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?

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

or

Part B) The dimensions are and

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

or

Part D) and

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

but

so

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

so

The area of the rectangle is equal to

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

The dimensions are

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

------>

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

so

Solve the quadratic equation

The formula to solve a quadratic equation of the form is equal to

in this problem we have

so

substitute in the formula

The value of x is equal to

the dimensions are

The ratio of blue marbles to red marbles is 35:15. To test his hypothesis in the best way, he should make sure that the total number of marbles he draws is 100. In other words, both sides of the ratio added together should equal 100. Right now, both sides equal 50 (35 + 15 = 50). To get to 100, double both sides of the ratio. Now, the ratio is 70:30. Based on the 50 marbles Sam drew, there are 70 blue marbles and 30 red marbles, meaning Sam's hypothesis is incorrect, and there are more blue marbles than red.