Answer:
16 years
Step-by-step explanation:
Let x represent the number of years. The suburb population is growing at a rate of 5000 per year after x years, it can be represented by the equation:
320000 + 5000x
The city population is declining at a rate of 14000 per year after x years, it can be represented by the equation:
624000 - 14000x
The number of years for the city and suburb population to be equal can be gotten from:
320000 + 5000x = 624000 - 14000x
14000x + 5000x = 624000 - 320000
19000x = 304000
x = 304000 / 19000
x = 16
In 16 years the populations of the suburb and the city be equal
Answer:
<em>The base is 24 cm long.</em>
Step-by-step explanation:
<u>Equations</u>
Let's call
b= base of the triangle
h=height of the triangle
The base is 9 cm longer than the height, thus:
b = h + 9
The area of the triangle is:


And its value is 180:

Multiplying by 2:

Operating:

Factoring:

The only valid positive solution is:
h = 15 cm
And b = h + 9 = 24
b = 24 cm
The base is 24 cm long.
Simplifying
8x + -10 = 62
Reorder the terms:
-10 + 8x = 62
Solving
-10 + 8x = 62
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '10' to each side of the equation.
-10 + 10 + 8x = 62 + 10
Combine like terms: -10 + 10 = 0
0 + 8x = 62 + 10
8x = 62 + 10
Combine like terms: 62 + 10 = 72
8x = 72
Divide each side by '8'.
x = 9
Simplifying
x = 9
Answer:
Step-by-step explanation:
general equation for a circle at the origin is
x² + y² = r²
if the circle center is (x₀, y₀), the formula is
(x - x₀)² + (y - y₀)² = r²
(x - 8)² + (y - 10)² = 36