Tyrone wants to save $10 000. He has $3250 in his savings account, and he plans on saving $1250 per year until he reaches his goal. A) Write an algebraic expression to represent this scenario. B) Solve the equation to determine how long it will take Tyrone to achieve his goal. C) How much faster would Tyrone achieve his goal if he saved $2500 per year, instead?

An answer will be appreciated!!

Answer:

{HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}

Step-by-step explanation:

To find the sample space of flipping a quarter three times, we need to list all possible outcomes or combinations of heads (H) and tails (T) when flipping the quarter.

Since we are flipping the quarter three times, we can use a tree diagram to help visualize the different possible outcomes.

Starting with the first flip, we have two possible outcomes: H or T. Each of these outcomes will have two possible outcomes for the second flip (H or T), resulting in four possible outcomes so far: HH, HT, TH, TT.

For the third flip, each of the four outcomes from the second flip will have two possible outcomes (H or T), resulting in a total of eight possible outcomes for the third flip.

Combining all of the outcomes from each flip, we get the following sample space:

{HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}

This is the complete list of all possible outcomes when flipping a quarter three times.

The distance between points A and B is 2 units.

To find the distance between two points in a coordinate plane, we can use the distance formula:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

Using this formula, we can find the distance between points A (-3,1) and B(-1,1) as follows:

distance = sqrt((-1 - (-3))^2 + (1 - 1)^2)

distance = sqrt(2^2 + 0^2)

distance = sqrt(4)

distance = 2

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Answer:

Perimeter:

[tex]2( \frac{2}{3} + \frac{1}{2} ) = 2( \frac{4}{6} + \frac{3}{6} ) = 2( \frac{7}{6} ) = \frac{7}{3} = 2 \frac{1}{3} [/tex]

The perimeter is 2 1/3 inches.

Area:

[tex] \frac{2}{3} \times \frac{1}{2} = \frac{1}{3} [/tex]

The area is 1/3 of a square inch.

Answer:

To dilate a triangle using a scale factor of 3.5, we multiply the distance between each vertex and the center of dilation (in this case, the origin) by 3.5.

Using this information, we can find the coordinates of each vertex of triangle A'B'C':

A' = (43.5, 33.5) = (14, 10.5)

B' = (33.5, -23.5) = (10.5, -7)

C' = (-33.5, 13.5) = (-10.5, 3.5)

Therefore, the vertex of point C' is (-10.5, 3.5).

So the correct answer is C′(−10.5, 3.5).

There are 504 boys at the school out of the total 720 students, and 168 of them are from poor homes.

We must first ascertain the number of female students in order to calculate the number of guys enrolled in the school. Since there are 30% more female students overall, we can compute percentage as follows:

216 girls is equal to 0.3 x 720 males.

The number of boys can be calculated as follows:

Total students - Number of girls equals Number of boys

Boys' number = 720 - 216

Amount of boys: 504

There are 504 guys enrolled in the school as a result. Furthermore, we are informed that 168 of these boys come from poor homes, which may be helpful for additional computations or research.

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The perimeter and the area of the regular polygon are 20 inches and 27.53 square inches.

The figure representing a regular polygon with five sides of same length, whose perimeter and area is well described by following formulas:

Perimeter

p = n · l

Area

A = (n · l · a) / 2

Where:

Where the apothema is:

a = 0.5 · l / tan (180° / n)

If we know that l = 4 in and n = 5, then the perimeter and the area of the polygon are:

Perimeter

p = 5 · (4 in)

p = 20 in

Area

a = 0.5 · (4 in) / tan (180° / 5)

a = 0.5 · (4 in) / tan 36°

a = 2.753 in

A = [5 · (4 in) · (2.753 in)] / 2

A = 27.53 in²

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Hence,the area of circle [tex]=144\pi[/tex][tex]cm^{2}[/tex]

In a plane all points  are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

The patch of size on a surface is determined by its area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, therefore  the area of a plane area or .plane region  refers to the area of a form  of plane lamina .

we know that ,

area of circle =[tex]\pi r^{2}[/tex]

according to question,

r= 12 cm.

