How do you write an equivalent logarithmic equation for e^4=x

Given polygons a right triangle and an isosceles triangle sometimes be similar.

As given ,

Given polygons : A right triangle and isosceles triangle.

Polygon a right triangle and isosceles triangle never be similar.

Reason:

Therefore, given polygons a right triangle and an isosceles triangle sometimes be similar.

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Answer:

10

Step-by-step explanation:

In a polygon

interior angle + interior angle = 180°, thus

exterior angle = 180° - 144° = 36°

The sum of the exterior angles in a polygon = 360°, thus

number of sides = \(\frac{360}{36}\) = 10

Answer:

10 sides

Step-by-step explanation:

A decagon is a 10-sided polygon, with 10 interior angles, and 10 vertices which is where the sides meet. A regular decagon has 10 equal-length sides and equal-measure interior angles. Each angle measures 144° and they all add up to 1,440°.

Answer:

3x=10-1

3x=9

x=9/3=3

x=3

the answer is 3

If you save $2,015.82 every year at an interest rate of 8%, you can retire in 30 years and live another 25 years while still having enough money to spend $80,000 per year.

To calculate the amount you need to save per year for the next 30 years, we can use the future value of an ordinary annuity formula.

The future value of an ordinary annuity formula is:

\(FV = P \cdot \left(\frac{(1 + r)^n - 1}{r}\right)\)

Where:

FV = Future value of the annuity

P = Payment amount per period

r = Interest rate per period

n = Number of periods

In this case:

P = Amount you need to save per year

r = 8% = 0.08 (annual interest rate)

n = 30 (number of years)

We want the future value (FV) to be equal to the amount needed to spend per year during retirement, which is $80,000.

Using the formula, we can calculate the amount you need to save per year:

\(\$80,000 = P \cdot \left[\left(1 + 0.08\right)^{30} - 1\right] / 0.08\$\)

Simplifying the equation:

\($80000 = P \cdot [1.08^{30} - 1] / 0.08$\)

$80,000 * 0.08 = P * [1.08³⁰ - 1]

$6,400 = P * [1.08³⁰ - 1]

Dividing both sides by [1.08³⁰ - 1]:

\($P = \dfrac{\$6400}{1.08^{30} - 1}$\)

Calculating [1.08³⁰ - 1]:

[1.08³⁰ - 1] ≈ 3.172024

Dividing $6,400 by 3.172024:

P ≈ \($\frac{6,400}{3.172024} \approx$ $2,015.82\) (rounded to the nearest cent)

Therefore, you need to save approximately $2,015.82 per year into your investment account at the end of each year for the next 30 years.

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The probability that calls to exactly two randomly selected households will both go unanswered is 0.1849

From the question, we have the following parameters that can be used in our computation:

Probabiity of answering, p = 57%

This means that the probability that no one answers the call is

q = 1 - 57%

Evaluate

q = 43%

So, the probability that both calls will go unanswered is

P = q²

This gives

P = (43%)²

Evaluate

P = 0.1849

Hence, the probability is 0.1849

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Answer:

It the volume

Step-by-step explanation:

Answer:

the answer is 1908.52

Step-by-step explanation:

The solution of the DTDS is xn = (0.63)^n * 41 grams, where n represents time in hours.

a) The updating function f(x) for the discrete time dynamical system (DTDS) can be derived from the given information that the body eliminates 37% of the alcohol present in the body per hour.

Since 37% of the alcohol is eliminated, the amount remaining after one hour can be calculated by subtracting 37% of the current amount from the current amount. This can be expressed as:

f(x) = x - 0.37x

Simplifying the equation:

f(x) = 0.63x

b) The initial condition for the DTDS is given as Peter having 41 grams of alcohol in his body after consuming three alcoholic drinks. Therefore, the initial condition is:

x0 = 41 grams

c) To find the solution of the DTDS with the given initial condition, we can use the updating function f(x) and iterate it over time.

