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GenaCL600 [577]
3 years ago
6

Find the surface area of the pyramid shown to the nearest whole number. The base is a regular hexagon.

Mathematics
1 answer:
Fiesta28 [93]3 years ago
8 0
The surface area of the pyramid will be given as follows:
Area of triangles:
A=1/2×base×height
A=1/2×12×18
A=108 m²
Area of 6 triangles is given by:
A=108×6=648 m²

Area of the hexagon:
A=6×1/2×12×6√3
A=374.123m²

Total surface area:
SA=648+374.123
SA=1022.123 m²~1022 m²

Answer: C] 1022 m²

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Solution:

we are given that

f(x+3)=4x+12

we have been asked to find f(x).

we can find the value of f(x) by re-writing the given function in the form of f(x+3) and thereafter we will replace (x+3) by x.

we can re-write the given function as below

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Hence the expression representing f(x) is f(x)=4x+3.

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What is the simplified form of x minus 2 over x squared plus x minus 6divided byx squared plus 5x plus 4 over x plus 4?
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\dfrac{1}{x^2+4x+3}

Step-by-step explanation:

You have asked for the simpilfied form of ...

x-\dfrac{2}{x^2}+x-\dfrac{6}{x^2}+5x+\dfrac{4}{x}+4

That would be ...

\dfrac{7x^3+4x^2+4x-4}{x^2}

We suspect that's not what you meant. Parentheses are required for grouping when you write math expressions in text form. They work best using math symbols instead of words. We think you mean

... ((x -2)/(x^2 +x -6))/((x^2 +5x +4)/(x +4))

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Maybe you want to simplify ...

\displaystyle\frac{\left(\frac{x-2}{x^2+x-6}\right)}{\left(\frac{x^2+5x+4}{x+4}\right)}=\frac{(x-2)(x+4)}{(x-2)(x+3)(x+4)(x+1)}\\\\=\frac{1}{(x+1)(x+3)}=\frac{1}{x^2+4x+3}

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<em>Comment on simplifying rational expressions</em>

Division of fractions works the same whether you're working with numbers or polynomials (or anything else). Dividing by something is the same as multiplying by its inverse (reciprocal).

(a/b)/(c/d) = (a/b)·(d/c)

I learned this as "invert and multiply". I've recently seen it referred to as "copy dot flip", meaning you copy the numerator, use a dot symbol to indicate multipication, then flip the denominator (make its reciprocal) to become what you're multiplying by.

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