What property is illustrated in if ∠ A ≅ ∠ B ∠ B ≅ ∠ C then ∠ A ≅ ∠ C?

According to the Question, The interest earned in 4 years is $1,954.83.

What is compounded quarterly?

A quarterly compounded rate indicates that the principal amount is compounded four times over one year. According to the compounding process, if the compounding time is longer than a year, the investors would receive larger future values for their investment.

The principal is $10,000.

The annual interest rate is 4.5%, which is compounded quarterly.

Since there are four quarters in a year, the quarterly interest rate can be calculated by dividing the annual interest rate by four.

The formula for calculating the future value of a deposit with quarterly compounding is:

\(P = (1 + \frac{r}{n})^{nt}\)

Where P is the principal

The annual interest rate is the number of times the interest is compounded in a year (4 in this case)

t is the number of years

The interest earned equals the future value less the principle.

Therefore, the interest earned can be calculated as follows: I = FV - P

where I = the interest earned and FV is the future value.

Substituting the given values,

\(P = $10,000r = 4.5/4 = 1.125n = 4t = 4 years\)

The future value is:

\(FV = $10,000(1 + 1.125/100)^{4 *4} = $11,954.83\)

Therefore, the interest earned is:

\(I = $11,954.83 - $10,000= $1,954.83\)

Thus, the interest earned in 4 years is $1,954.83.

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Answer: Answer is B

Step-by-step explanation:  

102.3 divided by 23.8 = 4.30 = 4

Answer: A function is a relation between domain and range such that each value in the domain corresponds to only one value in the range. Relations that are not functions violate this definition. They feature at least one value in the domain that corresponds to two or more values in the range.

Step-by-step explanation:

Answer

5 x (f + 9g)

Step-by-step explanation:

I can add my step by step if u want

Answer:

-55

Step-by-step explanation:

got it right on edge

Answer:

m = -3/2

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

Points (4, − 6) and (− 2, 3)

We see the y increase by 9 and the x decrease by 6, so the slope is

m = - 9/6 = -3/2

So, the slope of the line is -3/2

Answer:

5c + 2.12

Step-by-step explanation:

I hope this helps!

Answer:

The procedure for this case is add three, then divide by 5.

Step-by-step explanation:

if y=5x-3

to find the inverse, we exchange x and y then solve for the new y.

x=5y-3   add 3

x+3 = 5y   divide by 5

(x+3)/5 = y

or

inverse, y=(x+3)/5

The procedure for this case is add three, then divide by 5.

Answer:

x = 4 ± \(\sqrt{3}\)

Step-by-step explanation:

Given

x² - 8x + 13 = 0 ( subtract 13 from both sides )

x² - 8x = - 13

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 4)x + 16 = - 13 + 16

(x - 4)² = 3 ( take the square root of both sides )

x - 4 = ± \(\sqrt{3}\) ( add 4 to both sides )

x = 4 ± \(\sqrt{3}\)

Answer:

x = 4 + √3 or x = 4 - √3

Step-by-step explanation:

Use quadratic formula with a=1, b=-8, c=13.

x=−b ± √b2 − 4ac / 2a

x= −(−8) ± √(−8)2 − 4(1)(13) / 2(1)

x= 8 ± √12 / 2

x= 4 + √3 or x= 4 − √3

Answer:

Cone Volume = (PI * radius^2 * height) / 3

96 cc = (PI * radius^2 * 14) / 3

(96 * 3) / (PI * 14) = radius^2

radius ^ 2 = 6.5480890872

radius = 2.5589234235

diameter = radius *2 = 5.117846847  cm

diameter = 5.12 cm (rounded)

Step-by-step explanation:

Therefore , the solution of the given problem of equation comes out to be value of g is 12 .

In a math equation, the comparable symbol (=) is used to denote equality between two propositions. It is demonstrated that by using mathematical formulas, which have been expressions of reality, different numerical factors can be compared. The equal sign, for instance, splits the integer 12 or the equation y + 6 = 12 to 2 different halves. It is possible to determine how many characters each side of such a symbol has. It's common for symbols to have conflicting meanings.

Here,

Given :

=> g -3 = 9

To find the value of g :

=> g = 9 + 3

=> g = 12

Thus , value of g is 12.

Therefore , the solution of the given problem of equation comes out to be value of g is 12 .

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Answer:

5 and 6.

Step-by-step explanation:

5^2 = 25 and 6^2= 36

As we know, 32 is between 25 and 36, therefore √32 is between √25 and √36.

Answer:

the number of miles is 14,722

Step-by-step explanation:

The computation of the number of miles drive last year is shown below:

= Total cost ÷ cost per mile

= $1,560 + $3,740 ÷ $0.36 per mile

= $5,300 ÷ $0.36 per mile

= 14,722 miles

Hence, the number of miles is 14,722

To solve this problem, we can use algebraic equations. Let's say that the number of weeks it takes for Ted and Carly to have the same account balance is "w".