So,the area of circle

[tex]=\pi *12^{2} \\=\pi *144[/tex]

or the area of circle [tex]=144\pi[/tex][tex]cm^{2}[/tex]

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Answer:

26) 1.32

27) 90

28) 0.00845

29) 2.56x10^-1

30) 9.5x10^-3

31) 7.8x10

The coordinates of the vertices B, D and C after a reflection over the line x = 1 are B'(1,7), D'(1,6) and C'(-8, 7).

The picture M', whose coordinates are in the fourth quadrant and created when point M is mirrored in the x-axis, is (h, -k). As a result, we deduce that when a point is reflected along the x-axis, the x-coordinate stays constant while the y-coordinate changes to the negative.

As a result, M'(h, -k). is the image for point M (h, k)

Given data:

coordinates of the vertices before reflection:

B(1,7), D(1,6) and C(10, 7).

Reflection about x = 1.

As Point B and D lies on the line x = 1, their coordinates will  not change.

C is 9 units to the right of the line x = 1 at (10, 7)

Thus, after reflection C will be 9 units to the left of the line x = 1 at (-8, 7).

Therefore, the coordinates of the vertices B, D and C after a reflection over the line x = 1 are B'(1,7), D'(1,6) and C'(-8, 7).

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We can see that for c to be greater than 6, sin(C) must be greater than sin(70°). However, since sin(C) cannot be greater than 1, there are no possible values of C that satisfy this condition.

Based on the given information, we have:

[tex]a = 8[/tex] (length of side a)

[tex]b = 2[/tex] (length of side b)

[tex]A = 70^\circ[/tex] (angle A)

To determine whether the given information results in one triangle, two triangles, or no triangle at all, we can apply the triangle inequality theorem.

According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let's check if the given sides a, b, and angle A satisfy the triangle inequality theorem:

[tex]a + b > c[/tex]

[tex]8 + 2 > c[/tex]

[tex]10 > c[/tex]

[tex]c > |a - b|[/tex]

[tex]c > |8 - 2|[/tex]

[tex]c > 6[/tex]

where c is the length of the third side.

From the above inequalities, we can see that c must be greater than 6 and less than 10 in order to form a triangle. However, we also know that   [tex]A = 70^\circ[/tex], and the sum of the angles in a triangle is always 180°. So we can use the Law of Sines to find the length of side c:

[tex]sin(A) / a = sin(C) / c[/tex]

[tex]sin(70°) / 8 = sin(C) / c[/tex]

[tex]c = (8 \times sin(C)) / sin(70^\circ)[/tex]

Now we can find the possible values of c using the given information:

[tex]c = (8 * sin(C)) / sin(70^\circ)[/tex]

[tex]c = (8 \times sin(C)) / sin(70^\circ) > 6[/tex] (from triangle inequality)

Therefore,  We can see that for c to be greater than 6, sin(C) must be greater than sin(70°). However, since sin(C) cannot be greater than 1, there are no possible values of C that satisfy this condition.

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Two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle. Solve any triangle that result triangle(s). a=8, b=2, A=70°

The functions 7 are inverse functions while the functions 8 are not inverse functions

To verify that f and g are inverse functions, we need to show that:

Let's apply these conditions to the given functions:

f(x) = 5x + 2; g(x) = (x−2)/5

f(g(x)) = f((x−2)/5) = 5((x−2)/5) + 2 = x − 2 + 2 = x

g(f(x)) = g(5x + 2) = ((5x + 2) − 2)/5 = 5x/5 = x

Since f(g(x)) = x and g(f(x)) = x, we can conclude that f and g are inverse functions.

f(x) = ½x − 7; g(x) = 2x + 14

f(g(x)) = f(2x + 14) = ½(2x + 14) − 7 = x

g(f(x)) = g(½x − 7) = 2(½x − 7) + 14 = x − 7 + 14 = x + 7

Since f(g(x)) = x and g(f(x)) ≠ x, we can conclude that f and g are not inverse functions.

