Constructing parallel lines

What is the slope of the original line?


–1



What is the equation of the line that is parallel to the given line and passes through the given point?

Answers

Answer 1

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The slope of the lines is -1, and the equation of the parallel line is y = - x - 6.

Since, The parallel line passes through the points (-4,-2) and (-3,-3).

Therefore, the slope of the line is,

Slope = (-2 + 3) / (-4 + 3)

         = 1/-1

         = -1

Hence, The equation of the parallel line that is passing through point P is,

y = mx + c

y = -x + c

-3 = -(-3) + c

-3 -3 = c

c = -6

Hence, the slope of the lines is -1, and the equation of the parallel line is,

⇒ y = - x - 6.

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Constructing Parallel Lines What Is The Slope Of The Original Line?1What Is The Equation Of The Line

Related Questions

g(x)=3x^2+30x+78 minimum and maximum

Answers

The minimum value of the given function is 3 at x=-5.

By locating the vertex of the parabola that the function defines, we may determine the lowest or maximum value of G(x).

The x-coordinate of the vertex may be determined by using the formula x = -b/(2a), where a and b are the coefficients of the quadratic components in the function.

In this case, a = 3 and b = 30, so:

x = -b/(2a) = -30/(2*3) = -5

Now we can find the y-coordinate of the vertex by plugging in x = -5 into the function:

[tex]G(-5) = 3(-5)^2 + 30(-5) + 78 \\= 3(25) - 150 + 78 \\= 3(25) - 72 \\= 3(25 - 24) \\= 3(1) \\= 3[/tex]

Therefore, the minimum value of G(x) is 3 and there is no maximum value.

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Need help with this ASAP please​

Answers

Answer: The answer is Q1: 2.3+34, Q2: 5.7+8.9.

Step-by-step explanation: Please give Brainlist.

Hope this helps!!!!

I can answer more questions if you like.

(Expert Answered)

Find the probability of exactly 4 successes in 6 trials of a binomial experiment in which the probability of success is 40%

Answers

Answer:

  0.13824

Step-by-step explanation:

You want the probability of exactly 4 successes in 6 trials if the probability of success in each trial is 0.4.

Binomial probability

The probability of k successes in n trials with each having a probability of success of p is given by the formula ...

  P(k of n) = nCk·p^k·(1-p)^(n-k)

  P(4 of 6) = 6C4·0.4^4·0.6^2 = 15·0.0256·0.36 = 0.13824

The probability of exactly 4 successes is 0.13824.

__

Additional comment

The binomial coefficient nCk is computed as ...

  nCk = n!/(k!(n-k)!)

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How to find the perimeter of a composite shape with missing sides(rectangles)

Answers

Answer: You have to add up the lengths.

The volume of a triangular pyramid is 756 units3 . If the base and height of the triangle that forms its base are 18 units and 12 units respectively, find the height of the pyramid.

Answers

If the base and height of the triangle that forms its base are 18 units and 12 units respectively then the height of the pyramid is 21 units.

The formula for the volume of a triangular pyramid is:

V = (1/3) * base area * height

We are given that the volume of the pyramid is 756 units^3, the base of the pyramid is a triangle with base length 18 units and height 12 units, so its area is:

A = (1/2) * base * height = (1/2) * 18 * 12 = 108 units^2

Substituting the given values into the formula for the volume of a pyramid, we get:

756 = (1/3) * 108 * h

Multiplying both sides by 3 and dividing by 108, we get:

h = 756 / 36 = 21

Therefore, the height of the pyramid is 21 units.

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consider the data about the number of blocked intrusions in exercise 8.1, p. 240. (a) construct a 95% confidence interval for the difference between the average number of intrusion attempts per day before and after the change of firewall settings (assume equal variances). (b) can we claim a significant reduction in the rate of intrusion attempts? the number of intrusion attempts each day has approximately normal distribution. compute pvalues and state your conclusions under the assumption of equal variances and without it. does this assumption make a difference?

