Answer:
k = -1
Step-by-step explanation:
-3(k-8)-(k+5)=23
Distribute
-3k +24 -k-5 = 23
Combine like terms
-4k +19 = 23
Subtract 19 from each side
-4k +19-19 = 23-19
-4k = 4
Divide by -4
-4k/-4 = 4/-4
k = -1
Answer:
a
Step-by-step explanation:
because it is
Answer:
obtuse
Step-by-step explanation:
A "form factor" can be computed whose sign will tell you the classification of the triangle. For short sides a, b and long side c, the form factor is ...
f = a² +b² -c²
And the interpretation is ...
- f > 0 . . . acute
- f = 0 . . . right
- f < 0 . . . obtuse
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<h3>form factor</h3>
For the given side lengths, the form factor is ...
f = 11² +15² -20² = 121 +225 -400
f = -54
<h3>interpretation</h3>
The value is less than zero, signifying an obtuse triangle.
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<em>Additional comment</em>
The value f/(2ab) = -54/(2·11·15) = -9/55 is the cosine of the largest angle. Here, the largest angle is arccos(-9/55) ≈ 99.4°. This is greater than 90°, hence an obtuse angle.
This cosine relation comes from the Law of Cosines. The interpretation of the "form factor" can be developed by considering the Pythagorean theorem (f=0 ⇒ right triangle) and the relationship between sides and angles. If the longest side is longer than necessary for a right triangle, the largest angle will be greater than 90°.
Answer:
Read Exp:
Step-by-step explanation:
Exact Form:
- 99/20
Decimal Form:
- 4.95
Mixed Number Form:
- 4 19/20
Answer:
The volume of the rock is 13.368 cubic feet.
Step-by-step explanation:
The volume of the rock (), measured in gallons, is equal to the volume of the fish aquarium without the decorative rock () minus the volume of the fish aquarium with the decorative rock (), both measured in gallons.
Since the water flow is at constant rate, the volume of the rock is expressed by the following equation:
(1)
Where:
- Flow rate, measured in gallons per hour.
- Filling time of the fish aquarium without the decorative rock, measured in hours.
- Filling time of the fish aquarium with the decorative rock, measured in hours.
And the flow rate is:
The flow rate is 200 gallons per hour.
If we know that , and , then the volume of the rock is:
The volume of the rock is 13.368 cubic feet.