Algebraically find the x-coordinates where the line y=2x+3 intersects the circle (x-3)^2 + (y+6)= 50

Answers

Answer 1

The x-coordinates where the line y = 2x + 3 intersects the circle is equal to -2 and -4.

What is the equation of a circle?

Mathematically, the standard form of the equation of a circle is represented by this mathematical expression;

(x - h)² + (y - k)² = r²  

Where:

h and k represents the coordinates at the center of a circle.r represents the radius of a circle.

From the information provided, we have the following system of equations:

(x - 3)² + (y + 6)² = 50      ......equation 1.

y = 2x + 3              .............equation 2.

In order to determine the x-coordinates at the point of intersection, we would substitute the equation 2 into equation 1:

(x - 3)² + (2x + 3 + 6)² = 50

(x - 3)² + (2x + 9)² = 50

x² - 6x + 9 + 4x² + 36x + 81 - 50 = 0

5x² + 30x + 40 = 0

x² + 6x + 8 = 0

x² + 6x + 9 = 1

(x + 3)² = 1

Taking the square of both sides of the equation, we have;

x + 3 = ±1

x = ±1 - 3

x = -2 and -4

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Algebraically Find The X-coordinates Where The Line Y=2x+3 Intersects The Circle (x-3)^2 + (y+6)= 50

Related Questions

In Mr. Richard's class, 5/8 of the students like
to bake. Of those students, one-half prefer to
bake cookies. What fraction of the students
prefer to bake cookies?

Answers

Do you have answer choices?

I neeed help with middle school math

 I neeed help with middle school math

Answers

Multiple different forms in the picture attached - for these problems use Math-way is super easy
First is the exact form
 I neeed help with middle school math

Answer:

22/5*8/3

176/15

yep that's it

I think..



Myra wants to save at least $500 by the end of her summer vacation. She currently has $350 saved. She can earn $25 cutting a lawn in her neighborhood. Myra solves an inequality to determine the least number of lawns, n, she must cut to reach her goal.

What number is the minimum number of lawns Myra needs to mow to meet her goal?

Answers

Answer:

6 ≤ b.

(6).

Step-by-step explanation:

So, we are given in the question that the amount that Myra wants to say is $500 at the end of her summer vacation and she has saved up to $350. Thus, it remain ($500 - $350 = $150) for completion.

Also, "She can earn $25 cutting a lawn in her neighborhood."

Therefore, the total amount of money she wants to save = a = 500. Then,

Total amount of money, a = 350 + 25b.

500 = 350 + 25b.

=> 500 ≤ 350 + 25b.

Note that the ' =' sign has changed to '≤' sign since she wants that amount(at least). Also, the question specified that she used inequality.

Hence, the amount remaining for it to complete is $150. Therefore;

150 ≤ 25b.

6 ≤ b.

Thus, Myra will have to mow at least 6 lawns

Answer:

6

Step-by-step explanation:

Took the quiz on edge!

The computers of six faculty members in a certain department are to be replaced. Two of the faculty members have selected laptop machines and the other four have chosen desktop machines. Suppose that only two of the setups can be done on a particular day, and the two computers to be set up are randomly selected from the six (implying 15 equally likely outcomes; if the computers are numbered 1, 2, . . . , 6, then one outcome consists of computers 1 and 2, another consists of computers 1 and 3, and so on).

Required:
a. What is the probability that both selected setups are for laptop computers?
b. What is the probability that both selected setups are desktop machines?
c. What is the probability that at least one selected setup is for a desktop computer?
d. What is the probability that at least on computer of each type is chosen for setup?

Answers

Answer:

a. \(\frac{1}{15}\)

b. \(\frac{2}{5}\)

c. \(\frac{14}{15}\)

d. \(\frac{8}{15}\)

Step-by-step explanation:

Given that there are two laptop machines and four desktop machines.

On a day, 2 computers to be set up.

To find:

a. probability that both selected setups are for laptop computers?

b. probability that both selected setups are desktop machines?

c. probability that at least one selected setup is for a desktop computer?

d. probability that at least one computer of each type is chosen for setup?

Solution:

Formula for probability of an event E can be observed as:

\(P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}\)

a. Favorable cases for Both the laptops to be selected = \(_2C_2\) = 1

Total number of cases = 15

Required probability is \(\frac{1}{15}\).

b. Favorable cases for both the desktop machines selected = \(_4C_2=6\)

Total number of cases = 15

Required probability is \(\frac{6}{15} = \frac{2}{5}\).

c. At least one desktop:

Two cases:

1. 1 desktop and 1 laptop:

Favorable cases = \(_2C_1\times _4C_1 = 8\)

2. Both desktop:

Favorable cases = \(_4C_2=6\)

Total number of favorable cases = 8 + 6 = 14

Required probability is \(\frac{14}{15}\).

d. 1 desktop and 1 laptop:

Favorable cases = \(_2C_1\times _4C_1 = 8\)

Total number of cases = 15

Required probability is \(\frac{8}{15}\).