For n hours, the solution is given by:

xn = f^n(x0)

Applying the updating function f(x) repeatedly for n times:

xn = f(f(f(...f(x0))))

In this case, since the function f(x) is f(x) = 0.63x, the solution can be written as:

xn = (0.63)^n * x0

Substituting the initial condition x0 = 41 grams, the solution becomes:

xn = (0.63)^n * 41 grams

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Al-Fatihah is an Islamic prayer recited during the five daily prayers. Comparing radio and television in reading Al-Fatihah from its beginning requires an analysis of how each medium conveys the prayer to its audience. Radio precedes television in reading Al-Fatihah from its beginning.

This is because radio broadcasting began in the early 1900s while television broadcasting began in the late 1940s.

This delay can range from a few seconds to a few minutes depending on several factors such as the geographical location of the audience, the strength of the signal, and the quality of the receiver. Therefore, the time difference between radio and television in reading Al-Fatihah can vary depending on the factors mentioned above.

Mathematically, the time difference between radio and television can be calculated using the formula: d = s / tWhere d is the distance between the transmitter and the receiver, s is the speed of the signal, and t is the time it takes for the signal to reach the receiver.

In this case, d is the distance between the broadcasting station and the audience, s is the speed of the signal which is constant (i.e., the speed of light), and t is the time it takes for the signal to reach the audience. Since the speed of light is approximately 299,792,458 m/s, the time it takes for the signal to reach the audience can be calculated using the following formula:t = d / s

Therefore, the time difference between radio and television in reading Al-Fatihah can be calculated by subtracting the time it takes for the radio signal to reach its audience from the time it takes for the television signal to reach its audience. This difference can range from a few milliseconds to a few minutes depending on the factors mentioned above.

In network concepts, the time difference between radio and television in reading Al-Fatihah can be affected by the bandwidth of the network. The bandwidth is the amount of data that can be transmitted over a network in a given time. If the bandwidth is low, it can cause a delay in the transmission of the signal which can affect the time difference between radio and television.

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The expected time taken by the man to leave the maze is 15 minutes.

To find the expected time taken by the man to leave the maze, we'll first calculate the conditional expectation of time taken given that he chose each of the exits, and then use these conditional expectations to calculate the overall expectation.

Step 1: Calculate the conditional expectations :
- If he chooses Exit 1 (probability 1/3), he leaves the maze after 3 minutes.
- If he chooses Exit 2 (probability 1/3), he returns to the same room after 5 minutes and starts again. So, the expected time in this case is 5 + E(X).
- If he chooses Exit 3 (probability 1/3), he returns to the same room after 7 minutes and starts again. So, the expected time in this case is 7 + E(X).

Step 2: Calculate the overall expectation :
E(X) = (1/3)*(3) + (1/3)*(5 + E(X)) + (1/3)*(7 + E(X))

Now, we'll solve for E(X):
3E(X) = 3 + 5 + 7 + 2E(X)
E(X) = 15 minutes

The expected time taken by the man to leave the maze is 15 minutes.

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According to the problem, there are three possible exits (1, 2, and 3) from the room in the center of the maze. The probabilities of choosing each of these exits are equal.

Exit 1 leads to the outside of the maze, and it takes 3 minutes on average to reach it. Exit 2 leads back to the same room, so the man will need to start over again. Exit 3 also leads back to the same room, and it takes longer than exit 2 to get there (7 minutes).Let X be the time taken by the man to leave the maze from this room. Let Y be the exit he chooses first. Y belongs to {1, 2, 3}. Calculate the conditional expectation of the time taken to leave the maze given that he chose each of the exits. Then use these conditional expectations to calculate the expectation of the time taken to leave the maze.The expected value of X can be calculated as follows:() = ( | = 1) × ( = 1) + ( | = 2) × ( = 2) + ( | = 3) × ( = 3)Expected time to leave the maze through exit 1:( | = 1) = 3Expected time to leave the maze through exit 2:( | = 2) = 5 + ()Expected time to leave the maze through exit 3:( | = 3) = 7 + ()The probability of choosing each exit is 1/3, so:P(Y = 1) = 1/3P(Y = 2) = 1/3P(Y = 3) = 1/3Substituting these values into the equation for ():() = 3(1/3) + (5 + ())(1/3) + (7 + ())(1/3)() = 5 + (2/3)() + (7/3)()() = 15 minutes. Therefore, the expected time taken by the man to leave the maze is 15 minutes.

