Answer:
Infinitely many triangles.
Step-by-step explanation:
Given the lengths of two sides are 8 inches and 10 inches.
Let's assume third side = x inches.
Using the Triangle Inequalities given as follows:-
1. a+b > c,
2. b+c > a,
3. c+a > b.
Using the lengths given in the problem, we can write:-
1. x+8 > 10 ⇔ x > 10-8 ⇔ x > 2.
2. x+10 > 8 ⇔ x > 8-10 ⇔ x > -2.
3. 8+10 > x ⇔ x < 18.
So, the solution set is 2 < x < 18. It means third side can take any value in interval (2, 18).
Hence, there are infinitely many triangles.
Answer:
The ship is located at (3,5)
Explanation:
In the first test, the equation of the position was:
5x² - y² = 20 ...........> equation I
In the second test, the equation of the position was:
y² - 2x² = 7 ..............> equation II
This equation can be rewritten as:
y² = 2x² + 7 ............> equation III
Since the ship did not move in the duration between the two tests, therefore, the position of the ship is the same in the two tests which means that:
equation I = equation II
To get the position of the ship, we will simply need to solve equation I and equation II simultaneously and get their solution.
Substitute with equation III in equation I to solve for x as follows:
5x²-y² = 20
5x² - (2x²+7) = 20
5x² - 2y² - 7 = 20
3x² = 27
x² = 9
x = <span>± </span>√9
We are given that the ship lies in the first quadrant. This means that both its x and y coordinates are positive. This means that:
x = √9 = 3
Substitute with x in equation III to get y as follows:
y² = 2x² + 7
y² = 2(3)² + 7
y = 18 + 7
y = 25
y = +√25
y = 5
Based on the above, the position of the ship is (3,5).
Hope this helps :)
Answer:
min{5 x^2 - 20 x + 3} = -17 at x = 2
Step-by-step explanation: here's the graph
Answer: 16 percent
Step-by-step explanation:
