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erma4kov [3.2K]
3 years ago
8

If x = 8 units, y = 3 units, and h = 10 units, find the area of the trapezoid shown above using decomposition.

Mathematics
2 answers:
kondaur [170]3 years ago
8 0
If by decomposition you mean breaking it ino parts then

break it itno 2 triangles and 1 rectangle

left to right

triangle with base y and height h
h=10
y=3
area of traignel=1/2bh
aera=1/2(10)(3)
area=5(3)
area=15

rectangel of legnth x and height h
area=legnth timwe width
x=8
h=10
area=8 times 10
aera=80


last triangle
should be same as other sinces same base (y) and same height (h)
15

add
15+80+15=120
goldfiish [28.3K]3 years ago
5 0
A = ¹/₂h(b₁ + b₂)
A = ¹/₂(10)(3 + 14)
A = 5(22)
A = 110 units²

The answer is A.
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\frac{1}{5}x -  \frac{2}{3} y = 30  \\

Putting the value of Y = 15

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If f(x) = 2x^3 - 14x^2 + 38x -26 and x-1 is a factor of f(x) find all of the zeros of f(x) algebraically.
Anestetic [448]

Answer:

Step-by-step explanation:

First confirm that x = 1 is one of the zeros.

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=========================

next perform a long division

x -1  || 2x^3 - 14x^2 + 38x - 26 || 2x^2 - 12x + 26

          2x^3 - 2x^2

          ===========

                    -12x^2 + 28x

                     -12x^2 +12x

                     ==========

                                  26x -26

                                  26x - 26

                                 ========

                                      0

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The discriminate of the quadratic is negative. (36 - 4*1*13) = - 16

So you are going to get a complex result.

x = -(-6) +/- sqrt(-16)

     =============

                 2

x  = 3 +/- 2i

f(x) = 2*(x - 1)*(x - 3 + 2i)*(x - 3 - 2i)

The zeros are

1

3 +/- 2i

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_________________________________________________________

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