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The equation for the bob's horizontal location is x(t) = -A sin(ωt) and the bob is 3.47cm after 0.9 seconds

Since the distance a from the equilibrium position can be described by a cosine function, we have:

a(t) = Acos(ωt + φ)

where A is the amplitude of the motion, ω is the angular frequency, and φ is the phase constant. We are given that the amplitude A = 7.5/2 = 3.75 cm (half the width of the swing) and the period T = 1.1 seconds. The angular frequency is related to the period by:

ω = 2π/T

so we have:

ω = 2π/1.1 ≈ 5.72 rad/s

To find the phase constant φ, we need to use the initial condition that the pendulum bob is released from its farthest right position. This means that at t = 0, a = A, so we have:

A = Acos(φ)

which implies:

cos(φ) = 1

Since we want a positive value of a when the bob is to the right of the equilibrium position, we choose φ = 0. Therefore, the equation for the bob's horizontal location is:

x(t) = -A sin(ωt)

where we have used the fact that the bob's motion is in a vertical plane and the angle between the vertical and the string of the pendulum is a right angle.

To find where the bob is after 0.9 seconds, we substitute t = 0.9 into the equation for x(t) and get:

x(0.9) = -3.75 sin(5.72 × 0.9) ≈ -3.47 cm

So the pendulum bob is about 3.47 cm to the left of the equilibrium position after 0.9 seconds.

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Using a trigonometric relation we can see that the correct option is the last one;

4. 348.5 ft​

We have a right triangle, so we can use trigonometric relations.

The angle at the top of the triangle is a, and it must solve the equation:

a + 19° = 90°

a = 90° - 19° = 71°

Now we can use the trigonometric relation:

tan(a) = (opposite cathetus)/(adjacent cathetus)

REplacing what we know:

tan(71) = ?/120 ft

120ft*tan(71) = ? = 348.5ft

That is the distance.

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If sandbox is 4 ft long, 3 ft wide, and 1 ft deep, then the number of "sand-bags" which are needed to fill the sandbox is 20 bags.

The "Volume" of a cuboid is defined as a measure of the amount of three-dimensional space it occupies. The volume of a cuboid can be calculated using the formula : Volume = Length × Width × Height,

To find out how many bags of sand are needed to fill the sandbox, we first need to calculate the volume of the sandbox.

The sandbox is 4 feet long, 3 feet wide, and 1 foot deep.

So, its volume can be calculated as : Volume = Length × Width × Depth,

Substituting the values,

We get,

⇒ Volume = 4 ft × 3 ft × 1 ft = 12 cubic feet

So, Volume of the sandbox is 12 cubic feet.

Next, we divide the "total-volume" of sandbox by "volume of each bag" of sand (0.6 cubic feet) to determine the number of bags needed,

⇒ Number of bags = (Total volume)/(Volume per bag),

⇒ Number of bags = 12/0.6 = 20 bags,

Therefore, 20 bags of sand are needed to fill the sandbox.

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A(n) "spanned" volume is similar to a primary partition, but in fact, is not a primary partition.

A spanned volume is similar to a primary partition, but in fact, is not a primary partition. In a spanned volume, you can combine free space from multiple disks to create a larger logical storage unit, while a primary partition is a segment of a hard disk drive that the operating system recognizes as a separate logical storage unit. A volume can span multiple partitions depending on how it is configured, or it can encompass a single partition. Different operating systems have different ways of configuring and managing volumes.

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Answer:

35° 21

Step-by-step explanation:

In an isosceles triangle, the angles opposite to the equal sides of an isosceles triangle are equal in measurement1. Therefore, if ∠A = 110° and ABC is an isosceles triangle, then ∠B = ∠C = (180° - ∠A)/2 = (180° - 110°)/2 = 35° 21.

