Ram borrowed Rs. 250000 from sit a at the rate of 21%: per annum. At the end of monts, how much should he pay compounde à half yearly ?​

the answer for the question that you are asking will possibly be 17

Answer:

-3[tex]x^{6}[/tex] + 5

Step-by-step explanation:

3 - 3[tex]x^{6}[/tex] + 2 = ?

-3[tex]x^{6}[/tex] + 5

So, the answer is -3[tex]x^{6}[/tex] + 5

Answer:

To estimate the distance the train traveled in the first 20 seconds using four strips of equal width, follow these steps:

a) Calculate the average velocity for each strip by finding the average height of each strip.

b) Multiply the average velocity of each strip by the width (time) of each strip to obtain the distance covered by each strip.

c) Add up the distances covered by each strip to find the estimated total distance traveled in the first 20 seconds.

Regarding part b), to determine if the estimate is an overestimate or an underestimate, we need to analyze the graph. If the graph shows that the velocity increases during the 20-second period, then the estimate will be an underestimate because the actual distance covered would be greater than the estimation based on a constant velocity assumption. On the other hand, if the graph shows that the velocity decreases during the 20-second period, then the estimate will be an overestimate since the actual distance covered would be less than the estimation based on a constant velocity assumption.

Without seeing the graph, it's difficult to provide a definitive answer.

The area of the parallelogram is  189 square units

First, we have the determine the length of the base and height.

The distance between the lines x = 9 and f(x) = 9 + 2x is the height

We have that the line parallel to f(x) passes through (4, 11)

The equation in point-slope form is;

y - 11 = 2(x - 4

y = 2x + 3

Substitute x = 9 in the equation,  y = 2x + 3.

y = 2(9) + 3 = 21

The  points are then (9, 21) and (9, 0).

The distance between the y-axis and the line x = 9 is the base.

Base = 9 units.

The formula for calculating area of a parallelogram is given by ;

= base × height

= 9 × 21

= 189 square units.

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Answer:

f(x)=5x

g(x)=1/x-5

f(g)=5(1/x-5)

f(x)=5/x- 25

therefore domain is x=0

The lengths of the three sides of the pie-shaped lake-front lot are:

Shortest side: 100 feet

Second side: 400 feet

Third side: 600 feet

Let's denote the lengths of the three sides of the triangular lake-front lot as x, x + 300, and x + 500.

The perimeter of a triangle is the sum of its three sides, so we can set up an equation to represent the given information:

x+ (x + 300) + (x + 500) = 1,100

Simplifying the equation:

3x + 800 = 1,100

Subtracting 800 from both sides:

3x = 300

Dividing both sides by 3:

x = 100

Now that we have found the length of the shortest side, we can substitute this value back into the expressions for the other two sides:

Shortest side (x) = 100 feet

Second side (x + 300) = 100 + 300 = 400 feet

Third side (x + 500) = 100 + 500 = 600 feet

Therefore, the lengths of the three sides of the pie-shaped lake-front lot are:

Shortest side: 100 feet

Second side: 400 feet

Third side: 600 feet

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The average slope of the climb is approximately 0.404.

To find the average slope of the climb, we need to calculate the change in elevation divided by the horizontal distance covered.

Change in elevation = Final elevation - Initial elevation = 1943 ft - 875 ft = 1068 ft

Horizontal distance covered = 2645 ft

Average slope = Change in elevation / Horizontal distance covered = 1068 ft / 2645 ft

Using a calculator or dividing these values, we find that the average slope is approximately 0.404 to the nearest hundredth.

The average slope of the climb is approximately 0.404. This means that for every 1 foot of horizontal distance covered, the hiker ascends approximately 0.404 feet in elevation.

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The coefficient of x is -1, indicating that there is one fewer x term compared to the original expression. The constant term is -4, which is the result of subtracting 5 from -9.

To find the difference when subtracting 8x - 5 from 7x - 9, we can use the distributive property to distribute the negative sign to each term in 8x - 5:

(7x - 9) - (8x - 5) = 7x - 9 - 8x + 5

Next, we can combine like terms by adding or subtracting the coefficients of the same variables:

7x - 9 - 8x + 5 = (7x - 8x) + (-9 + 5) = -x - 4

Therefore, the expression that represents the difference when 8x - 5 is subtracted from 7x - 9 is -x - 4.

