You need to do this in several steps.
1) Using the given length and width of the rectangle, find its area.
2) Then using the base and height of the triangle, find its area.
3) Since the areas are equal, set the expressions equal to each other, and solve for x.
4) Using the value of x you found, find the length and width of the rectangle and find its perimeter.
1) The area of the rectangle is A = LW
Area of Rectangle = (x + 2)x = x^2 + 2x
2) The area of the triangle is A = (1/2)bh
Area of Triangle = (1/2)(24)x = 12x
3) Set the areas equal and solve for x
x^2 + 2x = 12x
x^2 - 10x = 0
x(x - 10) = 0
x = 0 or x = 10
Since a width cannot be 0, we discard x = 0, and keep x = 10.
4) The length is x + 2 = 10 + 2 = 12
The width is x = 10
The perimeter is 2(L + W) = 2(10 + 2) = 2(22) = 44
The perimeter is 44 cm.
Answer:
A) 3; B) 1116 m²; C) 24 m³; D) 1/27
Step-by-step explanation:
A) Scale factor
The scale factor is the ratio of the heights of the two pyramids.
h₂/h₁ = 24/8 = 3
B) Surface area
The ratio of the surface areas is the square of the scale factor.
A₂/A₁ = 3²
A₂/124 = 9
A₂ = 124 × 9 = 1116 m²
The volume of the larger pyramid is 1116 m².
C) Volume
The ratio of the volumes is the cube of the scale factor.
V₂/V₁ = 3³
648/V₁ = 27
648 = 27V₁
V₁ = 648/27 = 24 m³
The volume of the smaller pyramid is 24 m³.
D) Volume ratio
V₁/V₂ = 24/648 = 1/27
The volume ratio is 1/27.
That showed be 20/6 which is 3 with a reminder of 2
Answer:
vertex(-3,27)
Step-by-step explanation:
f(x)= x^2+ 6x + 36 ( a=1,b=6,c=36)
V(h,k)
h=-b/2a=-6/2=-3
k=f(-3)=3²+6(-3)+36
f(-3)=9-18+36=27
vertex(-3,27)
Given:
Initial population = 100 algae
Growth rate = 30% per day.
Time = 5 days
To find:
The future amount of population.
Solution:
The exponential growth model is
where, a is the initial value, r is the rate of interest in percent and t is time period.
Substituting the given values, we get
Now, solve this.
Therefore, the future value is 371.293 algae.