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We can say that the new area is given by 1600 square feet and the garden gets enlarged by 400 square feet.

The rectangular garden is 60 feet long and 20 feet wide.

To enlarge the garden while using the same fence, its shape is changed to a square.

The area of the rectangular garden is given by;

A = l × w

Where;

l = 60 feet

w = 20 feet

A = 60 × 20 = 1200 square feet.

To find the new area of the garden when it's changed to a square, we need to determine the length of one side of the square.

Since the square is formed by using the same fence that enclosed the rectangular garden, the perimeter of the square should be equal to the perimeter of the rectangular garden. Therefore;

Perimeter of rectangle = 2(l + w)

= 2(60 + 20)

= 2(80)

= 160 feet.

Perimeter of square = 160 feet.

Let s be the length of one side of the square. Then;

Perimeter of square = 4s

= 160 feet.

Divide both sides by 4;

4s/4 = 160/4

s = 40 feet.

New area of the garden is given by;

A = s²

= (40)²

= 1600 square feet.

The new area is 1600 square feet.

The garden enlarges by 1600 - 1200 = 400 square feet.

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Answer:

d

Step-by-step explanation:

CAFDYahi Sahi answer hai bhai

You can use linear equations and then can solve that system of linear equations to find the number of each type of coin Julio has got in the given condition.

The number of coin that Julio got in his pocket for each type are given as

Number of nickles = 12

Number of dimes = 14

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on  methods can be used to convert description to mathematical expressions.

Let Julio has got x amount of nickels and got y amount of dimes in his pocket. Then by the given description, we have got;

Number of dimes = twice the number of nickle - 10

\(y = 2x -10\)

Total amount in his pocket = $2.75

Total amount = amount by x nickles and amount by y dimes

\(2.75 = x \times 0.05 + y \times 0.1\) (since one nickle = $0.05, and one dime  = $0.1)

Thus, we got system of linear equations for given condition as:

\(y = 2x - 10\\0.05x + 0.1y = 2.75\)

Substituting value of y from first equation in the second equation, we get:

\(0.05x + 0.1(2x-10) = 2.75\\0.05x + 0.2x - 1 = 2.75\\0.25x = 3.75\\\\x = \dfrac{3.75}{0.25} = 12\)

Thus, there are 12 nickles in Julio's pocket

Putting this value in first equation, we get:

\(y = 2x - 10\\y = 2 \times 12 - 10\\y = 24 - 10 = 14\)

Thus,

The number of coin that Julio got in his pocket for each type are given as

Number of nickles = 12

Number of dimes = 14

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Reported to the proper number of significant figures, is 551.56 which has five significant figures.

The given expression is:(2115 - 2101) × (5.11 × 7.72)

Now let's evaluate the given expression to solve for the unknown. For that, we have to perform the mathematical operations in the following order according to the proper order of operations or the PEMDAS rule:

Parentheses or Brackets Exponents or Powers Multiplication or Division (from left to right) Addition or Subtraction (from left to right). So, let's solve the given expression by using the above rule.

(2115 - 2101) × (5.11 × 7.72)= 14 × (5.11 × 7.72)= 14 × 39.3972= 551.5608 ≈ 551.56

The answer, reported to the proper number of significant figures, is 551.56 which has five significant figures.

The first significant figure is 5 (it comes before decimal point), and the next four significant figures are 5, 1, 5, and 6 (they come after decimal point). The final answer should have no more than five significant figures because the least precise number given in the expression (2101) has four significant figures.

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I think that for a its 1.12 and for b its 39424

100 + 12 = 112
112/100 = 1.12

35200 * 1.12 = 39424

Let 'x' represent the cost of the garden table.

Let 'y' represent the cost of the bench.

Therefore, from the first statemenet

From the second statement,

Substitute x = y - 77 into equation 1

Collect like terms

Divide both sides by 2

Therefore, the cost of the bench is 325.

