Use the graph at the right to determine whether each system has no solution, one solution, or infinitely many solutions.

Dado dos ángulos complementarios, uno mide (2x + 10) y el otro (x + 20),

rusak2 [61]

Answer:

El valor de x es igual a 20 o x = 20.

Step-by-step explanation:

Lo primero que se debe saber es que dos ángulos complementarios suman un ángulo recto o 90º.

Supongamos que el valor de un ángulo $\\ \alpha$ y un ángulo $\\ \beta$ valen:

$\\ \alpha = 2x + 10$ [1]

$\\ \beta = x + 20$ [2]

Como la suma de $\\ \alpha + \beta = 90$ [3]

Entonces

$\\ \alpha + \beta = (2x + 10) + (x + 20) = 90$

Sumamos los factores comunes entre si:

$\\ (2x + x) + (10 + 20) = 90$

Para la primera expresión debemos recordar que se suman sólo los coeficientes. Así:

$\\ (2 + 1)x + (10 + 20) = 90$

$\\ 3x + 30 = 90$

Para despejar la incógnita x, debemos tener en cuenta que una igualdad no se altera si se suma, se resta, se multiplica o divide un mismo valor a cada lado de ella. Por esta razón, para despejar 3x, lo primero que podemos hacer es sumar -30 a cada lado de la expresión (lo que es igual a restar 30 a cada lado de la misma). Así tenemos:

$\\ 3x + 30 - 30 = 90 - 30$

$\\ 3x + 0 = 90 - 30$

$\\ 3x = 60$

Ahora dividimos cada miembro de la igualdad entre 3 (o multiplicamos cada lado de la igualdad por $\\ \frac{1}{3}$ ):

$\\ \frac{3}{3}x = \frac{60}{3}$

Como sabemos que:

$\\ \frac{3}{3} = 1$

Entonces:

$\\ 1*x = \frac{60}{3}$

$\\ x = \frac{60}{3}$

$\\ x = 20$

De esta manera, el valor de x es igual a 20 o x = 20.

Lo anterior lo podemos comprobar considerando las ecuaciones [1], [2] y [3]. Así tenemos que:

$\\ \alpha = 2x + 10$ [1]

Sustituimos x por el valor de 20:

$\\ \alpha = 2*20 + 10 = 40 + 10 = 50$

$\\ \beta = x + 20$ [2]

Hacemos lo mismo para [2]:

$\\ \beta = 20 + 20$

$\\ \beta = 40$

De esta manera:

$\\ \alpha + \beta = 90$ [3]

$\\ 50 + 40 = 90$

4 0

3 years ago

Evaluate the line integral, where c is the given curve. C xeyz ds, c is the line segment from (0, 0, 0) to (2, 3, 4)

Arada [10]

The value of line integral is, 73038 if the c is the given curve. C xeyz ds, c is the line segment from (0, 0, 0) to (2, 3, 4)

<h3>What is integration?</h3>

It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.

The parametric equations for the line segment from (0, 0, 0) to (2, 3, 4)

x(t) = (1-t)0 + t×2 = 2t

y(t) = (1-t)0 + t×3 = 3t

z(t) = (1-t)0 + t×4 = 4t

Finding its derivative;

x'(t) = 2

y'(t) = 3

z'(t) = 4

The line integral is given by:

$\rm \int\limits_C {xe^{yz}} \, ds = \int\limits^1_0 {2te^{12t^2}} \, \sqrt{2^2+3^2+4^2} dt$

$\rm ds = \sqrt{2^2+3^2+4^2} dt$

After solving the integration over the limit 0 to 1, we will get;

$\rm \int\limits_C {xe^{yz}} \, ds = \dfrac{\sqrt{29}}{12} (e^{12}-1)$ or

= 73037.99 ≈ 73038

Thus, the value of line integral is, 73038 if the c is the given curve. C xeyz ds, c is the line segment from (0, 0, 0) to (2, 3, 4)

Learn more about integration here:

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7 0

2 years ago

Simplify -2√-45 please

algol [13]

Answer:

l-4l+l-3l??

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

What expression is equivalent to (4-x)+3

sattari [20]

The answer would be B

5 0

3 years ago

She used a graphing tool to display the data in a scatter plot, with x representing the number of ice cubes and y representing t

azamat

The glass will contain 89.086 milliliters of juice with 7 ice cubes, using the equation of the line of best fit, y = -29.202x + 293.5.

In the question, we are informed that the equation of the line of best fit, for the, scatter plot with x representing the number of ice cubes and y representing the milliliters of juice is given as y = -29.202x + 293.5.

We are asked to tell how many milliliters of juice will be in a glass with 7 ice cubes based on the line of best fit.

To find the milliliters of juice in the glass with 7 ice cubes, we substitute x = 7, in the equation of the line of best fit, to get a value of y, representing the milliliters of juice in the glass.

Thus,

y = -29.202x + 293.5,

or, y = -29.202(7) + 293.5 {Substituting x = 7},

or, y = -204.414 + 293.5,

or, y = 89.086.

Thus, the glass will contain 89.086 milliliters of juice with 7 ice cubes, using the equation of the line of best fit, y = -29.202x + 293.5.

Learn more about the equation of the line of best fit at

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4 0

2 years ago