Ted's account balance after "w" weeks can be represented by:

300 + 4w

Carly's account balance after "w" weeks can be represented by:

16w

We want to find out when their account balances will be equal, so we can set these two equations equal to each other:

300 + 4w = 16w

Simplifying this equation, we get:

300 = 12w

Dividing both sides by 12, we get:

25 = w

Therefore, it will take 25 weeks for Ted and Carly to have the same account balance.

The results of the expressions involving logarithms are listed below:

Case 1: 1 / 2

Case 2:

Subcase a: 0

Subcase b: 11 / 2

Subcase c: - 11 / 2

In this problem we have a case of an expression involving logarithms that must be simplified and three cases of expressions involving logarithms that must be evaluated. Each case can be solved by means of the following logarithm properties:

㏒ₐ (b · c) = ㏒ₐ b + ㏒ₐ c

㏒ₐ (b / c) = ㏒ₐ b - ㏒ₐ c

㏒ₐ cᵇ = b · ㏒ₐ c

Now we proceed to determine the result of each case:

Case 1

㏒ ∛8 / ㏒ 4

(1 / 3) · ㏒ 8 / ㏒ 2²

(1 / 3) · ㏒ 2³ / (2 · ㏒ 2)

㏒ 2 / (2 · ㏒ 2)

1 / 2

Case 2:

Subcase a

㏒ [b / (100 · a · c)]

㏒ b - ㏒ (100 · a · c)

㏒ b - ㏒ 100 - ㏒ a - ㏒ c

3 - 2 - 2 + 1

0

Subcase b

㏒√[(a³ · b) / c²]

(1 / 2) · ㏒ [(a³ · b) / c²]

(1 / 2) · ㏒ (a³ · b) - (1 / 2) · ㏒ c²

(1 / 2) · ㏒ a³ + (1 / 2) · ㏒ b - ㏒ c

(3 / 2) · ㏒ a + (1 / 2) · ㏒ b - ㏒ c

(3 / 2) · 2 + (1 / 2) · 3 + 1

3 + 3 / 2 + 1

11 / 2

Subcase c

㏒ [(2 · a · √b) / (5 · c)]⁻¹

- ㏒ [(2 · a · √b) / (5 · c)]

- ㏒ (2 · a · √b) + ㏒ (5 · c)

- ㏒ 2 - ㏒ a - ㏒ √b + ㏒ 5 + ㏒ c

- ㏒ (2 · 5) - ㏒ a - (1 / 2) · ㏒ b + ㏒ c

- ㏒ 10 - ㏒ a - (1 / 2) · ㏒ b + ㏒ c

- 1 - 2 - (1 / 2) · 3 - 1

- 4 - 3 / 2

- 11 / 2

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Part A) The cost function is C(x) = 12x + 5000 and the revenue function would be R(x) = 25x.

Part B) Muffins A-plenty 385 months to make its first profit.

Part C) Profit after 10 months of operation is $4970.

What is the cost function?

A cost function is a mathematical function that represents the total cost of producing a certain number of goods or services.

Part A:

The cost function for Muffins A-plenty is given by:

C(x) = 12x + 5000

This represents the total cost of producing x muffins. The cost of each muffin is $12, and there is a fixed cost of $5000.

The revenue function for Muffins A-plenty is given by:

R(x) = 25x

This represents the total revenue from selling x muffins at a price of $25 per muffin.

Part B:

The profit function for Muffins A-plenty is given by:

P(x) = R(x) - C(x) = 25x - (12x + 5000) = 13x - 5000

To determine the number of months it takes for Muffins A-plenty to make its first profit, we need to find the first value of x such that P(x) > 0.

Substituting x = 0, we get P(0) = -5000, which is negative.

Substituting x = 1, we get P(1) = 13 - 5000 = -4987, which is also negative.

Substituting x = 2, we get P(2) = 26 - 5000 = -4974, which is still negative.

However, when we substitute x = 385, we get P(385) = 5000, which is the first time P(x) is greater than zero. This means that it takes Muffins A-plenty 385 months to make its first profit.

Part C:

To predict the profit after 10 months of operation, we need to substitute x = 10 into the profit function:

P(10) = 4970

This means that the profit after 10 months of operation is $4970. This is a loss, as the profit is negative.

Hence,

Part A) The cost function is C(x) = 12x + 5000 and the revenue function would be R(x) = 25x.

Part B) Muffins A-plenty 385 months to make its first profit.

Part C) Profit after 10 months of operation is $4970.

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A story that can be represented using the equation y=x+1/5x is "John has an apple and he cut another apple into 5 equal parts and took on part. What's the rural fraction of apple that he has?

