A line passes through the points (-4,-3) and (2, 6). Determine the slope of the line.

• m = 2/3
O The slope is undefined.
Om = 0
Om =3/2

Answers

Answer 1

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-4)}}} \implies \cfrac{6 +3}{2 +4} \implies \cfrac{ 9 }{ 6 } \implies {\Large \begin{array}{llll} \cfrac{ 3 }{ 2 } \end{array}}[/tex]


Related Questions

as an avid fisherman, nick was curious if the advertised strength of fishing line is accurate. to investigate, he used "6 pound" fishing line to hang a bucket, which he then filled with weights until the line broke. then nick measured the total weight of the bucket and its contents to determine the breaking strength of that piece of fishing line. after trying this with many different sections of the fishing line, he estimated that the distribution of breaking strength for this type of line is approximately normal with a mean of 6.44 pounds and a standard deviation of 0.75 pound.

Answers

Using the normal distribution, it is found that this type of fishing line have a breaking strength less than the advertised 6 pounds 27.76% of the time.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by the following rule:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score measures how many standard deviations the measure X is above or below the mean, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X.

The mean and the standard deviation for the breaking strengths are given as follows:

[tex]\mu = 6.44, \sigma = 0.75[/tex]

The proportion of times with breaking strength less than 6 inches is given by the p-value of Z when X = 6, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (6 - 6.44)/0.75

Z = -0.59

Z = -0.59 has a p-value of 0.2776.

Hence the percentage is of 27.76%.

What is the missing information?

The question is:

How often will this type of fishing line have a breaking strength less than the advertised 6 pounds.

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if you finish these both ill give u a cookie

Answers

1. 135, 205, 330, 275, and 365 are divisible by 5.

2.  1, 4, and 7 can be filled in the blank space to make it divisible by 3.

3. 1, 2, 3, 5, 6, 10, 15, and 30 are the factors.

4. 81 is the only composite number all the other nos. are prime.

What is the divisibility rule?

Divisibility rules are methods for determining whether a number is divisible by a certain number or not without actually dividing.

We know numbers that are divisible by 5 are those numbers

having 5 or 0 in their unit place.

∴ 135, 205, 330, 275, and 365 are divisible by 5.

A number is divisible by 3 if the sum of all the digits is divisible by 3.

∴ 3,71_ has a digit sum of 11, so 1, 4, 7 can be filled in the blank space to make it divisible by 3.

A list of all the factors of 30 is those numbers that divide 30 completely.

∴ 1, 2, 3, 5, 6, 10, 15, and 30 are the factors.

We know composite numbers are those numbers that are not prime.

∴ 81 is the only composite number all the other nos. are prime and they have only two factors 1 and the number itself.

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Ryan invests $7,000 for 9 months at a simple interest rate of 8.3%. The amount of interest received is found by
I=PRT
Since R=0.083,
I=0.083 x P x T
What are P and T?

Answers

P, which is the principal invested is $7,000 whereas the T is 0.75

What is simple interest?

The simple interest on an investment such as that of Ryan, can be determined as the principal multiplied by the simple interest  rate and the time whose formula is as given below:

I=PRT

I=simple interest amount in dollars=unknown

P=principal investment=actual amount invested on simple interest basis=$7000

R=annual simple interest rate=8.3%

T=period of investment measured in years=9/12=0.75(9months divided by 12months in a year gives 0.75 years)

I=$7000*0.083*0.75

I=$435.75

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an executive in an engineering firm earns a monthly salary plus a christmas bonus of 5700 dollars. if she earns a total of 83500 dollars per year, what is her monthly salary in dollars?

Answers

The monthly salary of an executive is $6483.

What is monthly salary?

A salary is the amount of money that an employee receives from their employer each month, particularly when they work in a profession like education, law, or medical.

Given: An executive in an engineering firm earns a monthly salary plus a Christmas bonus of 5700 dollars. She earns a total of 83500 dollars per year.

To find the salary for each month.

First to subtract the Christmas bonus from the total amount.

83500 - 5700 = 77800.

So, the salary from each month is,  77800/12 = 6483

Therefore, the salary for each month is, $6483.

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Solve for x 6 + 2x = 2(x - 3)

Answers

Answer:

No solution

Step-by-step explanation:

6 + 2x = 2(x - 3)

6 + 2x = 2x-6

No solution

Find the distance between the two points rounding to the nearest tenth (if necessary).
(4, -4) \text{ and } (9, -2)
(4,−4) and (9,−2)

Answers

The distance between two points having coordinates (4, -4) and (9, -2) plotted on the cartesian plane, and rounded to the nearest tenth, will be 5.40 units.

