A square play area has an area of 5625m2. How long is each side

The area of the circle of radius r centered at the origin is π[tex]a^{2}[/tex]

Since the circle is symmetrical in relation to the x and y axes, we can calculate the area of a quarter of a circle and multiply it by 4 to get the entire circle's area.

The equation y y = + mn [a 2 - x 2] must be solved.

Y = [a 2 - x 2] = a [1 - x 2 / a 2] is the equation for the upper semicircle (y positive).

Using integrals, we can calculate the area of the circle's top right quarter as shown below.

(1 / 4) Circle's area is equal to 0a a [1 - x 2 / a 2]. dx

Let's replace x/a with sin t to make sin t equal to x/a, dx equal to a cos t dt, and the area is given by

The formula for area of a circle is (1 / 4) Area of circle = 0/2 a 2 (1 - sin2 t) cos t dt

Now that t can range from 0 to /2, we utilize the trigonometric identity [1 - sin2 t] = cos t, which equals (1 / 4) Circle area equals 0/2 a 2 cos2 t dt.

To linearize the integrand, use the trigonometric equation cos2 t = (cos 2t + 1) / 2;

(1 / 4) Circle's area is equal to 0/2 a (cos 2t + 1) / 2 dt.

the integral (1 / 4) be evaluated. Circle's area is equal to (1/2) a2 [(1/2) sin 2t + t]. 0π/2\s= (1/4) π a 2

The circle's entire area is calculated by multiplying by 4.

Area of a circle is equal to 4 * (1/4) a 2 a 2. additional references on integrals and calculus applications.

Area of circle = 4 * (1/4) π a 2 = π a 2 More references on integrals and their applications in calculus.

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Answer:

y = 3x + 3

Step-by-step explanation:

The slope is 3

change in y over the change in x.  As the y increases by 3, the x increases by 1.  [tex]\frac{3}{1}[/tex] = 3

Use any of the points from the table to write the equation in the slope intercept form

Let's use the first point (0,3)  Any point would give us the same answer.

We will use the x from the point which is 0 and use the y from the point which is 3.  We will also use the slope of 3.  We will plug all of these into the equation and solve for b or the y-intercept.

y = mx + b

3 = 3(0) + b

3 = 0 + b

3 = b

y = 3x + 3

As a result, 4.8 litres of water will be in the fish tank after three minutes if the water release rate is 1.6 gallons per minute.

A linear system is a mathematical representation of a system in systems theory that relies on the application of a linear operator. Compared to nonlinear systems, linear systems often have significantly simpler traits and properties. Linear systems are widely used in automatic control theory, signal processing, and telecommunications as a mathematical abstraction or idealization.

for 0.5 minutes , 0.8 gallons of water is required

To convert to gallons per minute, multiply by 2.

1.6 gallons per minute (0.8 x 2)

Gallons per minute multiplied by three minutes

3.0 minutes = 4.8 liters (1.6 x 3)

Therefore, 4.8 litres of water will be in the fish tank after 3 minutes if per minute water released is 1.6 gallons

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The complete question is:
How many gallons of water will be in the fish tank after 3 minutes? 0.5 mins = 0.8 gallons

Equation that can be used to represent the number of visits Violet must make to earn a free movie ticket is:

2.5v+45=75

A formula that expresses the equality of two expressions, by connecting them with the equals sign '= 'is called an equation

Unknowns are the variables for which the equation is solved and  unknown values that satisfy the equation are called solutions.

Firstly, multiply 2.5 by the number of visits (v) to calculate how many points Violet earned in total.

Now add 75 to the product of 2.5(v) because Violet started with 75 points.

To find out how many times Violet would require to visit the movie theater to get a free movie ticket:

Subtract 45 from 75,  that leaves you with 30, and after dividing that by 2.5, the number of points per visit comes out to be 12

Violet would need to visit the theater 12 times to earn a free movie ticket.

To check if that's right, substitute the value of 'v' in the equation,

12*2.5 + 45 = 75

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Answer:

8/25

Step-by-step explanation:

change the 5/4 into a 4/5 and change the divide into a mulltiple while you do this

then multiply 2 x 5 = 8

                      5 x 5 = 25

Answer: AAS

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Answer:

Step-by-step explanation:

Problem 2:

Count the blocks.

