MATHEMATICS HIGH SCHOOL

A square is inscribed in an equilateral triangle that is inscribed in a circle. A square is inscribed in an equilateral triangle that is inscribed in a circle. The square and circle are shaded.

Which represents the area of the shaded region?

area of the circle – area of the square – area of the triangle
area of the triangle – area of the square + area of the circle
area of the triangle + area of the square + area of the circle
area of the circle – area of the triangle + area of the square

Answers

Answer 1

Answer:

The area of the shadedregion is (area of the circle) - (area of the square) - (area of the triangle)

Option A is the correct answer

What is a triangle?

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

The shadedregion consists of the area inside the circle but outside the square, as well as the area inside the equilateral triangle but outside the square.

Now,

The area of the circle is πr²

Since the square is inscribed in the circle, the diameter of the circle is equal to the diagonal of the square.

Let's say the side length of the square is s.

By the Pythagorean theorem,

s² + s² = (diameter)²

2s² = (2r)²

s² = r²

The area of the square is s² = r².

The area of an equilateraltriangle with side length s is √(3)/4 x s².

Since the side length of the square is equal to the height of the equilateral triangle, the side length of the equilateral triangle is also equal to s.

The area of the shadedregion.

= (area of the circle) - (area of the square) - (area of the triangle)

Thus,

The area of the shadedregion is (area of the circle) - (area of the square) - (area of the triangle)

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Answer 2

Answer: A is square due to ots shape

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For the following exercises, use this scenario: A biologist recorded a count of 360 bacteria present in a culture after 5 minutes and 1000 bacteria present after 20 minutes. Rounding to six significant digits, write an exponential equation representing this situation. To the nearest minute, how long did it take the population to double

Answers

Answer:

$P(t)=256*e^(0.068185t)$

10 minutes for the population to double.

Step-by-step explanation:

The general formula for the population equation, P(t), is:

$P(t)=A*e^(nt)$

We are given that for t =5 minutes and t = 2 minutes:

$P(5)=360=A*e^(5n)\nP(20)=1,000=A*e^(20n)\n\n$

Solving for A and n:

$ln(360)=ln(A)+5n\nln(1,000)=ln(A)+20n\nln(1,000)-4ln(360)=ln(A)-4ln(A)+20n-20n\nln(A)=5.5455536\nA=256\nn=(ln(360)-ln(256))/(5)\nn=0.068185$

The exponential equation that represents this situation is:

$P(t)=256*e^(0.068185t)$

The population will double when P(t) = 512 bacteria:

$512=256*e^(0.068185t)\nln(2)=0.068185t\nt=10.17\ minutes$

To the nearest minute, it takes roughly 10 minutes for the population to double.

Help me please
It about linear equations

Answers

Answer:

plant 1 i think

Step-by-step explanation:

Answer:

Plant 2 grew faster

Step-by-step explanation:

The slope of plant 1 is 3

(each day the plant grew 3cm)

The slope of plant 2 is 5

(each day the plant grew 5cm)

The slope of plant 3 is 1.5

(each day the plant grew 1.5cm)

The zeros of the function f(x) =(x+2) to the second power minus 5

Answers

$(x+2)^2-5=0\n (x+2)^2=5\n x+2=-\sqrt5 \vee x+2=\sqrt5\n x=-2-\sqrt5 \vee x=-2+\sqrt5$

Mark can make 42 birthday cakes in 7 days how many cakes can mark make in 5 days

Answers

Mark can make 30 cakes in 5 days.

How many cakes can mark make in 5 days?

Given that Mark can make 42 birthday cakes in 7 days.

In 5 days Mark can make,

If the ratio can be 42 : 7

42/ 7 = x/ 5

where, x can be the number of cakes,

x = 30

So, 30 cakes can be done in 7 days.

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42:7 ratio
42/7=x/5
you cross multiply to get 30 cakes
42 times 5 divided by 7

Why do all verified people who answer, are always wrong

Answers

Answer:

they probably do it just to get more answer points or whatever the brianily thing is called

Step-by-step explanation:

A model for a proposed computer chip measures 1/9 inch by 1 4/9 inches. Find its area.