In this expression, the coefficient of x is -1, indicating that there is one fewer x term compared to the original expression. The constant term is -4, which is the result of subtracting 5 from -9.

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Using the future value formula and an equation, we can see that Larry must deposit $263.48 each month.

To determine how much Larry should deposit each month into his account so that both men will have the same amount of money at age 65, we need to calculate the monthly deposit amount for Larry.

Let's break down the problem into steps:

Step 1: Calculate the number of months each person will be making deposits.

Both Ben and Larry will make monthly deposits for (65 - 21) * 12 = 528 months.

Step 2: Calculate the future value of Ben's account at age 65.

Using the formula for the future value of an ordinary annuity:

[tex]FV = P * [(1 + r)^n - 1] / r[/tex]

where:

Since Ben has been depositing $200 at the end of each month for 528 months, we can substitute the values into the formula:

[tex]FV_Ben = 200 * [(1 + 0.035/12)^{528} - 1] / (0.035/12)[/tex]

Step 3: Calculate the future value of Larry's account at age 65.

Larry started depositing 5 years after Ben, so he will only be making deposits for (65 - 21 - 5) * 12 = 456 months.

Using the same formula, we can calculate the future value for Larry:

[tex]FV_Larry = P * [(1 + 0.035/12)^{456} - 1] / (0.035/12)[/tex]

Step 4: Set up an equation to find the monthly deposit amount for Larry.

Since both Ben and Larry will have the same amount at age 65, we equate the future values:

FV_Ben = FV_Larry

[tex]200 * [(1 + 0.035/12)^{528} - 1] / (0.035/12) = P * [(1 + 0.035/12)^{456} - 1] / (0.035/12)[/tex]

Step 5: Solve the equation for P (the monthly deposit amount for Larry).

[tex]P = [200 * [(1 + 0.035/12)^{528} - 1] / [(1 + 0.035/12)^{456} - 1]\\\\P = 263.48[/tex]

That is how much he must deposit per month.

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The quotient of the division is x² - 6x + 43 and the remainder is 0

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

P(x) = x³ + 4x² - 17x + 430

d(x)= x + 10

Using the long division method of quotient, we have

x + 10 | x³ + 4x² - 17x + 430

The division steps are as follows

           x² - 6x + 43

x + 10 | x³ + 4x² - 17x + 430

           x³ + 10x²

--------------------------------------------------------------

                     -6x² - 17x + 430

                     -6x² - 60x

--------------------------------------------------------------

                                 43x + 430

                                 43x + 430

--------------------------------------------------------------

                                         0

Hence, the quotient is x² - 6x + 43 and the remainder is 0

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Answer:

x = 10

Step-by-step explanation:

the figure inscribed in the circle is a cyclic quadrilateral , all 4 vertices lie on the circumference.

the opposite angles in a cyclic quadrilateral sum to 180° , that is

6x + 1 + 10x + 19 = 180

16x + 20 = 180 ( subtract 20 from both sides )

16x = 160 ( divide both sides by 16 )

x = 10

a. The distribution of X is X ~ N(68, 14).

b. The corresponding area to the right of 0.9286, which is approximately 0.1772.

c. The longest amount of time a patron can spend and still receive the discount is approximately 48.5654 minutes.

d. The Inter Quartile Range (IQR) for time spent at the hot springs is approximately 21.373 minutes.

a. The distribution of X is X ~ N(68, 14), where X represents the amount of time a person spends at Grover Hot Springs, 68 is the mean, and 14 is the standard deviation.

b. To find the probability that a randomly selected person stays longer than 81 minutes, we need to calculate the area under the normal curve to the right of 81.

Using the z-score formula: z = (x - μ) / σ, where x is the value (81), μ is the mean (68), and σ is the standard deviation (14).

Plugging in the values, we have z = (81 - 68) / 14 = 0.9286.

Using a standard normal distribution table or a calculator, we can find the corresponding area to the right of 0.9286, which is approximately 0.1772.

c. To find the longest amount of time a patron can spend at the hot springs and still receive the discount, we need to find the value that corresponds to the lowest 8% of the distribution.

Using a standard normal distribution table or a calculator, we can find the z-score that corresponds to the 8th percentile, which is approximately -1.4051.

Using the z-score formula, we can calculate the longest amount of time: x = μ + z [tex]\times[/tex] σ = 68 + (-1.4051) [tex]\times[/tex] 14 = 48.5654 minutes.

Therefore, the longest amount of time a patron can spend and still receive the discount is approximately 48.5654 minutes.

d. The Inter Quartile Range (IQR) is a measure of the spread of the data and represents the range between the first quartile (Q1) and the third quartile (Q3).

To find Q1 and Q3, we can use the z-score formula and the standard normal distribution table.

For Q1, we find the z-score corresponding to the 25th percentile, which is approximately -0.6745.

Using the formula Q1 = μ + z [tex]\times[/tex] σ, we have Q1 = 68 + (-0.6745) [tex]\times[/tex] 14 = 57.053.

Therefore, Q1 is approximately 57.053 minutes.

For Q3, we find the z-score corresponding to the 75th percentile, which is approximately 0.6745.

Using the formula Q3 = μ + z [tex]\times[/tex] σ, we have Q3 = 68 + (0.6745) [tex]\times[/tex] 14 = 78.426.

Therefore, Q3 is approximately 78.426 minutes.

Finally, we can calculate the IQR by subtracting Q1 from Q3: IQR = Q3 - Q1 = 78.426 - 57.053 = 21.373 minutes.

Therefore, the Inter Quartile Range (IQR) for time spent at the hot springs is approximately 21.373 minutes.

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a) The fruit vendor sold 3/10 of the grapefruits on Saturday, b) The vendor had 100 grapefruits at first, and c) 40 grapefruits were sold on Friday.

a) On Saturday, the fruit vendor sold 1/2 of the remaining grapefruits. Since 2/5 of the grapefruits were sold on Friday, there are 3/5 of the original amount left. Therefore, on Saturday, the vendor sold (1/2) x (3/5) = 3/10 of the grapefruits.

b) To find the original number of grapefruits, we need to calculate the total amount remaining after Friday's sales. Since there were 60 grapefruits left after Saturday's sales and 3/5 of the original amount remained, we can set up the equation (3/5) [tex]\times[/tex]x = 60, where x represents the original number of grapefruits.

Solving for x, we have x = (60 x 5) / 3 = 100 grapefruits. Therefore, the fruit vendor had 100 grapefruits at first.

c) To find the number of grapefruits sold on Friday, we subtract the amount remaining after Friday's sales from the original number. 2/5 of the grapefruits were sold on Friday, so the number sold is (2/5) x 100 = 40 grapefruits.

In summary, a) the fruit vendor sold 3/10 of the grapefruits on Saturday, b) the vendor had 100 grapefruits at first, and c) 40 grapefruits were sold on Friday.

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Inferences about the interaction between Anna and Mrs. Morgan are supported by the information in paragraphs 7 and 8 are as follows: Mrs. Morgan is not very patient with Anna and is trying to get rid of her.Mrs. Morgan thinks Anna is lying and is not telling the truth.

Mrs. Morgan appears to be strict and unkind towards Anna, as well as being skeptical about her intentions. She is not really interested in Anna's concerns and is rather impatient and dismissive, trying to get rid of her as soon as possible. Additionally, Mrs. Morgan doesn't believe Anna, thinking she is lying and hiding something from her.

This suggests that Mrs. Morgan might not be a trustworthy person and has a negative impression of Anna without even knowing her well.

The textual evidence used to support these inferences is the description of Mrs. Morgan's tone and behavior towards Anna as well as her verbal responses, such as the abruptness of her question about the purse and her insistence on Anna leaving.

These actions suggest that Mrs. Morgan is not open to listening to Anna's story and is only interested in getting her out of the way, as well as indicating that she doesn't believe Anna's story.

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Answer:

the possible length and width b:

1 and 20

10 and 2

5 and 4

120 = 1*20*6

120 = 10*2*6

120 = 5*4*6

The possible length and width for Derek's rectangular prism with a volume of 120 cubic inches and a height of 6 inches is 6 inches and 20 inches, respectively.

To find the possible length and width of Derek's rectangular prism, we can use the formula for the volume of a rectangular prism:

Volume = Length x Width x Height

Given that the volume is 120 cubic inches and the height is 6 inches, we can substitute these values into the formula:

120 = Length x Width x 6

To find the possible values for length and width, we need to factorize 120 and check the combinations that satisfy the equation. Let's find the factors of 120:

1 x 120

2 x 60

3 x 40

4 x 30

5 x 24

6 x 20

8 x 15

10 x 12

Now let's substitute these factors into the equation and solve for the missing dimension:

For the combination 1 x 120:

120 = 1 x 120 x 6

This does not work because the width would be 120 inches, which is not feasible.

For the combination 2 x 60:

120 = 2 x 60 x 6

This does not work because the width would be 60 inches, which is not feasible.

For the combination 3 x 40:

120 = 3 x 40 x 6

This does not work because the width would be 40 inches, which is not feasible.

For the combination 4 x 30:

120 = 4 x 30 x 6

This does not work because the width would be 30 inches, which is not feasible.

For the combination 5 x 24:

120 = 5 x 24 x 6

This does not work because the width would be 24 inches, which is not feasible.

For the combination 6 x 20:

120 = 6 x 20 x 6

This works because the width would be 20 inches:

120 = 6 x 20 x 6

120 = 720

This combination satisfies the equation.

For the combination 8 x 15:

120 = 8 x 15 x 6

This does not work because the width would be 15 inches, which is not feasible.

For the combination 10 x 12:

120 = 10 x 12 x 6

This does not work because the width would be 12 inches, which is not feasible.

Therefore, the possible length and width for Derek's rectangular prism with a volume of 120 cubic inches and a height of 6 inches is 6 inches and 20 inches, respectively.

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The second pair of points representing the solution set of the system of equations is (-6, 29).

To find the second pair of points representing the solution set of the system of equations, we need to substitute the x-coordinate of the second point into one of the equations and solve for y.

Given the system of equations:

y = x^2 - 2x - 19

y + 4x = 5

Substituting the x-coordinate of the second point (-6) into equation 2:

y + 4(-6) = 5

y - 24 = 5

y = 5 + 24

y = 29

Therefore, the second pair of points representing the solution set of the system of equations is (-6, 29).

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Question

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.

y = x2 − 2x − 19

y + 4x = 5

The pair of points representing the solution set of this system of equations is (-6, 29) and

_________.

a. The critical points of f are x = π/2, x = 2π/3, and x = 4π/3.

b. f is increasing on the intervals (0, π/2) and (2π/3, 2π).

  f is decreasing on the interval (π/2, 2π/3) and (4π/3, 2π).

c. f assumes a local maximum at x = π/2 and x = 4π/3.

  f assumes a local minimum at x = 2π/3.

a. The critical points of f occur where the derivative f'(x) equals zero or is undefined.

Note that the derivative is defined for all values of x in the given interval:

0 ≤ x ≤ 2π

Therefore, we need to find the values of x where f'(x) = 0:

  f'(x) = (8 sin x - 8)(2 cos x + 1) = 0

Setting each factor equal to zero gives us:

  8 sin x - 8 = 0   ==>   sin x - 1 = 0 ==>  sin x = 1

                                                                      x = π/2 + 2πk,

                                                                      where k is an integer.

  2 cos x + 1 = 0   ==>   cos x = -1/2  

                                            x = 2π/3 + 2πk or x = 4π/3 + 2πk,

                                            where k is an integer.

  Therefore, the critical points of f are x = π/2, 2π/3, and 4π/3.

b. To determine where f is increasing or decreasing, we can examine the sign of the derivative f'(x) within different intervals. The intervals can be defined by the critical points we found in part (a):

Interval (0 ≤ x < π/2):

In this interval, sin x and cos x are positive. Thus, both factors in f'(x) are positive, resulting in f'(x) > 0.

Therefore, f is increasing on this interval.

Interval (π/2 < x < 2π/3):

In this interval, sin x is positive, but cos x is negative. Thus, the first factor in f'(x) is positive, while the second factor is negative, resulting in f'(x) < 0.

