In June 2003, an Italian named Giancarlo Bellingrath set a world record when
he held his breath for 12 minutes and 47 seconds. How many seconds is
this?

Answer:

I don't need to prove it, I already believe you

Answer:

240

Step-by-step explanation:

You have to find the area of each indivigual side and then add all the areas together. So like 9x5 is 45 so you take 45 and multiply it by 4 since there are 4 sides identical to that side and then you get 180. Then you multiply 6x5 and that gives you 30 which you then multiply by 60, so then all you gotta do is 60+180=240.

Answer:

\(\textsf{1.(a)} \quad x^2-14x+\boxed{49}=\left(x-\boxed{7}\right)^2\)

\(\textsf{1.(b)} \quad 9x^2 + 30x +\boxed{25}= \left(3x +\boxed{5}\right)^2\)

\(\begin{aligned}\textsf{2.(a)}\quad3x^2-24x+48&=3\left(x^2-\boxed{8}\:x+\boxed{16}\right)\\&=3\left(x-\boxed{4}\right)^2\end{aligned}\)

\(\begin{aligned}\textsf{2.(b)}\quad \dfrac{1}{2}x^2+8x+32&=\dfrac{1}{2}\left(x^2+\boxed{16}\:x+\boxed{64}\right)\\&=\dfrac{1}{2}\left(x+\boxed{8}\right)^2\end{aligned}\)

Step-by-step explanation:

(a) When completing the square for a quadratic equation in the form ax² + bx + c where the leading coefficient is one, we need to add the square of half the coefficient of the x-term:

\(x^2-14x+\left(\dfrac{-14}{2}\right)^2\)

\(x^2-14x+\left(-7\right)^2\)

\(x^2-14x+49\)

We have now created a perfect square trinomial in the form a² - 2ab + b². To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 -2ab + b^2 = (a -b)^2}\)

Therefore:

\(a^2=x^2 \implies a=1\)

\(b^2=49=7^2\implies b = 7\)

Therefore, the perfect square trinomial rewritten as a binomial squared is:

\(x^2-14x+\boxed{49}=\left(x-\boxed{7}\right)^2\)

(b) When completing the square for a quadratic equation where the leading coefficient is not one, we need to add the square of the coefficient of the x-term once it is halved and divided by the leading coefficient, and then multiply it by the leading coefficient:

\(9x^2 + 30x +9\left(\dfrac{30}{2 \cdot 9}\right)^2\)

\(9x^2 + 30x +9\left(\dfrac{5}{3}\right)^2\)

\(9x^2 + 30x +9 \cdot \dfrac{25}{9}\)

\(9x^2 + 30x +25\)

We have now created a perfect square trinomial in the form a² + 2ab + b². To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 +2ab + b^2 = (a +b)^2}\)

Therefore:

\(a^2=9x^2 = (3x)^2 \implies a = 3x\)

\(b^2=25 = 5^2 \implies b = 5\)

Therefore, the perfect square trinomial rewritten as a binomial squared is:

\(9x^2 + 30x +\boxed{25}= \left(3x +\boxed{5}\right)^2\)

\(\hrulefill\)

(a) Factor out the leading coefficient 3 from the given expression:

\(3x^2-24x+48=3\left(x^2-\boxed{8}\:x+\boxed{16}\right)\)

We have now created a perfect square trinomial in the form a² - 2ab + b² inside the parentheses. To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 -2ab + b^2 = (a -b)^2}\)

Factor the perfect square trinomial inside the parentheses:

                        \(=3\left(x-\boxed{4}\right)^2\)

(a) Factor out the leading coefficient 1/2 from the given expression:

\(\dfrac{1}{2}x^2+8x+32=\dfrac{1}{2}\left(x^2+\boxed{16}\:x+\boxed{64}\right)\)

We have now created a perfect square trinomial in the form a² + 2ab + b² inside the parentheses. To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2+2ab + b^2 = (a +b)^2}\)

Factor the perfect square trinomial inside the parentheses:

                        \(=\dfrac{1}{2}\left(x+\boxed{8}\right)^2\)

Step-by-step explanation:

Since ABCD is a rectangle

⇒ AB = CD and BC = AD

x + y = 30 …………….. (i)

x – y = 14 ……………. (ii)

(i) + (ii) ⇒ 2x = 44

⇒ x = 22

Plug in x = 22 in (i)

⇒ 22 + y = 30

⇒ y = 8

The perimeter of the given shape as represented in the task content is; 29 cm.

It follows from the task content that the perimeter of the given shape on the centimeter grid as required is to be determined.

Since each grid line has 1cm as it's length;

The perimeter of the shape is the sum of all side lengths of the shape;

Perimeter, P = 6+2+3+2+2+1+3+2+2+2+2+1

P = 29 cm

Hence, the perimeter of the shape is; 29 cm.