Answers

The 95% confidence interval for the difference between the average number of intrusion attempts per day before and after the change of firewall settings is (3.36, 13.78).

To construct a 95% confidence interval for the difference between the average number of intrusion attempts per day before and after the change of firewall settings, we can use a two-sample t-test with equal variances.

Let x₁ be the number of blocked intrusions per day before the change of firewall settings, and let x₂ be the number of blocked intrusions per day after the change of firewall settings. We have

x₂ = (56+47+49+37+38+60+50+43+43+59+50+56+54+58)/14 = 50.36

x₂ = (53+21+32+49+45+38+44+33+32+43+53+46+36+48+39+35+37+36+39+45)/20 = 40.95

s₁ = standard deviation of x₁ = 8.23

s₂ = standard deviation of x₂ = 8.98

The pooled standard deviation, sp, is given by

sp = √(((n₁-1)s₁² + (n₂-1)s₂²)/(n₁+n₂-2))

where n₁ and n₂ are the sample sizes. Since we assume equal variances, we use the formula for the pooled standard deviation. Substituting the values, we get:

sp = √(((14-1)8.23² + (20-1)8.98²)/(14+20-2)) = 8.63

The t-statistic for the difference between the means is given by

t = (x₁ - x₂) / (sp × √(1/n₁ + 1/n₂))

Substituting the values, we get

t = (50.36 - 40.95) / (8.63 × √(1/14 + 1/20)) = 2.28

We can use a t-distribution with degrees of freedom = n₁ + n₂ - 2 = 32 and a significance level of α = 0.05 to find the confidence interval. The confidence interval is given by

(x₂ - x₂) ± tsp√1/n₁ + 1/n₂)

Substituting the values, we get

(50.36 - 40.95) ± 2.0458.63√(1/14 + 1/20) = 8.57 ± 5.21

= (3.36, 13.78)

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The given question is incomplete, the complete question is:

The numbers of blocked intrusion attempts on each day during the first two weeks of the month were 56,47,49,37,38,60,50,43,43,59,50,56,54,58 After the change of firewall settings, the numbers of blocked intrusions during the next 20 days were 53,21,32,49,45,38,44,33,32,43,53,46,36,48,39,35,37,36,39,45. construct a 95% confidence interval for the difference between the average number of intrusion attempts per day before and after the change of firewall settings (assume equal variances).

Michael has a bag of smarties.He has 6 red smarties 4 blue smarties and 2 pink smarties.What is the probability he will pick 2 blue smarties two times

Answers

Answer:

Step-by-step explanation:

If he puts smarty back

because it's an "and" multiply by the 2 possibilities

4/12 *4/12

=1/3 *1/3

=1/9

If does not put smarty back

4/12 *3/11

=1/3*3/11

=3/33

can you guys please help me on this?

Answers

Answer: what do you need help with?

Step-by-step explanation:

You forgot to put an image!

Urgently need the answer please help!!

Answers

Answer:

A = 81

Step-by-step explanation:

Using the formulas

A=a2

P=4a

Solving forA

A=1

16P2=1

16·362=81

Answer:

[tex]36 {r}^{4} {s}^{5}[/tex]

Perimeter of the square

one side has a length of 9r⁴s⁵

area is equal to 9r⁴s⁵ × 9r⁴s⁵

= 81r⁸s¹⁰

or 81r⁸s¹⁰cm²

a team of soccer players spend an average of 15 minutes on weight weight training per practice session.how many minutes of weight trainingon an average would they have to complete in 116 practise?​

Answers

Answer:

The answer to your problem is, 1,740 minutes

Step-by-step explanation:

The time period of 116 trainings solutions;

The time period of 1 weight training that we know is 15 minutes. Time period of 116 weight is 5 x 116 = 1,740

Thus the answer to your problem is, 1,740

Answer:1,740 minutes

Step-by-step:

I first saw that I need to take 15 minutes and x it be the 116 Practices.

So 15 x 116 is 1,740.

1,740 minutes is your answer.

