Answer:
x ≥ 7
Step-by-step explanation:
|x - 7| = x - 7
A. For each absolute, find the intervals
x - 7 ≥ 0 x - 7 < 0
x ≥ 7 x < 7
If x ≥ 7, |x - 7| = x - 7 > 0.
If x < 7, |x - 7| = x - 7 < 0. No solution.
B. Solve for x < 7
Rewrite |x - 7| = x - 7 as
+(x - 7) = x - 7
x - 7 = x - 7
-x + 14 = x
14 = 2x
x = 7
7 ≮7. No solution
C. Solve for x ≥ 7
Rewrite |x - 7| = x - 7 as
+(x - 7) = x - 7
x - 7 = x - 7
True for all x.
D. Merge overlapping intervals
No solution or x ≥ 7
⇒ x ≥ 7
The diagram below shows that the graphs of y = |x - 7| (blue) and of y = x - 7 (dashed red) coincide only when x ≥ 7.
Answer:
186 cm²
Step-by-step explanation:
<em>*First we can move the shape around a bit to make it simpler to solve. If we take the triangle from the left side and move it over to the right, it connects with the other piece to create a rectangle. This leave two rectangles total which is much easier to solve.</em>
<em>*To find the length of the right rectangle, you take the 22 cm at the bottom and subtract the 12 cm (which is being used as the length for the left rectangle). This will give you a length of 10 cm long.</em>
<u>Left rectangle:</u>
A = lh
A = 12 (8)
A = 96 cm²
<u>Right rectangle:</u>
A = lh
A = 10 (9)
A = 90 cm²
<u>Total:</u>
A = 90 + 96
A = 186 cm²
Answer: 3
Step-by-step explanation:
