why would someone choose to use a graphing calculator to solve a system of linear equations instead of graphing by hand? explain

2.75; a kitten who is just born is predicted to weigh 2.75 ounces.

What is Statistics?

Statistics is a branch of mathematics that involves collecting, analyzing, interpreting, presenting, and organizing data. It enables the identification of trends, patterns, and relationships within the data. The goal of statistics is to make meaningful inferences and predictions based on the data.

It is used in a wide range of fields, including business, economics, social sciences, healthcare, and engineering. The main tools of statistics include probability theory, statistical inference, and statistical modeling.

2.75; a kitten who is just born is predicted to weigh 2.75 ounces.

The w-intercept of the line of fit represents the weight of a kitten at birth, which is the value of w when d equals zero. In this case, the intercept is 2.75, which means that a kitten who is just born is predicted to weigh 2.75 ounces.

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The probability that none of the 3 detectors would work if there was smoke in the factory is 0.25³, or 0.015625 (1.56%).

Probability is a branch of mathematics that deals with the likelihood of certain outcomes or events occurring. Probability is a measure of how likely an event is to occur, expressed as a number between 0 and 1. An event that is certain to occur has a probability of 1, while an event that is impossible to occur has a probability of 0. The probability of an event occurring can be calculated by dividing the number of successful outcomes by the total number of possible outcomes.

This probability indicates that the factory does have a safety problem, as there is a 1.56% chance that none of the smoke detectors would sound an alarm if there was smoke present. This presents a significant risk to the factory, as it could lead to an undetected fire that may cause damage to the facility or put employees in danger.

The company should look into ways to reduce the risk of the smoke detectors not working. One way to do this would be to increase the number of smoke detectors in the factory room, as the more detectors there are, the lower the probability that none of them will work. The company could also consider using more reliable smoke detectors that have a higher probability of working correctly when needed. Ultimately, the company should seek to reduce the risk of none of the detectors working by taking steps to increase the probability that at least one of them will sound an alarm in the event of smoke or a fire.

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Answer:

Let's say that the class has a total of 7x students, where 2x wear glasses and 5x don't.

After 5 of the students who didn't wear glasses now do, the number of students who don't wear glasses becomes 5x - 5.

So, the new ratio of students who wear glasses to those who don't wear glasses is:

2x : (5x - 5)

We can simplify this ratio by dividing both terms by the greatest common factor, which is x:

2 : (5 - 5/x)

We can't simplify this any further, but we can see that the ratio is not fixed and depends on the value of x.

a) The monthly interest rate for the $40,000 loan repaid monthly over 20 years with a monthly payment of $544.53 is 0.00153. b) The monthly interest rate for the $40,000 loan repaid monthly over 20 years with a monthly payment of $544.53 comes out as 0.00153 percent

To find the monthly payment needed to repay a $40,000 loan over 20 years with a 0.5% interest rate per month, we can use the following formula: Monthly payment = (Loan amount * Monthly interest rate) / (1 - (1 + Monthly interest rate)^-Number of payments)

Plugging in the given values: Monthly payment = ($40,000 * 0.005) / (1 - (1 + 0.005)^-240) Monthly payment = $200 / (1 - 0.334) Monthly payment = $200 / 0.666, Monthly payment = $300.30

Therefore, the monthly payment needed to repay the $40,000 loan over 20 years with a 0.5% interest rate per month is $300.30.To find the monthly interest rate for a $40,000 loan repaid monthly over 20 years with a monthly payment of $544.53, we can use the same formula and rearrange it to solve for the monthly interest rate:

Monthly interest rate = (Monthly payment * (1 - (1 + Monthly interest rate)^-Number of payments)) / Loan amount. Plugging in the given values:

0.005 = ($544.53 * (1 - (1 + 0.005)^-240)) / $40,000

0.005 * $40,000 = $544.53 * (1 - (1 + 0.005)^-240)

$200 = $544.53 * (1 - (1 + 0.005)^-240)

$200 / $544.53 = 1 - (1 + 0.005)^-240

0.367 = 1 - (1 + 0.005)^-240

(1 + 0.005)^-240 = 0.633

1 + 0.005 = 0.633^-240

0.005 = 0.633^-240 - 1

0.005 = -0.367

Monthly interest rate = -0.367 / -240

Monthly interest rate = 0.00153

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1. The probability of getting a z-score of 0.189 or less is 0.5753.  

2. The probability of getting a z-score of 1.13 or less is 0.8708.

3. The probability of getting a z-score of 3.02 or less is 0.9982.

Normally distributed data refers to data that follows a normal distribution, also known as a Gaussian distribution or bell curve.

In a normal distribution, the data is symmetric around the mean and the majority of the data is clustered around the mean with decreasing density as the data moves further away from the mean.

Here we have

The mean price for liquid crystal display (LCD) computer monitors is $ 170  and the standard deviation is $ 53.  

Find the z-score associated with $ 180 using the formula:

z = (x - μ) / σ

where x is the value we need to find the probability, μ is the mean, and σ is the standard deviation.

z = (180 - 170) / 53

z = 0.189

Hence, using a standard normal distribution table or calculator, we can find that the probability of getting a z-score of 0.189 or less is 0.5753.  

To find the probability that the mean cost of 9 randomly selected LCD computer monitors is less than $ 180, find the standard deviation σ/√n.

The standard deviation of the sample means is σ/√n = $53/√9 = $17.67.

Now we need to find the z-score associated with $ 180 using the formula:

z = (x - μ) / σ/√n

where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

z = (180 - 170) / (53 / √9)

z = 1.13

Hence, using a standard normal distribution table or calculator, we can find that the probability of getting a z-score of 1.13 or less is 0.8708.  

To find the probability that the mean cost of 36 randomly selected LCD computer monitors is less than $ 180, we can use the same formula as in part 2, with n = 36:

z = (x - μ) / σ/√n

z = (180 - 170) / (53 / √36)

z = 3.02

Hence, using a standard normal distribution table or calculator, we can find that the probability of getting a z-score of 3.02 or less is 0.9982.

Therefore,

1. The probability of getting a z-score of 0.189 or less is 0.5753.  

2. The probability of getting a z-score of 1.13 or less is 0.8708.

3. The probability of getting a z-score of 3.02 or less is 0.9982.

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Answer:

Step-by-step explanation:

We can rewrite the situation using cost equations for the two companies

If c1 and c2 represent the total costs for companies 1 and 2 respectively and w the weight of sugar transported

For the first company we have
c1 = 2804 + 100.50w

For the second company
c2 = 275.75w

Costs are the same when c1 = c2

or

2804 + 100.50w = 275.75w

To Solve:

At 16 tons of sugar, the costs will be the same for both companies

At this tonnage, the cost is
275.75 x 16 = $4412

The area of rectangle S is 84.15 square unit.

Area is the region enclosed by the shape of an object. The space covered by a figure or any two-dimensional geometric shape in the plane is the area of ​​the shape, or

Area is a measure of the surface area of ​​a shape. To find the area of ​​a rectangle or square, you need to multiply the length and width of the rectangle or square.

Solution according to the given information in the question:

Area of rectangle R = 187

Ratio of rectangle R = 17

Ratio of rectangle S = 7.65

Area of rectangle S = (7.65/17)×187

                                 = 84.15 square unit

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The parent functions that have an infinite number of zeroes are sine and cosine.  A zero of a function is a value of x for which the function equals zero. For example, the function f(x) = x has a zero at x = 0, because f(0) = 0.

The parent functions sine and cosine have an infinite number of zeroes because they are periodic functions, meaning they repeat their values at regular intervals.

The sine function has zeroes at every multiple of π, or 0, π, 2π, 3π, etc. The cosine function has zeroes at every odd multiple of π/2, or π/2, 3π/2, 5π/2, etc.

In contrast, the other parent functions listed have a finite number of zeroes. The linear function has one zero, the quadratic function has at most two zeroes, the exponential function has at most one zero, the reciprocal function has no zeroes, the absolute value function has at most one zero, and the square root function has at most one zero.

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The shortest distance from a point to a line can be found by using the formula:
d = |Ax + By + C| / √(A² + B²)

where A, B, and C are the coefficients of the line equation and x and y are the coordinates of the point.

In this case, A = 2, B = 3, C = -1, x = 6, and y = 5.
Plugging these values into the formula, we get:
d = |(2)(6) + (3)(5) - 1| / √(2² + 3²)
d = |17| / √(13)
d = 17 / √(13)
d = √(13) * 17 / 13
d = √(13) * √(13) / √(13)
d = √(13)
Therefore, the shortest distance from the point (6,5) to the line 2x+3y=1 is √(13).

