The longest possible altitude of the third altitude (if it is a positive integer) is 83.
According to statement
Let h is the length of third altitude
Let a, b, and c be the sides corresponding to the altitudes of length 12, 14, and h.
From Area of triangle
A = 1/2*B*H
Substitute the values in it
A = 1/2*a*12
a = 2A / 12 -(1)
Then
A = 1/2*b*14
b = 2A / 14 -(2)
Then
A = 1/2*c*h
c = 2A / h -(3)
Now, we will use the triangle inequalities:
2A/12 < 2A/14 + 2A/h
Solve it and get
h<84
2A/14 < 2A/12 + 2A/h
Solve it and get
h > -84
2A/h < 2A/12 + 2A/14
Solve it and get
h > 6.46
From all the three inequalities we get:
6.46<h<84
So, the longest possible altitude of the third altitude (if it is a positive integer) is 83.
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Answer:
look at picture
Step-by-step explanation:
x: adult tickets
y: student tickets
<span>The definition of a perfect cube is a number that is the result of multiplying an integer by itself three times
Hope it helps</span>
Answer: Under the given option, the following is true of algorithms and heuristics for solving real-life problems: <u><em>Heuristics are shortcut strategies. </em></u>
Algorithms are known as step by step plan of action for resolving a issue. It leads to a specific solution, methodically.
whereas;
Heuristics are known as short‐cut, step‐saving reasoning scheme or generalization that bring forth a solution speedily but possibly with an error.
<u><em>Therefore, the correct option is (a)</em></u>
Answer:
Step-by-step explanation:
<u>Modeling With Functions</u>
It's a common practice to try to mathematically represent the relation between two or more variables. It allows us to better understand the behavior of the phenomena being observed and, more importantly, to be able to predict future values.
The specific situation stated in the question relates how Taylor buys nail polish for $3.95 each, with a maximum of $30 to spend. If x is the number of nail polish purchased, then the total cost will be
But we know Taylor has a limited budget of $30, so the total cost cannot exceed that amount
Solving the inequality for x
We round down to
Of course, the lower limit of x is 0, because Taylor cannot purchase negative quantities of nail polish
Our model is now complete if the state the limits of x, or its domain