Solve the system of equations using substitution 6x-9=y and y=-3x

Answers

Answer:

y = -3

x = 1

Step-by-step explanation:

To solve the system of equations using substitution, we need to isolate one variable in terms of the other in one of the equations and substitute this expression into the other equation. We can then solve for the remaining variable.

In this case, we are given two equations:6x - 9 = y

y = -3x

We can substitute the expression for y from the second equation into the first equation to get:

6x - 9 = -3x

Now we can solve for x:

6x + 3x = 9

9x = 9

x = 1

We can substitute this value of x back into one of the original equations to solve for y. Using the second equation, we have:

y = -3(1) = -3

Therefore, the solution to the system of equations is x = 1 and y = -3.

To verify the solution, we can substitute the values of x and y into the original equations and check if they are satisfied:

6x - 9 = y

6(1) - 9 = -3

-3 = -3

This equation is true, so x = 1 and y = -3 satisfy the first equation.

y = -3x

-3 = -3(1)

This equation is also true, so x = 1 and y = -3 satisfy the second equation.

Since x = 1 and y = -3 satisfy both equations, they are the solution to the system of equations using substitution.

which is the best estimate of 7.21x3.86/10.09

Answers

Answer:

7.21x3.86/10.09

7 x 4 / 10

28 / 10

2.8

3. AKLO is similar to ANMO.
a. Which side corresponds to side KO?
AC IS
b. Write a proportion that you could use to find MN.
c. What is MN?
3cm
units.
M
3 cm
K-
2.5 cm
O
L
7.5 cm

Answers

a. Since AKLO is similar to ANMO, we know that the corresponding sides are proportional. Therefore, the side that corresponds to side KO must be the side of ANMO that is similar to side KL of AKLO. Looking at the two figures, we can see that this corresponds to side NO of ANMO.

b. To find MN, we can use the fact that the sides of similar triangles are proportional. In particular, we can use the proportion:

MN/2.5cm = 3cm/7.5cm

This proportion compares the length of MN to the length of KO (which is 2.5 cm in the smaller triangle and 7.5 cm in the larger triangle). We can solve for MN by cross-multiplying and simplifying:

MN/2.5cm = 3cm/7.5cm
MN = (2.5cm)(3cm)/7.5cm
MN = 1cm

c. Therefore, MN is 1 cm.

a tugboat goes 200 miles upstream in 10 hours. the return trip downstream takes 4 hours. find the speed of the tugboat without a current and the speed of the current.

Answers

The speed of the tugboat without the current is 35 miles per hour, and the speed of the current is 15 miles per hour.


Let t be the speed of the tugboat without the current and c be the speed of the current.
Upstream, the tugboat moves against the current, so its speed is (t - c).
Downstream, the tugboat moves with the current, so its speed is (t + c).
The upstream distance is 200 miles in 10 hours, so the upstream speed is 200/10 = 20 miles per hour.
The downstream distance is also 200 miles, but it takes 4 hours, so the downstream speed is 200/4 = 50 miles per hour.
Now, we have two equations with two variables:
  a. t - c = 20
  b. t + c = 50
Solve these equations simultaneously:
  a. Add the two equations to eliminate the variable c: 2t = 70
  b. Divide both sides by 2 to get t: t = 35 miles per hour
  c. Substitute the value of t back into one of the equations (e.g., t - c = 20): 35 - c = 20
  d. Solve for c: c = 15 miles per hour

Hence, The speed of the tugboat without the current is 35 miles per hour, and the speed of the current is 15 miles per hour.

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Circumference of circle Q

Answers

The circumference of circle be 60 in.

Give that,

Angle of sector = 60 degree

Arc length  = 10 inch

Arc length of circle = (Θ/360) x 2πr

Put the values

10 = (60/360)x2πr

⇒ r = 60/2π

Since circumference of circle = 2πr

Therefore,

circumference of the given circle = 2π x (60/2π)

                                                       = 60 in.

