Triangle ΔABC has side lengths of a = 18, b=\(18\sqrt{3}\), and c = 36 inches.

Part A: Determine the measure of angle A.

Part B: Show how to use the unit circle to find tan A.

Part C: Calculate the area of ΔABC.

Answer:

She will have $375,769.33 in her retirement plan at the time of retirement.

Explanation:

According to the question,

Periodic Payments(P) = $200

Rate of Return(r) = 12%(annual)

                           \(=\frac{12}{12}%\)  

                           = 1% monthly

                           = 0.01

Number of payments(n) = 65 - 40

                                        = 25(annual)

                                        = 25 × 12 monthly

                                        = 300 monthly

Future value =?

The formula for calculating future value is:

Future Value = \(P[\frac{(1+i)^{n}-1 }{i}]\)

                      = \(200[\frac{(1+0.01)^{300}-1 }{0.01}]\)

                      = \(200[\frac{19.7884663-1}{0.01}]\)

                      = 200[1878.84663]

                      = 375,769.326

                      = 375,769.33

Final Answer:

Therefore, the future value of her retirement when she retires is

$ 375,769.33 .

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Saving for a down payment was worth it for Isabel. It reduces the total amount paid for the car by lowering the loan amount, resulting in less interest paid over time.

When evaluating whether saving for a down payment on a car was worth it for Isabel, we need to consider the difference in the total amount paid for the car in two scenarios: with a down payment and without a down payment. Let's analyze the two scenarios to make a judgment.

Scenario 1: With a down payment

In this scenario, Isabel saved up and made a down payment on the car. As a result, her monthly loan payment fits within her budget. By making a down payment, she reduces the principal amount borrowed and, subsequently, the interest charged on the loan.

The benefits of saving for a down payment include:

Lower loan amount: By making a down payment, Isabel reduces the total amount borrowed from the lender.

Reduced interest: With a lower loan amount, the interest charged on the loan is also reduced.

Shorter loan term: A down payment can help Isabel secure a shorter loan term, reducing the overall interest paid over time.

Scenario 2: Without a down payment

In this scenario, Isabel does not make a down payment and finances the entire purchase price of the car. As a result, her monthly loan payment may be higher, as she is borrowing a larger sum and potentially paying more interest over the loan term.

The drawbacks of not saving for a down payment include:

Higher loan amount: Without a down payment, the entire purchase price is financed, leading to a higher loan amount.

Increased interest: With a higher loan amount, more interest may accumulate over the loan term, resulting in a higher total cost of the car.

By comparing the two scenarios, we can assess the impact on the total amount paid for the car. Generally, having a down payment reduces the loan amount, decreases interest charges, and may result in a shorter loan term. This, in turn, can lead to substantial savings in the long run.

To determine the exact difference in the total amount paid for the car in each scenario, we would need specific details such as the purchase price of the car, the interest rate, and the loan term. With these figures, we could calculate the total cost of the car, including interest, in both scenarios and compare the results. Based on this analysis, we can then determine if saving for a down payment was worth it for Isabel.

In conclusion, saving for a down payment on a car can offer financial benefits such as lower loan amounts, reduced interest charges, and potentially shorter loan terms. Considering the potential cost savings and improved financial stability, it is generally advisable for Isabel to save for a down payment, making it worth the effort and consideration.

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Question

The down payment makes the monthly loan payment fit into Isabel's budget. Besides this benefit, do you think saving for a down payment on the car was worth it for Isabel? Use each monthly payment with and without a down payment) to find the difference of the total amount paid for the car in each scenario to justify your answer.

It will take approximately 28.67 years for Talwar's investment of R5,800 to grow to R26,100 at a simple interest rate of 12.2% per annum.

To calculate the number of years it will take for Talwar's investment to grow to R26,100 at a simple interest rate of 12.2% per annum, we can use the formula for simple interest:

Simple Interest = Principal × Rate × Time

Given that the principal (P) is R5,800, the rate (R) is 12.2% (or 0.122 as a decimal), and the desired amount (A) is R26,100, we need to find the time (T) it will take. Rearranging the formula, we get:

Time = (Amount - Principal) / (Principal × Rate)

Plugging in the values, we have:

Time = (R26,100 - R5,800) / (R5,800 × 0.122)

= R20,300 / R708.6

≈ 28.67 years

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The equilibrium point for James T-shirt business is (P, Q) = (7, 24).

