The distance from point Y to the flag post measures 38.13 m. Step-by-step explanation: Assuming point Y is located at the intersection of both lines shown. Point X is positioned 34 meters east of point Y. The flagpole at point X is observed at a bearing of N18°W, meaning it creates an angle of 18° to the west from the north at point X. Conversely, at point Y, the flagpole has a bearing of N40°E, which makes a 40° angle towards the east from the north.
Considering ∆ AXY as a right triangle, the angle FXY is established. Then, concerning ∆ BYX as another right triangle, the angle FYX is also determined. To find the third angle ∠YFX in triangle FYX, the angle sum property of triangles can be applied:
∠YFX + ∠FYX + ∠FXY = 180°
Thus, we have: ∠YFX + 50° + 72° = 180° leading to ∠YFX = 58°.
Now we can calculate the distance FY using the sine rule.
To start, calculate the return for each
price per unit
Return = quantity sold x price
per unit
Return1 = 5000 units x Php 900
Return1 = Php 4,500,000
Next, figure out the return for the other price per
unit
Return2 = quantity sold x
price per unit
Return2 = (5000 + 1500 units) x (
Php 900 – 100)
Return2 = Php 5,200,000
Thus, a price of Php 800 per unit will result in a higher return.
Let’s define x as the amount invested by Sam in the first year.
Here are the corresponding expressions derived from the provided descriptions for Sam's investments.
For Sam:
2nd year: investment = 5x/2 - 2000
3rd year: investment = x/5 + 1000
The total Sam invested is:
x + (5x/2 - 2000) + (x/5 + 1000)
Next, we can form the expressions for Sally’s investments.
For Sally
1st year: investment = 3x/2 - 1000
2nd year: investment = 2x - 1500
3rd year: investment = x/4 + 1400
Thus, Sally's total investment is,
total = (3x/2 - 1000) + (2x - 1500) + (x/4 + 1400)
Setting both totals equal gives us:
(x) + (5x/2 - 2000) + (x/5 + 1000) = (3x/2 - 1000) + (2x - 1500) + (x/4 + 1400)
Solving for x,
x = 2000
For Sally's investment for the third year:
investment = x/4 + 1400 = (2000/4 + 1400) = 1900
RESULTS:
Sam's first year = $2000
Sally's third year = $1900
Given: AD ≅ BC and AD ∥ BC
Prove: ABCD is a parallelogram.
Statements Reasons
1. AD ≅ BC; AD ∥ BC 1. provided
2. ∠CAD and ∠ACB are alternate interior angles 2. definition of alternate interior angles
3. ∠CAD ≅ ∠ACB 3. congruence of alternate interior angles
4. AC ≅ AC 4. reflexive property
5. △CAD ≅ △ACB 5. SAS congruency theorem
6. AB ≅ CD 6. Congruent triangles have congruent corresponding parts (CPCTC)
7. ABCD is a parallelogram 7. theorem for sides of parallelograms
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