As per the question statement, two points having coordinates (4, -4) and

(9, -2) plotted on the cartesian plane.

We are required to calculate the distance between the above mentioned two points, rounded to the nearest tenth.

To solve this question,  we need to know the Distance-formula which goes as,

"The distance between any two points (x₁, y₁) and (x₂, y₂) can be given by √[(x₂ - x₁)² + (y₂ - y₁)²]"

Assuming that [(x₁, y₁) = (4, -4)] and [(x₂, y₂) = (9, -2)], and substituting these values in the above-mentioned distance formula, we get,

√[(9 - 4)² + {(-2) - (-4)}²]

= √[(9 - 4)² + {(-2) + 4}²]

= √[(9 - 4)² + (4 - 2)²]

=√[(5)² + (2)²]

=√(25 + 4)

=√29

= 5.38 units.

Therefore, rounding (5.38) to the nearest tenth, we get, 5.40.

That is, the distance between two points having coordinates (4, -4) and (9, -2) plotted on the cartesian plane, and rounded to the nearest tenth, will be 5.40 units.

Distance: In Mathematics, physics or daily life, distance is a numerical or occasionally qualitative measurement of how far objects or points are from each other.Coordinates: In geometry, coordinates are a pair of numbers that can uniquely determine the position of points or other geometric elements on a Euclidean or Cartesian Plane.

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over the set of integers factor the expression 4x^3 - x^2+16x-4 completely

Answers

The factorized expression of the equation of the function given as lf(x) = 4x³ - x² + 16x - 4 is f(x) = (x² + 4)(4x - 1)

How to determine the factor of the expression?

The equation of the function is given as

f(x) = 4x³ - x² + 16x - 4

Factor out x from the equation of the function

So, we have

f(x) = 4x³ - x² + 16x - 4

Group the terms in 2's

f(x) = (4x³ - x²) + (16x - 4)

Factorize the expression in the bracket

So, we have

f(x) = x²(4x - 1) + 4(4x - 1)

Factor out 4x - 1

So, we have

f(x) = (x² + 4)(4x - 1)

Hence, the factorized expression is f(x) = (x² + 4)(4x - 1)

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how many solutions does the equation 7x+3-8=2(5x-4) have

Answers

The number of solutions in the equation where the equation is given as 7x + 3 - 8 = 2(5x - 4)  is one solution

How to determine the number of solutions in the equation?

The equation is given as

7x + 3 - 8 = 2(5x - 4)

The above equation is a linear function with one variable

So, we have

7x + 3 - 8 = 2(5x - 4)

Open the brackets

So, we have

7x + 3 - 8 = 10x - 8

Subtract 10x from both sides of the equation

So, we have

-3x + 3 - 8 = - 8

Subtract (3 - 8) from both sides of the equation

So, we have

-3x = - 3

Divide by -3

x = 1

The above equation is true because it has a definite solution

Hence, the number of solutions in the equation is one

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paula invited some friends to dinner, and she plans to make fajitas. at the grocery store, she spends $2.56 on red bell peppers and $1.92 on green bell peppers. if both types of bell peppers cost $1.60 per pound, how many total pounds of bell peppers does she buy?write your answer as a whole number or decimal. pounds

Answers

Answer:

2.8 pounds

Step-by-step explanation:

she spends on both types of bell peppers =

$2.56+$1.92=$4.48

$1.60 = 1 pound

$4.48 = ?

= 4.48/1.60

= 2.8 pounds

What values of x and y satisfy the system
y = −2x + 3
y = 5x - 4

Answers

The most appropriate choice for simultaneous linear equation will be given by -

x = 1, y = 1

What is simultaneous linear equation?

At first it is important to know about linear equation

Equation shows the equality between two algebraic expressions by connecting the two algerbraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.

Here,

y = −2x + 3

y = 5x - 4

So, -2x + 3 = 5x - 4

5x  + 2x = 3 + 4

7x = 7

[tex]x = \frac{7}{7}\\x = 1[/tex]

Putting the value of x in the first equation'

y = [tex]- 2\times 1 +3[/tex]

y = 1

So, x = 1, y = 1

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i need help, what is 4x+14≤38

Answers

Answer:

x ≤ 6 I think!

Answer: [tex]x\leq 6[/tex]

Step-by-step explanation: [tex]4x\leq 38-14[/tex]. Move the 14 to the right side first.

Then you would get [tex]4x\leq 24[/tex]

Divide 4 on both side

[tex]x\leq 6[/tex]

The distance to your cousin's house is 666 miles, and the distance to Chicago is 37 miles. If it took 18 hours to drive to your cousin's house. howlong would you estimate the drive to Chicago to take?

Answers

We know that it took 18 hours to drive 666 miles. If we divide the distance by the hours (666 miles)/(18 hours)

We find that 666/18= 37 miles per hour . which means we travel 37 miles each hour.

So, we can estimate that driving 37 miles it will take 1 hour (the distance to Chicago).

Answer:

666/18=37miles/hour

it would take 1 hour to drive 37 miles

A projectile is fired vertically upward and can be modeled by the function h(t)=−16t2+900t+175. During what time interval will the projectile be more than 9000 feet above the ground? Round your answer to the nearest hundredth.

Answers

Calculating a projectile's vertical upward firing is possible using the function h(t)=-16t²+900t+175.  12.65<t<43.59 will the projectile be above the ground at a height more than 9000 feet.

Given that,

Calculating a projectile's vertical upward firing is possible using the function h(t)=-16t²+900t+175.

We have to find how long will the projectile be above the ground at a height more than 9000 feet.

Answers should be rounded to the closest hundredth.

The function is

h(t)=-16t²+900t+175

-16t²+900t+175>9000

-16t²+900t+175-9000>0

-16t²+900t-8825>0

The simplest method for locating a quadratic equation's roots is the quadratic formula. There are some quadratic equations that are difficult to factor, and in these cases we can quickly discover the roots by using the quadratic formula.

Gives the roots of a quadratic equation ax² + bx + c = 0.

x = [-b ± √(b² - 4ac)]/2a.

Now, We get

t= [-900 ± √((900)² - 4(-16)(-8825))]/2(-16)

t=[-900 ± √(810000-564800)]/-32

t=[-900 ± √(245200)]/-32

t=[-900 ± 495.17]/-32

First,

t=[-900 + 495.17]/-32

t=[-404.83]/-32

t=12.65

Second,

t=[-900 - 495.17]/-32

t=[-1395.17]/-32

t=43.59

Therefore, 12.65<t<43.59 will the projectile be above the ground at a height more than 9000 feet.

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Which of the following is a geometric sequence?
O 0, 2, 6, 12, 72,
1 2 3 4 5
2'3'4'5'6'
O4, 9, 14, 19, 24,
O
O 1, 3, 9, 27, 81,

Answers

The geometric sequence is option(D) i.e, 1, 3, 9, 27, 81,..

What is Geometric sequence ?

A geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

In this, the last option have the geometric sequence. since, there is a common ration between each term. If you multiplying the previous term in the sequence by 3 gives the next term.

Hence, The geometric sequence is 1, 3, 9, 27, 81,

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Solve...........................................

Answers

The sum of 25 and 35 using their greatest common factor is 60.

What are factors?

It should be noted that factors simply means the numbers that.van be multiplied with another number which is also a factor to get the original number.

In this case, it should be noted that the sum of 25 + 25 based on their factor will be:

= 5(5) + 5(7)

= 5(12)

= 60

The sum is 60.

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(1) Solve x² + x + 2 = 0 by formula method.​

Answers

The roots of the quadratic equation  x² + x + 2 = 0  is [tex]-1+\sqrt{-7} /2[/tex] and[tex]-1-\sqrt{-7} /2[/tex]

What are roots?

Roots: In mathematics, a solution to an equation, usually expressed as a number or an algebraic formula. The square root of a number is a value that can be multiplied by itself to give the original number. The square root of 9 is 3, because when 3 is multiplied by itself, you get 9.

given quadratic equation is,  x² + x + 2 = 0

to find the roots we have formula method ,

x=[tex]-b+\sqrt{b^2-4ac}[/tex][tex]/2a[/tex]

x=[tex]-b-\sqrt{b^2-4ac}[/tex][tex]/2a[/tex]

a=1, b=1 and c=2

sub the values in the above equation

x=[tex]-1+[/tex][tex]\sqrt{1-4(1)(2)}[/tex][tex]/2[/tex]

x=[tex]-1-\sqrt{1-4(1)(2)} /2[/tex]

x= [tex]-1+\sqrt{-7}/2[/tex] and x=[tex]-1-\sqrt{-7} /2[/tex] are the roots of the quadratic equation

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11.04 = 1/2 (a + 0) 1.5

Answers

Answer: the value of a = 14.72 and if you evaluate it.