Determine the relationship between the measure of angle ADE and the measure of arc AE by circling one of the statements below.

Determine the relationship between the measure of angle ADE and the measure of arc AE by circling one

Answers

Answer:

The answer c is correct.  

Step-by-step explanation:

When two chords share an endpoint, the inscribed angle has half of the measure of the intercepted arc.   In this example, ADE is the inscribed angle, so its measure is one half of the arc AE's measure. m<ADE= 1/2(mAE)

i hope this helped :)

The relationship between the measure of angle ADE and the measure of arc AE is  m∠ADE  = \(\frac{1}{2}\) m (arc AE) .

What seems to be the relationship between an inscribed angle and its intercepted arc?

The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of its intercepted arc. Inscribed angles that intercept the same arc are congruent. This is called the Congruent Inscribed Angles Theorem

According to the question

The relationship between the measure of angle ADE and the measure of arc AE .

∠ADE  is a  inscribed angle

arc AE  is a  intercepted arc

According to Inscribed Angle Theorem

∠ADE  = \(\frac{1}{2}\) arc AE

Hence, the relationship between the measure of angle ADE and the measure of arc AE is  m∠ADE  = \(\frac{1}{2}\) m (arc AE) .

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A young executive is going to purchase a vacation property for investment purposes. She needs to borrow $128,000.00 for 25 years at a 5.3% annual interest rate, with interest compounded monthly, and will make monthly payments of $770.82. (Round all answers to 2 decimal places.)
Create an amortization table to answer the following:

a) What is the unpaid balance after 9 months? $


b) Over the 9 months in part (a), how much total interest did she pay?

Answers

Answer:

(a) After 9 months, the unpaid balance is $125,874.09.

(b) Over the 9 months, she paid a total of $4,918.56 in interest.

To create the amortization table, we can use the formula for calculating the monthly payment of a loan:

P = (r * A) / (1 - (1 + r)^(-n))

where:

P = monthly payment

r = monthly interest rate

A = loan amount

n = total number of payments

In this case, we have:

A = $128,000.00

n = 25 years * 12 months/year = 300 months

r = 5.3% / 12 = 0.00441666667

Using the formula, we can calculate the monthly payment:

P = (0.00441666667 * $128,000.00) / (1 - (1 + 0.00441666667)^(-300))

P = $770.82

Now, we can create the amortization table:

A young executive is going to purchase a vacation property for investment purposes. She needs to borrow

If √ 24 + √ 96 7 √600 = y√ 6, find the value of y. -​

Answers

Solution :

\(y = 2(1 + 5 \sqrt{967} )\)

Step by Step explanation:

1.Switch sides\(y\sqrt{6} = \sqrt{24 } + \sqrt{967} \sqrt{600} \)2.Simplify√24 + √967 √600

\(y \sqrt{6} = 2 \sqrt{6} + 10 \sqrt{5802} \)

3.Divide both side by √6

\( \frac{y \sqrt{6} }{ \sqrt{6} } = \frac{2 \sqrt{6} }{ \sqrt{6 } } + \frac{10 \sqrt{5802} }{ \sqrt{6} } \)4.Simplify\(y = 2(1 + 5 \sqrt{967} )\)

Suppose U = The set of one digit numbers and A = {x: x is an even natural number less than or equal to 9} Describe each of the sets by complete listing method: A'​

Answers

The sets U and A are U = {0, 1, 2, 3.....,9} and A = {2, 4, 6, 8}

How to list the set elements?

The sets are given as:

U = The set of one-digit numbers

A = {x: x is an even natural number less than or equal to 9}

One-digit numbers are numbers 0 - 9.

So, we have

U = {0, 1, 2, 3.....,9}

Natural numbers are numbers from 1.