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The cost of 36 watches is ₹179100. Find the cost of one watch

Answers

The cost of one watch is ₹4975. The answer we got was obtained by dividing the total amount for 36 watches by the number of watches

To find the price of one watch, we can divide the total fee of 36 watches by way of the quantity of number of watches:

Price of 1 watch = general cost of 36 watches / 36

We are given that the price of 36 watches is about ₹179100, so we can now do the replacement of this value in to the formulation:

Value of one watch Is = ₹179100 / 36

When we will Simplify this expression, we get:

Value of 1 watch = ₹4975

Therefore, the cost of one watch is ₹4975.

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Chen and Megan have a parcel Chen’s parcel weighs 1 1/2kg Megan’s parcel weighs 1. 2kg how many more grams does Chen’s parcel weigh than Megan’s parcel

Answers

Chen’s parcel weighs 0.3 kg more than Megan’s parcel

What is the difference in fraction?

When working with fractions and decimals, it is good to use only one unit for ease of solving.

We are given the weights as:

Weight of Chen’s Parcel = 1¹/₂ kg

Weight of Megan's Parcel = 1.2 kg

Now, let us convert the weight of Chen’s Parcel from fraction to decimal to get 1.5 kg

Thus:

Difference in weight = 1.5 kg - 1.2 kg

= 0.3 kg

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Solve the following equation and check your result (2n)/3 + 1 = (7n)/15 + 3

Answers

both sides are equal, we can conclude that n = 150/29 is the correct solution.

What is an Equations?

Equations consist of two algebraic expressions separated by an equal (=) sign, representing the equality between the expressions on the left and right sides. Solving equations helps to find the value of a variable that represents an unknown quantity. If there is no "equal to" symbol, a statement cannot be considered an equation and is instead considered an expression.

(2n)/3 + 1 = (7n)/15 + 3 // subtract 1 from both sides

(2n)/3 = (7n)/15 + 2 // multiply both sides by 15 to eliminate fractions

10n = 3(7n)/5 + 30 // multiply both sides by 3

10n = 21n/5 + 30 // subtract 21n/5 from both sides

50n/5 - 21n/5 = 30 // simplify fractions

29n/5 = 30 // multiply both sides by 5/29

n = 150/29

To check the solution, we substitute n = 150/29 back into the original equation and see if both sides are equal:

(2n)/3 + 1 = (7n)/15 + 3

(2(150/29))/3 + 1 = (7(150/29))/15 + 3

100/29 + 1 = 70/29 + 3

129/29 = 129/29

Since both sides are equal, we can conclude that n = 150/29 is the correct solution.

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the professor for a different section of the multi-section course reported his students’ exam scores as z-scores. a student in this section, katie, received a z-score of 2.2. what percentage of the students in her section did katie outscore?

Answers

Katie outscored approximately 1.39% of the students in her section.

How to calculate percentage of the students in her section did katie outscore?

If Katie received a z-score of 2.2, this means that her score was 2.2 standard deviations above the mean of the exam scores for her section.

We can use a standard normal distribution table or calculator to find the percentage of scores that fall above a z-score of 2.2.

Using a standard normal distribution table, we can find the proportion of scores that fall below a z-score of 2.2, and then subtract this from 1 to find the proportion of scores that fall above a z-score of 2.2.

The table value for a z-score of 2.2 is approximately 0.9861, which means that approximately 98.61% of the scores fall below a z-score of 2.2. Therefore, approximately:

1 - 0.9861 = 0.0139, or 1.39%

of the scores fall above a z-score of 2.2.

This means that Katie outscored approximately 1.39% of the students in her section.

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which equations represent exponential growth? which equations represent exponential decay? drag the choices into the boxes to complete the table

Answers

The equations that represent exponential growth are [tex]A = 20,000(1.08)^t[/tex], [tex]A = 40(3)^t,[/tex] [tex]P = 1700(1.07)^t[/tex] and the equations that represent exponential decay are [tex]A = 80(1/2)^t, A = 1600(0.8)^t,[/tex] and [tex]P = 1700(0.93)^t.[/tex]

The mathematical function used to calculate the exponential growth or decay of a given set of data is an exponential function. we can calculate changes in population, loan interest charges, bacterial growth, radioactive decay, or the spread of disease by using the exponential functions.

An exponential function is of the form:

[tex]f(x) = a ^x[/tex]

The function represents an exponential decay If b < 1

The function represents an exponential growth If b > 1

From the given data about equations, we have;

Exponential Growth is;

The equation with the values b < 1 is:

[tex]A = 20,000(1.08)^t[/tex]

[tex]A = 40(3)^t[/tex]

[tex]P = 1700(1.07)^t[/tex]

Exponential Decay is;

The equation with the values b > 1 is:

[tex]A = 80(1/2)^t[/tex]

[tex]A = 1600(0.8)^t[/tex]

[tex]P = 1700(0.93)^t[/tex]

Therefore, The equations that represent exponential growth are[tex]A = 20,000(1.08)^t[/tex], [tex]A = 40(3)^t[/tex], and[tex]P = 1700(1.07)^t[/tex]  the equations that represent exponential decay are [tex]A = 80(1/2)^t[/tex], [tex]A = 1600(0.8)^t\\[/tex], and [tex]P = 1700(0.93)^t.[/tex]

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The complete question is

Which equations represent exponential growth? which equations represent exponential decay? drag the choices into the boxes to complete the table

help pls don’t need to do work for it jist give answer

Answers

Answer:

A. 25%

B. Candidate B

C. 60% of voters chose Candidate A and Candidate C

Step-by-step explanation:

A. 25%

B. Candidate B

C. 60% of the voters

for the grand opening, al's furniture store offered a spin the wheel for a discount to its customers. customers would spin the wheel and receive a discount on a single item of purchase. the wheel is divided into 12 equal slices. 6 slices awarded a 10% discount, 3 slices awarded a 20% discount, 2 slices awarded a 40% discount, and 1 slice awarded a 100% discount. what is the probability that a customer gets a 10% or 20% discount?

Answers

At the grand opening, al's furniture store, there is offering spin wheel for discount. The probability that a customer gets a 10% or 20% discount is equals to the 0.75.

At the grand opening, al's furniture store, it offered a spin the wheel for a discount to its customers. The wheel is divided into 12 equal slices.

The percentage of discount awarded by 6 slices = 10%

The percentage of discount awarded by 3 slices = 20%

The percentage of discount awarded by 2 slices = 40%

The percentage of discount awarded by 1 slices

= 100%

We have to determine the probability that a customer gets a 10% or 20% discount. As we see all slices are independent to each other so events related to these also independent.

We have total 12 slices. Since, 6 slices awarded for 10% discount i.e. chances of getting 10% discount is equal = 6/12

Similarly, 3 slices awarded for 20% discount i.e. chances of getting 20% discount is 3/12.

Hence chances of getting 10% or 20% discount is

= P( X = 20%) + P( X= 10%)

= 6/12 + 3/12

= 1/2 + 1/4

= 0.50 + 0.25

= 0.75

Hence, required value is 0.75.

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The debate over pipelines and the use of oil sands is far from over. There is likely to be another
application for a pipeline to bring oil from Alberta to Texas or a proposal to pipe oil across Canada
.
to ships that could take it to refineries in Asia. What do you think should be done? Explain your
answer using complete sentences.

Answers

The decision of whether or not to build pipelines to transport oil from Alberta to Texas or other parts of Canada is a complex one that involves multiple factors.

From a mathematical perspective, the debate over pipelines and oil sands can be analyzed in terms of supply and demand. On the other hand, opponents of pipelines argue that the supply of oil is finite and that the continued extraction and transportation of oil will have long-term negative consequences for the environment.

In addition to the economic and environmental factors, there are also geopolitical considerations to take into account. For example, some argue that building a pipeline to transport oil from Alberta to Texas would reduce Canada's reliance on foreign oil and would increase our energy independence.

