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3 years ago

Dec 23, 8:45:08 PM

Mathematics

1 answer:

Gemiola [76]3 years ago

3 0

Answer:

3, 5, 7

Step-by-step explanation:

Let the first of the three positive consecutive odd numbers be $x$ .

Now, the second odd number = $x+2\\$

And, the third odd number = $x+4$

As per question statement, the multiplication of the first and third odd number is 9 lesser than the 6 times the second integer.

Writing the equation, we get:

$x(x+4) = 6(x+2)-9\\\Rightarrow x^{2} +4x=6x+12-9\\\Rightarrow x^{2} +4x-6x = 3\\\Rightarrow x^{2} -2x - 3=0\\\text{Solving the above equation by factorization method:}\\\Rightarrow x^{2} -3x +x - 3=0\\\Rightarrow x(x -3) + 1(x - 3)=0\\\Rightarrow (x -3) (x+ 1)=0\\\Rightarrow x =3, -1$

As, we got a quadratic equation, so we have two solutions here.

One is positive integer and other one is negative.

So, solution is $x=3$

First number is 3.

Second number is 3 + 2 = 5

Third number is 5 + 2 = 7

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Ostrovityanka [42]

Answer:

6 cm²

Step-by-step explanation:

Since 3 side lengths are given, I assume that this figure is a triangle. The area of a triangle can be determined by using hero's formula.

$\text{Area of triangle} = \sqrt{\text{s(s - a)(s - b)(s - c)}$

⇒ s = Perimeter/2

⇒ a, b, and c = side lenths of triangle

Replacing a, b, and c as the given side lengths:

$\implies \text{Area of triangle} = \sqrt{\text{s(s - 5)(s - 3)(s - 4)}$

Determining the perimeter of the triangle:

$\text{Perimeter of triangle = Sum of it's side lengths}$

$\implies \text{Perimeter of triangle =}\ 5 + 4 + 3$

$\implies \text{Perimeter of triangle =}\ 12 \ \text{cm}$

Determining the half of perimeter:

$\text{Half of perimeter} = s = \dfrac{\text{Perimeter}}{2}$

$\implies s = \dfrac{12}{2}$

$\implies s = 6$

Replacing the value of "s" in the formula:

$\implies \text{Area of triangle} = \sqrt{\text{6(6 - 5)(6 - 3)(6 - 4)}$

Evaluating the area:

$\implies \text{Area of triangle} = \sqrt{\text{6(6 - 5)(6 - 3)(6 - 4)}$

$\implies \text{Area of triangle} = \sqrt{\text{6(1)(3)(2)}$

$\implies \text{Area of triangle} = \sqrt{\text{6(6)}$

$\implies \text{Area of triangle} = 6 \ \text{cm}^{2}$

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Answer to 4.
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3 years ago

The base of a triangle is seven less than twice its height. If the area of the triangle is 100cm^2 find the length of the base

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4 years ago

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How to answer this question

12345 [234]

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3 years ago

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Find constants a and b such that the function y = a sin(x) + b cos(x) satisfies the differential equation y'' + y' − 7y = sin(x)

Elza [17]

The first thing we must do in this case is find the derivatives:
y = a sin (x) + b cos (x)
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Substituting the values:
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We rewrite:
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From here we get the system:
-b-8a = 1
a-8b = 0
Whose solution is:
a = -8 / 65
b = -1 / 65
Answer:
constants a and b are:
a = -8 / 65
b = -1 / 65

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