You can find 1 1000 block

You can find 2 100 block

You can find 3 10 block

You can find 6 1 block.

Together it is 1236.

Problem 3:

Expanded notation is the number listed in groups of base 10. To solve, just put the number of blocks and the block number.

(1 x 1000)+(2 x 100)+(3 x 10) + (6 x 1)

Problem 4:

Find the number between the clues.

Since A is close to 100 and less than 100, you could put 75, which is close to 100 but not quite enough.

Since B is pretty close to a 100 but greater than 100, you could put 110.

Since C is in the middle of both 100 and 200, you could put 150 because it's in the middle of both numbers.

Since D is in between C which is 150 and 200, you could put 175 as that is half of both numbers.

Since E is close to 200 but bigger than D which is 175, you could put 180.

Answer: 5

Step-by-step explanation: Substitute the value of the variable into the expression and simplify

Answer:

C. t = 3/5

Step-by-step explanation:

[tex]10t + 4 - 2t = 2 - 2(t - 4)[/tex]

[tex]4 + 8t = 2 - 2t + 8[/tex]

[tex]4 + 8t = 10 - 2t[/tex]

[tex]4 + 10t = 10[/tex]

[tex]10t = 6[/tex]

[tex]t = .6 = \frac{3}{5} [/tex]

The equation the function after the transformation is  g(x) = -4x² - 8

The equation of the function is given as

f(x) = x²

The sequence of transformations is given as follows:

When the above transformations are combined, we have:

So, we have

g(x) = -4(x² + 2)

Expand

g(x) = -4x² - 8

Hence, the function g(x) is g(x) = -4x² - 8

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Answer: (-2, -2)

Step-by-step explanation:

Since both equations are set equal to y,

[tex]2x+2=-\frac{1}{2}x-3\\\\\frac{5}{2}x=-5\\\\x=-2\\\\\implies y=2(-2)+2=-2\\\\\therefore (x,y)=(-2, -2)[/tex]

Answer:

Acute angle

OLN angle

Step-by-step explanation:

The inequality  x > 0 ,  x all real numbers .

What do you mean by inequality?

= 3(x-2) + 12x + 2(x+2)

= 3x - 6 + 12x + 2x + 4

= 12x + 2x + 3x -6 + 4

=  17x - 2

17x - 2 = 0

x = 2/17

x > 0 ,  x all real numbers ..

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Doug dives a total distance of 6.8 meters from the platform to the bottom of the sea.

A numerical expression is algebraic information stated in the form of numbers and variables that are unknown. Information can is used to generate numerical expressions.

We have been given that a Doug dives from a platform that is 5 meters above the water.

His dive takes him 1.8 meters below the surface of the water.

To determine the total distance Doug dived, add the height of the platform above water and the distance he dived below water.

= (5 + 1.8) meters.

= 6.8 meters.

Thus, Doug dives a total distance of 6.8 meters from the platform to the bottom of the sea.

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Answer:

I'll assume m2 is m^2

m = ±4

Step-by-step explanation:

1.  m = ±4  m^2 = 16  YES.  Both -4 and 4, when squared, are equal to 16

2.  m = 4   This also works, but it doiesn't allow for the possibility that m is a -4

3.  m = ±8  8^2 = 64  and (-8)^2 = 64 Don't work.

4.  m = 8   8^2 = 64  Doesn't work.

Answer: 9

Step-by-step explanation:

1. To divide by 2 you need an even number, and the closest even number below 19.5 is 18.

2. 18 feet divided by 2 feet per piece of rope equals nine pieces of rope.

The correct answer is options A and E.

f(x) = 6x + 4

f(1) = 6(1) + 4 = 10

f(2) = 6(2) + 4 = 16

f(3) = 6(3) + 4 = 22

Clearly, options A and E are the same sequences.

The missing value in the solution to the equation y = -2x+4y is y.

According to the question,

We have the following information:

y = -2x+4y

y equals minus 2 x plus 4.

Now, look at the equation, we know that the solution of y is -2x+4y.

Now, the statement that is given is incomplete because we have 4 is multiplied by y.

(More to know: this equation can be further solved. We have y = -2x+4y. Now, we can move the same variables to one side. So, we have -3y = -2x. Now, the two negative signs when divided gives the positive result.)

