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earnstyle [38]
3 years ago
14

3- A rectangle has an area of 30 square meters arm a perimeter of 34 meters the dimensions , of the rectangle I 9 , a J v ft HA

4, _ friar .7 V .,,. , ( I i . est Practice w square has a perimeter of 28 feet 38 //

Mathematics
1 answer:
Leto [7]3 years ago
4 0
If you are looking for the answer to the question above you have to ask yourself what two numbers multiply to 30 and equal 17 when added up. We halve the perimeter to make this easier. So your answer is 15 and 2 because 15 *2=30. If the sides are 15 and 2 then, 15(2) +2(2)=34. There is your answer. 
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Q.6. The equation of the ellipse whose centre is at the origin and the x-axis, the major axis, which passes
azamat

<h3>Answer:</h3>

Equation of the ellipse = 3x² + 5y² = 32

<h3>Step-by-step explanation:</h3>

<h2>Given:</h2>

  • The centre of the ellipse is at the origin and the X axis is the major axis

  • It passes through the points (-3, 1) and (2, -2)

<h2>To Find:</h2>

  • The equation of the ellipse

<h2>Solution:</h2>

The equation of an ellipse is given by,

\sf \dfrac{x^2}{a^2} +\dfrac{y^2}{b^2} =1

Given that the ellipse passes through the point (-3, 1)

Hence,

\sf \dfrac{(-3)^2}{a^2} +\dfrac{1^2}{b^2} =1

Cross multiplying we get,

  • 9b² + a² = 1 ²× a²b²
  • a²b² = 9b² + a²

Multiply by 4 on both sides,

  • 4a²b² = 36b² + 4a²------(1)

Also by given the ellipse passes through the point (2, -2)

Substituting this,

\sf \dfrac{2^2}{a^2} +\dfrac{(-2)^2}{b^2} =1

Cross multiply,

  • 4b² + 4a² = 1 × a²b²
  • a²b² = 4b² + 4a²-------(2)

Subtracting equations 2 and 1,

  • 3a²b² = 32b²
  • 3a² = 32
  • a² = 32/3----(3)

Substituting in 2,

  • 32/3 × b² = 4b² + 4 × 32/3
  • 32/3 b² = 4b² + 128/3
  • 32/3 b² = (12b² + 128)/3
  • 32b² = 12b² + 128
  • 20b² = 128
  • b² = 128/20 = 32/5

Substituting the values in the equation for ellipse,

\sf \dfrac{x^2}{32/3} +\dfrac{y^2}{32/5} =1

\sf \dfrac{3x^2}{32} +\dfrac{5y^2}{32} =1

Multiplying whole equation by 32 we get,

3x² + 5y² = 32

<h3>Hence equation of the ellipse is 3x² + 5y² = 32</h3>
8 0
3 years ago
If two triangles are congruent, which of the following statements must be true?
PSYCHO15rus [73]

Answer:

The correct options are A, B, C and D.

Step-by-step explanation:

A figure said to be congruent if:

Two figures are said to be congruent if they have same size and same shape.

If two figure are congruent that means the corresponding sides will also be congruent.

If two figure are congruent that means the the corresponding angles will also be congruent.

Now consider the provided option.

By the above definition it is clear that all the options are correct.

Hence, the correct options are A, B, C and D.

7 0
3 years ago
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Answer:

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Step-by-step explanation:

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5 = -1/3(3) + b

5 = -1 + b

6 = b

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