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3 years ago

A town has a population of 2000 and grows at 4% every year write an equation to represent the scenario

Mathematics

1 answer:

vfiekz [6]3 years ago

7 0

Answer: $P=2000(1.04)^t$ .

Step-by-step explanation:

It is given that,

Initial population of a town = 2000

Growth rate = 4% = 0.04 per year

The exponential growth function for population is

$P=P_0(1+r)^t$

where, $P_0$ is initial population, r is growth rate and t is number of years.

Substitute $P_0=2000,r=0.04$ in the above equation.

$P=2000(1+0.04)^t$

$P=2000(1.04)^t$

Therefore, the required equation is $P=2000(1.04)^t$ , where P is population after t years.

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Step-by-step explanation:

$-4x+7(3x+15)=20\\ -4x+21x+105=20\\ 17x+105=20\\ 17x=20-105\\ 17x=-85\\ x=-5$

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PLEASE HELP!!-What two rotations would provide the following images.

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3 years ago

Solve 5x^2 - 7x + 2 = 0 by completing the square.

Reika [66]

Answer: The correct option is (c) $\dfrac{49}{100}.$

Step-by-step explanation: We are given to solve the following quadratic equation by the method of completing the square:

$5x^2-7x+2=0~~~~~~~~~~~~~~~~~~~(i)$

Also, we are to find the constant added on both sides to form the perfect square trinomial.

We have from equation (i) that

$5x^2-7x+2=0\\\\\Rightarrow x^2-\dfrac{7}{5}x+\dfrac{2}{5}=0\\\\\\\Rightarrow x^2-2\times x\times \dfrac{7}{10}+\left(\dfrac{7}{10}\right)^2+\dfrac{2}{5}=\left(\dfrac{7}{10}\right)^2\\\\\\\Rightarrow \left(x-\dfrac{7}{10}\right)^2=\dfrac{49}{100}-\dfrac{2}{5}\\\\\\\Rightarrow \left(x-\dfrac{7}{10}\right)^2=\dfrac{49-40}{100}\\\\\\\Rightarrow \left(x-\dfrac{7}{10}\right)^2=\dfrac{9}{100}\\\\\\\Rightarrow x-\dfrac{7}{10}=\pm\dfrac{3}{10}\\\\\\\Rightarrow x=\pm\dfrac{3}{10}+\dfrac{7}{10}.$

So,

$x=\dfrac{3}{10}+\dfrac{7}{10},~~~~~~~~x=-\dfrac{3}{10}+\dfrac{7}{10}\\\\\\\Rightarrow x=\dfrac{10}{10},~~~~~~~~\Rightarrow x=\dfrac{-3+7}{10}\\\\\\\Rightarrow x=1,~-\dfrac{2}{5}.$

Thus, the required solution is $x=1,~-\dfrac{2}{5}.$ and the value of the constant added is $\dfrac{49}{100}.$

Option (c) is correct.

3 0

3 years ago

Can someone help meeeeee

11Alexandr11 [23.1K]

Answer:

Area of shaded rectangle = 42 cm²

55%

Step-by-step explanation:

The length of the shaded area is equal to the length of the white rectangle.

Therefore, length of shaded rectangle = 7 cm

The width of the shaded rectangle is equal to the length of the white rectangle <u>minus</u> two widths of the white rectangle.

Therefore, width = 7 - (2 x 0.5) = 6 cm

Area of shaded rectangle = width x length

= 6 x 7

= 42 cm²

----------------------------------------------------------------------------------------------

Perimeter of a square = 4 × side length

If the perimeter of the square is 40 cm,
then the side length = 40 ÷ 4 = 10 cm

Area of a square = side length x side length

⇒ area of this square = 10 x 10 = 100 cm²

To determine the shaded area, calculate the areas of the 2 white triangles and subtract these from the area of the square.

Area of a triangle = 1/2 x base x height

⇒ area of left triangle = 1/2 x (10 - 7) x 10 = 15 cm²

⇒ area of right triangle = 1/2 x 10 x (10 - 4) = 30 cm²

Therefore, shaded area = 100 - 15 - 30 = 55 cm²

To calculate the percentage, divide the shaded area by the area of the square and multiply by 100:

(55 ÷ 100) × 100% = 55%

7 0

3 years ago

What is the fourth number if three of the numbers are 80, 95, and 85?

Strike441 [17]

100 because it goes up 15 and 5

3 0

4 years ago

Read 2 more answers

A town has a population of 2000 and grows at 4% every year write an equation to represent the scenario​

A town has a population of 2000 and grows at 4% every year write an equation to represent the scenario