Answer:28inches & 84inches
First, lets write an equation that fits the data given. The string is 112 inches long. When the two pieces are cut, the first piece will be three times as long as the second piece. If we use the variable, x, to represent the second piece, we can create the following equation...
112=3x+x
Now lets solve for x.
112=4x
divide both sides by 4
28 inches=x
Now we know that the second piece is 28inches long. Since the first piece is three times as long, simply multiply 28*3 and we'll know the length of the first piece.
28*3=84 inches
28+84=112
Answer:
a = 1/2 (b) (h)
Step-by-step explanation:
Use Pythagorean theorem for sub triangle on the left: 8^2 + h^2 = 22^2
Use Pythagorean again for sub triangle on the right: x^2 + h^2= 31^2
Find your base: 8+x=b
Find entire area: a = 1/2 (b) (h)
The population Pa of insect A after t years is given by the equation
Pa = 1.3(1-0.038)^t
while the population Pb of insect B after t years is
Pb = 2.1(1-0.046)^t
We equate the above expressions to find the number of years t it will take the two populations to be equal:
Pa = Pb
1.3(1-0.038)^t = 2.1(1-0.046)^t
1.3(0.962)^t = 2.1(0.954)^t
These are the equations that can be used to determine how long it will be before the populations of the two species are equal.
We can now solve for t:
(0.962)^t / (0.954)^t = 2.1/1.3
(0.962/0.954)^t = 2.1/1.3
After taking the log of both sides of our equation, number of years t is
t = log (2.1/1.3) / log (0.962/0.954)
t = 57 years
Therefore, it will take 57 years for the population of insect A to equal the population of insect B.
Answer:
The answer is "
"
Step-by-step explanation:
The whole question can be found in the file attached.
Subtracting the 
from both sides of the equations:
