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Given the following data of a quadrilateral: ∠ABC=104°, ∠BCD=89°, ∠ABD=60°, ∠ACD=53°, and AD=1000 m

1.)Determine the length of line BC (in meters, 2 decimal place):   

2.)Determine ∠CAD:

3.)Determine ∠BDA:

3. If BEJO is a square, m∠𝐵𝑂𝐽 = 4𝑥 − 6 and 𝐵𝑂= 2x- 8, find 𝐽𝑂.

7. What is the volume of the prism ? 8 cm 5.8 cm A. 29 cm ^ 3 B. 87 cm ^ 3 15.2 cm C. 512.3 cm ^ 3 D. 705.3 cm ^ 3

It was decided to put 20 street lights on a lonely road in order to secure the area at night. Each light was in the shape of a right circular cone mounted on a right circular cylinder having base radius 40 cm. Height of cylindrical part is 45 cm and that of conical part is 30 cm. Based on the above information in the statement of the question, find the surface area of a street light and if it costs `15 per 100 cm2? What will be the cost to install above mentioned lights?

15. A math teacher at Vallivue High School measured the angle of elevation from the ground to the flag at

the top of the school’s flagpole. She took the measurement from the ground 25 feet away from the

flagpole, and found that it was a 50 ◦ angle of elevation. When the flag was lowered to half-staff, she

found the angle decreased by 18 ◦. How much was the flag lowered, in feet? Draw a diagram to

support your answer.

The undefined objects are trees.

P1: There exists at least one tree.

Definition 1. A row is a non-empty collection of trees.

P2: Each tree belongs to at least one row.

P3: Any two distinct tress belong to a unique row.

Definition 2. A given row is called separate from another given row if these two rows have no tree in common.

P4: For each row, there is one and only one row separate from it.

Using only these postulates, prove the following theorems.

Theorem 4. Every row contains at least two trees.

Aaron is installing a ceiling fan in his bedroom. Once the fan is in motion, he needs to know the area the fan will cover. Which formula will he use?

Find T4, T7 and T9 for each of the following geometric progressions :3, 6,12,24

Brian made a burger. The diameter of the burger was 6 cm. What was the area of the burger?

Rectangular diagonals intersection point coincides with the center of the circle.
The length of the rectangle is equal to 8 and the width is equal to 2√2. The length of the circle radius is 2. Calculate the rectangle and
the area of ​​the common part (area of circle inside rectangle) of the circle.