Therefore, f is decreasing on this interval.

Interval (2π/3 < x < 4π/3):

In this interval, sin x and cos x are negative. Both factors in f'(x) are negative, resulting in f'(x) > 0.

Therefore, f is increasing on this interval.

Interval (4π/3 < x ≤ 2π):

In this interval, sin x is negative, but cos x is positive. The first factor in f'(x) is negative, while the second factor is positive, resulting in f'(x) < 0.

Therefore, f is decreasing on this interval.

c. To find the points where f assumes local maximum or minimum values, we need to consider the critical points we found in part (a) and check the behavior of the function around these points.

  At x = π/2: Since f'(x) changes from positive to negative as we move from the left side of π/2 to the right side, this implies that f has a local maximum at x = π/2.

  At x = 2π/3: Since f'(x) changes from negative to positive as we move from the left side of 2π/3 to the right side, this implies that f has a local minimum at x = 2π/3.

  At x = 4π/3: Since f'(x) changes from positive to negative as we move from the left side of 4π/3 to the right side, this implies that f has a local maximum at x = 4π/3.

Therefore, the function f has local maximum values at x = π/2 and 4π/3, and a local minimum value at x = 2π/3.

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the answer is D

The figure can be divided into a rectangle and 2 triangles

The point on the number line that is 5/7 of the way from A = -4 to B = 17 is approximately -1.8571.

To find the location of a point on the number line that is a certain fraction of the way from one point to another, we can use the concept of linear interpolation.

In this case, we want to find the point that is 5/7 of the way from A = -4 to B = 17.

To calculate this point, we can use the formula:

Point = A + (Fraction × Distance)

where A is the starting point, Fraction is the desired fraction, and Distance is the total distance between the two points.

In this case, A = -4, B = 17, and the desired fraction is 5/7. The distance between A and B can be calculated as:

Distance = B - A = 17 - (-4) = 21

Plugging in these values, we have:

Point = -4 + (5/7 × 21)

Simplifying the expression, we get:

Point = -4 + (15/7) = -4 + 2.1429 ≈ -1.8571

Therefore, the point on the number line that is 5/7 of the way from A = -4 to B = 17 is approximately -1.8571.

Among the given options, none of them match the calculated value. However, the closest option is C. 9.

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The calculated percentage error with the assumed answer of 10%

To find the percentage error in actual weights, we can use the formula:

Percentage Error = [(|Measured Value - Expected Value|) / Expected Value] * 100%

In this case, the expected weight is 4 ounces. Let's assume the measured value is 10% off from the expected value. So the measured value would be:

Measured Value = Expected Value + (10% of Expected Value)

              = 4 ounces + (10/100) * 4 ounces

              = 4 ounces + 0.4 ounces

              = 4.4 ounces

Now we can calculate the percentage error:

Percentage Error = [(|4.4 ounces - 4 ounces|) / 4 ounces] * 100%

               = [(0.4 ounces) / 4 ounces] * 100%

               = (0.4/4) * 100%

               = 0.1 * 100%

               = 10%

Comparing the calculated percentage error with the assumed answer of 10%, we can see that they are the same.

The percentage error represents the deviation from the expected value as a percentage of the expected value itself. In this case, it indicates that the actual weights deviate by 10% from the expected weight of 4 ounces. The calculated percentage error with the assumed answer of 10%

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The best description of the fees he is charged for renting or the cost per mile would be = He is charged an initial rate of $55.60 for renting the van. That is option E.

To determine the best description for the cost per mile, the following steps needs to be taken as follows:

The average cost per mile he was given for renting the trucks would be calculated by addition of the total cost divided by the miles driven.

Total cost = 55.60+53.22+51.16+54.97+52.38/

= 267.33

Total miles driven = 80+46+23+71+34 = 254

The average = 267.33/254 = 1.1

Therefore since the initial price given = $55.60, the best statement = He is charged an initial rate of $55.60 for renting the van

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Replacement cost of the minibus in 4 years' time, considering the trade-in of the old minibus, is R9,411.70.