Have a good day

pls help it's very urgent !!​

Answers

For given function the rule obtained when finding f^(-1) is ±√[(x + 4)/3]

In this question, we have been given a function f(x) = 3x² - 4

We need to write the rule obtained when finding f^(-1)

Le f(x) = y          ........(1)

y =   3x² - 4

We find the value of x.

3x² = y + 4

x² = (y + 4)/3

x = ±√[(y + 4)/3]

From (1),

f^{-1}(y) = ±√[(y + 4)/3]

Since the choice of the variable is arbitrary, we can write this as ,

f^{-1}(x) = ±√[(x + 4)/3]

Therefore, for given function the rule obtained when finding f^(-1) is  ±√[(x + 4)/3]

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thanks help bhjjjdjshshshsyshdh

Answers

Answer:

14.90 $ 527.86- 349.11 = 178.75 divided by 12 pta members is 14.89 rounded would be 14.90 the answer depends if u want to round it

Step-by-step explanation:

sub to imaginefn in utube

in a study by giacobbi et al. (2014), it was determined that about 60% of the participants found imagery very helpful in enhancing their physical activity, but 40% said they would no longer use imagery in their exercise. the implication from these results is that

Answers

Before offering imaging programs, practitioners need to be aware of the reasons why exercise participants are doing it.

Define imagery in sports.

When we use imagery, we simulate an actual situation in our minds rather than actually going through it. It differs significantly from daydreaming or simply thinking about anything because it is a cognitive activity that is consciously used by an athlete or exerciser to accomplish a certain task.

In this study, an analysis of secondary data from a recently published randomized controlled trial. In a community-based, group-mediated physical activity intervention for sedentary people 50 and older, the Active Adult Mentoring Program (AAMP) tested the effectiveness of peer volunteers as delivery agents. The AAMP was built on the social-cognitive and self-determination theories, and mentors were trained to lead discussions in groups that would help reinforce key ideas from both theories.

The adaptability of images makes it useful at different times and in varied settings. Athletes employ imagery most frequently right before a competition or during practice, but they do so during the entire season, including the off-season. Similar to how it's reported by athletes, visualization is frequently used before an activity session. For example, it would be more effective for a swimmer to mentally practice her race start by adopting the proper position on the starting block at the swimming pool, as opposed to sitting on a chair at home. Both types of people will typically imagine within the sport and exercise environment where the benefits of this technique are maximized.

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Ashley babysits for 6 hours for $73.50 on Friday and for 3 hours for $36.75 on Sunday. What constant of proportionality relates the number of hours and total pay?

Group of answer choices

$13.50

$12.25

$11.75

$14.25

Answers

Answer:

12.25

Step-by-step explanation:

a steamer sails 100 miles east and then 40 miles on a bearing of n60°e. how far is the steamer from its starting point, and at what angle has it traveled from its starting point? round your answer to the nearest thousandth.

Answers

how do i delete an answer?

Find the length of WY if WZ=128 ft and WX=YZ

Answers

Answer: 91 ft

Step-by-step explanation:

Since WZ=1287ft .XY=54ft

WX is congruent to YZ

so WX= 1/2 (128-54)

= 1/2 x(<—times) 74

=37ft

WY= WX + XY

=37+54

= 91ft

I need help with this question. Please help

Answers

A linear function which has the same y-intercept of 5 as the one that is represented by the graph is: table 1.

How to calculate the slope of a linear function?

Mathematically, the slope of any linear function can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

At points (-3, -4) and (-1, 2), the slope of the line is given by:

Slope, m = (2 + 4)/(-1 + 3)

Slope, m = 6/2

Slope, m = 3.

Note: The y-intercept of the line shown on the graph is 5.

At points (-3, -4), the y-intercept of this line can be calculated by using the slope-intercept form:

y = mx + c

Where:

x and y represents the points.m represents the slope.c represents the y-intercept.

Making y-intercept (c) the subject of formula, we have:

y-intercept, c = y - mx

y-intercept, c = -4 - 3(-3)

y-intercept, c = -4 + 9

y-intercept, c = 5.

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Complete Question:

Which linear function has the same y-intercept as the one that is represented by the graph?

23. graph 6x=-90
pls anwser need to turn in asap

Answers

Answer:

Step-by-step explanation:

Step: 1

-Graph the 6x: It will start at (0,0) and will have a rise of 6 and a run of 1

Step: 2

-Graph the 90: From what I understand it should be a horizontal line with its point on 90y

Sorry if this doesn't help very late where I am.