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The equation for the total cost of all adult tickets (a) and student tickets (s).

4a + 2.5s = 2,820  

a + s = 900

The number of adults ticket and student tickets is 380 and 520.

We have,

Adults ticket cost = $4

Student ticket cost = $2.5

Now,

Total amount earned = $2,820

The equation for the total cost of all adult tickets (a) and student tickets (s).

4a + 2.5s = 2,820   ______(1)

And,

The number of tickets sold = 900.

We can write as equation as:

a + s = 900 ______(2)

Now,

We have two equations.

4a + 2.5s = 2820

a + s = 900

Solving for s.

s = 900 - a

Substituting in (1)

4a + 2.5(900 - a) = 2820

Simplifying and solving for a.

4a + 2250 - 2.5a = 2820

1.5a = 570

a = 380

Now,

a + s = 900

380 + s = 900

s = 520

Therefore,

The number of adults ticket and student tickets is 380 and 520.

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First take a time derivative of a function describing motion,

\(\frac{d}{dt}h(t)=\frac{d}{dt}-4.9t^2+19.6t-14.6=-9.8t+19.6\).

Finding the maxima of the function is obtained by determining where the critical points are. You can find the critical points by equating the derivative with 0 and solving for t,

\(\frac{d}{dt}h(t)=0\)

\(-9.8t+19.6=0\implies t=\frac{19.6}{9.8}=\boxed{2}\).

So at 2 seconds the ball peaks in height.

To find out the height feed 2 to the function h.

\(h(2)=-4.9\cdot2^2+19.6\cdot2-14.6=\boxed{5}\).

So at 2 seconds the ball reaches maximum height of 5 meters.

Hope this helps :)

The inverse of the function → f(x) = 2x + 5  is → f⁻¹(x) = (x/2) - (5/2).

Inverse of a function can be calculated by following the steps mentioned below -

According to the question, the equation given is as follows

y = f(x) = 2x + 5

y = 2x + 5

Replace 'y' with 'x', we get -

x = 2y + 5

Now, solve for y -

2y = x - 5

y = (x/2) - (5/2)

Replace 'y' with f⁻¹(x) -

f⁻¹(x) = (x/2) - (5/2)

Hence, the inverse of the function → f(x) = 2x + 5  is → f⁻¹(x) = (x/2) - (5/2).

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Answer:

22 1/2

Step-by-step explanation:

Answer: −200y−125

Step-by-step explanation:

Answer:

8/9. 5/9+1/3 L.C.M =9 ANS= 8/9.

Answer:

Step-by-step explanation:

148 people

The equations are

Solve the equations for varaible x.

Since each side of the equation is equal to each other. So lines overlap each other and there are infinitely many solution for the equations.

Answer:

lol i hope this helps:

Step-by-step explanation:

:3 (look at the photo!!!)

Answer:

\(\huge\boxed{\sf 18^{-3}}\)

Step-by-step explanation:

\(\displaystyle \frac{18^4}{18^7}\)

So, the expression becomes:

= \(18 ^{4-7}\)

= \(18^{-3}\)

\(\rule[225]{225}{2}\)

a) The total cost of being on the team is; $1192

b) Ralph average cost is; $119.20

c)  The standard deviation of the distribution of his 10 weekly paychecks is; $0

We are given the costs of the travel team as listed below;

Uniform - $67.00

Registration - $50.00

Tournaments -$775.00

Travel - $300.00

a) To find the total cost of being on the team, we will simply add all the individual costs as given to get;

Total Cost = 67 + 50 + 775 + 300

Total Cost = $1192

b) If Ralph takes a summer job and works 10 weeks over the summer, then his average cost is;

Average Cost = 1192/10

Average Cost = $119.20

c) If he is paid at a flat rate of exactly q dollars each week, the standard deviation of the distribution of his 10 weekly paychecks is;

$0

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Answer:

Step-by-step explanation:

first one is wrong and I don’t know the answer yet

Answer:

perimeter: 2

Step-by-step explanation:

8x-3 = 6x

8x – 6x = 3

2x = 3

x = 3/2

The required algebraic expression that represents the difference between the perimeter of Tamara's suitcase and the perimeter of Anna's suitcase is 5x - 5.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
The difference between the perimeter of Tamara's suitcase and Anna's suitcase can be found by subtracting the expression for the perimeter of Anna's suitcase from the expression for the perimeter of Tamara's suitcase:

(8x - 3) - (3x + 2)

Simplifying the expression by removing the parentheses and combining like terms, we get:

8x - 3 - 3x - 2

= 5x - 5

Therefore, the algebraic expression that represents the difference between the perimeter of Tamara's suitcase and the perimeter of Anna's suitcase is 5x - 5.

