Aperson stands 10 meters from a lamppost at night. if the person is 2 meters tall and the lamppost is 6 meters tall, how long is their shadow cast by the lamp?

  5 meters

Step-by-step explanation:

The height of the lamppost above the person is twice the height of the person, so the distance between the lamppost and person is twice the length of the person's shadow. (A diagram can help you see this.)

The person's shadow is (10 m)/2 = 5 m long.

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Check

The tip of the shadow is 15 m from the lamppost, 2.5 times the height of the lamp. The tip of the shadow is also 5 m from the person, 2.5 times the height of the person. The triangles involved are similar.

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

answer: 414,377,008

step-by-step explanation:

just multiply it