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Anit [1.1K]
2 years ago
11

What is x? I am no good at math and am trying to help a friend.

Mathematics
1 answer:
Rainbow [258]2 years ago
4 0

Remark

This one isn't easy. There are a lot of steps.

Step One

Multiply the entire equation through by 4*(x - 1)(x + 2)

4*(x - 1)(x + 2)[1/(x - 1) + 1/(x + 2) = 5/4]

4(x +2) + 4(x - 1) = 5*(x + 2)(x - 1)       If you don't see how I got this step, leave a note. Remove the brackets on the left

4x + 8 + 4x - 4 = 5(x +2)(x - 1)

8x + 4 = 5(x + 2)(x - 1)               Expand the right side. Use FOIL

8x + 32 = 5 (x^2 + 2x  - x - 2)

8x + 32 = 5( x^2 +x - 2)            Remove the brackets on the right.

8x + 32 = 5x^2 + 5x - 10          Subtact 8x + 32  from both sides.

0 = 5x^2 + 5x - 8x - 32 - 10

0 = 5x^2 - 3x - 42

Now you have to factor this mess. You need two numbers that multiply to 5 which can only be 5 and 1. You also need 2 numbers which multiply to 42. That's not so easy. 6 and 7 are your best bet because you need something close to get 3.

It turns out that none of these numbers work. So you have to use the quadratic formula

a = 5

b = - 3

c = - 42

\text{x = }\dfrac{ -b \pm \sqrt{b^{2} - 4ac } }{2a}

\text{x = }\dfrac{ -3 \pm \sqrt{(-3)^{2} - 4(1)(-42)} }{10}

\text{x = }\dfrac{ -3 \pm \sqrt{9 + 840} }{10}

x = 3.12

x = -2.61

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Answer:

7) 28.8 in

8) 80.6 mm

9) 68.3 cm

(All answers to the nearest tenth)

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7) The traingle is a right-angled triangle since the 4 angles of a rectangle are right angles.

Applying Pythagoras' Theorem,

x²= 16² +24²

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8) Applying Pythagoras' Theorem,

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x= 80.6 mm (nearest tenth)

9) See the attached picture for better understanding.

1st picture shows the simplified diagram of the question, indicating where line x lies in the rectangular prism.

Now, if we cut the prism into half diagonally so that we obtain 2 equal triangular prism, we would obtain 2 prisms that look like the one drawn in picture 2.

Now zoom in to the blue face of the prism, we would get a triangle as shown in picture 3.

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y²= 40² +54²

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Look at picture 2 again at focus at the pink shaded triangle. It has been re-drawn in picture 4.

Now we know that y= √4516.

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2 years ago
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