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:
They are SIMILAR triangles
Step-by-step explanation:
Given triangles MNL and FHG with two of their angles to be 51° and 36° respectively. Their third angle is expressed as:
180°-(51°+36°)
= 180°-87°
= 93°
Their third angle is 93°
Since both triangles have the same angles in them, both triangles are considered as similar triangle even though the value of their sides are different due to angle differences in both.
Note that individual triangles are scalene triangles since their angles are not the same but the both triangles are similar triangles based on their relationship.
Answer:
25.2
Step-by-step explanation:
6/5 is 1.2, so it takes 1.2 minutes to run one lap.
This means 21 x 1.2 = the minutes it takes to run 21 laps around the track.
Therefore it takes 25.2 minutes to run around the track 21 times.
Answer:
A.
While D is partially correct, A is the way to go, because samples are easier to collect than whole populations. The internet quotes, "It is a much quicker process and is more time efficient." This proves the theory why A is the correct answer.
