Mathematics, 30.06.2019 12:00 kaylallangari549

Aun cuadrado se le aumenta 7 cm de largo y 3 de ancho con lo que se forma un rectángulo cuya área ¿cuáles en las dimensiones del rectángulo construido? ¿si las medidas de las dimensiones del rectángulo cambian aunmentando en 6 de largo del cuadrado y en 3 el ancho del cuadrado cuál será el área del nuevo rectángulo? ¿el área que encontraste del rectángulo anterior se iguala a cuarenta, encuentra la medida de los lados?

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Answer from: sajasolo3467

The question in English

A) A square is increased by 7 cm in length and 3 cm in width, forming a rectangle whose area is...

B) What are the dimensions of the constructed rectangle?

C) If the measures of the dimensions of the rectangle change joining in 6 of length of the square and in 3 the width of the square what will be the area of the new rectangle?

D) The area you found of the previous rectangle equals forty, does it find the measure of the sides?

Part A) the area of the rectangle is equal to

A=(x+7)(x+3) or $A=x^{2} +10x+21$

Part B) The dimensions are Length=x+7 and Width=x+3

Part C) the new area of the rectangle is equal to

A=(x+6)(x+3) or $A=x^{2} +9x+18$

Part D) $Length=8\ units$ and $Width=5\ units$

Step-by-step explanation:

Let

x------> the length of the original square

y--------> the width of the original square

we know that

the area of a square is equal to

A=xy

but

x=y

$A=x^{2}$

Part A) A square is increased by cm in length and cm in width

x=x+7

y=x+3

The area of the rectangle is equal to

A=(x+7)(x+3)

$A=x^{2} +3x+7x+21$

$A=x^{2} +10x+21$

Part B) What are the dimensions of the constructed rectangle?

The dimensions are

Length=x+7

Width=x+3

Part C) If the measures of the dimensions of the rectangle change joining in of length of the square and in the width of the square what will be the area of the new rectangle?

The new dimensions will be

Length=x+6

Width=x+3

A=(x+6)(x+3)

$A=x^{2} +3x+6x+18$ ------> $A=x^{2} +9x+18$

Part D) The area you found of the previous rectangle equals forty, does it find the measure of the sides?

$A=x^{2} +9x+18$

$A=40\ units^{2}$

$x^{2} +9x+18=40$

$x^{2} +9x-22=0$

Solve the quadratic equation

The formula to solve a quadratic equation of the form $ax^{2} +bx+c=0$ is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$x^{2} +9x-22=0$

$a=1\\b=9\\c=-22$

substitute in the formula

$x=\frac{-9(+/-)\sqrt{9^{2}-4(1)(-22)}} {2(1)}$

$x=\frac{-9(+/-)\sqrt{169}} {2}$

$x=\frac{-9(+/-)13} {2}$

$x=\frac{-9+13} {2}=2$

$x=\frac{-9-13} {2}=-11$

The value of x is equal to $x=2\ units$

the dimensions are

$Length=x+6=2+6=8\ units$

$Width=x+3=2+3=5\ units$

Answer from: Quest

hi! i think the answer is 1/2 : )

Answer from: Quest

First step is to get rid of the square root. remember that a square root is the same as raising to the (1/2) power. see below: $\sqrt{\frac{ {72x}^{16} }{ {50x}^{{{36} }}}} = \frac{ { \sqrt{72}x}^{ {16}^{ (\frac{1}{2}) } } }{ { \sqrt{50} x}^ {{36}^{ (\frac{1}{2}) } }}$ multiply exponents per exponent rules to get: $\frac{ { \sqrt{72}x}^{8} }{ { \sqrt{50}x}^{18} }$ remember you subtract exponents from the denominator and add exponents in the numerator so: $\sqrt{ \frac{72}{ 50}} \times ( {x}^{(8 - 18) } ) = \sqrt{ \frac{36}{25} } \times ( {x}^{ - 10} )$ simplify further: $\frac{6}{5} {x}^{ - 10} = \frac{6}{5 {x}^{10} }$ so a is the correct choice. if you don't understand this google exponent rules and it will you understand. look at the image results.
Plz hurrywhat is the simplified form of ? assume x ≠ 0.

Plz hurrywhat is the simplified form of  ? assume  x  ≠ 0.

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Aun cuadrado se le aumenta 7 cm de largo y 3 de ancho con lo que se forma un rectángulo cuya área ¿...

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