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

In this case, if John has an apple and he cut another apple into 5 equal parts and took on part.

This can be illustrated as:

y = x + 1/5x

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Answer:

1590 minutes

Step-by-step explanation:

November 17 ends on 12:00, which is 8 hours after 4:00 pm. The time from the beginning of November 18 to noon is 12 hours, and the distance from noon to 6:30 is 6 hours and 30 minutes, so the total time in hours is 8+12+6 +1/2=26 1/2.

Because we know that one hour is 60 minutes, 26 hours is going to be 60*26, which is equal to 60*20+60*6=1560.

1/2 * 60 = 30. 1560+30=1590, so the value of minutes is 1590 minutes.

2.87 units

The volume of a cone is found by using the formula, V = (1/3)(pi)(h)r^2

Substituting values:

3 = (1/3)(3.14)(h)(1)

2.87 = h

Answer: The answer is 5

Answer:

B

Step-by-step explanation:

If you distribute:

2(x) + 2(10)

that gives you:

2x + 20

Answer:

B. 2x +20

Step-by-step explanation:

Answer:

carry out laws and put them in action

Answer:11.52

Step-by-step explanation:

Answer: 11.52

Step-by-step explanation:

Answer:

( 3 , − 10 )

Step-by-step explanation:

Answer:

-3,10

Step-by-step explanation:

First, follow PEMDAS, then you will have your answer

Answer:

B. 0

Step-by-step explanation:

The slope of a straight horizontal line is always equal to 0.

To support the above statement, we can show working out:

m = slope of the line

m = ( y1 - y2 ) / ( x1 - x2 )

Two points on line = ( 0 , - 2 ) , ( 1 , - 2 )

y1 = - 2

y2 = - 2

x1 = 0

x2 = 1

m = [ ( - 2 ) - ( - 2 ) ] / [ ( 0 ) - ( 1 ) ]

m = ( - 2 + 2 ) / ( 0 - 1 )

m = 0 / - 1

m = 0

The y values on a horizontal line will always be the same. When calculating the subtraction of y values in the numerator of the formula for the slope of a line, a number subtracted by itself will always equal to 0. 0 divided by any number will always equal to 0. Hence, the slope of a straight horizontal line will always equal to 0.

we find that the numerical approximation using Euler's method gives y(2) ≈ 1.865, while the analytical solution gives y(2) = 2.5.

Using the formula y(n+1) = y(n) + Δx * f(x(n), y(n)), where f(x, y) = x² √y, we can calculate the values of y at each step. Here's the step-by-step calculation:

Step 1: For x = 0, y = 1 (initial condition).

Step 2: For x = 0.2, y = 1 + 0.2 * (0.2)² * √1 = 1.008.

Step 3: For x = 0.4, y = 1.008 + 0.2 * (0.4)² * √1.008 = 1.024.

Step 4: For x = 0.6, y = 1.024 + 0.2 * (0.6)² * √1.024 = 1.052.

Step 5: For x = 0.8, y = 1.052 + 0.2 * (0.8)² * √1.052 = 1.094.

Step 6: For x = 1.0, y = 1.094 + 0.2 * (1.0)² * √1.094 = 1.155.

Step 7: For x = 1.2, y = 1.155 + 0.2 * (1.2)² * √1.155 = 1.238.

Step 8: For x = 1.4, y = 1.238 + 0.2 * (1.4)² * √1.238 = 1.346.

Step 9: For x = 1.6, y = 1.346 + 0.2 * (1.6)² * √1.346 = 1.483.

Step 10: For x = 1.8, y = 1.483 + 0.2 * (1.8)² * √1.483 = 1.654.

Step 11: For x = 2.0, y = 1.654 + 0.2 * (2.0)² * √1.654 = 1.865.

Therefore, using Euler's method with a step size of Δx = 0.2, we approximate y(2) to be 1.865.

To obtain the analytical solution to the ODE, we can separate variables and integrate both sides:

∫(1/√y) dy = ∫x² dx

Integrating both sides gives:

2√y = (1/3)x³ + C

Solving for y:

y = (1/4)(x³ + C)²

Using the initial condition y(0) = 1, we can substitute x = 0 and y = 1 to find the value of C:

1 = (1/4)(0³ + C)²

1 = (1/4)C²

4 = C²

C = ±2

Since C can be either 2 or -2, the general solution to the ODE is:

y = (1/4)(x³ + 2)² or y = (1/4)(x³ - 2)²

Now, let's evaluate y(2) using the analytical solution:

y(2) = (1/4)(2³ + 2)² = (1/4)(8 + 2)² = (1/4)(10)² = 2.5

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Answer:

undefined

Step-by-step explanation:

y2-y/x2-x1=

(11/7-4/7)/(2/3-2/3) =(3/11)/0

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Answer:

I have to show the work gimme a sec

Step-by-step explanation: