Which ordred pair is in the solution set of 4x + 8y>16 ?

The area of the square is 144 \(cm^{2}\).

Let x be the side of the square. Then the length of the triangle is (x+4). Perimeter is the length of all sides of a geometric figure combined. For an equilateral triangle, it's equal to thrice the length of one side. For a square, it's four times the length of one side. The Perimeter of the Triangle is 3(x+4) & the Perimeter of the square is 4x.

We know, both these perimeters are equal. Hence,

4x = 3(x+4)

To further simplify the above equation.

4x = 3x + 12

x = 12

Hence, the length of one side of the square is 12 cm. The area of the square can be calculated as follows:

Area = \((side)^{2}\)

Area = 12 * 12

Area = 144 \(cm^{2}\)

Hence, the Area of the Square is 144 \(cm^{2}\)

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Answer:

a(x+y)+2by

Step-by-step explanation:

pick up a from the expression:

a(x+y) +by+by

sum by:

a(x+y)+2by

Step-by-step explanation:

An = -2 * An-1

What this means is that you multiply -2 to the term to get the next term.

Since our 1st term (A1) is -2, we have:

A2 = -2 * A1 = -2 * (-2) = 4,

A3 = -2 * A2 = -2 * (4) = -8,

A4 = -2 * A3 = -2 * (-8) = 16,

A5 = -2 * A4 = -2 * (16) = -32,

A6 = -2 * A5 = -2 * (-32) = 64.

Hence our first 6 terms in the GP are

-2, 4, -8, 16, -32 and 64.

Both the expressions from parts are correct.

In calculus, integration by substitution, also known as μ substitution, inverse chain rule, or change of variables , is a method of evaluating integrals and antiderivatives. This is the counterpart of the chain rule for differentiation and can loosely be thought of as using the chain rule backwards.

In first option we integrate the equation

Consider the integral

∫7x(x²+1) dx

A. First, rewrite the integral by multiplying out the integrand:

∫7 x (x² + 1) dx = ∫(7x^3)+(7x)

Then evaluate the resulting integral term-by-term:

∫7x(x²+1)dx = 7(x^4/4+x^2/2)+C

B. Next, rewrite the integral using the substitution w =(x² + 1):

∫7 x (x² + 1) dx= ∫1/(2sqrt(w-1))

Evaluate this integral (and back-substitute for w) to find the value of the original integral:

∫7x(x²+ 1) dx = 7x^4/4+7x^2/2+7/4+C

C. How are your expressions from parts (A) and (B) different? What is the difference between the two? (Ignore the constant of integration.)

(answer from B)-(answer from A) = 7/4

And in second way we used substitution so both the methods are correct.

Therefore both the Answers are correct .

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Answer:v = y(1-n)dv/dx = (1-n)y-n dy/dxso dy

Step-by-step explanation:

volume = l x w x h

- plug in the numbers

14 X 6 X 3 = 252 yards^3

The balance of the account after 2.4 years is 975.22.

To find the balance of the account, we need to calculate the interest earned over 2.4 years and add it to the initial principal of 925.

The formula for simple interest is:

I = P × r × t

where:

I = interest earned

P = principal (initial amount of money)

r = annual interest rate (as a decimal)

t = time (in years)

Plugging in the values given in the problem, we get:

I = 925 × 0.023 × 2.4

I = 50.22

Therefore, the interest earned over 2.4 years is 50.22.

To find the balance of the account, we need to add the interest earned to the initial principal:

Balance = Principal + Interest

Balance = 925 + 50.22

Balance = 975.22

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Perimeter of the soccer field is 306 meters.

A shape's perimeter  is defined as the total length of its bounds. The perimeter of a shape is determined by summing all sides and side lengths that enclose the shape. It is measured in linear measurement units such as centimeters, meters, inches, and feet.

Given,

Length of the soccer field = 98 meters

Width of the soccer field = 55 meters wide

Perimeter of rectangle = 2(Length + Width)

Perimeter of soccer field = 2(98 + 55)

Perimeter of soccer field = 2(153)

Perimeter of soccer field = 306 meters

Hence, 306 meters is the perimeter of the soccer field.