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The values of the length and angle are;

AD = 22 units

m < ADC = 106 degrees

The properties of a kite are given as;

From the information given, we have that;

AB = 8x - 2

AD = 6x + 4

Equate the sides

8x - 2 = 6x + 4

collect like terms

2x = 6

x = 3

AD = 22 units

Also,

m < ABC = m < ADC

Substitute the values

12x + 10 = 15x - 14

collect like terms

-3x = -24x

x = 8

m < ADC = 106 degrees

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Answer: AD = 22 units

Step-by-step explanation:

m < ADC = 106 degrees

AB = 8x - 2

AD = 6x + 4

Equate any sides

8x - 2 = 6x + 4

Collect terms

2x = 6

x = 3

AD = 22 units

m < ABC = m < ADC

Substitute the values

12x + 10 = 15x - 14

Collect terms

-3x = -24x

x = 8

m < ADC = 106 degrees

The result of blending 50 percent of each animation of the pairs that follow will be a new animation that combines the features of both animations. This is known as "root motion blending" and is used to create smooth transitions between different animations.

The new animation will have a duration that is the average of the two animations being blended (for example, blending IDLE and WALK_1 will result in a 3s duration animation) and will include features from both animations. For example, blending WALK_1 and WALK_2 will result in a walking animation that is at a pace between relaxed and fast. Similarly, blending SPRINT_1 and SPRINT_2 will result in a sprinting animation that includes both a straight sprint and a slight right turn. The root motion of the new animation will be the average of the root motions of the two animations being blended.

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Answer:The father's position relative to the surface of the water is 4.2 meters below the surface of the water.

Step-by-step explanation:

What is an expression?

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The height relative to the water surface is calculated as:-

Height from iceberg to water surface = 0.5 meters

The height from iceberg to deep inside the water is = 4.7 meters

Father's height relative to the water surface is,

H= 4.7 - 0.5 = 4.2 meters.

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Rounding to the nearest whole number, we can estimate that about 566.49 visitors would be expected to buy no costume when there are 1200 visitors to the website.

The first 10 integers are known as the fundamental numbers in mathematics. These fundamental integers are given from 0 to 9. Basic integers in the 0 to 9 range include 0 through 1, 2, 3, 4, 5, 6, 7 and 8.

According to the information given, 93 visitors purchased no costume, 94 visitors purchased one costume, and 10 visitors purchased more than one costume. Let's calculate the total number of costumes purchased:

Total number of costumes purchased = 1(94) + 2(10) = 114

Next, let's calculate the total number of visitors to the website:

Total number of visitors = 93 + 94 + 10 = 197

To estimate the number of visitors who are likely to purchase no costume when there are 1200 visitors to the website, we can use a proportion:

93/197 = x/1200

x = (93/197) * 1200 ≈ 566.49

Rounding to the nearest whole number, we can estimate that about 566.49 visitors would be expected to buy no costume when there are 1200 visitors to the website.

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The area of the circle which is drawn by tracing around the edge of the quarter on a sheet of paper is 0.78 in.²

All points in a plane that are at a specific distance from a specific point, the centre, 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.

Each of the four equally sized pieces that make up a circle is known as a quarter of a circle. The quadrant of the circle is the name given to each quarter. One-fourth of the total area of the circle is represented by the area of a quarter circle.

Given,

the diameter of the quarter  = 1 in.

When we trace around the edge of the quarter on a sheet of paper, we get a circle of diameter 1 in.

So the radius of the circle r = 1/2 = 0.5 inches

Area of the circle on the paper = πr² = 3.14 × 0.5² = 0.78 in.²

Therefore the area of the circle which is drawn by tracing around the edge of the quarter on a sheet of paper is 0.78 in.²

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Answer:

Let's assume that Mia's present age is x.

According to the problem, Rosie is 6 years older than Mia, so Rosie's present age is x + 6.

In 4 years, Mia's age will be x + 4, and Rosie's age will be (x + 6) + 4 = x + 10.

The problem also states that Rosie's age in 4 years will be three times Mia's present age, so we can write the equation:

x + 10 = 3x

Simplifying this equation, we can subtract x from both sides to get:

10 = 2x

Dividing both sides by 2, we get:

x = 5

Therefore, Mia is currently 5 years old. To check, we can verify that in 4 years, Rosie will be three times Mia's age:

Rosie's age in 4 years = (5 + 6) + 4 = 15

Mia's age in 4 years = 5 + 4 = 9

Rosie's age in 4 years is indeed three times Mia's age, so our solution is correct.

