Rania solves the equation below by first squaring both sides of the equation.

-5=

3x - 7

What extraneous solution does Rania obtain?

The extraneous solution is 4.

Step-by-step explanation:

First, let us calculate the value of 'x' without squaring both side of the expression. This is illustrated below:

-5 = 3x - 7

Collect like terms

-5 + 7 = 3x

2 = 3x

Divide both side by 3

x = 2/3.

Now, let us calculate the value of 'x' by squaring both side of the expression. This is illustrated below:

(-5)^2 = (3x - 7)^2

25 = (3x - 7)(3x - 7)

25 = 9x^2 - 21x - 21x + 49

9x^2 - 42x + 49 - 25 = 0

9x^2 - 42x + 24 = 0

Solving by factorisation:

Multiply the first term i.e 9x^2 and 3rd term i.e 24 together. The result is 216x^2.

Next, we shall obtain two factors of 216x^2 such that when we add them together, it will give the 2nd term i.e -42x in the equation. These factors are: -6x and -36x

Now we can write the above equation as:

9x^2 - 42x + 24 = 0

9x^2 - 6x - 36x + 24 = 0

3x(3x - 2) - 12(3x - 2) = 0

(3x - 12)(3x - 2) = 0

3x - 12 = 0 or 3x - 2 = 0

3x = 12 or 3x = 2

x = 12/3 or x = 2/3

x = 4 or 2/3.

We can see that when we solve the question without squaring both side, the value of x is 2/3. But when we solve by squaring both side, the value of x are 4 and 2/3.

Therefore, the extraneous solution to the question is 4.

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.