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Answer:

2.06

Step-by-step explanation:

The formula for critical value = Margin of Error / Standard Error

Margin of Error = z × Standard deviation/√n

Mean for the month of March = $305.30

Standard deviation = $46.50

n = number of samples = 26 homes

z score for 95% confidence interval = 1.96

= 1.96 × $46.50/√26

= 17.874024556

Standard error = standard deviation/√n

= $46.50/√26

= 9.1194002839

Critical value = Margin of Error/Standard Error

= 17.874024556/9.1194002839

= 2.06

Answer:

Answer is B

Step-by-step explanation:

Answer:θ ≈ 2.57 radians

θ ≈ 0.58 radians

Step-by-step explanation:We can solve this quadratic equation in sin(θ) by factoring:

4sin^2(θ) + 7sin(θ) - 5 = 0

(4sin(θ) - 1)(sin(θ) + 5) = 0

Therefore, either:

4sin(θ) - 1 = 0

sin(θ) = 1/4

or:

sin(θ) + 5 = 0

sin(θ) = -5 (not possible, since sin(θ) is between -1 and 1)

So, we have sin(θ) = 1/4. Since 0 ≤ θ < 2π, we can find the two solutions in the interval [0, 2π) by using the inverse sine function:

θ = arcsin(1/4)

Using a calculator, we find:

θ ≈ 0.2531 or θ ≈ 2.8887

Therefore, in radians, the solutions for θ are approximately:

0.2531 (which is less than 2π)

2.8887 (which is greater than 2π)

So the only answer that satisfies 0 ≤ θ < 2π is:

Answer:

below

Step-by-step explanation:

x = one number

x+23 = second number       <======added together the equal  -14

x   +    x+23    =   -14

2x = -37

x = -18.5       other number = x+23 =  4.5

The composite function f·g(x) is 4x⁴+24x³.

The given functions are f(x)=x²+6x and g(x)=4x².

We need to find f·g(x).

We know that, f·g(x)=f(x)×g(x)

Here, f·g(x)=(x²+6x)×4x²

= x²×4x²+6x×4x²

= 4x⁴+24x³

Therefore, the composite function f·g(x) is 4x⁴+24x³.

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The expression "F = {(x, y) : φ(x, y, p)}" represents a set of ordered pairs (x, y) that satisfy a condition defined by the function φ. The interpretation and nature of the set F depend on the specific function φ and the parameter p, which determine the relationship between the variables x, y, and p.

The expression "F = {(x, y) :  φ(x, y, p)}" represents a set F consisting of ordered pairs (x, y) that satisfy a particular condition defined by the function  φ, which takes the variables x, y, and p as inputs.

To fully understand the meaning of F, we need to delve into the function  φ and its relationship with the variables x, y, and p. The function φ could represent a wide range of mathematical relationships or conditions that determine the inclusion of certain pairs (x, y) in the set F.

For instance, let's consider a specific example where vraphi(x, y, p) is defined  φ(x, y, p) = \(x^2 + y^2 - p^2.\)In this case, F = {(x, y) : \(x^2 + y^2 - p^2\)= 0} represents a set of ordered pairs (x, y) that satisfy the equation \(x^2 + y^2 - p^2 = 0.\) This equation represents a circle with radius p centered at the origin (0, 0). Consequently, F corresponds to all the points lying on the circumference of this circle.

It is important to note that the specific meaning and implications of F heavily rely on the nature of the function  φ and the parameter p. Different functions and parameters will yield distinct sets F with their own unique characteristics and interpretations.

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Answer:

It’s blurry but I think it’s an obtuse triangle

Step-by-step explanation:

Maybe a right triangle

Answer:

p = 5

Step-by-step explanation:

-3(-3-4p) = 69

-3×(-3) + -3× (-4p) = 69

9 + 12p = 69

12p + 9 - 9 = 69 - 9

12p = 60

p = 5

Hope this helps!!!

Answer:

i think its A

Step-by-step explanation:

The probability that the slope of the line determined by p and the point (5/8, 3/8) is greater than or equal to 1/2 is 5/8.

Let the coordinates of point p be (x,y). Then, the slope of the line determined by p and the point (5/8, 3/8) is:

For the slope to be greater than or equal to 1/2, we must have:

Solving for y, we get:

Graphing this inequality on the unit square, we see that the region satisfying this inequality is a trapezoid with vertices (5/8,3/8), (1,1/2), (1,1), and (3/4,1).

The area of this trapezoid is (1/2)*((5/8 - 3/4) + (1 - 5/8) + (1 - 1/2) + (3/8 - 3/16)) = 5/16.

The area of the unit square is 1, so the probability we seek is 5/16.

Hence, the answer is 5/16 written as a fraction in its simplest form, which is 5/16.

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