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:
The measure of ∠EFG is 52°
Step-by-step explanation:
Given line m is parallel to line p. m∠HEF = 39º and m∠IGF = 13º.we have to find m∠EFG.
In ΔJFG,
By angle sum property of triangle, which states that sum of all angles of triangle is 180°
m∠FJG+m∠JGF+m∠JFG=180°
⇒ 39°+13°+m∠JFG=180°
⇒ m∠JFG=180°-39°-13°=128°
As JFE is a straight line ∴ ∠JFG and ∠EFG forms linear pair
⇒ m∠JFG+m∠EFG=180°
⇒ 128°+m∠EFG=180°
⇒ m∠EFG=52°
The measure of ∠EFG is 52°
If the point P(x, y) partitions the segment AB in the ratio 1 : 1, then the point P is midpoint of segment AB.
The formula of a midpoint of segment:
We have:
Answer: C. (4, -1)
