Find the area of the sector in terms of pi. 24 180° Area = [?] T Enter Find the area of the sector in terms of pi . 24 180 ° Area = [ ? ] T​

The simplified form of √([2m5z6]/[xy]) is (√2m√5z√6) / (√x√y).

To simplify the expression √([2m5z6]/[xy]), we can break it down step by step:

Simplify the numerator:

√(2m5z6) = √(2) * √(m) * √(5) * √(z) * √(6)

= √2m√5z√6

Simplify the denominator:

√(xy) = √(x) * √(y)

Combine the numerator and denominator:

√([2m5z6]/[xy]) = (√2m√5z√6) / (√x√y)

Thus, the simplified form of √([2m5z6]/[xy]) is (√2m√5z√6) / (√x√y).

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\(\displaystyle\bf\\If~p=-8.4~and~q=3.2~find~r~when~r= 8.4q-p\\\\Solution: \\\\r= 8.4q-p=\\\\= 8.4\times3.2-(-8.4)=\\\\= 8.4\times3.2+8.4=\\\\= 26.88+8.4=35.28\\\\\boxed{\bf r=35.28}\)

The number of steps they climbed can be represented by positive

From the question, we understand that they climbed up

Upward movements are usually represented by the positive sign

This means that:

Steps = 125 or +125

Hence, the number of steps they climbed can be represented by positive

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Answer:

5

Step-by-step explanation:

2x²y³ + 4y³ = 149 + 3x²

\( 2x^2y^3 - 3x^2 = 149 - 4y^3 \)

\( x^2(2y^3 - 3) = 149 - 4y^3 \)

\( x^2 = \dfrac{149 - 4y^3}{2y^3 - 3} \)

\( x = \pm \sqrt{\dfrac{149 - 4y^3}{2y^3 - 3}} \)

Try y = 1

\(x = \pm \sqrt{\dfrac{149 - 4(1)}{2(1)^3 - 3}} = \pm \sqrt{-145} = i\sqrt{145}\)

For y = 1, x is imaginary.

Try y = 2

\( x = \pm \sqrt{\dfrac{149 - 4(2)^3}{2(2)^3 - 3}} = \pm \sqrt{9} = \pm 3\)

Since x and y are positive integers, ignore x = -3.

When x = 3, y = 2.

x + y = 3 + 2 = 5

The value of x + y is 5.

Polynomials are expressions which consist of variables, constants, coefficients and exponents.

We have the equation,

2x²y³ + 4y³ = 149 + 3x²

2x²y³ - 3x² = 149 - 4y³

x² (2y³ - 3) = 149 - 4y³

x² = (149 - 4y³) / (2y³ - 3)

x = √[(149 - 4y³) / (2y³ - 3)]

Now, we have to find two positive integers.

We can use trial and error method here.

Trial putting y = 1.

x = √[(149 - 4 × 1³) / (2 × 1³ - 3)]

  = √[145 / (-1)]

  = √(-145)

There is no real root for √(-145). So y = 1 is not applicable.

Trial putting y = 2.

x = √[(149 - 4 × 2³) / (2 × 2³ - 3)]

  = √[117 / 13]

  = √(9)

  = ± 3

But we need positive integers. So we ignore -3.

So x = 3 and y = 2 ⇒ x + y = 5

Hence x + y = 5.

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The solution of x in the inequality is x > 2

The inequality is given as:

5x + one third(3x + 6) > 14

Rewrite properly as:

5x + 1/3(3x + 6) > 14

Open the brackets

5x + x + 2 > 14

Subtract 2 from both sides of the inequality

5x + x + 2 - 2> 14 - 2

Evaluate the difference

5x + x > 12

Evaluate the like terms

6x > 12

Divide both sides of the inequality by 2

x > 2

Hence, the solution of x in the inequality is x > 2

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Answer:

x > 2, like the other guy said

Step-by-step explanation:

I hope this helps

During halftime of a basketball game, a slingshot launches T-shirts at the crowd.

What is the maximum height?

Generally, To find the time it takes the T-shirt to reach its maximum height, we need to find the time when the height of the T-shirt stops increasing and starts decreasing. At this point, the velocity of the T-shirt will be 0, since it is not moving up or down.