Hence, the statement can be completed by y.

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Answer:

5/12

Step-by-step explanation:

answers are in the picture above

Answer: 5

Step-by-step explanation: This equation appears in the Slope-Intercept form, which is Y=Mx+B. In which Y is the coordinate, M is the slope, X is the coordinate and B is the Y-Intercept, or where the line passes the Y-Axis.

Answer: the slope of this equation is 5

Step-by-step explanation: the term "5x" represents the slope of this equation.

slope-intercept form: y = mx + b

m = slope

b = y-intercept

Answer:C = 1.75f

Step-by-step explanation:

C = Cost
F = Fabric in yards
Depending on the amount of fabric in yards she will buy that is the amount she spends.

Step-by-step explanation:

you can ask questions for clarification

17/28 of all the letters are X's.

The actual distance between Dallas and Austin in miles is 180 miles.

Conversion of units means to convert between different units of measurement for the same quantity. Example of units are - m, cm, litre.

Given is the distance between Dallas and Austin on a map is about 9 centimeters. The map uses a scale in which 1 centimeter represents 20 miles.

The maps use scale in order to depict large distances with very small length measurements. As mentioned in the question - 1 cm represents 20 miles. This scale shrinks 20 miles of distance into 1 cm

Distance between Dallas and Austin on a map - 9 cm

On map - 1 cm = 20 miles

Therefore, 9 cm will be equivalent to (9 x 20) or 180 miles.

Hence, the actual distance between Dallas and Austin in miles is 180 miles.

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A graph represents the inequality 2.5 is less than the product of −0.5 and a number is: D. number line with open circle on point negative 5 and arrow shaded to the right.

A number line can be defined as a type of graph with a graduated straight line which is composed of both positive and negative numbers that are placed at equal intervals along its length.

In order to solve this word problem, we would assign a variable to the number and then translate the word problem into an algebraic equation as follows: Let x represent the number.

Translating the word problem into an algebraic equation, we have;

2.5 < -0.5x

Next, we would solve the given inequality as follows:

2.5/0.5 < -0.5x/0.5

5 < -x

x > -5

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The car will catch up the cyclist 3 hours after it starts moving.

The cyclist travels at 9 miles per hour, and travels for 4 hours before the car starts moving, so the equation for the position of the cyclist as a function of time, t, is:

C(t) = 9*4 + 9*t = 36 + 9*t

And the car moves at 21 miles per hour, then the position is:

P(t) = 21*t

The car will catch the cyclist when:

C(t) = P(t), this gives:

36 + 9*t = 21*t

36 = 21*t - 9*t = 12*t

36/12 = t

3 = t

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Answer:

A.    Bank B

Step-by-step explanation:

First the formulae necessary to calculate compound and simple interest

P = principal = amount deposited

r = interest rate as a decimal (i%  interest => r = i/100)

t = number of years

n = number of times compounded

[tex]\text{Compound Interest }= P\left(1 + \dfrac{r}{n}\right)^{nt} - P[/tex]

In this case, we have P = 800
r = 8/100 = 0.08
n = 12 since the interest is compounded monthly
t = 2 years

So compound interest

[tex]CI = 800\left(1 + \dfrac{0.08}{12}\right)^{12 \times 2} - 800\\\\CI = 800(1.00667)^{24} - 800\\\\\\CI = 938.31 - 800\\\\CI = $138.31[/tex]

For Bank B, the interest is calculated at 9% annually and the interest is given by the formula
SI = P x r x t
SI = 800 x 0.09 x 2    (r = 9%/100 = 0.09)

SI =  $144.00

So depositing in bank B is preferred

In the given triangle,

sides vx and vw are equal,

and ∠v = 40°

∠w = ∠x (Adjacent angles of the equal sides of a triangle are equal)

Also, ∠v + ∠w + ∠x = 180° (Angle sum property of a triangle)

⇒ 40° + ∠x + ∠x = 180°

⇒ 2∠x = 140°

⇒∠x = 70°

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Answer:

Step-by-step explanation

Third, second, first.

The third has 5% chance that it will get the investor its money back, second having a 34% of the investor getting its money back, and the first having a 54% chance. Hope this was quick enough for you!