20points
arianna claims that the rectangles shown below are similar, while miguel claims that they are not similar.

a. miguel is correct because the two rectangles are not oriented in the same direction.

b. arianna is correct because the four angles of the smaller rectangle are the same as the four angles of the larger rectangle.

c. arianna is correct because the smaller rectangle has side lengths that are half the size of the side lengths of the larger rectangle.

d. miguel is correct because the measures of the sides of the smaller rectangle are not proportional to the measures of the sides of the larger rectangle.

D. Miguel is correct because the measures of the sides of the smaller rectangle are not proportional to the measures of the sides of the larger rectangle.

Step-by-step explanation:

We need to understand when the two rectangles are similar

For the two rectangles to be similar to each other, their sides must be proportional (forming an equal ratio). The ratio of the longer sides should be equal to the ratio of the shorter sides.  

As we can see in the attached photo,

The long side of the big rectangle is 10 units

The long side of the small rectangle is 6 units

=>  their ratio is 10 : 6 or 5:3 units

The short side of the big rectangle is 4 units

The short side of the small rectangle is 2 units

=>  their ratio is 4 : 2 or 2 : 1 units

So the two rectangles are not similar, we choose D. Miguel is correct because the measures of the sides of the smaller rectangle are not proportional to the measures of the sides of the larger rectangle.

the polynomial is a perfect square trinomial of the form a^2-2ab+b^2:

option a. true

step-by-step explanation:

9x^2-12x+4

comparing with the form a^2-2ab+b^2

1.) a^2=9x^2

solving for a: square root both sides of the equation:

sqrt(a^2)=sqrt(9x^2)

a=sqrt(9) sqrt(x^2)

a=3x

2.) b^2=4

solving for b: square root both sides of the equation:

sqrt(b^2)=sqrt(4)

b=2

to be a perfet square trinomial 2ab must be equal to 12x. let's check:

2ab = 2 (3x) (2)

2ab = 12x

correct