What is the solution to this equation7x-12x-5= -45+15

Mathematics

1 answer:

balandron [24]3 years ago

6 0

Answer:

-5x-5 = -50

-5x = -45

x = 9

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Please help!! Find BD

Temka [501]

Answer: $8\sqrt{2}$

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Work Shown:

Focus entirely on triangle ABD (or on triangle BCD; both are identical)

The two legs of this triangle are AB = 8 and AD = 8. The hypotenuse is unknown, so we'll say BD = x.

Apply the pythagorean theorem.

$a^2 + b^2 = c^2\\\\c = \sqrt{a^2 + b^2}\\\\x = \sqrt{8^2 + 8^2}\\\\x = \sqrt{2*8^2}\\\\x = \sqrt{8^2*2}\\\\x = \sqrt{8^2}*\sqrt{2}\\\\x = 8\sqrt{2}\\\\$

So that's why the diagonal BD is exactly $8\sqrt{2}\\\\$ units long

Side note: $8\sqrt{2} \approx 11.3137$

6 0

3 years ago

A pole that is 3m tall casts a shadow that is 1.22m long. At the same time, a nearby building casts a shadow that is 38.5m long.

vichka [17]

Refer to the diagram shown below.

The height of the pole is CD (3 m), and its shadow is AB (1.22 m).
The height of the building is h m, and its shadow is AD (38.5 m).

The two triangles ΔABC and ΔADE are similar because of AAA.
Therefore
$\frac{DE}{BC} = \frac{AD}{AB} \\\\ \frac{h}{3} = \frac{38.5}{1.22}$

Cross multiply.
1.22 h = 3*38.5 = 115.5
h = 115.5/1.22 = 140.91 m

Answer: 141 m (nearest meter)