However, others argue that building a pipeline would tie us more closely to the United States and would not necessarily benefit Canada in the long run.

Regardless of the decision that is ultimately made, it is clear that pipelines will continue to play a significant role in our energy infrastructure for many years to come.

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The value of a mountain bike y (in dollars) can be approximated by the model y=200(0.75)t, where t is the number of years since the bike was new. Would this table show growth or a decline (decay)? How do you know? Identify the annual percent increase or decrease in the value of the bike. Estimate when the value of the bike will be $50.​

Answers

Answer:

Step-by-step explanation:

To determine if the table shows growth or decay, we can look at the coefficient of the exponential function y = 200(0.75)^t. The coefficient is 0.75, which is less than 1. This means that the value of the bike decreases over time, so the table shows decay.

To identify the annual percent increase or decrease in the value of the bike, we can compare the value of the bike after one year to its initial value. Plugging in t = 1 into the model, we get:

y = 200(0.75)^1

y = 150

So after one year, the value of the bike is $150. This represents a decrease of $50 from its initial value of $200. To find the percent decrease, we can use the formula:

percent decrease = (amount of decrease / initial value) x 100%

Plugging in the values, we get:

percent decrease = (50 / 200) x 100%

percent decrease = 25%

Therefore, the value of the bike decreases by 25% each year.

To estimate when the value of the bike will be $50, we can set y = 50 in the model and solve for t:

50 = 200(0.75)^t

0.25 = 0.75^t

log(0.25) = t log(0.75)

t = log(0.25) / log(0.75)

t ≈ 4.2

Therefore, the value of the bike will be $50 approximately 4.2 years after it was new.

Dave drove 6,000 miles in his car last year. The total of fixed costs was $1,250.00 and of variable costs was $1,000.00.

Answers

Total annual cost for Dave's car driving 6,000 miles last year is $2,250.00 with fixed cost of $1,250.00 plus variable cost of $1,000.00.

Based on the given information, we can use the formula for total cost

Total Cost = Fixed Cost + (Variable Cost per unit x Number of units)

In this case, we know the fixed cost is $1,250.00, and the variable cost per mile is $1,000.00 / 6,000 miles = $0.1667/mile. Therefore, we can calculate the total annual cost as

Total Cost = $1,250.00 + ($0.1667/mile x 6,000 miles)

Total Cost = $1,250.00 + $1,000.20

Total Cost = $2,250.20

So, Dave's total annual cost of driving his car for 6,000 miles is $2,250.20.

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--The given question is incomplete, the complete question is given

" Dave drove 6,000 miles in his car last year. The total of fixed costs was $1,250.00 and of variable costs was $1,000.00. What is the total annual cost?"--

find the equation of a circle passing through the points (1, 2), (0, 3)and (-2, 7)

Answers

To find the equation of a circle passing through three given points, we can use the general equation of a circle, which is:

(x - h)^2 + (y - k)^2 = r^2

where (h, k) is the center of the circle, and r is the radius.

We can find the center and radius of the circle by solving a system of equations using the three given points. Here's how:

First, we can find the equations of the perpendicular bisectors of the line segments connecting the three points. The intersection of these bisectors will be the center of the circle.

The midpoint of the line segment connecting (1, 2) and (0, 3) is:

((1+0)/2, (2+3)/2) = (1/2, 5/2)

The slope of the line segment is:

(3-2)/(0-1) = -1

The slope of the perpendicular bisector is the negative reciprocal of the slope of the line segment, which is:

1/(-1) = -1

So the equation of the perpendicular bisector is:

y - (5/2) = (-1)(x - 1/2)
y = -x + 6

The midpoint of the line segment connecting (0, 3) and (-2, 7) is:

((0-2)/2, (3+7)/2) = (-1, 5)

The slope of the line segment is:

(7-3)/(-2-0) = -2

The slope of the perpendicular bisector is the negative reciprocal of the slope of the line segment, which is:

1/(-2) = -1/2

So the equation of the perpendicular bisector is:

y - 5 = (-1/2)(x + 1)
y = (-1/2)x + (11/2)

The intersection of these two lines is the center of the circle. Solving for x and y, we get:

-x + 6 = (-1/2)x + (11/2)
x = 1

Substituting x = 1 into either equation, we get:

y = -1 + 6 = 5

So the center of the circle is (1, 5).