I hope this helps!

Answer:

A

Step-by-step explanation:

Equation of a line is:    y = mx + b    where  m = slope    b = y axis intercept

      To find the slope between any two of the given points :

  say   18, 100   and     27, 85

    m = slope =  (y1-y2) / (x1-x2) = (85-100) / ( 27-18)  = -15/12 = -5/3  

so now you have

   y = - 5/3 x   + b       we still need to find the value of b

                                        use any point to calculate b

                              say    15, 106

     106 = - 5/3 (15) + b    

          b = ~ 131

the equation is then     y = - 5/3 x + 131     closest  to answer 'A'

Answer:

6 inches

Step-by-step explanation:

Specific function is not provided. To calculate, we need to find predict, and determine population.

1. Growth rate: This is the rate at which the population increases or decreases over time.

2. Measures: In this context, "measures" refers to the way the population is represented in the function, which is in millions.

3. Function: This is a mathematical relationship that describes how the population of Japan changes with respect to time (years since 2000).

To answer your question with a given function, follow these steps:

Step 1: Find the population in 2007.
Plug in the value of the number of years since 2000 (7) into the function and calculate the population in millions.

Step 2: Predict the population in 2020.
Plug in the value of the number of years since 2000 (20) into the function and calculate the population in millions.

Step 3: Determine when the population reaches 2 billion.
Set the function equal to 2000 (since 2 billion people = 2000 million) and solve for the number of years since 2000. Convert this result to the actual year by adding the number of years to 2000.

Once you have the specific function, you can follow these steps to find the answers to your questions.

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The growth rate continues, the population of Japan will reach 2 billion people in approximately the year

2226 (adding 226.3 to 2000).

To find the population in 2007, we simply need to substitute 7 for t in the function:

[tex]P(7) = 127.7(1.002)^7 ≈ 127.7(1.015) ≈ 129.6 million[/tex]

Therefore, the population of Japan in 2007 was approximately 129.6 million.

To predict the population in 2020, we substitute 20 for t in the function:

[tex]P(20) = 127.7(1.002)^20 ≈ 127.7(1.044) ≈ 133.2 million[/tex]

Therefore, the predicted population of Japan in 2020 is approximately 133.2 million.

To find the year in which the population of Japan reaches 2 billion people, we need to solve for t in the equation:

[tex]2,000 = 127.7(1.002)^t[/tex]

Taking the natural logarithm of both sides and solving for t:

ln(2,000/127.7) = t ln(1.002)

t ≈ 226.3

Therefore, if the growth rate continues, the population of Japan will reach 2 billion people in approximately the year

2226 (adding 226.3 to 2000). However, it is important to note that this is a theoretical calculation and does not take

into account any changes in the growth rate or other factors that may affect population growth in Japan.

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The ratio of the probability of flipping a tail to the probability of flipping a head when the probability of getting three heads is the same as the probability of getting exactly two tails in three flips is 1/3.

Let p be the probability of flipping a head and q be the probability of flipping a tail.

The probability of getting three heads in three flips is [tex](p)^3.[/tex]

The probability of getting exactly two tails in three flips is 3pq².

Given that these probabilities are equal, we have:

[tex](p)^3[/tex]= 3pq²

Simplifying this equation gives:

p = 3q

Dividing both sides by q gives:

p/q = 3

Therefore, the ratio of the probability of flipping a tail to the probability of flipping a head is 1/3.

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Let x be the length of the pen and y be the width of the pen.

