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Tom [10]
3 years ago
13

If ABCD is a rectangle, calculate x as a function of α

Mathematics
2 answers:
shusha [124]3 years ago
7 0

Answer:

x = 90 - 2α

Step-by-step explanation:

Solution:-

- Consider the right angled triangle " ABD ". The sum of angles of an triangle is always "180°".

                       < BAD > + < ADB > + < ABD > = 180°

                       < ABD > = 180 - 90° - α

                        < ABD > = 90° - α

- Then we look at the figure for the triangle "ABE". Where " E " is the midpoint and intersection point of two diagonals " AC and BD ".

- We name the foot of the perpendicular bisector as " F ":  " BF " would be the perpendicular bisector. The angle < BAE > is equal to < ABD >.

                    < ABD > = < BAE >  = 90° - α   ... ( Isosceles triangle " BEA " )

Where, sides ( BE = AE ).

- Use the law of sum of angles in a triangle and consider the triangle " BFA " as follows:

                     < ABF> + < BFA > + < BAF > = 180°

                     < ABF > = 180 - (90° - α) - 90°

                    < ABF > = α  

Where,       < BAF > = < BAE >

- The angle < ABD > = < ABE > is comprised of two angles namely, < ABF > and < FBE >  = x.

                        < ABD > = < ABE > = < ABF > + x

                         90° - α = α + x

                        x = 90 - 2α   ... Answer

Yanka [14]3 years ago
4 0

Answer:

Step-by-step explanation:

The length of this triangle is 10 squares

and the width is 4 squares

The diagonals divide the rectangle into four triangles

These traingles are isoceles

Each two triangles facing each others are identical

<B = 90 degree

B = alpha + Beta

Let Beta be the angle next alpha

The segment that is crossing Beta is its bisector since it perpendicular to the diagonals wich means that:

Beta = 2x

Then B = alpha + 2x

90 = alpha +2x

90-alpha = 2x

x = (90-alpha)/2

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ehidna [41]

Answer:

The planning value for the population standard deviation is of 4330.

Step-by-step explanation:

Uniform probability distribution:

The uniform probability distribution has two bounds, a and b. The standard deviation is given by:

S = \sqrt{\frac{(b-a)^2}{12}}

Annual starting salaries for college graduates with degrees in business administration are generally expected to be between 20000 and 35000.

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Which of the following statements is true?
sdas [7]

Answer:

Option The product of (-x+4)(x^2+3x-3) is

-x^3+x^2+15x-12 is correct.

That is (-x+4)(x^2+3x-3)=-x^3+x^2+15x-12

Step-by-step explanation:

Given expression is (-x+4)(x^2+3x-3)

To find the product of the given expression :

(-x+4)(x^2+3x-3)

( By using the distributive property each term in the factor is multiplied by each term in the another factor )

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=-x^3+x^2+15x-12

Therefore (-x+4)(x^2+3x-3)=-x^3+x^2+15x-12

Therefore Option The product of

(-x+4)(x^2+3x-3) is -x^3+x^2+15x-12 is correct.

That is (-x+4)(x^2+3x-3)=-x^3+x^2+15x-12

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