To find the equilibrium point (P, Q) for James T-shirt business

we need to set the demand function equal to the supply function and solve for the values of P and Q.

Demand function: P = -Q + 31

Supply function: P = Q - 17

Setting them equal:

-Q + 31 = Q - 17

Adding Q to both sides and subtracting 31 from both sides:

2Q = 48

Dividing both sides by 2:

Q = 24

Now, we can substitute this value of Q into either the demand or supply function to find the corresponding value of P.

P = Q - 17

P = 24 - 17

P = 7

Therefore, the equilibrium point for James T-shirt business is (P, Q) = (7, 24).

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The formula for perimeter is 2(Length) + 2(width)

Fill in the known information:

22 = 2(6.5)+ 2(width)

Simplify:

22 = 13 + 2(width)

Subtract 13 from both sides:

9 = 2(width)

Divide both sides by 2:

Width = 4.5m

Therefore , the answer to this problem is that planned delivery time is the amount of time required to get material.

Time scheduling is a group of methods for creating and presenting schedules that indicate when work will be done. All of these methods' outcomes are typically displayed as activities or bars on a timeline known as a Gantt chart.

Here,

Obtaining the substance requires the following scheduling if it is externally manufactured.

So ,

When a material is purchased outside, the planned delivery time is the amount of time required to get the material.

Therefore , the answer to this problem is that planned delivery time is the amount of time required to get material.

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The complete question is "which of the following scheduling times is needed to obtain the material if it is externally produced or not ?

a.In-house production time.

b.Goods issue processing time.

c.  Planned delivery time.

d. Goods receipt processing time."

Answer:

1/2 < 3/4.

Step-by-step explanation:

if you draw two rectangles, and split them accordingly, 3/4 will be more than 1/2.

hope this helps!

Answer: 9

Step-by-step explanation: To divide we need to flip the second fraction we are dividing by. For example:

10/1 divided by 1/4 = 10/1 times 4/1. So in this case, the answer is 40.

Now lets try it with 1/9.

X divided by 1/9 = X times 9/1.

So dividing by 1/9 is equal to multiplying by 9.

Answer:

We don't know the initial value of the principal but we do know that the accumulated value is double (twice) the principal. It takes 9.9 years for money to double if invested at 7% continuous investment

Answer:

Not a lot of information given but if you are looking for the difference in price it is 31 CHF

It is 31 more CHF in Manchester than in Switzerland.

Step-by-step explanation:

1.55(145) = 224.75

224.75-193.75 = 31

Fraction which are equivalent to the given fractions are as follow:

a. 4 /6 is equivalent to 2/3, 8/12, 12/18 ,...

b. 4/8 is equivalent to 1/2 , 8/16, 12/24,.....

c. 2/6 is equivalent to 1/3 , 4/12, 6/18,....

d. 2/4 is equivalent to 1/2, 4/8, 6/12,...

e. 3/4 is equivalent to 6/8, 9/12, 12/16,...

As given in the question,

Equivalent fraction are the fractions which when reduced have the same numerator and denominator.

Multiply or divide by 2/2, 3/3, 4/4, 5/5,...so on to all numerator and denominators of the given fractions to get equivalent fraction.

a. 4/6 divide by 2 both numerator and denominator we get

4/6 = 2/3

Now multiply by both numerator and denominator by 2/2, 3/3,...so on.

4/6 is equivalent to 2/3 , 8/12, 12/18,...

Multiply and divide by same numbers in the numerator and denominator of all the fractions to get equivalent

b. b. 4/8 is equivalent to 1/2 , 8/16, 12/24,.....

c. 2/6 is equivalent to 1/3 , 4/12, 6/18,....

d. 2/4 is equivalent to 1/2, 4/8, 6/12,...

e. 3/4 is equivalent to 6/8, 9/12, 12/16,...

Therefore, equivalent fractions of the given fractions are :

a. 4 /6 is equivalent to 2/3, 8/12, 12/18 ,...

b. b. 4/8 is equivalent to 1/2 , 8/16, 12/24,.....

c. 2/6 is equivalent to 1/3 , 4/12, 6/18,....

d. 2/4 is equivalent to 1/2, 4/8, 6/12,...

e. 3/4 is equivalent to 6/8, 9/12, 12/16,...