The velocity of the T-shirt at any time t can be found by taking the derivative of the equation for height:

v(t) = dh/dt = -32t + 72

Setting the velocity to 0 and solving for t, we get:

0 = -32t + 72 32t = 72 t = 72/32 t = 9/4

So it takes the T-shirt 9/4 seconds, or approximately 2.25 seconds, to reach its maximum height.

To find the maximum height, we plug this value back into the equation for height:

h(t) = -16(9/4)^2 + 72(9/4) + 4 h(t) = -81 + 162 + 4 h(t) = 77

The maximum height of the T-shirt is 77 feet.

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Given:

Let's again recall the rule: The negative exponent in the numerator rule tells us that a number with a negative exponent should be put to the denominator, and vice versa.

In other worths, if the exponent of a number or variable is negative, we should reciprocate it and remove the negative sign.

We get,

Therefore, the answer is:

Answer:

4506.4369

Step-by-step explanation:

welcome

The area of the rhombus, obtained from the dimensions, of the diagonals, found from the trigonometric of sines of the angle can be presented as follows;

Area = 8·√3

The area of a plane figure is the two dimensional space occupied by the figure on a plane.

The measure of the angle ABC, m∠ABC = 60°

The length of the segment AE = 2 units

The diagonals of a rhombus bisect each other at right angles, and the right angles through which they pass, therefore;

BE = ED, m∠AEB = 90°

m∠ABE = 30°

sin(30°) = AE/AB

sin(30°) = 2/AB

AB = 2/(sin(30°)) = 4

AB = 4

BE = √(4² - 2²) = √(12) = 2·√3

Therefore; AC = 2 + 2 = 4

BD = 2·√3 + 2·√3 = 4·√3

The area of a rhombus = (1/2) × The product of the length of the diagonals

Therefore;

Area of the rhombus = (1/2) × (4·√3) × 4 = 8·√3

The area of the rhombus = 8·√3

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Answer:

No these these result do not differ at 95% confidence level  

Step-by-step explanation:

From the question we are told that

  The first concentrations is  \(c _1= 30.0 \ g/m^3\)

      The second concentrations is  \(c _2 = 52.9 \ g/m^3\)

  The first sample size is  \(n_1 =  32\)

    The second sample size is  \(n_2 =  32\)

   The  first standard deviation is \(\sigma_1 =  30.0 \)

     The  first standard deviation is \(\sigma_1 =  29.0 \)

The mean for  Turnpike is  \(\= x _1 = \frac{c_1}{n} = \frac{31.4}{32} = 0.98125\)

The mean for   Tunnel is  \(\= x _2 = \frac{c_2}{n} = \frac{52.9}{32} = 1.6531\)

The  null hypothesis is  \(H_o : \mu _1 - \mu_2 = 0\)

The  alternative hypothesis is  \(H_a : \mu _1 - \mu_2 \ne 0\)

Generally the test statistics is mathematically represented as

              \(t = \frac{\= x_1 - \= x_2}{ \sqrt{\frac{\sigma_1^2}{n_1} +\frac{\sigma_2^2}{n_2} }}\)

         \(t = \frac{0.98125 - 1.6531}{ \sqrt{\frac{30^2}{32} +\frac{29^2}{32} }}\)

        \(t = - 0.0899\)

Generally the degree of freedom is mathematically represented as

     \(df = 32+ 32 - 2\)

     \(df = 62\)

The  significance \(\alpha\)  is  evaluated as

      \(\alpha = (C - 100 )\%\)

=>   \(\alpha = (95 - 100 )\%\)

=>   \(\alpha =0.05\)

The  critical value  is evaluated as

      \(t_c = 2 * t_{0.05 , 62}\)

From the student t- distribution table  

        \(t_{0.05, 62} = 1.67\)

So

     \(t_c = 2 * 1.67\)

=>  \(t_c = 3.34\)

given that

       \(t_c > t\) we fail to reject the null hypothesis so  this mean that the result do  not differ

Answer:

90 PLEASE MARK ME BRAINLLIEST

Step-by-step explanation:

289.76-54.88-54.88=180/2=90

Perimeter is the sum of the length of the sides used to make the given figure. The length of the field is 90 meters.

Perimeter is the sum of the length of the sides used to make the given figure.

Given that the width of the field is 54.88 meters and the perimeter of the field is 289.76 meters. Therefore, we can write the perimeter as,

Perimeter = 2(Length + Width)

289.76 meters = 2(Length + 54.88 meters)

289.76meters / 2 = Length + 54.88 meters

144.88metes = Length + 54.88 meters

Length = 144.88 meters - 54.88 meters

Length = 90 meters

Hence, the length of the field is 90 meters.

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Given in the question:

a.) A washer and a dryer cost $649 combined.

b.) The washer costs $51 less than the dryer.

From the given description, let's transform them into an equation.

Let,

x = Cost of washer

y = Cost of dryer

a.) A washer and a dryer cost $649 combined.

b.) The washer costs $51 less than the dryer.

From the generated equation, substitute x = y - $51 to x + y = $649.

We get,

Therefore, the cost of the dryer is $350.

Let's find the cost of the washer.

Therefore, the cost of the washer is $299.

Answer:

5:47

Step-by-step explanation:

in my opinion audience means young adult

Step-by-step explanation:

It may help you

Jordan spend 25 minutes writing each dayNoHow much time does Jordan spend writing each dayFrom the question, we have the following parameters that can be used in our computation:D + W = 75W + 25 = DSo, we haveW + W + 25 = 75EvaluateW = 25This means that Jordan spends 25 minutes on writing is it possible?Based on the answer in (a), the truth statement is No

Exponential growth is a type of growth that occurs when the rate of increase is proportional to the current amount.

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The general solution for the equation 5tan(θ) - 6cos(θ) = 0 is:

θ = sin⁻¹(2/3) + nπ, where n is an integer.

To determine the general solution of the trigonometric equation 5tan(θ) - 6cos(θ) = 0, we can use algebraic manipulation and trigonometric identities to simplify and solve for θ.

Starting with the given equation:

5tan(θ) - 6cos(θ) = 0

First, we can rewrite the tangent function in terms of sine and cosine:

5(sin(θ)/cos(θ)) - 6cos(θ) = 0

Next, multiply through by cos(θ) to eliminate the denominator:

5sin(θ) - 6cos²(θ) = 0

Using the identity sin²(θ) + cos²(θ) = 1, we can express cos²(θ) as 1 - sin²(θ):

5sin(θ) - 6(1 - sin²(θ)) = 0

Expanding and rearranging terms:

5sin(θ) - 6 + 6sin²(θ) = 0

Rearranging the equation:

6sin²(θ) + 5sin(θ) - 6 = 0

Now, we have a quadratic equation in terms of sin(θ).

We can solve this quadratic equation by factoring or using the quadratic formula.

However, since this equation is not easily factorable, we will use the quadratic formula:

sin(θ) = (-b ± √(b² - 4ac)) / 2a

For our equation:

a = 6, b = 5, c = -6

Plugging these values into the quadratic formula and simplifying, we get:

sin(θ) = (-5 ± √(5² - 4(6)(-6))) / (2(6))

sin(θ) = (-5 ± √(25 + 144)) / 12

sin(θ) = (-5 ± √169) / 12

sin(θ) = (-5 ± 13) / 12.

This gives us two possible solutions for sin(θ):

sin(θ) = (13 - 5) / 12 = 8/12 = 2/3

sin(θ) = (-13 - 5) / 12 = -18/12 = -3/2

Since the range of the sine function is -1 to 1, the second solution (-3/2) is not valid.

Now, to find the values of θ, we can use the inverse sine function (sin⁻¹) to solve for θ:

θ = sin⁻¹(2/3)

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The pair of numbers that yields the maximum product when their sum is 24 is (12, 12), and the maximum product is 144. The corresponding quadratic function is P(x) = -x^2 + 24x, and the parabola opens downwards.

To find a pair of numbers whose sum is 24 and whose product is as large as possible, we can use the concept of maximizing a quadratic function.

Let's denote the two numbers as x and y. We know that x + y = 24. We want to maximize the product xy.

To solve this problem, we can rewrite the equation x + y = 24 as y = 24 - x. Now we can express the product xy in terms of a single variable, x:

P(x) = x(24 - x)

This equation represents a quadratic function. To find the maximum value of the product, we need to determine the vertex of the parabola.

The quadratic function can be rewritten as P(x) = -x^2 + 24x. We recognize that the coefficient of x^2 is negative, which means the parabola opens downwards.

To find the vertex of the parabola, we can use the formula x = -b / (2a), where a = -1 and b = 24. Plugging in these values, we get x = -24 / (2 * -1) = 12.

Substituting the value of x into the equation y = 24 - x, we find y = 24 - 12 = 12.

