Answer:
The population changed by 20% in 3 years
Step-by-step explanation:
The percentage change, is given by the following equation;
The given parameters are;
The initial population of the town = 35,000
The final population of the town = 42,000
The percentage change in the population is therefore;
The population changed (increase) by 20% in 3 years.
The solutions to the given system of equations is (0, -6) and (1, -5)
<h3>Simultaneous equations</h3>
From the question, we are to determine the solutions to the given system of equations
The equations are
x − y = 6 --------- (1)
y = x² −6 ---------- (2)
From equation (1)
x - y = 6
∴ x = 6 + y ------- (3)
Substitute into equation (2)
y = x² −6
y = (6+y)² −6
y = (6+y)(6+y) -6
y = 36 + 6y + 6y +y² -6
y = 36 + 12y + y² - 6
Simplifying
y² + 12y - y + 30 = 0
y² + 11y + 30 = 0
Solve quadratically
y² + 11y + 30 = 0
y² + 6y + 5y + 30 = 0
y(y +6) +5 (y +6) = 0
(y + 5)(y + 6) = 0
y + 5 = 0 OR y + 6 = 0
y = -5 OR y = -6
Substitute the values of y into equation (3)
x = 6 + y
When y = -5
x = 6 + (-5)
x = 6 -5
x = 1
When y = -6
x = 6 + (-6)
x = 6 -6
x = 0
∴ When x = 0, y = -6 and when x = 1, y = -5
Hence, the solutions to the given system of equations is (0, -6) and (1, -5)
Learn more on Solving simultaneous equations here: brainly.com/question/16863577
#SPJ!
Answer:
(7x + 10y)
Step-by-step explanation:
To find this add (3x - 4y) to itself to calculate to lengths of the shorter sides.
(3x - 4y) + (3x - 4y) = 6x - 8y
Subtract this from (20x + 12y)
(20x + 12y) - (6x - 8y) = 14x + 20y Divide this by two to get the length of one side
14x + 20y / 2 = 7x + 10y
If this answer is correct, please make me Brainliest!
Perimeter is the sum of all the sides. So we can set up an equation:
Now solve for 'x', combine like terms:
When it comes to terms with variables it's just like normal addition but we keep the variable:
So we have:
Add:
Subtract 7x to both sides:
Subtract 4 to both sides:
Divide 5 to both sides:
To determine the time it takes for the penny to reach the ground, we use the relation of height and time given above. We do as follows:
<span>
0 =−4.9t^2+(0)t+150
t = sqrt( 150/4.9)
t = 5.53 s
Hope this answers the question. Have a nice day.</span>
