Answer: Art students are painting replicas of a print of Michael Jackson by Fine Art America. Unfortunately, I am not able to see the picture you are referring to. However, I can help you with the math problem you have provided.
A) To determine the value of c that will result in a perfect square trinomial, we need to complete the square. We can do this by adding and subtracting the square of half the coefficient of w from the left-hand side of the equation:
w^2 + 6w + (6/2)^2 - (6/2)^2 + c = 130 + c
Simplifying this expression gives:
(w + 3)^2 - 9 + c = 130 + c
To obtain a perfect square trinomial, we need to eliminate the constant term on the left-hand side of the equation. We can do this by adding 9 to both sides:
(w + 3)^2 + c = 139
Therefore, c = -9.
B) To rewrite the equation as a perfect square binomial, we can use the formula:
(a + b)^2 = a^2 + 2ab + b^2
In this case, we have:
(w + 3)^2 - 9 = w^2 + 6w
Therefore, (w + )² = (w + 3)².
C) The area of the painting is given as 260 in². We know that:
Area = width x height
Since we don’t know the height of the painting, we can express it in terms of w:
Area = w x height
We also know that:
Area = 260 in²
Therefore:
260 in² = w x height
We are asked to find the width w of the painting. To do this, we need to solve for w. We can rearrange the equation as follows:
w = 260 in² / height
To find height, we can use our result from part B:
(w + )² = (w + 3)²
Expanding both sides gives:
w^2 + 6w + 9 = w^2 + 6w + 9
Therefore, height must be equal to (w+3).
Substituting this expression for height in our equation for w gives:
w = 260 in² / (w+3)
We can solve for w numerically using a calculator or computer software. The width of the painting is approximately 20.1 inches when rounded to one decimal place.