Simplify the following: 2x3 - 2x2 - 4x / (over)

Mathematics

1 answer:

Marina86 [1]3 years ago

8 0

$\frac{2x^3-2x^2-4x}{3x^3-12x}$

$\frac{2x.(x^2-x-2)}{3x.(x^2-4}$

$\frac{2}{3}.\frac{x^2-x-2}{x^2-4}$

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A photographer is 6 feet tall and cast a shadow that is 2 feet long. He is photographing a palm tree with a shadow that is 7 fee

Novay_Z [31]

Answer: The height of the tree is 21 feet.

Step-by-step explanation:

Here we can assume that the angle at which the sun impacts the photographer and the tree to be the same angle.

Then we can think in both cases as triangles rectangles, where the height is a cathetus, and the shadow is the other cathetus.

Then we will have a relationship like:

Tg(angle) = shadow/height

height = shadow/Tg(angle)

Now, because for both triangles we have the same angle, then Tg(angle) will be the same number for both cases, and we can just think of it as constant K

Tg(angle) = K

Then we have the equation:

Height = Shadow/K

We know that the photographer is 6ft tall, and his shadow is 2 ft long, we can replace those two things in the above equation and find the value of k:

6ft = 2ft/K

K = 2ft/6ft = (1/3)

Now we know that the shadow of the tree is 7ft long, then the height will be:

height = 7ft/(1/3) = 7ft*3 = 21ft

The tree is 21 ft tall.

6 0

3 years ago

Please help me with number ten and twelve

jasenka [17]

Answer: $93,\ 34^{\circ}$

Step-by-step explanation:

Given

For figure (i) both triangles are congruent

$\therefore 8x-27=4x+33\\\Rightarrow 8x-4x=33+27\\\Rightarrow 4x=60\\\Rightarrow x=15$

$\Rightarrow PQ=8x-27\\\Rightarrow PQ=93$

For figure (ii)

Two triangles WXZ and WZY are congruent

$\therefore 9x-28=5x-8\\\Rightarrow 4x=20\\\Rightarrow x=5^{\circ}\\\Rightarrow \angle YWX=2(9x-28)\\\Rightarrow \angle YWX=2(17)\\\Rightarrow \angle YWX=34^{\circ}$