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Ksju [112]
3 years ago
6

A two digit number is 4 times the sum of its digits and twice the product of its digit.FIND THE NUMBER

Mathematics
1 answer:
Dmitrij [34]3 years ago
5 0
X - tenths digit
y - units digit

10x+y=4(x+y)\\
10x+y=2xy\\\\
10x+y=4x+4y\\
10x+y=2xy\\\\
6x=3y\\
10x+y=2xy\\\\
3x=y\\
10x+y=2xy\\\\
10x+3x=2x\cdot3x\\
13x=6x^2\\
6x^2-12x=0\\
6x(x-2)=0\\
x=0 \vee x=2\\\\
y=3\cdot2\\
y=6\\\\
10\cdot2+6=\boxed{26}
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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
Find all missing sides and angles with work
Fed [463]

Answer:

Please see attached picture for full solution.

Right angle= 90°

The sum of all the angles in a triangle is 180°.

3 0
3 years ago
Which of the following is the solution to the inequality below? 2x−4≤12
Afina-wow [57]

Answer:

x   ≤ 8

Step-by-step explanation:

Given

2x - 4 ≤ 12

Isolate the term in x by adding 4 to both sides

2x ≤ 16 ( divide both sides by 2 )

x ≤ 8 ← is the solution

8 0
3 years ago
Read 2 more answers
When five times a number is decreased by 8, the result is 7. What is the number?<br> The number is
kumpel [21]

Answer:

3

Step-by-step explanation:

5x - 8 = 7

5x = 7+8

5x = 15

x = 15 ÷ 5

x = 3

6 0
3 years ago
Someone Help me solve these by substitution please !
PSYCHO15rus [73]
I think the answer is:

X=3

Y=-2
8 0
2 years ago
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