Which system of equations does this graph represent?

The system of equations is y = x - 4 and y = x² - 6

Step-by-step explanation:

The graph has a linear equation represented by a line and a quadratic equation represented by a parabola

The form of the linear equation is y = m x + b, where m is the slope and b is the y-intercept

The form of the quadratic equation is y = a(x - h)² + k, where (h, k) are the coordinates of its vertex point and a is the coefficient of x²

let us use the graph to find each equation

→ Equation the line

∵ The line passes through points (-1, -5) and (2, -2)

∵ m =

∴ m =

∴ m = 1

∵ The line intersected the y-axis at point (0, -4)

∵ b is the value of y at x = 0

∴ b = -4

→ Substitute the values of m and b in the form of the equation above

∴ y = (1)x + (-4)

∴ y = x - 4

→ Equation the parabola

∵ The vertex of the parabola is (0, -6)

∴ h = 0 and k = -6

→ Substitute them in the equation

∴ y = a(x - 0)² + -6

∴ y = ax² - 6

→ To find a choose any point on the parabola and substitute x and y

   by its coordinated

∵ The point (2, -2) lies on the parabola

∴ x = 2 and y = -2

∵ -2 = a(2)² - 6

∴ -2 = 4a - 6

→ Add 6 to both sides

∵ -2 + 6 = 4a - 6 + 6

∴ 4 = 4a

→ Divide both sides by 4

∴ 1 = a

∴ y = (1)x² - 6

∴ y = x² - 6

The system of equations is y = x - 4 and y = x² - 6

never fear papaguy is here

answer

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt