What is the solution to the equation One-third (x minus 2) = one-fifth (x + 4) + 2? x = 12 x = 14 x = 16 x = 26

Mathematics

1 answer:

Elena L [17]3 years ago

3 0

Answer:

x = 26

Step-by-step explanation:

Given

$\frac{1}{3}$ (x - 2) = $\frac{1}{5}$ (x + 4) + 2

Multiply through by 15 to clear the fractions

5(x - 2) =3(x + 4) + 30 ← distribute and simplify both sides

5x - 10 = 3x + 12 + 30, that is

5x - 10 = 3x + 42 ( subtract 3x from both sides )

2x - 10 = 42 ( add 10 to both sides )

2x = 52 ( divide both sides by 2 )

x = 26

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The base of a right triangle is increasing at a rate of 2 meters per hour and the height is decreasing at a rate of 3 meters per

STatiana [176]

Answer:

dL/dt = - 2,019 m/h

Step-by-step explanation:

L² = x² + y² (1) Where x, and y are the legs of the right triangle and L the hypotenuse

If the base of the triangle, let´s call x is increasing at the rate of 2 m/h

then dx/dt = 2 m/h. And the height is decreasing at the rate of 3 m/h or dy/dt = - 3 m/h

If we take differentials on both sides of the equation (1)

2*L*dL/dt = 2*x*dx/dt + 2*y*dy/dt

L*dL/dt = x*dx/dt + y*dy/dt (2)

When the base is 9 and the height is 22 according to equation (1) the hypotenuse is:

L = √ (9)² + (22)² ⇒ L = √565 ⇒ L = 23,77

Therefore we got all the information to get dL/dt .

L*dL/dt = x*dx/dt + y*dy/dt

23,77 * dL/dt = 9*2 + 22* ( - 3)

dL/dt = ( 18 - 66 ) / 23,77

dL/dt = - 2,019 m/h

6 0

4 years ago

What is the factored form of 6x2 13x 6? (x 4)(x 9) (2x 3)(3x 2) (2x 6)(3x 1) (6x 1)(6x 1).

snow_tiger [21]

Polynomial are expressions. The factored form of the polynomial 6x²+13x+6 is (3x+2)(2x+3).

<h3>What are polynomial?</h3>

Polynomial is an expression that consists of indeterminates(variable) and coefficient, it involves mathematical operations such as addition, subtraction, multiplication, etc, and non-negative integer exponentials.

In order to find the factored form of the given quadratic equation, we will break constant b(13) into two parts such that the sum of the parts is 13, while their product is equal to the product of the constant a(6) and c(6).

Therefore, the solution of the polynomial is,

$6x^2+13x+6\\\\= 6x^2 + 9x + 4x + 6\\\\= 3x(2x+3)+2(2x+3)\\\\=(3x+2)(2x+3)\\$