The explicit formula for the nth term of the sequence 7, 35, 175 is:

[tex]a_n = 7 * 5^{n-1}[/tex]

What is the geometric sequence?

A geometric sequence is a sequence of numbers in which each term after the first is found by multiplying the previous term by a fixed number called the common ratio. The general formula for a geometric sequence is:

a, ar, ar², ar³, ...

where a is the first term and r is the common ratio.

To find the explicit formula for the sequence 7, 35, 175, we need to identify the pattern in the sequence.

Notice that each term is obtained by multiplying the previous term by 5. Specifically, the first term (7) is multiplied by 5 to get the second term (35), and the second term is multiplied by 5 to get the third term (175).

So, the sequence is a geometric sequence with a common ratio of 5.

To find the explicit formula for a_n, we can use the formula:

[tex]a_n = a_1 * r^{n-1}[/tex]

where a1 is the first term, r is the common ratio, and n is the term we want to find.

In this case, a1 = 7 and r = 5.

Substituting these values into the formula, we get:

[tex]a_n = 7 * 5^{n-1}[/tex]

Therefore, the explicit formula for the nth term of the sequence 7, 35, 175 is:

[tex]a_n = 7 * 5^{n-1}[/tex]

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Answer:

75:77

Step-by-step explanation:

5 is 2 more than 3

3+72=75

5+72=77

therefore: 3:5 = 75:77

If that's not what you meant, then I don't understand the question

There are 15 blue counters in the bag.

Two quantities are compared to form a ratio. An equality of two ratios is a proportion.

We know that the initial ratio of red counters to blue counters was 4:5. Therefore, we can write:

4x : 5x

We also know that 10 more red counters were added to the bag. Therefore, the new number of red counters in the bag is:

4x + 10

The ratio of red counters to blue counters then became 6:5. Therefore, we can write:

(4x + 10) : y = 6 : 5

We can simplify this equation by cross-multiplying:

5(4x + 10) = 6y

20x + 50 = 6y

Dividing both sides by 6, we get:

y = (20x + 50)/6

Simplifying, we get:

y = (10x + 25)/3

Since y has to be a whole number, 10x + 25 has to be divisible by 3. The only value of x that satisfies this condition is x = 2.

Therefore, the initial number of red counters was 4x = 8, and the initial number of blue counters was 5x = 10.

After adding 10 more red counters, the new number of red counters was 18, and the new ratio of red counters to blue counters was 6:5.

To find the new number of blue counters, we can use the equation we derived earlier:

y = (10x + 25)/3

Substituting x = 2, we get:

y = (10(2) + 25)/3 = 15

Therefore, there are 15 blue counters in the bag.

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Answer:

62

Step-by-step explanation:

x2 a 4 - 91

kejejej

ejejdjej

ejjeej

There are a total of 32 possible sequences because there are two alternatives for each stage. Since there are more than seven distinct ways to mount the stairs, the priestess can do so every day for a week.

(a) Every day, the priestess at the temple of Horus must climb a flight of five stairs, which she can do by taking one or two steps at a time. The amount of ways she can up the stairs on any given day can be represented by a binary digit, where 1 denotes a two-step ascent and 0 denotes a one-step ascent. For each of the five steps, for instance, 00101 reflects the order of her one- and two-step climbs.

(b) The same regulations apply. The entire number of potential sequences, using the same binary digit format, is 213 = 8,192. There are therefore more than 365 possible ways to mount the grand staircase, allowing the priest to do so every day for a whole year.

In conclusion, the number of alternative binary sequences, where each digit denotes a one- or two-step climb, may be used to determine the number of ways the priestess can ascend the five-step flight of stairs and the number of ways the priest can ascend the thirteen-step grand staircase.

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X = 7 & -7/2

First, use the distributive property to simplify the equation:

2 - 5/(x+7) = -7/(x-3)(x+7)

2(x-3)(x+7) - 5(x-3) = -7(x+7)

2x2 + 7x - 6x - 15 = -7x - 49

2x2 -13x - 49 = 0

This equation can be solved by factoring the binomial:

2x2 -13x - 49 = 0

2x(x-7) - 7(x-7) = 0

(2x-7)(x-7) = 0

Therefore, the solution for x is x = 7 and x = -7/2.