1. Calculate the depreciation of the minibus over 4 years:

  Depreciation = Original cost * (1 - Rate of depreciation) Number of years

  Depreciation = R241,000 * (1 - [tex]0.22)^4[/tex]

  Depreciation = R241,000 * [tex]0.78^4[/tex]

  Depreciation ≈ R91,073.17

2. Calculate the remaining value of the minibus after 4 years:

  Remaining value = Original cost - Depreciation

  Remaining value = R241,000 - R91,073.17

  Remaining value ≈ R149,926.83

3. Calculate the inflated cost of a new minibus in 4 years:

  Inflated cost = Original cost * (1 + Rate of inflation) Number of years

  Inflated cost = R241,000 * (1 + [tex]0.15)^4[/tex]

  Inflated cost = R241,000 * [tex]1.15^4[/tex]

  Inflated cost ≈ R421,731.04

4. Calculate the replacement cost by subtracting the remaining value and adding the inflated cost:

  Replacement cost = Remaining value + Inflated cost

  Replacement cost = R149,926.83 + R421,731.04

  Replacement cost ≈ R571,657.87

5. Calculate the trade-in value by subtracting the depreciation from the replacement cost:

  Trade-in value = Replacement cost - Depreciation

  Trade-in value = R571,657.87 - R91,073.17

  Trade-in value ≈ R480,584.70

6. Therefore, the replacement cost of the minibus in 4 years' time, considering the trade-in, is approximately R480,584.70.

For the second question:

1. Determine the number of months until the first payment is made:

  Number of months = 4 years * 12 months/year - 3 months

  Number of months = 48 months - 3 months

  Number of months = 45 months

2. Use the formula for the future value of a series of payments to calculate the required monthly payment:

  Monthly payment = (Future value * Interest rate) / ((1 + Interest rate) Number of periods - 1)

  Monthly payment = (Replacement cost * Monthly interest rate) / ((1 + Monthly interest rate) Number of months - 1)

  Monthly payment = (R480,584.70 * 0.086/12) / ((1 + [tex]0.086/12)^4^5[/tex] - 1)

  Monthly payment ≈ R9,411.70

3. Therefore, the required monthly payment to the sinking fund for the purchase of a new minibus in 4 years' time, with the first payment made three months after the original bus was purchased, is approximately R9,411.70.

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Answer:

Step-by-step explanation:

65x2-26x

The postulate or theorem that proves that two triangles are congruent if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle. Of the above choices, only ASA satisfies this condition. So the answer is (C).

ASA Congruence Theorem explains that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

This theorem is a part of triangle congruence criteria in Euclidean geometry. It states that if two angles and the included side of one triangle are equal to the corresponding two angles and included side of another triangle, then the two triangles are congruent, meaning they have the same shape and size.

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(3a) The equation that can be used to determine the cost, C is C = 2.55 + 1.85x.

(3b) The cost of 3 miles taxi ride is $8.1.

(3a) The equation that can be used to determine the cost, C is calculated by applying the following equation as follows;

C = f + nx

where

C = 2.55 + 1.85x

(3b) The cost of 3 miles taxi ride is calculated as follows;

C = 2.55 + 1.85x

where;

C = 2.55 + 1.85 (3)

C = $8.1

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Answer:

(8,5)(0,-3)

Step-by-step explanation:

-y=-x+3

y=x-3

Substitute for y:

(x-3)^2-2x=9

x^2-6x+9-2x=9

x^2-8x=0

x(x-8)=0

x=0,8

if x=0,

0-y=3

y=-3

if x=8

8-y=3

-y=-5

y=5

Answer :

x - y = 3

x = 3 + y

y^2 - 2x = 9

y^2 - 2(3+y) = 9

y^2 - 2y -6 -9 = 0

y^2 - 2y -15 = 0

Factorize

y = -3 y = 5

when y = -3

x -(-3) = 3

x = 0

when y = 5

x - 5 = 3

x = 8

Answer:

1.255 seconds

Step-by-step explanation:

We can use the formula:

time = distance ÷ speed

to find the driver's time. Here, the distance is 200 miles and the speed is 159.5 miles per hour. Substituting these values into the formula, we get:

time = 200 miles ÷ 159.5 miles per hour

time = 1.255 seconds