Answer:
The distance added to each dimension is 2 yards.
Step-by-step explanation:
The initial dimensions of the rectangular fence is 8 yards by 4 yards.
The initial area of the rectangular fence = area of a rectangle
area of a rectangle = length x width
So that,
The initial area of the fence = 8 x 4
= 32
The initial area of the fence is 32 square yards.
But, with the new dimensions, area = 60 square yards.
(4 + x) x (8 + x) = 60
+ 12x + 28 = 60
+ 12x - 32 = 0
(x + 14) = 0 or (x - 2) = 0
x = -14 or x =2
Thus, x = 2
The distance added to each dimension is 2 yards.
The polygons are similar.
This is because dividing the corresponding sides forms the same ratio, as shown by the three equations below
35/28 = 1.25
25/20 = 1.25
(15.5)/(12.4) = 1.25
So the larger figure on the right has side lengths that are 1.25 times larger compared to the corresponding sides of the figure on the left.
You'll need to flip the figure on the left so that the side labeled "20" is along the top, and the "28" is along the bottom.
After this flip happens, also note that the angle arc markings match up. The bottom pairs of angles of each figure are shown with a single arc, while the top angles are shown as double arcs. This helps visually show which angles pair up and are congruent to one another.
Because we have similar proportions as discussed earlier, and congruent pairs of angles like this, this shows the two figures are similar quadrilaterals. The one on the right is simply an enlarged scaled up copy of the figure on the left.
Answer:
a^2 + b^2 = c^2
a^2 + 32^2 = 58^2
a^2 + 1024 = 3364
a^2 = 2340
a = 48.37
Step-by-step explanation:
Answer:
87,000 ; 10.6%
Step-by-step explanation:
Given the function :
P(t)=87,000e^0.106t
P(t) is an exponential function ; comparing the given function to the general form of an exponential function :
y = Ae^rt
Where,
A = initial amount ; r = growth rate ; t = time
The Given function models t years after 2010, that is the 2010 population is the initial population of the city.
Comparing the general exponential equation with the function given:
A = 87,000 = population of city in 2010
The growth rate :
rt from the general equation compares to 0.106t in the given function.
rt = 0.106t
r = 0.106
Hence, the rate of change = 0.106 * 100% = 10.6%
