its 7/4 decimal 1.75 add the numbers; 4+2+1=7
Answer:
yes, parallelogram ABCD is a square.
Step-by-step explanation:
Given information: ABCD is parallelogram with vertices A(0,4), B(2, 2), C(4,4), and D(2,6).
We need to check whether this parallelogram is a square or not.
The opposite side of a parallelogram are parallel and congruent. If the interior angles a parallelogram are right angles then the parallelogram is square.
Formula for slope:
Now, find the slopes of each side.
The product of slopes of two perpendicular line is -1.
The product of slopes of any two consecutive sides is -1. It means all interior angles are right angle.
Therefore, the parallelogram ABCD is a square.
Point B on the ground is 5 cm from point E at the entrance to Ollie's house.
Ollie is at a distance of 2.45 m from the entrance to his house when he first activates the sensor.
The complete question is as follows:
Ollie has installed security lights on the side of his house that is activated by a sensor. The sensor is located at point C directly above point D. The area covered by the sensor is shown by the shaded region enclosed by triangle ABC. The distance from A to B is 4.5 m, and the distance from B to C is 6m. Angle ACB is 15°.
The objective of this information is:
- To find angle CAB and;
- Find the distance Ollie is from the entrance to his house when he first activates the sensor.
The diagrammatic representation of the information given is shown in the image attached below.
Using cosine rule to determine angle CAB, we have:
Here:
∠CAB = Sin⁻¹ (0.3451)
∠CAB = 20.19⁰
From the diagram attached;
- assuming we have an imaginary position at the base of Ollie Standing point called point F when Ollie first activates the sensor;
Then, we can say:
∠CBD = ∠GBF
∠GBF = (CAB + ACB)
(because the exterior angles of a Δ is the sum of the two interior angles.
∠GBF = 15° + 20.19°
∠GBF = 35.19°
Using the trigonometric function for the tangent of an angle.
BF = 2.55 m
Finally, the distance of Ollie║FE║ from the entrance of his bouse is:
= 5 - 2.55 m
= 2.45 m
Therefore, we can conclude that Ollie is at a distance of 2.45 m from the entrance to his house when he first activates the sensor.
Learn more about exterior angles here:
I think it’s 0.33 inches per mile, but I’m not positive