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Answer:21.87

Step-by-step explanation:

196.83 divided by 9

Answer:

They each cost $21.87

Step-by-step explanation:

If each hose costs the same you can just divide the total (196.83) by the number of hoses (9) to get 21.87.

The three conditions for a function to be continuous at a point x=a are:

a) The function is defined at x=a.

b) The limit of the function as x approaches a exists.

c) The limit of the function as x approaches a is equal to the value of the function at x=a.

The continuity of a function can be analyzed by observing its graph. However, as the graph is not provided, a specific discussion about its continuity cannot be made without further information. It is necessary to examine the behavior of the function around the point in question and determine if the three conditions for continuity are satisfied.

The function f(x) = { *** is not defined in the question. In order to discuss its continuity, the function needs to be provided or described. Without the specific form of the function, it is impossible to analyze its continuity. Different functions can exhibit different behaviors with respect to continuity, so additional information is required to determine whether or not the function is continuous at a particular point or interval.

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Answer:

Step-by-step explanation:

Sum of all angles of pentagon = (5-2)*180 = 3 *180 = 540

4x + 2 +6x - 6 + 4x - 10 + 5x - 11 + 5x + 13 = 540

4x + 6x  + 4x + 5x + 5x + 2 - 6 - 10 - 11 + 13 = 540

                                                     24x  -12 = 540

                                                            24x = 540 + 12

                                                             24x = 552

                                                                 x = 552/24

                                                                  x = 23

∠P = 4x + 2

     = 4*23 + 2

     = 92 + 2

    = 94°

Answer:

It is right

Step-by-step explanation:

good job whatever your name is! you are very smart

Answer:

Given:

Use identity:

Apply to the given expression, substitute cosθ:

Square both sides:

Find cosθ:

Find tanθ:

Find cotθ:

Answer:

9.33 feet = 111.96 inches

Step-by-step explanation:

If we have similar triangles, the rate between matching sides is the same.

So the length of the smaller ladder (18 ft) over the length of the taller ladder (24 ft) is equal to the distance from the bottom of the smaller ladder to the tree (7 ft) over the distance from the bottom of the taller ladder to the tree (x ft):

18 / 7 = 24 / x

x = 7 * 24 / 18

x = 9.33 feet

To find this measure in inches, we just need to multiply by 12:

x = 9.33 * 12 =  111.96 inches

Answer:

Step-by-step explanation:

13 feet 6 inches

Options a, d, and e could describe a binary search tree while the rest doesn't.

In a binary search tree (BST), every element 'a' has certain properties regarding its position relative to other elements in the tree. Let's analyze it:

a. "Lesser than all elements in its left subtree": This statement would hold true in a BST. In a BST, the left subtree contains elements that are smaller than the current element.

b. "Greater than all elements in its left subtree": This statement would not hold true in a BST. In a BST, the left subtree contains elements that are smaller than the current element, so 'a' cannot be greater than all elements in its left subtree.

c. "Lesser than all elements in its right subtree": This statement would not hold true in a BST. In a BST, the right subtree contains elements that are greater than the current element, so 'a' cannot be lesser than all elements in its right subtree.

d. "Greater than all its descendants": This statement would hold true in a BST. In a BST, all elements in the left subtree are smaller than the current element, and all elements in the right subtree are greater. Therefore, 'a' would be greater than all its descendants.

e. "Greater than all elements in its right subtree": This statement would hold true in a BST. In a BST, the right subtree contains elements that are smaller than the current element, so 'a' can be greater than all elements in its right subtree.

In summary, options a, d, and e could describe a binary search tree, while options b and c would not accurately describe a binary search tree.

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If 4 less than a certain integer is multiplied by 5 more than the integer, the product is 3 less than the square of the integer. The integer is 8

To find the value of the integer, let's call it 'x.' According to the given information, when 4 less than 'x' is multiplied by 5 more than 'x,' the resulting product is 3 less than the square of 'x.' Mathematically, we can represent this as (x - 4) * (x + 5) = x^2 - 3.