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Answer: To determine the effective rate of Zoe's loan, we can use the formula:

Effective rate = (1 + (nominal rate/number of compounding periods))^number of compounding periods - 1

Since the nominal rate is compounded monthly, the number of compounding periods is 12.

Plugging in the values, we get:

Effective rate = (1 + (0.039/12))^12 - 1

Effective rate = 0.0407 or 4.07%

Therefore, the effective rate of Zoe's loan is 4.07%, rounded to the nearest hundredth. The correct response is 3.97%.

Step-by-step explanation:

The function value and the indicated trigonometric value are not specified in the question. Additionally, the specified quadrant is not mentioned. Therefore, it is not possible to provide an accurate answer to this question.

However, generally speaking, to find the indicated trigonometric value in a specified quadrant using a function value, you can use the following steps:

1. Identify the function and the quadrant in which the value is to be found.
2. Use the function value to find the reference angle in the first quadrant.
3. Use the reference angle and the specified quadrant to find the indicated trigonometric value.

For example, if the function value is sin(θ) = 1/2 and the specified quadrant is II, you can use the following steps to find the indicated trigonometric value:

1. Identify the function and the quadrant: sin(θ) and II.
2. Find the reference angle in the first quadrant: θ = 30°.
3. Use the reference angle and the specified quadrant to find the indicated trigonometric value: sin(150°) = 1/2.

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Answer:

1. around 4.86 or 4.9 for the nearest tenth

2. 17 months

Step-by-step explanation:

1. (1.7×10^6)/(3.5×10^5) = (1.7/3.5)×(10^6/10^5) = 0.4857×10 = 4.857

Therefore, 1.7×10^6 is about 4.857 times as great as 3.5×10^5.

2.  start by finding out how much Erica still owes after the down payment:

Total cost - Down payment = $1,867 - $320 = $1,547

divide the amount still owed by the monthly payment to find out how many months Erica will be paying:

$1,547 ÷ $91 per month = 17 months (rounded up)

Therefore, Erica will be paying for the bike for 17 months

Both f(g(x)) and g(f(x)) equal x, we can determine that the functions f(x) and g(x) are inverses.

To determine if the functions f(x) and g(x) are inverses using composition, we need to find f(g(x)) and g(f(x)) and see if they both equal x.

First, let's find f(g(x)):
f(g(x)) = f((3)/(2)x+12)
= (2)/(3)((3)/(2)x+12)-8
= (2)/(3)(3)/(2)x + (2)/(3)(12) - 8
= x + 8 - 8
= x

Now, let's find g(f(x)):
g(f(x)) = g((2)/(3)x-8)
= (3)/(2)((2)/(3)x-8) + 12
= (3)/(2)(2)/(3)x - (3)/(2)(8) + 12
= x - 12 + 12
= x

Since both f(g(x)) and g(f(x)) equal x, we can determine that the functions f(x) and g(x) are inverses.

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The values of k that make the system inconsistent are k = 0 and k = 2.

The system obtained from the given augmented matrix is:
```
1 2 -1 | 4
0 -1 1 | 3
0 0 k^2-2k | -3k-3
```
For the system to be inconsistent, the last equation must be a contradiction, meaning that the coefficients of the variables are all zero but the constant term is nonzero. In other words, we need `k^2-2k = 0` and `-3k-3 ≠ 0`.

Solving for k in the first equation, we get:
```
k^2-2k = 0
k(k-2) = 0
```
So k = 0 or k = 2.

However, we also need `-3k-3 ≠ 0`, which means that k ≠ -1. Therefore, the values of k that make the system inconsistent are k = 0 and k = 2.

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Difference in the medians as a multiple of the IQR = 5.

The Interquartile Range (IQR) formula computes the median of a set of data. One of the smallest statistical measurements of dispersion is the interquartile range. The interquartile range refers to the spread between the upper and lower quartiles.

The interquartile range is defined as Upper Quartile - Lower Quartile.

According to the question,

Data set of Mount Vernon= 55, 60, 65, 70, 75, 80, 85, 90

Data set of Lakewood= 65, 70, 75, 80, 85

Data sets are already in ascending order.

Median for Mount Vernon = 70+75/2 = 77.5

Median for lower half of set= 55+60+65+70/4 = 62.5

Median for upper half of set= 75+80+85+90/4 = 82.5

IRQ for Mount Vernon = 82.5-62.5 = 20

Now similarly in case of Lakewood,

Median= 75.

