Part A The Pythagorean Theorem states that for any given right triangle, a2 + b2 = c2. Using the Pythagorean Theorem, what should be the relationship between the areas of the three squares?

Part B
Using squares 1, 2, and 3, and eight copies of the original triangle, you can create squares 4 and 5. Keep the square 4 and square 5 window open. You will need them to complete the rest of the tasks in this section.

What are the side lengths of square 4 and square 5 in terms of a and b? Do the two squares have the same area?

Part C
Write an expression for the area of square 4 by combining the areas of the four triangles and the two squares.

Part D
Write an expression for the area of square 5 by combining the areas of the four triangles and the one square.

Part E
Since the areas of square 4 and square 5 are the same, set the two expressions equal.

Part F
Which term is on both sides of the equal sign? Since it’s on both sides of the equal sign, you can cancel it out. What is the expression after canceling out the common term?

Part G
What does the equation show after you cancel out a common term?

the graph in the attached figure

step-by-step explanation:

we have

using a graphing tool

the graph in the attached figure

the roots are ( x-intercepts) x=-0.5,x=1,x=3

the y-intercept is the point (0,3)

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;

the surface area is 124cm²

step-by-step explanation:

length: 4cm

width: 9cm

height:   2cm

a, b, c, d are correct.

step-by-step explanation:

we have g(x) = 3 and are required to find which option is a translation of g(x).

now, 'translation' is a transformation which means to shift the function in any direction and the general form of translation is g(x) + k, where k is any real number.

so, according to the options we see that all are correct as they satisfy the general form of translation.

also, it can be seen from the graph below that the function g(x) = 3 is shifted from its position in all the four options.