To find the radius of the circle, we can use the distance formula between one of the given points and the center of the circle. Let's use (1, 2):

r^2 = (1 - 1)^2 + (2 - 5)^2
r^2 = 9
r = 3

Therefore, the equation of the circle passing through the points (1, 2), (0, 3), and (-2, 7) is:

(x - 1)^2 + (y - 5)^2 = 9

PLEASE HELP, NEED IT BY TODAY

Write three equations. Each equation must include the numbers 3 and 30.3 and must be easy to solve by inspection. Solve your equations.

Answers

The three equations are:

3x = 30.3

30.3 - x = 27.3

3x + 30.3 = 63.6

We have,

Equation 1:

3x = 30.3

Solving for x, we can divide both sides by 3:

x = 10.1

Equation 2:

30.3 - x = 27.3

Solving for x, we can subtract 27.3 from both sides:

x = 3

Equation 3:

3x + 30.3 = 63.6

Solving for x, we can first subtract 30.3 from both sides:

3x = 33.3

Then, we can divide both sides by 3:

x = 11.1

Thus,

The three equations are:

3x = 30.3

30.3 - x = 27.3

3x + 30.3 = 63.6

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is 3 greater than 3 and a Half (3>< 3 1\2

Answers

Answer:

3 and a half would be greater than 3

Step-by-step explanation:

3 and a half would be 3.5 which is .5 more than just 3.

through Buzz under the assignment.
1. lan deposits $2,400 each quarter for 3 years. The annuity earns 10% interest and is compounded quarterly. Find the present value of the annuity.
Using the Present Value of Ordinary Annuity Table, the correct factor for 12 compounding periods at 2.5% interest is 10.25776.

Answers

Answer:

$56,577.12

Step-by-step explanation:

To find the present value of the annuity, we can use the formula for the present value of an ordinary annuity, which is:

PV = PMT x [1 - (1 + r/n)^(-n*t)] / (r/n)

Where:

PV = present value

PMT = payment amount per compounding period

r = annual interest rate

n = number of compounding periods per year

t = total number of years

Plugging in the given values, we get:

PV = 2400 x [1 - (1 + 0.10/4)^(-4*3)] / (0.10/4)

PV = 2400 x [1 - (1.025)^(-12)] / (0.025)

PV = 2400 x [1 - 0.610355] / 0.025

PV = 2400 x 23.5742

PV = $56,577.12 (rounded to the nearest cent)

Therefore, the present value of the annuity is $56,577.12, assuming the interest is compounded quarterly and the annuity earns a 10% interest rate.

Jim and Avery compare the number of points they scored during a game. Explain your answer mathematically
Jim notices that when he doubles his number of points, then subtracts 10 from that number, the result is the same as the number of points Avery scored. Write an expression representing the number of points
Avery scored, in terms of the number of points Jim scored, j. Enter your expression in the response box

Answers

The expression representing the number of points Avery scored in terms of the number of points Jim scored is 2j - 10.

Let's assume that Jim scored 'j' points during the game. According to the given information, when Jim doubles his number of points and subtracts 10 from that number, the result is the same as the number of points Avery scored. Therefore, we can write an equation as follows:

2j - 10 = number of points scored by Avery

To find the expression representing the number of points Avery scored in terms of the number of points Jim scored, we simply solve the above equation for Avery's points:

number of points scored by Avery = 2j - 10

Therefore, the expression representing the number of points Avery scored in terms of the number of points Jim scored is 2j - 10.

In summary, Jim scored 'j' points during the game and when he doubles his number of points and subtracts 10 from that number, he gets the same result as the number of points Avery scored.

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