Rory has a handful of Skittles. He has 5 red, 8 yellow, 6 purple, 4 green, and 11 orange.
What is the ratio of red and orange to the other Skittles?

Answers

The most appropriate choice for ratio will be given by-

Ratio of red and orange to the other Skittles  = 8 : 9

What is ratio?

Ratio determines how many times one number is bigger than the other number, provided both the numbers has the same unit.

The first part of the ratio is called antecedent and the second part of the ratio is called consequent

Here,

Number of red Skittles Rory has = 5

Number of yellow Skittles Rory has = 8

Number of purple Skittles Rory has = 6

Number of green Skittles Rory has = 4

Number of orange Skittles Rory has = 11

Total number of red and orange skittles = 5 + 11

                                                                   = 16

Total number of other skittles = 8 + 6 + 4

                                                  = 18

Ratio of red and orange to the other Skittles = 16 : 18

                                                                         = 8 : 9

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Determine the range of f(x) = |x + 5|.

Answers

Answer:

f(x) ≥ 0

In interval notation Range:  [0, ∞]

Step-by-step explanation:

Regardless of the value of x, |x+5| ≥ 0 and there is no upper bound on f(x)

Answer: C

Step-by-step explanation: Got it right for my test

Vince took out a $500 loan to buy a new
couch. He paid back the loan in 2 years and
paid a total of $570. What was the simple
interest rate for his loan?

Answers

Answer:

Step-by-step explanation:

The requried, simple interest rate for Vince's loan was 7%.

What is simple interest?

Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan.

Amount = Principal [1 + rate×time]

We can use the simple interest formula to solve this problem, where:

Simple interest = Principal x Rate x Time

In this case, the principal is $500, and the time is 2 years. We can rearrange the formula to solve for the rate:

Rate = Simple interest / (Principal x Time)

The total amount paid back, including the principal and the interest, is $570. So, the simple interest can be calculated as:

Simple interest = Total amount paid - Principal

Simple interest = $570 - $500

Simple interest = $70

Substituting these values into the formula, we get:

Rate = $70 / ($500 x 2)

Rate = $70 / $1000

Rate = 0.07 or 7%

Therefore, the simple interest rate for Vince's loan was 7%.

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The population of a village is 6400. The population is decreasing exponentially at a rate of r% per year. After 22 years, the population will be 2607. Find the value of r.

Answers

[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\dotfill & \$2607\\ P=\textit{initial amount}\dotfill &6400\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{elapsed time}\dotfill &22\\ \end{cases} \\\\\\ 2607=6400(1 - \frac{r}{100})^{22} \implies \cfrac{2607}{6400}=\left( \cfrac{100-r}{100} \right)^{22} \implies \sqrt[22]{\cfrac{2607}{6400}}=\cfrac{100-r}{100}[/tex]

[tex]\cfrac{r-100}{100}=-\sqrt[22]{\cfrac{2607}{6400}}\implies r-100=-100\sqrt[22]{\cfrac{2607}{6400}} \\\\\\ r=100-100\sqrt[22]{\cfrac{2607}{6400}}\implies {\Large \begin{array}{llll} r\approx 4 \end{array}}[/tex]

Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options.



The radius of the circle is 3 units.
The center of the circle lies on the x-axis.
The center of the circle lies on the y-axis.
The standard form of the equation is (x – 1)² + y² = 3.
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

Answers

The correct statement are;

1. The radius of the circle is 3 units.

2. The center of the circle lies on the x-axis.

3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

What is Circle?

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

The equation of circle will be;

⇒ x² + y² - 2x - 8 = 0

The standard form of the equation of circle is;

⇒ x² + y² + 2gx + 2fy + c = 0

Where,

The center of circle = (-g , -f)

The radius of circle = √g² + f² - c

Since, The equation of circle will be;

⇒ x² + y² - 2x - 8 = 0

Compare with the standard form of circle, we get;

⇒ 2gx = - 2x

⇒ g = - 1

And, 2fy = 0

⇒ f = 0

Hence, The center = ( -g , -f) = (- (-1) , 0)

                                           = (1, 0)

Clearly, This shows the center of circle is lies on x - axis.

Radius of circle = √g² + f² - c

Substitute all the values we get;

Radius of circle = √g² + f² - c = √(-1)² + 0 - (-8)

                                            = √9

                                            = 3

Thus, The radius of the circle is 3 units.

Now, For the equation of circle x² + y² = 9,

Radius = √9 = 3 units.

So, The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

Therefore, The correct statement are;

1. The radius of the circle is 3 units.

2. The center of the circle lies on the x-axis.

3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

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