The equation y = −2x + 3 is the boundary line for the inequality y ≤ −2x + 3. which sentence describes the graph of the inequality?

a. the region shaded above a dashed boundary line.

b. the region shaded above a solid boundary line.

c. the region shaded below a solid boundary line.

d. the region shaded below a dashed boundary line.

Option C

Step-by-step explanation:

The point-slope form of the equation of the line is:

Where m is the slope and b is the intersection with the y-axis.

In the line , you can identify that:

The symbol of the inequality "" indicates that you must shade the region below the boundary line and for the symbols of inequalities "" and "" the line must be solid (Observe the graph attached).

Then the answer is the option C.

C. The region shaded below a solid boundary line.

Step-by-step explanation:

The given inequality is

The boundary line for this inequality is .

Since the inequality involve , we use a solid boundary line.

After graphing the boundary line; we test the origin to determine which half -plane to be shaded. This is because the boundary lie is not passing through the origin.

Testing the origin yields .

This implies that;  . This statement is true.

Hence we shade the lower half-plane of the solid boundary line.

The correct choice is C.

See graph

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)