So the pair of numbers that yields the maximum product is (12, 12). The maximum product is obtained by evaluating the quadratic function at the vertex: P(12) = 12(24 - 12) = 12(12) = 144.

Therefore, the maximum product is 144. This quadratic function has a maximum value because the parabola opens downwards.

To graph the function, you can plot several points and connect them to form a parabolic shape. Here is an uploaded image of the graph of the quadratic function: [Image: Parabola Graph]

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\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$2000\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &20 \end{cases}\)

\(A = 2000\left(1+\frac{0.03}{12}\right)^{12\cdot 20}\implies A=2000(1.0025)^{240} \implies \boxed{A \approx 3641.51} \\\\\\ 3641.51~~ - ~~2000~~ \approx~~ \stackrel{earned~interest}{\boxed{1641.51}}\)

Answer:

1.5

Step-by-step explanation:

The scale factor can be found by dividing the side length from triangle ABC by the corresponding side length from triangle ABC

so the scale factor would be equal to

12/8 and 9/6

9/6 = 1.5

12/8 =1.5

so we can conclude that the scale factor is 1.5

Answer:

Step-by-step explanation:

She has  5 dimes, 2 pennies, and 3 nickels in her pocket.

So 5+2+3 = 10 coins total.

For the first coin is a dime, the probability = number of dimes/total number of coins

= 5/10

= 1/2

After that, 9 coins are left with 4 dimes, 2 pennies and 3 nickels.

For the second coin is a penny, the probability = number of penny / total number of coins

= 2/9

Combining the above, probability that the first coin is a dime and the second coin is a penny

= 1/2 * 2/9

= 1/9

Answer:

i think sequence bye 4567890

I don't know if you have any questions

The function g(x) in the form a(x-h)^2 + k is: \(g(x) = (x + 2)^2 - 4\)

Starting with\(f(x) = x^2\), the translation 2 units left and 4 units down would result in the following transformation:

g(x) = f(x + 2) - 4

Substituting\(f(x) = x^2:\)

\(g(x) = (x + 2)^2 - 4\)

Expanding the square:

\(g(x) = x^2 + 4x + 4 - 4\)

Simplifying:

\(g(x) = x^2 + 4x\)

Now we need to rewrite this expression in the form \(a(x-h)^2 + k.\) To do this, we will complete the square:

\(g(x) = x^2 + 4x\\g(x) = (x^2 + 4x + 4) - 4\\g(x) = (x + 2)^2 - 4\)

Therefore, the function g(x) in the form a(x-h)^2 + k is:

\(g(x) = (x + 2)^2 - 4\)

Where a = 1, h = -2, and k = -4.

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Answer:

Below

Step-by-step explanation:

Rate of change (aka the slope) = 2/5

Y Intercept = 10

Step-by-step explanation:

M(x) = 4x^3 - 3

let M(x) = Y

Y = 4x^3 - 3...swap places of x & y.

X = 4y^3 - 3

look for x in terms of y.

4y^3 = x + 3

Y^3 = x + 3 / 4...put both sides under cube root.

y = ( x + 3 / 4 )^1/3

Answer: C)

Step-by-step explanation:

If you subtract .5 to y you get x

Answer:

the answer is B put the point 1 in the equation you will get 0 hence proved

∠G+∠H+∠J=180 and ∠K+∠L+∠M=180 from the angle sum property of triangle, ∠H=∠L (3rd Angle Theorem) and ∆GHJ≅∆KLM from ASA congruency theorem.

In the given question we have to prove ∆GHJ congrurnce ∆KLM.

Given that: ∠G≅∠K, ∠J≅∠M, \(\over{HJ}\) ≅ \(\over{LM}\).

As given that;

∠G≅∠K

∠J≅∠M

\(\over{HJ}\) ≅ \(\over{LM}\)

So from the angle sum property of triangle

∠G+∠H+∠J=180................(1)

∠K+∠L+∠M=180.................(2)

Now equation equation 1 and 2

∠G+∠H+∠J=∠K+∠L+∠M

As we know that ∠G=∠K, ∠J=∠M

So now the expression is

∠G+∠H+∠J=∠G+∠L+∠J

After solving ∠H=∠L (3rd Angle Theorem)

Since, ∠H=∠L, HJ=LM and ∠G=∠K, so from the theorem Angle Side Angle(ASA) congruency,

∆GHJ≅∆KLM

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