Answer:
C. (see the attachment)
Step-by-step explanation:
Both inequalities include the "or equal to" case, so both boundary lines will be solid. That excludes choices A and D.
The first inequality is plotted the same way in all graphs, so we must look at the second inequality. The relationship of y and the comparison symbol is ...
-y ≥ (something)
If we multiply by -1, we get ...
y ≤ (something else)
This means the solution space will be <em>on or below (less than or equal to) the boundary line</em>. This is the shaded area in graph C. (Graph B shows shading <em>above</em> the line.)
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<em>Further comment</em>
Since the boundary for the second inequality is fairly steep, "above" and "below" the line can be difficult to see. Rather, you can consider the relationship of x to the comparison symbol. For the second inequality, that is ...
x ≥ (something)
indicating the solution space is <em>on or to the right of the boundary line</em>.
The polynomial function of lowest degree with lead coefficient 1 and roots 1 and 1 + i is f(x) = x3 - 3x2 + 4x - 2.
Answer:
The rule used to reflect Δ ABC to its image is Reflect over y = x ⇒ B
Step-by-step explanation:
- If the point (x, y) reflected across the x-axis
, then its image is (x, -y)
- If the point (x, y) reflected across the y-axis
, then its image is (-x, y)
- If the point (x, y) reflected across the line y = x
, then its image is (y, x)
- If the point (x, y) reflected across the line y = -x
, then its image is (-y, -x)
From the given figure
∵ The coordinates of point A are (-4.5, 6)
∵ The coordinates of point A' are (6, -4.5)
→ The coordinates are switched ⇒ 3rd rule
∴ Point A is reflected over the line y = x
∴ Δ ABC is reflected over the line y = x
∴ The rule used to reflect Δ ABC to its image is Reflect over y = x
<em>Note: Point B' on the graph should be C' and point C' should be B' (correct it)</em>
Answer:
5
Step-by-step explanation:
The gradient is the ratio of the change in y to the change in x:
m = ∆y/∆x = (16 -6)/(2 -0) = 10/2 = 5
The gradient of the line segment is 5.
Answer:
The slope from point O to point A is 3 times the slope of the line from point A to point B.
Step-by-step explanation:
The slope of the entire line is 1. The slope from point A to point B is also 1. 1 multiplied by 3 is still 1, which means that the slope from point O to point A is also 1.