The total cost of the pen is given by:

Cost = 3x + 5y = 300

3x + 5y = 300

3x = 300 - 5y

x = (300 - 5y)/3

The area of the pen is given by:

Area = xy = (300 - 5y)/3 * y

The equation of the line shown in the given graph is y = x/2 + 4

From the question, we are to write the equation for the line shown in the graph

To write the equation of the line we will use the two points given on the line, (-2, 3) and (2, 5)

Using the formula,

(y - y₁) / (x - x₁) = (y₂ - y₁) / (x₂ - x₁)

Then,

The equation becomes

(y - 3) / (x - (-2)) = (5 - 3) / (2 - (-2))

(y - 3) / (x + 2) = (5 - 3) / (2 + 2)

(y - 3) / (x + 2) = 2 / 4

(y - 3) / (x + 2) = 1/2

Cross multiplication

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

2y - 6 = x + 2

2y = x + 2 + 6

2y = x + 8

Divide through by 2

y = x/2 + 4

Hence,

The equation is y = x/2 + 4

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As a result, if a bicycle covers 50 miles in 25 minutes, their speed is 120 miles per hour.

Speed is defined in physics as the distance covered in a unit of time. What determines the velocity vector's magnitude is a scalar quantity. An item is said to be travelling faster or slower depending on its speed. It has zero speed if it isn't moving at all.

Therefore, a bicycle travelling 50 miles in 25 minutes is moving at a speed of 120 miles per hour.

Miles might mean two different things. As a noun, it refers to a linear measurement unit that is 1,760 yard. It also has the adverbial meanings of greatly or far.

When the distance is 50 miles, the relationship between speed, s, and time, t, can be written as follows:

s = d/t

where d is the distance traveled, and t is the time it takes.

The distance is 50 miles in this instance, and the travel time is 25 minutes, or 25/60 hours.

When we enter these values into the formula above, we obtain:

120 miles per hour is equal to s = 50/(25/60).

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Martha travels 8 miles per hour, which is the same as saying that she covers 8 miles in one hour.

We can express Martha's weekend bicycling information as a rate by dividing the distance traveled by the time taken. In this case, her rate would be:

[tex]\frac{12 miles}{1.5 hours} = $8 miles per hour[/tex]

This tells us that Martha travels 8 miles for every hour that she spends bicycling.

We can express Martha's weekend bicycling information as a unit rate by dividing the distance traveled by the time taken and expressing the result in terms of one unit of time (usually one hour). In this case, her unit rate would be:

[tex]$\frac{12 miles}{1.5 hour}. \frac{1 hour}{1} = \frac{8 miles}{1 hour}[/tex]

This tells us that Martha travels 8 miles per hour, which is the same as saying that she covers 8 miles in one hour.

Expressing information as a rate or a unit rate allows us to compare different situations more easily. In this case, we could compare Martha's weekend bicycling rate with her weekday bicycling rate, or with the rates of other bicyclists, to see how they differ.

Therefore, Martha travels 8 miles per hour, which is the same as saying that she covers 8 miles in one hour.

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The area of the paper remains  is 238.14 cm².

Area is the region bounded by a plane shape.

To calculate the area of the paper that remains, we use the formula below.

Formula:

Where:

From the diagram in the question,

Given:

Substitute these values into equation 1

Hence, the area  is 238.14 cm².

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Answer:

QR=8

Step-by-step explanation:

When two lines are perpendicular, they form two 90-degree angles. So:

m∠QSR = m∠QSP = 90°

We also know that the line segment PS is congruent to the line segment SR.

Lastly, by the reflexive property, QS is congruent to itself.

Thus, ΔPSQ ≅ ΔRSQ by SAS (side-angle-side).

Now that we know these triangles are congruent, we can further state that PQ is congruent to QR by CPCTC (corresponding parts of congruent triangles are congruent).

If PQ is congruent to QR, then their measures are also congruent, and we can get this equation (by using substitution and algebra):

[tex]3n-1=5n-7=\\6=2n=\\n=3[/tex]

Plug in n to the length of QR:

[tex]5n-7=\\5(3)-7=\\15-7=\\8[/tex]

So, QR=8.