Simplifying the equation, we expand the product on the left side: x^2 + 5x - 4x - 20 = x^2 - 3. By combining like terms, the equation becomes x^2 + x - 20 = x^2 - 3.

Next, we eliminate the x^2 terms by subtracting x^2 from both sides of the equation: x^2 - x^2 + x - 20 = x^2 - x^2 - 3. This simplifies to x - 20 = -3.

To isolate the 'x' term, we add 20 to both sides: x - 20 + 20 = -3 + 20. This yields x = 17.

Therefore, the value of the integer 'x' is 17.

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The MATLAB program uses the fixed-point iteration method to find a real root of the equation 4x + cos(x) - e* = 0. It starts with an initial approximation of xo = 1 and iteratively applies the function g(x) = e* - cos(x) until convergence. The program also calculates the absolute and relative percentage error for the obtained root.

Here is an example MATLAB program that implements the fixed-point iteration method to find the real root of the given equation:

function root = fixedPointIteration()

   e_star = % Enter the desired value for e* here

   xo = 1; % Initial approximation

   % Set the tolerance for convergence

   tolerance = 1e-6;

   % Initialize variables

   x = xo;

   previous_x = xo;

   iteration = 0;

   % Perform the fixed-point iteration

   while true

       iteration = iteration + 1;

       x = e_star - cos(previous_x);

       % Calculate the absolute and relative percentage errors

       abs_error = abs(x - previous_x);

       rel_error = abs_error / abs(x);

       % Check for convergence

       if abs_error < tolerance

           break;

       end

       previous_x = x;

   end

   % Display the results

   disp('Root:')

   disp(x)

   disp('Absolute Error:')

   disp(abs_error)

   disp('Relative Error (%):')

   disp(rel_error * 100)  

   root = x;

end

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The length of the curve is approximately 0.52334 units.

To set up an integral for the length of the curve, we can use the arc length formula:

L = ∫ from y₁ to y₂  √{1 +{dx}/{dy})²} dy

In this case, we have the equation of the curve in terms of (x) and (y), but we need it in terms of (y) only.

To do this, we can solve for (x) in terms of (y) as follows:

2x = cos(3y)

x = 1/2 cos 3y

Now we can find dx/dy using the chain rule:

dx/dy = - 3/2 sin 3y

We need to find the values of (y) that correspond to the endpoints of the curve.

From the equation 2x = cos(3y), we can see that the curve starts at x = 1/2 when (y = 0), and it ends at (x = -1/2 when (y = π/6.

Therefore, we have (y₁ = 0) and (y₂ = π/6

Now we can substitute these expressions into the arc length formula and simplify:

L = ∫ from y₁ to y₂  √{1 +{dx}/{dy})²} dy

= ∫ from 0 to π/6  √{1 +(- 3/2 sin 3y)²} dy

To graph the curve, we can plug in the equation 2x = cos(3y)) into a graphing calculator or software.

Finally, we can use a graphing calculator software to evaluate the integral numerically.

Doing so, we get

L = 0.52334.

Therefore, the length of the curve is approximately 0.52334 units.

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The equation of the circle with center (5,-8) containing the point (14,-17) is (x - 5)² + (y + 8)² = 162.

The general equation of a circle with center (h,k) and radius r is given by:

(x - h)² + (y - k)² = r²

Given that:  the center of the circle is (5, -8) and the circle contains the point (14, -17).

We can use these values to find the radius, r, and then substitute them into the equation of a circle to obtain the final answer.

The radius r is simply the distance between the center (5,-8) and the point (14,-17). We can use the distance formula to calculate it:

r = √[ (14 - 5)² + (-17 + 8)²]

r = √[ 81 + 81 ]

r = √162

r = 9√2

Now that we have the value of the radius, we can substitute it into the equation of a circle to obtain the final answer:

(x - 5)² + (y + 8) = (  9√2 )²

(x - 5)² + (y + 8)² = 162

Therefore, the equation of the circle is (x - 5)² + (y + 8)² = 162.

