<span>The side of one square is 2 cm longer than the side of a second square.
If the combined area of the squares is 100 square cm, find the dimensions
of each square.
:
The area of the two squares
x^2 + (x+2)^2 = 100
x^2 + x^2 + 4x + 4 = 100
2x^2 + 4x + 4 - 100 = 0
2x^2 + 4x - 96 = 0
Simplify, divide by 2
x^2 + 2x - 48 = 0
Factors to
(x+8)(x-6) = 0
the positive solution
x = 6
:
6 by 6 the small square
8 by 8 the large square
;
:
Check: 36 + 64 = 100 Does this make sense to you?</span>
Answer:
y = 10852 bacteria
Step-by-step explanation:
The equation is exponential growth
y = a b^x where a is the initial amount , b is the growth rate and x is the time
At time 0, we have 5000 bacteria
5000 = a * b^0
5000 = a *1
a = 1
At 4 hours, we have 6000 bacteria
6000 = 5000 * b^4
Divide each side by 5000
6000/5000 = b^4
6/5 = b^4
Take the 4th root of each side
(6/5)^(1/4) = (b^4)^(1/4)
1.046635139 = b
Our equation is
y = 5000 (1.046635139) ^ x
We want to find the number of bacteria present after 17 hours
y = 5000 (1.046635139)^17
y=10851.51313
To the nearest whole number
y = 10852 bacteria
Answer:
I think the answer would be p > -20
Step-by-step explanation:
5 + 4p > -75
4p + 5 > -75
(4p + 5) + (-5) > -75 + (-5)
4p + 5 - 5 > -75 - 5
4p > 80
4p/4 > -80/4
p > 2^4 • 5/2^2
p > -(2^4 - 2 • 5)
p > -(2^2 • 5)
p > -(4 • 5)
p > -20