Answer:
B. {16, 19, 20}
Step-by-step explanation:
The <em>triangle inequality</em> requires for any sides a, b, c you must have ...
a + b > c
b + c > a
c + a > b
The net result of those requirements are ...
- the sum of the two shortest sides must be greater than the longest side
- the length of the third side lies between the difference and sum of the other two sides
__
If we look at the offered side length choices, we see ...
A: 8+11 = 19 . . . not > 19; not a triangle
B: 16+19 = 35 > 20; could be a triangle
C: 3+4 = 7 . . . not > 8; not a triangle
D: 5+5 = 10 . . . not > 11; not a triangle
The side lengths {16, 19, 20} could represent the sides of a triangle.
_____
<em>Additional comment</em>
The version of triangle inequality shown above ensures that a triangle will have non-zero area.
The alternative version of the triangle inequality uses ≥ instead of >. Triangles where a+b=c will look like a line segment--they will have zero area. Many authors disallow this case. (If it were allowed, then {8, 11, 19} would also be a "triangle.")
If you would like to expand and simplify 3 * (x + 2) + 2 * (x - 1), you can do this using the following steps:
3 * (x + 2) + 2 * (x - 1) = 3 * x + 3 * 2 + 2 * x - 2 * 1 = 5 * x + 6 - 2 = 5 * x + 4
The correct result would be 5 * x + 4.
Let the height of the building be x. Let the initial distance of the ant from the building be y, then
tan 32 = x/y
y = x/tan 32 . . . . . . . . (1)
tan 22 = x/(y + 66)
y tan 22 + 66 tan 22 = x
y = (x - 66 tan 22)/tan 22 . . . . . . . . (2)
Equating (1) and (2), we have
x/tan 32 = (x - 66 tan 22)/tan 22
x tan 22 = x tan 32 - 66 tan 22 (tan 32)
x(tan 32 - tan 22) = 66 tan 22 (tan 32)
x = (66 tan 22 (tan 32))/(tan 32 - tan 22) = 66(0.4040)(0.6249)/(0.6249 - 0.4040) = 16.6626/0.2208 = 75.4
Therefore, the height of the building is 75.4 feet.
Answer:
False
Step-by-step explanation:
to get from 3 to 15, you multiply by 5
So theoretically, if you multiply 7 and 5, you should get the other missing value.
7 x 5 ≠ 45
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-Chetan K
Answer:
D. 5267
Step-by-step explanation:
In the triangle XY and XZ are tangent to circle C. This means that the length has of XY and XZ are congruent.
So first you have to set the equations to each other to find what b equals to.
85b+83=91b-283
Add 283 to both sides
85b+366=91b
Subtract 85b on both sides
366=6b
Divide by 6
B=61.
Then you substitute 61 as b in the equation for XY.
85b+83
85(61)+83
5185+83
5268