Note that for setting (a), use the chi-square test of independence to compare texting behavior between age groups. For setting (b), use the chi-square test of homogeneity to compare accident rates between age groups in a manufacturing plant.

a) The appropriate chi-square test for this setting is the test of independence. This is because we are comparing the responses of two groups (less than 30 and at least 30 years old) to two categories (more texts and more phone calls), and we want to see if there is an association between age and texting behavior.

The test of independence allows us to determine if there is a significant relationship between two categorical variables.

b) The appropriate chi-square test for this setting is the test of homogeneity. This is because we are comparing two groups (older and younger employees) with respect to the same categorical variable (accident type), and we want to see if the proportion of accidents is the same for both groups.

The test of homogeneity allows us to determine if there is a significant difference between two or more populations with respect to a categorical variable.

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Histogram would be the most appropriate graphical representation for the collected data,  because it shows each individual data point.

A histogram is a graphical representation of a distribution of continuous data that is used to visualize the underlying frequency distribution of a set of data. Here are the general steps to plot a histogram:

1. Choose the appropriate number of bins: The first step in creating a histogram is to choose the number of bins or intervals that the data will be divided into. This decision is based on the number of data points and the range of the data.

2. Determine the range of the data: Determine the range of the data, which is the difference between the largest and smallest values in the data set.

3. Calculate the width of each bin: Divide the range of the data by the number of bins to determine the width of each bin.

4. Plot the horizontal axis: The horizontal axis of the histogram represents the range of the data and is divided into the chosen number of bins.

5. Plot the vertical axis: The vertical axis of the histogram represents the frequency or density of the data.

6. Count the number of observations: Count the number of observations that fall into each bin.

7. Plot the bars: Plot the bars of the histogram such that the height of each bar corresponds to the number of observations in each bin.

8. Label the axes and title: Finally, label the horizontal and vertical axes appropriately and give the histogram an appropriate title.

Histogram would be the most appropriate graphical representation for the collected data of milligrams of Vitamin C from 100 different gummy vitamins sold in the world.

A histogram is a graph that displays the distribution of a continuous data set using bars. It is useful for showing the frequency distribution of a large data set and helps to identify patterns or outliers in the data.

In this case, the milligrams of Vitamin C is a continuous variable, and the histogram would display the frequency of different milligram ranges. It would show the concentration range of the vitamin C in the gummy vitamins sold worldwide and provide an overall picture of the distribution of the data.

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Step-by-step explanation:

24 times, as there are no orange marbles in the set.

so, every pull will produce a marble that is not orange with 100% certainty.

in general, we have 12 marbles.

let's change the problem description into picking a marbles that is not blue.

we have 6 blue marbles.

the chance to pick a blue marble is therefore 6/12 = 1/2.

and the probability to not pick a blue marbles is 1 - 1/2 = 1/2.

so, in 24 pulls, we expect 24× 1/2 = 12 times to get a marble that is not blue.

or change it to "not green" marbles.

5 green marbles.

the probability to pick a green marble is 5/12.

the probabilty to not pick a green marble = 1 - 5/12 = 7/12.

in 24 pulls we expect 24 × 7/12 = 14 times to get a marble that is not green.

it change it to "not purple" marbles.

1 purple marble.

the probability to pick a purple marble is 1/12.

the probabilty to not pick a purple marble = 1 - 1/12 = 11/12.

in 24 pulls we expect 24 × 11/12 = 22 times to get a marble that is not purple.

Answer:

X; Y

Step-by-step explanation:

Let I be the midpoint of UV

Coordinates of midpoint: x = (5-7)÷2 = -1;   y = (8-6)÷2 = 1

(W) has center I(-1,1) and radius = IU = [tex]\sqrt{(5-(-1))^2+(8-1)^2}=\sqrt{85}[/tex]

Equation of (W): [tex](x+1)^2+(y-1)^2=85[/tex]

We see that X(8,3); Y(6,-5) satisfy the equation of (W)