Which veal represents the functions ?

Si a los lados de un cuadrado se le aumenta en 3 y 5 m respectivamente la superficie del nuevo rectangulo es 440m .Encontrar el

Ivahew [28]

Answer:

El lado del cuadrado inicial es 17 m.

Step-by-step explanation:

El área de un rectángulo se calcula a partir de los dos lados diferentes. Siendo a y b el valor de ambos lados, el área de la figura es el producto de los dos lados contiguos del rectángulo.

A los lados de un cuadrado se le aumenta en 3 y 5 m respectivamente la superficie del nuevo rectángulo es 440 m². Siendo x el lado del cuadrado inicial, entonces el área del rectángulo se puede expresar como:

(x+3)*(x+5)= 440 m²

Resolviendo:

x*x + 5*x + 3*X + 3*5= 440

x² + 8*x + 15=440

x² + 8*x + 15 -440= 0

x² + 8*x -425= 0

Una función cuadrática de la forma a*x² + b*x + c= 0 se puede resolver mediante la expresión:

$\frac{-b+-\sqrt{b^{2}-4*a*c } }{2*a}$

En este caso, a=1, b=8 y c=425. Reemplazando:

$\frac{-8+-\sqrt{8^{2}-4*1*(-425) } }{2*1}$

Resolviendo:

$\frac{-8+\sqrt{8^{2}-4*1*(-425) } }{2*1}= \frac{-8+\sqrt{64+1700} }{2*1}= \frac{-8+\sqrt{1764 } }{2}= \frac{-8+42 }{2}= \frac{34}{2} = 17$

y

$\frac{-8-\sqrt{8^{2}-4*1*(-425) } }{2*1}= \frac{-8-\sqrt{64+1700} }{2*1}= \frac{-8-\sqrt{1764 } }{2}= \frac{-8-42 }{2}= \frac{-50}{2} = -25$

Como las longitudes no pueden ser negativas, el lado del cuadrado inicial es 17 m.

3 0

2 years ago

I’m not sure how to do this

Brums [2.3K]

Answer: lim as x → -5 of f(x) and g(x) = 300

Domain of f(x) and g(x) is All Real Numbers

f(-5) = 200

g(-5) = 300

Step-by-step explanation:

The limit of f(x) as x approaches -5:

$f(x) =\dfrac{4x^3+500}{x+5}\\\\\\.\qquad =\dfrac{4(x^3+125)}{x+5}\\\\\\.\qquad =\dfrac{4(x^3+5^3)}{x+5}\qquad \text{we can factor the cubic}\\\\\\.\qquad =\dfrac{4(x+5)(x^2-5x+25)}{x+5}\\\\\\.\qquad =4(x^2-5x+25)\\\\\\\text{as x approaches -5, f(x) = }4[(-5)^2-5(-5)+25]\\\\.\qquad \qquad \qquad \qquad \qquad =4(25 + 25 + 25)\\\\.\qquad \qquad \qquad \qquad \qquad =4(75)\\\\.\qquad \qquad \qquad \qquad \qquad =300$

The limit of g(x) as x approaches -5:

g(x) = 4x² - 20x + 100

= 4(-5)² - 20(-5) + 100

= 100 + 100 + 100

= 300

There is a restriction at x = -5 for f(x), however, that discontinuity has been filled with the 200 at x = -5. So the domain is ALL REAL NUMBERs.

There are no restrictions on x for g(x) so the domain is ALL REAL NUMBERs.

5 0

2 years ago

9. Jack is learning to save, spend, and give his money away to charities. He has determined to give 10% of his summer job earnin

Kamila [148]

Answer:

$2560

Step-by-step explanation:

if 10%=256

then 10 times the amount 100% is 2560

4 0

2 years ago

What are the solutions to the quadratic equation x2 - 16 = 0?

enot [183]

X=4 x=-4 Due to the difference in squares theorem

7 0

3 years ago

After a holiday dinner, there are 3 1/3 apple pies left and 2 5/6 pumpkin pies left.

leonid [27]

Hi! I'm pretty sure this is correct so here it goes:
A. 3/6
B. 12 4/6

4 0

2 years ago