Median for lower half of set = 65+70/2 = 67.5

Median for upper half of set = 80+85/2 = 82.5

IRQ = 82.5 - 67.5 = 15.

Hence, difference in IRQ = 20-15 = 5.

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The exact value of the following trig expression tan(11pi/12) is (18sqrt(3) + 18sqrt(2-sqrt(2)))/(8-9sqrt(3)*sqrt(2-sqrt(2))).

The exact value of the following trig expression tan(11pi/12) can be found using trig identities and the special points on the unit circle.

First, we can use the double angle formula for tangent:

tan(2x) = 2tan(x)/(1-tan^2(x))

We can then use this formula to rewrite the given expression:

tan(11pi/12) = tan(2*11pi/24) = 2tan(11pi/24)/(1-tan^2(11pi/24))

Next, we can use the sum formula for tangent to rewrite the expression in the numerator:

tan(11pi/24) = tan(7pi/24 + 4pi/24) = (tan(7pi/24) + tan(4pi/24))/(1-tan(7pi/24)*tan(4pi/24))

We can then use the special points on the unit circle to find the exact values of these expressions:

tan(7pi/24) = tan(pi/3 + pi/8) = (tan(pi/3) + tan(pi/8))/(1-tan(pi/3)*tan(pi/8)) = (sqrt(3) + sqrt(2-sqrt(2)))/(1-sqrt(3)*sqrt(2-sqrt(2)))

tan(4pi/24) = tan(pi/6) = sqrt(3)/3

Plugging these values back into the original expression, we get:

tan(11pi/12) = 2(sqrt(3) + sqrt(2-sqrt(2)))/(1-sqrt(3)*sqrt(2-sqrt(2)))/(1-(sqrt(3)/3)^2) = 2(sqrt(3) + sqrt(2-sqrt(2)))/(1-sqrt(3)*sqrt(2-sqrt(2)))/(8/9) = (2(sqrt(3) + sqrt(2-sqrt(2))))*(9/(8-9sqrt(3)*sqrt(2-sqrt(2))))

Simplifying further, we get:

tan(11pi/12) = (18sqrt(3) + 18sqrt(2-sqrt(2)))/(8-9sqrt(3)*sqrt(2-sqrt(2)))

Therefore, the exact value of the following trig expression tan(11pi/12) is (18sqrt(3) + 18sqrt(2-sqrt(2)))/(8-9sqrt(3)*sqrt(2-sqrt(2))).

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Jean-Luc's account will be worth approximately $740.55 after 5 years of continuous  at a compounding annual interest rate of 1.6%.

Compound interest is the addition of interest to the principal amount of a loan or investment. In other words, it is the interest earned on both the principal amount and any accumulated interest from previous periods.

Interest rate is the amount charged by a lender to a borrower for the use of money or the amount earned by an investor for lending money or investing in an asset. It is usually expressed as a percentage of the principal amount and is typically calculated on an annual basis.

In the given question,

The formula for continuous compounding is:

A = Pe^(rt)

where A is the amount of money in the account after t years, P is the principal amount (the initial deposit), r is the annual interest rate (as a decimal), and e is the mathematical constant approximately equal to 2.71828.

Plugging in the given values, we get:

A = 625 * e^(0.016*5)

Simplifying this expression, we get:

A = 625 * e^(0.08)

Using a calculator, we can evaluate this expression to get:

A ≈ $740.55

Therefore, Jean-Luc's account will be worth approximately $740.55 after 5 years of continuous compounding at an annual interest rate of 1.6%.

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The equation of a circle with center at (4, 8) and passing through (-10, -5) is [tex](x-4)^2 + (y-8)^2 = (6)^2.[/tex]

To find this equation, we need to use the distance formula: [tex]d = sqrt((x2-x1)^2 + (y2-y1)^2).[/tex]

We can substitute in the coordinates of the center of the circle and the point it passes through:

[tex]d = sqrt((-10-4)^2 + (-5-8)^2)[/tex]
[tex]d = sqrt( (6)^2 + (13)^2 )[/tex]

d = sqrt(36 + 169)

d = sqrt(205)

d = 14.2

Now, we have the radius of the circle. We can use this to form the equation of the circle:

[tex](x-4)^2 + (y-8)^2 = (14.2)^2[/tex]

[tex](x-4)^2 + (y-8)^2 = (6)^2[/tex]

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