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\(\mathbb{FINAL\:ANSWER:}\)

\(\huge\boxed{\sf{y=4x+3}}\)

\(\mathbb{SOLUTION\:WITH\:STEPS:}\)

Hi! Hope you are having a nice day!

We are given the slope of the line and its y-intercept.

So, let's find the equation.

The y-intercept is written in the form (0, b).

No worries! b is the y-intercept.

Thus, the y-intercept equals 3.

Now, let's find the equation of the line with a slope of 4 and a y-intercept of 3.

We can write the equation in Slope-intercept form:

y=mx+b, where m stands for the slope and b stands for the y-intercept.

Since we have both m and b, we can just plug the given values:

y=4x+3 ✓

Hope you could understand everything.

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Using the Pythagoras theorem, the longest leg has the length of 24 feet.

Given that,

A ladder of length (2x+6) feet is positioned x feet from a wall.

Height of the ladder = (2x + 6) feet

Distance of ladder from the wall = x feet

Height of the wall that the ladder is placed = (2x + 4) feet

These three lengths form s right triangle where (2x + 6) feet is the hypotenuse.

Longest leg is (2x + 4) feet

Using the Pythagoras theorem,

(2x + 6)² = (2x + 4)² + x²

4x² + 24x + 36 = 4x² + 16x + 16 + x²

4x² + 24x + 36 = 5x² + 16x + 16

x² - 8x - 20 = 0

(x - 10) (x + 2) = 0

x = 10 or x = -2

x = 2 is not possible.

So x = 10

Longest leg = 2x + 4 = 20 + 4 = 24 feet

Hence the length of the longest leg is 24 feet.

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The sprinter will complete the race in approximately 17.07 seconds.

To calculate the time for the race, we need to consider two parts: the acceleration phase and the constant velocity phase.

Acceleration Phase:

The acceleration of the sprinter is 1.64 m/s², and the distance covered during this phase is 25 m. We can use the equation of motion to calculate the time taken during acceleration:

v = u + at

Here:

v = final velocity (which is the velocity at the end of the acceleration phase)

u = initial velocity (which is 0 since the sprinter starts from rest)

a = acceleration

t = time

Rearranging the equation, we have:

t = (v - u) / a

Since the sprinter starts from rest, the initial velocity (u) is 0. Therefore:

t = v / a

Plugging in the values, we get:

t = 25 m / 1.64 m/s²

Constant Velocity Phase:

Once the sprinter reaches the end of the acceleration phase, the velocity remains constant. The remaining distance to be covered is 100 m - 25 m = 75 m. We can calculate the time taken during this phase using the formula:

t = d / v

Here:

d = distance

v = velocity

Plugging in the values, we get:

t = 75 m / (v)

Since the velocity remains constant, we can use the final velocity from the acceleration phase.

Now, let's calculate the time for each phase and sum them up to get the total race time:

Acceleration Phase:

t1 = 25 m / 1.64 m/s²

Constant Velocity Phase:

t2 = 75 m / v

Total race time:

Total time = t1 + t2

Let's calculate the values:

t1 = 25 m / 1.64 m/s² = 15.24 s (rounded to two decimal places)

Now, we need to calculate the final velocity (v) at the end of the acceleration phase. We can use the formula:

v = u + at

Here:

u = initial velocity (0 m/s)

a = acceleration (1.64 m/s²)

t = time (25 m)

Plugging in the values, we get:

v = 0 m/s + (1.64 m/s²)(25 m) = 41 m/s

Now, let's calculate the time for the constant velocity phase:

t2 = 75 m / 41 m/s ≈ 1.83 s (rounded to two decimal places)

Finally, let's calculate the total race time:

Total time = t1 + t2 = 15.24 s + 1.83 s ≈ 17.07 s (rounded to two decimal places)

Therefore, the sprinter will complete the race in approximately 17.07 seconds.

