The table of values represents a linear function g(x), where x is the number of days that have passed and g(x) is the balance in the bank account:
x g(x)
0 5600
3 5720
6 5840
Part A: Find and interpret the slope of the function (3 points)
Part B: Write the equation of the line in point-slope, slope-intercept, and standard forms (3 points)
Part C Write the equation of the line using function notation. (2 points)
Part D: What is the balance in the bank account after 7 days? (2 points)

A. 4

B. Point-slope: y - 5600 = 40(x-0)

Slope-intercept: y = 40x +5600

Standard: y - 40x = 5600

C. g(x) = 40x + 5600

D. 5880

Step-by-step explanation:

Part A

m = (y2-y1)/(x2-x1)

m = (5720-5600)/(3-0)

m = (120)/(3)

m = 40

Part B

Point-slope: y - 5600 = 40(x-0)

Slope-intercept: y = 40x +5600

Standard: y - 40x = 5600

Part C

g(x) = 40x + 5600

Part D

g(x) = 40(7) + 5600

g(x) = 280 + 5600 = 5880

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).