25\,\%

The percent of the area under the density curve where x is more that 3 is 25 %.

7 0
3 years ago
Add (13x – 4) and (–6x + 15)
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7x + 11

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