Answer:
Part a) The ratio of the perimeters is 
Part b) The ratio of the areas is 
Step-by-step explanation:
Part A) What is the value of the ratio (new to original) of the perimeters?
we know that
If two figures are similar, then the ratio of its perimeters is equal to the scale factor
Let
z-----> the scale factor
x-----> the perimeter of the new triangle
y-----> the perimeter of the original triangle
we have
substitute
Part B) What is the value of the ratio (new to original) of the areas?
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
Let
z-----> the scale factor
x-----> the area of the new triangle
y-----> the area of the original triangle
we have
substitute
Answer:
B. (1, 16) and (6, 1)
Step-by-step explanation:
These make the most since because one is at the peek of the graph and the other one is at the bottom of the graph, also, these two points are on opposite sides of the graph.
Answer:
X=31
Step-by-step explanation:
-21+31=10
31 - 21 = 10
The volume of a cylinder is given by the formula <em>V</em>=π<em>r</em>²<em>h</em>². In this instance, <em>r</em> is 4 and the height is 47-12 (the height of the cone at the bottom is 12 mm and the sand goes up to 47 mm on the top portion of the hourglass, including both the cone and cylinder) or 35 mm.
<em>V</em>=π(4²)(35)=560π mm³.
The volume of a cone is given by the formula <em>V</em>=1/3π<em>r</em>²<em>h</em>². In this instance, <em>r</em> is 4 and the height is 12 mm.
<em>V</em>=1/3π(4²)(12)=π(1/3)(12)(4²)=π(4)(4²)=64π mm³.
This gives a total volume of 560π+64π=624π mm³ of sand.
Since the sand goes down to the bottom at a rate of 10π mm³/second, it will take 624π/10π=62.4 seconds for the sand to all drain out.
