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2 years ago

14

Suppose a population of 140 crickets doubles in size every month. The function f(x) = 140∗2x gives the population after x months

. How many crickets will there be after 2 years?

1 answer:

Tema [17]2 years ago

8 0

The equation would then be f(x) = 140 x 2(24)

There will be 6,720 crickets in 2 years

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<img src="https://tex.z-dn.net/?f=4x%20%7B%7D%5E%7B2%7D%20%20%2B%2020x%20%2B%2025" id="TexFormula1" title="4x {}^{2} + 20x + 25

BigorU [14]

$\sf{\qquad\qquad\huge\underline{{\sf Answer}}}$

Let's Solve ~

$\qquad \sf \dashrightarrow \: 4 {x}^{2} + 20x + 25$

$\qquad \sf \dashrightarrow \: 4 {x}^{2} + 10x + 10x + 25$

$\qquad \sf \dashrightarrow \: 2x(2x + 5) + 5(2x + 5)$

$\qquad \sf \dashrightarrow \: (2x + 5) (2x + 5)$

$\qquad \sf \dashrightarrow \: (2x + 5) {}^{2}$

or

$\sf{\qquad \sf \dashrightarrow \: 4x² + 20x + 25 }$

$\sf{\qquad \sf \dashrightarrow \: (2x)² + (2 \sdot 2x \sdot 5) + (5)²}$

[ it's similar to expression - a² + 2ab + b² that is equal to (a + b)² ]

so, let's use this identity here to factorise :

$\sf{\qquad \sf \dashrightarrow \: (2x + 5)²}$

I hope it was helpful ~

3 0

1 year ago

irina [24]

Answer:

160 m²

384 m²

Step-by-step explanation:

The area of a trapezium is given by :

A = 1/2(a + b)h

h = height ; a and b = lengths

From the diagram :

A = 1/2(12 + 20)10

A = 1/2(32)10

A = 16 * 10

A = 160 m²

2.)

Area of parallelogram = base * height

Base = 24 ; h = 16

A = 24 * 16

A = 384 m²

7 0

2 years ago

HELPPPP What is the volume of the square pyramid? Use Pythagorean’s Theorem to find the height of the pyramid

aalyn [17]

Answer: 4,111.7 mm³

Step-by-step explanation:

You need to use this formula to calculate the volume of the square pyramid:

$V=\frac{s^2h}{3}$

Where "s" is the lenght of any side of the square base and "h" is the height of the pyramid.

Find the height with the Pythagorean Theorem:

$a^2=b^2+c^2$

Where "a" is the hypotenuse and "b" and "c" are the legs of the right triangle. Let be "c" the height of the pyramid.

You can identify in the figure that:

$a=26mm\\\\b=\frac{23mm}{2}=11.5mm\\\\c=h$

Then, you can find the height:

$(26mm)^2=(11.5mm)^2+h^2\\\\h=\sqrt{(26mm)^2-(11.5mm)^2}\\\\h=23.318mm$

Then, knowing that:

$s=23mm\\h=23.318mm$

You can calculate the volume:

$V=\frac{(23mm)^2(23.318mm)}{3}=4,111.7mm^3$

3 0

2 years ago

Fill in the blanks for each box

Aliun [14]

Answer:

hi

Step-by-step explanation:

7 0

2 years ago

How many centimeters make up a triangle.

Eva8 [605]

Answer:

120cm

Step-by-step explanation:

A triangle has a perimeter of 120 cm and two sides of 30 cm and 40 cm. Calculates the area. A right triangle has a cathetus of 10 cm and the hypotenuse 26 cm.

3 0

2 years ago