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Answer:

Step-by-step explanation:

Try n = 2

2n = 4

n^2 = 4

n+5 = 7   That works. It will make a triangle since the 2 smallest numbers are bigger than 7

Try n = 3

2n = 6

n^2 = 9

n + 5 = 8     That works. Same reason as above.

n = 4

2n = 8

n^2 = 16

n + 5 = 9    That works. Same reason.

n = 5

2n = 10

n^2 = 25

n+5 = 10   Aha! That doesn't work. the two smaller numbers only = 20.

There are likely many numbers that don't work. I'll try one more

n = 6

2n = 12

n + 5 = 11

n^2 = 36   This won't work either. Same reason as n = 5.

Answer:

52 meters

Step-by-step explanation:

each percent is 1, so 50m plus 4 percent equals 52

an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is then instantly teleported to the point $(x,x)$. finally, it heads directly to $b$ at 2 units per second. what value of $x$ should the ant choose to minimize the time it takes to travel from $a$ to $b$?an ant travels from the point $a (0,-63)$ to the point $b (0,74)$ as follows. it first crawls straight to $(x,0)$ with $x \ge 0$, moving at a constant speed of $\sqrt{2}$ units per second. it is t minimize the time it takes to travel from $a$ to $b$?

Answer:

\( \frac{x + 2}{x - 2} \)

Step-by-step explanation:

This is much easier to solve actually since both expressions have the same denominator.

To solve it therefore,just sum the numerators

(x²-4x-2)+(8x+6)

x²+4x+4 Now divide by the common denominator

x²+4x+4/x²-4

Factorize both numerator and denominator

(x+2)(x+2)/(x-2)(x+2)

Cancel out common terms

x+2/x-2

The area of triangle EFG, to the nearest square inch, is approximately 1061 square inches.

To find the area of triangle EFG, we can use the formula:

\(Area = (1/2) \times base \times height\)

In this case, the base of the triangle is FG, and the height is the perpendicular distance from vertex E to side FG.

First, let's find the length of FG. We can use the law of cosines:

FG² = EF² + EG² - 2 * EF * EG * cos(∠F)

EF = 72 inches

EG = 34 inches

∠F = 21°

Plugging these values into the equation:

FG² = 72² + 34² - 2 * 72 * 34 * cos(21°)

Solving for FG, we get:

FG ≈ 83.02 inches

Next, we need to find the height. We can use the formula:

height = \(EF \times sin( \angle F)\)

Plugging in the values:

height = 72 * sin(21°)

height ≈ 25.52 inches

Now we can calculate the area:

\(Area = (1/2) \times FG \times height\\Area = (1/2)\times 83.02 \times 25.52\)

Area ≈ 1060.78 square inches

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Number of seats in the nth row = 38 + (n - 1) * 7.  The row with 290 seats is the 37th row.

a) To determine the type of sequence represented by the increasing number of seats in each row, let's examine the differences between consecutive terms: Second row - First row: 38 - 45 = -7, Third row - Second row: 45 - 38 = 7. We can see that the differences alternate between -7 and 7. This suggests that the sequence follows an arithmetic pattern. Specifically, it is an arithmetic sequence with a common difference of 7.

Now, let's find the function rule to determine the number of seats in the nth row. We can use the formula for the nth term of an arithmetic sequence: nth term = first term + (n - 1) * common difference. In this case, the first term is 38, and the common difference is 7. Plugging in these values, the function rule in simplified form becomes: Number of seats in the nth row = 38 + (n - 1) * 7

b) To find which row has 290 seats using the function rule, we can set up an equation and solve for n: Number of seats in the nth row = 290. 38 + (n - 1) * 7 = 290, Simplify the equation: 38 + 7n - 7 = 290, 7n + 31 = 290, 7n = 259, Divide both sides by 7: n = 259 / 7 ≈ 37. Therefore, the row with 290 seats is the 37th row.

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Answer:

the third one

Step-by-step explanation:

because if we calcul Δ

we get a negative number

Answer:

Step-by-step explanation:

Using Pythagorean Theorem : A² = B²+C².

→x² = 5²+12² = 25+144 = 169.

→x = √169 = 13.

Step-by-step explanation:

Simplify the expression

Answer:

0

Step-by-step explanation: