Let the length of second side be x" ,
So,
Length of first side = 2" shorter than second = ( x - 2 )"
Length of third side = 5" longer than second = ( x + 5 )"
=×=×=×=×=×=×=×=×=×=×=×=×=×=×=×=×=

Given, perimeter = 33"
= > first side + second side + third side = 33"
= > ( x - 2 ) + x + ( x + 5 ) = 33
= > x - 2 + x + x + 5 = 33
= > 3x + 3 = 33
= > 3x = 30

= > x = 10
Hence, length of each side is
First side = ( x - 2 )" = ( 10 - 2 )" = 8 inches
Second side = x " = 10 inches
Third side = ( x + 5 )" = ( 10 + 5 )" = 15 inches
The first choice is the correct answer
12 in by 22 in by 4 in
the explanation is as shown in the figure
The dimension will be x , 20 - 2x , 30 -2x
the volume= v = x(20-2x)(30-2x) = 4x³ - 100x² + 600x
differentiating with respect to x and equating to zero
dv/dx = 12x² - 200x + 600 = 0
solve for x using calculator
x = 12.7 (unacceptable) or x = 3.92 ≈ 4
∴ The dimension will be 4 , 12 , 22
No because you need another angle. angle QRP and TRS are congruent because they are vertical angles. if you add that then you will get ASA which proves congruency
True - since the outlier is way off it will cause your average to mess up which is why we test multiple times to make sure we are more accurate with our numbers
You answer is a^10
when multiplying by exponents, you really add them