Answer:

\({a}^{2} - {b}^{2}= {(80)}^{2} -{(45)}^{2} \\(a + b)(a - b) = (80 + 45)(80 - 45) \\ = 125 \times 35 = \boxed{ 4375}✓\)

The value of the 9 in 964,352 is 90 times greater than the value of the 9 in 290,481 .

The value of the 9 in 964,352 can be written as 900,000

The value of the 9 in 290,481 is 90, 000

Then to know the the number of times that  value of the 9 in 964,352is greater than the value of the 9 in 290,481 , then we can express it as

900,000/90, 000= 90

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An equation is formed of two equal expressions. The value of x is 6, while the value of y is 13.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The corresponding sides of the kite are of the same length, therefore, the length of the lower two sides are equal and the length of the upper two sides are equal as well. Thus, the equation for length can be written as,

2x + 3 = x + 9

2x - x = 9 - 3

x = 6

Similarly, the equation for the upper two sides of the kite can be written as,

y - 5 = x + 2

y - 5 = 6 + 2

y - 5 = 8

y = 8 + 5

y = 13

Hence, the value of x is 6, while the value of y is 13.

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The solutions to the quadratic equation x² = -7x - 8 are x equals  \(\frac{-7 - \sqrt{17}}{2}, \frac{-7 + \sqrt{17}}{2}\).

Given the quadratic equation in the question:

x² = -7x - 8

To find the solutions of the quadratic equation x² = -7x - 8, we can rearrange it into standard quadratic form, which is ax² + bx + c = 0, and apply the quadratic formula.

x² = -7x - 8

x² + 7x + 8 = 0

a = 1, b = 7 and c = 8

Plug these into the quadratic formula: ±

\(x = \frac{-b \± \sqrt{b^2 -4(ac)}}{2a} \\\\x = \frac{-7 \± \sqrt{7^2 -4(1*8)}}{2*1} \\\\x = \frac{-7 \± \sqrt{49 -4(8)}}{2} \\\\x = \frac{-7 \± \sqrt{49 - 32}}{2} \\\\x = \frac{-7 \± \sqrt{17}}{2} \\\\x = \frac{-7 - \sqrt{17}}{2}, \frac{-7 + \sqrt{17}}{2}\)

Therefore, the values of x are \(\frac{-7 - \sqrt{17}}{2}, \frac{-7 + \sqrt{17}}{2}\).

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The first derivatives for the given functions are:

For \(y = 3x^2 + 5x + 10,\) the first derivative is dy/dx = 6x + 5.

For  \(y = 100200x + 7x,\) the first derivative is dy/dx = 100207.

For \(y = ln(9x^4),\) the first derivative is dy/dx = 4/x.

To find the first derivative for each of the given functions, we'll use the power rule, constant rule, and chain rule as needed.

For the function\(y = 3x^2 + 5x + 10:\)

Taking the derivative term by term:

\(d/dx (3x^2) = 6x\)

d/dx (5x) = 5

d/dx (10) = 0

Therefore, the first derivative is:

dy/dx = 6x + 5

For the function y = 100200x + 7x:

Taking the derivative term by term:

d/dx (100200x) = 100200

d/dx (7x) = 7

Therefore, the first derivative is:

dy/dx = 100200 + 7 = 100207

For the function \(y = ln(9x^4):\)

Using the chain rule, the derivative of ln(u) is du/dx divided by u:

dy/dx = (1/u) \(\times\) du/dx

Let's differentiate the function using the chain rule:

\(u = 9x^4\)

\(du/dx = d/dx (9x^4) = 36x^3\)

Now, substitute the values back into the derivative formula:

\(dy/dx = (1/u) \times du/dx = (1/(9x^4)) \times (36x^3) = 36x^3 / (9x^4) = 4/x\)

Therefore, the first derivative is:

dy/dx = 4/x

To summarize:

For \(y = 3x^2 + 5x + 10,\) the first derivative is dy/dx = 6x + 5.

For y = 100200x + 7x, the first derivative is dy/dx = 100207.

