The 5x and the combination of (40° + x) are "vertical angles".
Vertical angles are equal.
So
5x = 40° + x
Subtract 'x' from each side: 4x = 40°
Divide each side by 4 : x = ?
Answer:
1. 9 < s < 17
2. 5 < MN < 19
3. AD > BD
Step-by-step explanation:
1. The triangle inequality tells you the sum of any two sides of a triangle must exceed the length of the other side. (Some versions say, "must be not less than ..." rather than "must exceed.") In practice, this means two things:
- the sum of the shortest two sides is greater than the length of the longest side
- the length of any side lies between the sum and the difference of the other two sides
Here, we can use the latter fact to write the desired inequality. The difference of the given sides is 13 -4 = 9; their sum is 13 +4 = 17. The third side must lie between 9 and 17. If that side length is designated "s", then ...
9 < s < 17
(If you don't mind a "triangle" that looks like a line segment, you can use ≤ instead of <.)
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2. Same as (1) using different numbers.
12 -7 < MN < 12 +7
5 < MN < 19
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3. Side CD is congruent to itself, and side CA is shown congruent to side CB. This means the requirements of the Hinge Theorem are met. That theorem tells you the longer side is opposite the greater angle:
AD > BD
The greatest number of friends who can receive a necklace is 6. The reason why is because 6 is the greatest common factor of 72 and 42.
Each friend will have 12 blue beads and 7 red beads. If you divide 6 (GCF) with both numbers you get 12 and 7.
Hope this helps :3
Answer:
Option D
Step-by-step explanation:
Given is a table which gives the order pair of x and y for a function f(x)
We have to find the local minimum of the function f(x)
We have from the table the values of different f(x)
Of all we find the least value is -15 and for this x value is -2 or +2
Hence f(x) has minimum at two points
(-2,-15) and (2,-15)
Out of 4 options given we find that (2,-15) appears in IV option
Hence option D is right answer
