Answer:
The height of the prism is 16 yards
Step-by-step explanation:
To get the height of the prism, we simply divide the volume of the prism by its base area
Mathematically, we have this as;
128/8 = 16 yards
The distance from a port Huron to the Indiana state line = 271 miles (approx)
We have to express the given distance into kilometers.
Since, 1 mile = 1.61 kilometers.
To convert the unit "miles" to "kilometer", we have to multiply the given miles by 1.61 to get the required kilometers.
Therefore, distance in kilometers = 
kilometers
= 436.3 kilometers.
Therefore, the distance from a port Huron to the Indiana state line in kilometers is 436.3 kilometers.
Note: Consider the side of first triangle is TQ instead of TA.
Given:
Triangles TQM and TPN which share vertex T.
To find:
The theorem which shows that 
.
Solution:
In triangle TQM and TPN,
[Given]
[Given]
[Given]
Since two sides and their including angle are congruent in both triangles, therefore both triangles are congruent by SAS postulate.
[SAS]
Therefore, the correct option is C.
Answer:
11. x = -3+√37 ≈ 3.08276
12. x = 11.2
13. x = -6 +6√5 ≈ 7.41641
Step-by-step explanation:
In each case, the relation of interest is ...
(distance to circle near) × (distance to circle far) = (distance to circle near) × (distance to circle far)
When there is only one point of intersection of the secant with the circle—because it is a tangent—then the product is the square of the length of the tangent.
11. 2(2+12) = x(x +6)
x² +6x -28 = 0
(x +3)² -37 = 0
x = -3+√37 ≈ 3.08276
12. 5(5+x) = 9(9)
5x +25 = 81
x = 56/5 = 11.2
13. x(x +12) = 12(12)
x² +12x -144 = 0
(x +6)² -180 = 0
x = -6 +√180 ≈ 7.41641
_____
<em>Comment on this secant rule</em>
This rule turns out to apply whether the point of intersection of the secant lines is outside the circle (as in these problems) or inside the circle (as in problem 9). The product of the two distances from the point of intersection to the circle is a constant for a given pair of intersecting secants/chords.
Answer:
7.5$
Step-by-step explanation:
This is because 11.25*3 = 33.75
and 8.25*5 = 41.25
41.25-33.75=7.5