For\(y = ln(9x^4),\) the first derivative is dy/dx = 4/x.

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Answer:

700%

Step-by-step explanation:

504/72 = 7

7 * 100 = 700

Answer:

3

Step-by-step explanation:

the answer

Answer:

Width = 44 yards

Length = 171 yards

Step-by-step explanation:

given data

length of the field = 5 yards

Perimeter of the rectangular field = 430 yards.

solution

we consider here length of the field = L

and width of the field = W

as we know length of the field 5yards less than quadruple the width

so here

L = 4W - 5       .....................................1

and  

Perimeter (P) will be here

P = 2(L + W)      ............................................2

put here equation 1 value

430 = 2(4W - 5 + W)  

solve it we get

W = 44

so here put value in eq 1 we het

L = 4W - 5          

L = 4(44) - 5

L = 171

so, length of the field is 171 yards

Answer:

Step-by-step explanation:

Emily buys 3 pencils for 51p

Work out the price of 4 pencils.

51 : 3 * 4 = 68p

Answer:

68

Step-by-step explanation:

We can write a ratio to solve

3 pencils      4 pencils

------------- = -------------

51 p                x

Using cross products

3x = 51*4

3x = 204

Divide by 3

3x/3 = 204/3

x = 68

The length of SR to the nearest hundredth is approximately 13.12 units.

What is Pythagoras theorem?

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

We can use the Pythagorean theorem to find the length of QR, which is the hypotenuse of right triangle PQR:

PQ² + QR² = PR²

Substituting in the given values:

(9+x)²+ QS² = 16²

We know that QS is the altitude from Q to PR, which means it is also the height of triangle PQR. We can use the area of triangle PQR to find the length of QS:

area of PQR = (1/2) * PQ * QS = (1/2) * 9 * QS

area of PQR = (1/2) * QR * QS = (1/2) * 16 * QS

Since the area of PQR is the same, we can set these two equations equal to each other and solve for QS:

(1/2) * 9 * QS = (1/2) * 16 * QS

9QS = 16QS

QS = (16/9) * x

Substituting this value for QS into the equation we set up earlier:

(9+x)²+ [(16/9)*x]²= 16²

Simplifying and solving for x:

81 + 18x + x²+ 256x²/81 = 256

x²+ 18x + 81 + 256x²/81 - 256 = 0

81x² + 1458x + 6561 + 20736x² - 20736(81) = 0

2889x² + 1458x - 127008 = 0

Using the quadratic formula:

x = (-b ± sqrt(b² - 4ac)) / 2a

where a = 2889, b = 1458, and c = -127008

x = (-1458 ± sqrt(1458² - 4(2889)(-127008))) / 2(2889)

x = (-1458 ± sqrt(5872034)) / 5778

x ≈ 13.12 or x ≈ -21.89

Since x represents a length, we take the positive value as our answer:

x ≈ 13.12

Therefore, the length of SR to the nearest hundredth is approximately 13.12units.

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The given vectors are linearly independent and are False. The vectors are linearly dependent

To determine whether the given vectors (1, 1, 0), (0, 2, 3) and (1, 2, 3) in R₃ are linearly independent, we need to check if there exist scalars (constants) such that a linear combination of these vectors equals the zero vector (0, 0, 0) with all components being zero.

In this case, we can set up the equation:

a(1, 1, 0) + b(0, 2, 3) + c(1, 2, 3) = (0, 0, 0)

Expanding the equation component-wise, we get:

(a + c, a + 2b + 2c, 3b + 3c) = (0, 0, 0)

This equation has non-trivial solutions (other than a = b = c = 0), we can set up an augmented matrix:

[1 0 1 | 0]

[1 2 2 | 0]

[0 3 3 | 0]

By row-reducing this matrix, we find:

[1 0 1 | 0]

[0 1 1 | 0]

[0 0 0 | 0]

From the row-reduced form, we see that the third row (0 0 0 | 0) implies that there are infinitely many solutions, indicating linear dependence among the vectors.

Therefore, the statement The given vectors are linearly independent is False. The vectors are linearly dependent.

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