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Answer:

132 degrees

Step-by-step explanation:

answer : 48 degrees

method

1. opposite angles are the same , so CFG os the same as GAC - these two added up are 132 + 132 = 264

2. angles add up to 360 in a quadrilateral , so the sum of the two remaining angles is 360 - 264 = 96

3. because the two remaining angles , ACF and FGA , are opposite , those are equal too. so u just half to get one of them : 96 / 2 = 48

Answer:

I don't know what is the answer really sorry

Answer:

72%

Step-by-step explanation:

I hope this is right

Ik its 16 over something

IM sorry if it's not right

The value of 4 Superscript negative 4 is negative StartFraction 1 Over 4 Superscript negative 4 EndFraction.

In the given table, Tasha observed a pattern in the powers of 4. When the exponent decreases by 1, the previous value is divided by 4. Using this pattern, she determined the values for 4 squared, 4 Superscript 1, 4 Superscript 0, 4 Superscript negative 1, and 4 Superscript negative 2.

To find the value of 4 Superscript negative 3, she divided the previous value (StartFraction 1 Over 16 EndFraction) by 4, resulting in StartFraction 1 Over 64 EndFraction.

Similarly, for 4 Superscript negative 4, she divided the previous value (StartFraction 1 Over 64 EndFraction) by 4, yielding StartFraction 1 Over 256 EndFraction.

Finally, to rewrite the value for 4 Superscript negative 4, she expressed it as negative StartFraction 1 Over 4 Superscript negative 4 EndFraction.

Therefore, the value of 4 Superscript negative 4 is negative StartFraction 1 Over 4 Superscript negative 4 EndFraction, which simplifies to StartFraction 1 Over 256 EndFraction

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The recursive formula for p(n) is; p(n) = p(n-2) + p(n-3) for n >= 3. Case 1: The last square is painted white. If the last square is painted white, then the second to last square must be painted gold.

There are p(n-2) ways to paint the remaining n-2 squares of the checkerboard subject to the restriction.

Case 2: The last square is painted gold. If the last square is painted gold, then the second to last square can be painted either white or gold. If the second to last square is painted white, then there are p(n-3) ways to paint the remaining n-3 squares of the checkerboard subject to the restriction.

If the second to last square is painted gold, then there are p(n-2) ways to paint the remaining n-2 squares of the checkerboard subject to the restriction.

Therefore, the recursive formula for p(n) is: p(n) = p(n-2) + p(n-3) for n >= 3

with initial conditions p(1) = 2 and p(2) = 3.

The base case for the recursion is p(1) = 2 and p(2) = 3, which are the number of ways to paint a 1 x 1 checkerboard and a 1 x 2 checkerboard subject to the restriction, respectively.

The recursive formula counts the number of ways to paint a 1 x n checkerboard subject to the restriction by considering the last column of the checkerboard.

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We substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.

The given system of equations are 2x-1/3y = -2...(1)

3x+y=1...(2)

We solve this system of equations by using substitution method.

Let us solve for x in equation to substitute it in equation (2).

2x=-2+1/3y

Divide both sides of equation by 2.

x=-1+1/6y

Now plug in the value of x in equation 2.

Hence, we substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.

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42 , 16 values of sin and cos

Let's review some information regarding the sin function before learning the sin formula. The sine function, often known as the sin function, is a periodic function in trigonometry. The ratio of the hypotenuse's length to the perpendicular's length in a right-angled triangle is another way to describe the sine function. Sin is a periodic function that has a period of 2 and a domain and range of (, ), respectively. To determine the sides of a triangle, use the sin formula.

The Sin Formula: What Is It? The ratio of the perpendicular of a right-angled triangle to the hypotenuse is known as the sine of the angle. The following is the sin formula: sin = Perpendicular / Hypotenuse

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Answer:

$18.28

Step-by-step explanation:

To complete this problem is a straightforward answer:

First, you add 14.75 + 1.03 which equals $15.78 then, you'll want to add 2.50 to 15.78 and there you have your answer!!

A angle that is 171° will be in the 2nd quadrant

Its an acute triangle by angles.

Its a NONE by sides.

Answer:

12.5

Step-by-step explanation:

125% is equal to 1.25

10 x 1.25 = 12.5

12.5 is 125% of 10

Hope this helped :)

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Answer:

12.5

Step-by-step explanation:

To find 125% of 10 simply multiply the percent by 10

You first need to but the percent in decimal form. To do this, move the understood decimal to the left by 2 spaces

1.25 x 10 = 12.5

Answer:

-6 (sry if not right)

Step-by-step explanation

Answer:

Step-by-step explanation:

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