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3 years ago

Solve the equation: 5/6x - 10 = 1/3(x - 15)

Mathematics

1 answer:

Harlamova29_29 [7]3 years ago

4 0

Answer:

X =10

Step-by-step explanation:

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Dada la sucesión an = 1700 + 4,1· n2 + 304,9· n

shutvik [7]

Concluimos que la opción correcta es "Solo II".

Una expresión es una sucesión aritmética si y solo si existe entre dos elementos consecutivos cualesquiera de la serie la misma diferencia. La sucesión aritmética es definida por una expresión de la forma:

$a_{n} = a + b\cdot n$ , $n\in \mathbb{N}$ (1)

Donde $a,b$ son coeficientes de la sucesión.

Asimismo, una expresión es una sucesión geométrica si y solo si entre dos elementos consecutivos cualesquiera de la serie existe la misma razón. La sucesión geométrica es definida por una expresión de la forma:

$a_{n} = a\cdot r^{b\cdot n}$ , $n\in \mathbb{N}$ (2)

Donde $a, b, r$ son coeficientes de la sucesión.

Por último, una expresión es una sucesión monótona creciente si dados dos elementos consecutivos de una serie, el elemento posterior es siempre mayor que el elemento anterior. Matemáticamente, debe satisfacerse la siguiente condición:

$\frac{a_{n+1}}{a_{n}} > 1, n\in \mathbb{N}$ (3)

Esta claro por inspección directa que la sucesión dada no es aritmética ni geométrica y cabe comprobar si es monótona creciente. Valiéndonos de (3), realizamos las operaciones algebraicas pertinentes:

$r = \frac{1700 + 4,1\cdot (n+1)^{2}+304,9\cdot (n+1)}{1700 + 4,1\cdot n^{2}+304,9\cdot n}$

$r = \frac{1700+4,1\cdot (n^{2}+2\cdot n +1) +304,9\cdot (n+1)}{1700 + 4.1\cdot n^{2}+304,9\cdot n}$

$r = \frac{1700+4,1\cdot n^{2}+304,9\cdot n+4,1\dot (2\cdot n +1) +304.9}{1700+4,1\cdot n^{2}+304,9\cdot n}$

$r = 1 + \frac{8,2\cdot n +309}{1700 + 4,1\cdot n^{2}+304,9\cdot n}$

Como puede apreciarse, $r > 1$ . Por tanto, la sucesión es monótona y creciente.

En consecuencia, concluimos que la opción correcta es "Solo II".

Invitamos cordialmente a leer esta pregunta sobre sucesiones: brainly.com/question/21709418

4 0

3 years ago

Joe's summer camp had 81 attendees when it first opened and has grown by 92 attendees per year since then.

pychu [463]

Answer:

A = 92y + 81

Step-by-step explanation:

Because A = number of attendees and if it adds 92 each year, you times the number of years by 92 and add 81 for the ones that were already there

4 0

3 years ago

Please need help please

Marianna [84]

Answer:

D is the correct answer! Hope it hepls!

Step-by-step explanation:

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5 0

4 years ago

You travel from point A to point B in a car moving at a constant speed of 70 km/h. Then you travel the same distance from point

tankabanditka [31]

Answer:

Yes, the average speed for the entire trip from A to C is equal to $80\frac{km}{h}$

Step-by-step explanation:

The average speed of an object is defined as the distance traveled divided by the time elapsed. Velocity is a vector quantity, and average velocity can be defined as the displacement divided by the time. For the special case of straight line motion in the x direction, the average velocity takes the form:

$V_a_v_e_r_a_g_e=\frac{x_2-x_1}{t_2-t_1}=\frac{Δx}{Δt}$

If the beginning and ending velocities for the motion are known, and the acceleration is constant, the average velocity can also be expressed as:

$V_a_v_e_r_a_g_e=\frac{V_1+V_2}{2}$

We Know that:

$V_1=70\frac{km}{h} \\\\V_2=90\frac{km}{h}$

Replacing the values:

$V_a_v_e_r_a_g_e=\frac{70+90}{2} =\frac{160}{2}=80\frac{km}{h}$

5 0

3 years ago

Indicate the equation of the given line in standard form.The line containing the median of the trapezoid whose vertices are R(-1

maxonik [38]

RS => y - 5 = (8 - 5)/(1 - (-1)) (x - (-1))
y - 5 = 3/2 (x + 1) => slope = 3/2
ST => y - 8 = (-2 - 8)/(7 - 1) (x - 1)
y - 8 = -10/6 (x - 1) = -5/3 (x - 1) => slope = -5/3
TU => y - (-2) = (0 - (-2))/(2 - 7) (x - 7)
y + 2 = 2/5(x - 7) => slope = 2/5
UR => y = 5/(-1 - 2) (x - 2)
y = -5/3 (x - 2) => slope = -5/3

The median is the line joining the midpoints of the non-parallel sides.
Midpoint of RS = ((-1 + 1)/2, (5 + 8)/2) = (0, 13/2)
Midpoint of TU = ((7 + 2)/2, -2/2) = (9/2, -1)

Equation of the line joining (0, 13/2) and (9/2, -1) is given by y - 13/2 = (-1 - 13/2)/(9/2) x
y - 13/2 = (-15/2)/(9/2) x
y - 13/2 = -15/9x
18y - 117 = -30x
30x + 18y = 117

7 0

3 years ago