Solve this simultaneous equation x/2+ y/3=13/6 2x/7-y/4=5/14
1 answer:
9514 1404 393
Answer:
(x, y) = (3, 2)
Step-by-step explanation:
These look like solution using elimination or substitution could be tedious, so we'll use the "cross multiplication" technique for solution. This requires each equation be in general form: ax+by+c = 0.
The first equation can be multiplied by 6 and 13 subtracted.
x/2 +y/3 = 13/6
3x +2y = 13
3x +2y -13 = 0
The second equation can be multiplied by 28 and 10 subtracted.
2x/7 -y/4 = 5/14
8x -7y = 10
8x -7y -10 = 0
Now, an array of coefficients can be constructed. The last column is the same as the first.
Cross-multiplying adjacent columns, we can write the equation ...
1/(3(-7)-8(2)) = x/(2(-10)-(-7)(-13)) = y/(-13(8)-(-10)(3))
1/-37 = x/-111 = y/-74
Solving for x and y, we have ...
x = -111/-37 = 3
y = -74/-37 = 2
The solution is (x, y) = (3, 2).
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Answer:
Hence proved that m∠AOD = m∠BCD.
Step-by-step explanation:
Given:
A Trapezoid with AC and BD as diagonals with O as intersection point to it.
Four angles formed at A and D are equal.
To Prove:
m∠AOD = m∠BCD
Proof:
Consider a Quadrilateral ABCD as trapezoid with diagonals as AC and BD
(Refer the Attachment).
And AB=CD which means the Quadrilateral ABCD isosceles in nature
i.e. angle A=angle D
Now
Consider triangle AOD and triangle BCD
Apply sum of all angles of triangle is 180.
And also
m∠2+∠AOD+m∠3=180
∠AOD=180-m∠2-m∠3..............equation(1)
And for Triangle BCD
m∠BCD=180-m∠3-m∠4,.....................Equation(2)
∠A=∠D................ as Quadrilateral is Isosceles.
i.e.∠2=∠3
That means by transitive property,
∠1=∠4=∠3=∠2
Using this values in above equation(1) we get ,
∠AOD=180-∠3-∠4.......................(3)
Now comparing equation 2 and 3 we get
RHS is equal for both equation that means LHS is also equal .
Therefore ∠AOD=∠BCD
Hence proved.
Option D is correct.
Figures are missing in the question.
The images below shows the missing figures of question.
<h3>Solution:</h3>For congruent figures, we need the same shape, same area, and inverse direction.
Congruent figures have congruency. That seems simple enough, but congruent figures need not be turned the same way or face the same direction to be congruent.
In the case of geometric figures, line segments with the same length are congruent and angle with the same measure are congruent.
In elementary geometry the word congruent is often used as follows. The word equal is often used in place of congruent for these objects.
In this sense, two plane figures are congruent implies that their corresponding characteristics are "congruent" or "equal" including not just their corresponding sides and angles, but also their corresponding diagonals, perimeters, and areas.
The figure in option D satisfies all these conditions. Hence, Option D is correct.
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