Answer:
The transformed points of the triangle ABC are
,
, 
Step-by-step explanation:
The new points after applying the scale factor are, respectively:






Answer:
(D) is the right answer
Step-by-step explanation:
The cross section will be a quadrilateral when the intersecting plane forms a closed four sided polygon along with the pyramid.
A triangular pyramid has four faces. So, to form four straight lines and therefore a quadrilateral, the intersecting plane must intersect all four faces.
A. In this case the plane will only intersect one side of the pyramid so four sided polygon can't be formed.
B. It will only intersect the two sides of the pyramid but the cross section will not be a quadrilateral.
C. In this case the plane will intersect three sides of the pyramid so the cross section will be a triangle not a quadrilateral.
D. In this case the plane intersects all the four faces forming a closed polygon of 4 straight lines so the cross section will be a quadrilateral.
So, the Correct Option is (D) : When the plane intersects the base and all three lateral faces of the pyramid, the cross section of the triangular pyramid will be a quadrilateral.
Answer:
Tens
Step-by-step explanation:
It's in the tens place because, it's after the decimal point so don't worry about anything after the decimal. So it's just 59. 9 is the first digit making it in the ones place. So that leaves 5.
Well we can find the perimeter by using the formula P=2L + 2W
P=2(30) + 2(18) P=60+36 P=96
I believe we can divide the perimeter by 18 to find the total amount of lights needed.
96÷18=5.333333
So we know at least 5 lights are needed.
I'm not sure if I'm correct, but I hope this helped anyways :)
The height of the tree is 60 meters.
Explanation:
Let the height of the tree be x. The tree casts a shadow of
meters and the distance from the top of the tree to the end of the shadow is
meters.
The sides of the triangle are attached in the image below:
Using pythagoras theorem,

Expanding, we get,




Solving the equation using the quadratic formula
, we get,

Simplifying, we have,



Thus,
and 
where the value
is not possible because substituting the value
in
results in negative solution. Which is not possible.
Hence, the value of x is 60.
Thus, The height of the tree is 60 meters.