Even natural numbers can be divided by 2 without remainder'

So, we have

A = {2, 4, 6, 8}

Hence, the sets U and A are U = {0, 1, 2, 3.....,9} and A = {2, 4, 6, 8}

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Answer:

Step-by-step explanation:

Is the function f(x) = 9x-1 + 2
linear, quadratic, or exponential?
A. Linear
B. Quadratic
C. Exponential

Answers

Answer :

Is aB) Quadratic

The profits earned in a year by some companies in a city are shown $160,000 $140,000 $130,000 $1120,000 $150,000 based on the data should the mean, or the median Be used to make the inference about the profits earned by the companies

Answers

Answer:

Median

Step-by-step explanation:

In this data set, there's a huge outlier ($1,120,000) which would skew the results upwards. Using the mean to make an inference about the profits would better represent the whole data set since you'd get $150,000 which is more in line with the rest of the data point.

plzzzzzzzzzzzz i need help

plzzzzzzzzzzzz i need help

Answers

Answer:

27

Step-by-step explanation:

-5a-b

-5(-6)-3

30-3

2

-5a - b

a = -6

b = 3

(-5 * -6) - 3

30 - 3 = 27

Explain the box and whisker plot in detail.

Explain the box and whisker plot in detail.

Answers

Based on the box and whisker plot shown above, we can infer and logically deduce that the number of lepilemures have a minimum at 0 but are well spread.

What is a box and whisker plot?

A box and whisker plot is also referred to as boxplot and it can be defined as a type of chart that can be used to graphically represent the five-number summary of a data set with respect to locality, skewness, and spread. Also, the five-number summary include the following:

MinimumFirst quartileMedianThird quartileMaximum

By critically observing the box and whisker plot shown above, we can infer and logically deduce that the data (number of lepilemures) have a minimum at 0 but are well spread.

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compare these decimals 0.7______0.6999
1. >
2.<
3.=

Answers

> greater then since 0.7 is 0.0001 greater then 0.6999

Which table represents a linear function?
х
1
х
1
2
3
4
y
3
6
12
24
у
2
5
9
14
х
1
2
3
4
y
-3
-5
-7
-9
N
AWN
3
4
O
Х
y
1
2
3
4
Inolt
-2
-4
-2
0

Answers

Answer: the first one, top left corner

Step-by-step explanation:

The last table has a constant slope of -3, hence it represents a linear function.

What is Slope of Line?

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

To determine that, we must check which of the table has a constant rate of change

Looking at the last table;

Slope = -4-(-2)/2-1

Slope = -4+1/1

Slope = -3

Since the last table has a constant slope of -3, hence it represents a linear function.

Hence, the last table has a constant slope of -3, hence it represents a linear function.

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Which table represents a linear function?11234y361224259141234y-3-5-7-9NAWN34Oy1234Inolt-2-4-20

I need answers for problem solving

I need answers for problem solving

Answers

Answer:

243

Step-by-step explanation:

the answer is 243 for number 6

Answer:

all you gotta do is do 2430 divided by ten

Kyle owns an orchard nearby. He wants to charge one flat rate per pound for his apples no matter how much someone buys. He wants 16 pounds of apples at his orchard to cost $1.50 less than16 pounds of apples at Pam’s Orchard. How much should Kyle charge per pound?

Answers

Answer:

(P - 1.50) / 16

Step-by-step explanation:

Given that:

Intention = 16 pounds of apple at Kyle's orchard should be $1.50 less than 16 pounds of apple t Pam's orchard.

Let cost of 16 pounds apple at Pam's orchard = p

Kyle's charge per pound will be :

Cost of 16 pound apple at Kyle's orchard :

p - $1.50

If 16 pounds of apple cost p - 1.50

1 pound of apple will cost :

(P - 1.50) / 16

What is the slope of the line passing through the points (-5,7) and (-3,5)

Answers

Answer:

Slope of  the line passing through the points (-5,7) and (-3,5) is -1.

Step-by-step explanation:

slope of line passing through point (x1,y1) and (x2,y2) is given by

m = (x2-x1)/(y2-y1)

____________________________________________

In the problem given  points are (-5,7) and (-3,5)

using the formula for finding slop ewe have

m = (-3-(-5))/(5-7)

=> m = (-3+5)/-2

=> m = 2/-2

=> m = -1

Thus, slope of  the line passing through the points (-5,7) and (-3,5) is -1.

Subtract: (c ^ 2 - 4c + 7) from (7c ^ 2 - 5c + 3)

Answers

subtracting (c ^ 2 - 4c + 7) from (7c ^ 2 - 5c + 3) would give 6c² - 9c -4

Substracting algebraic expressions

Given the expressions as

(c ^ 2 - 4c + 7)

(7c ^ 2 - 5c + 3)

We are to substract expression 2 from expression 1

In doing this, we need to know the BODMAS rule ( bracket, of, division, multiplication, addition and subtraction). This would help in finding the solution

(7c ^ 2 - 5c + 3) -  (c ^ 2 - 4c + 7)

Expand the bracket

7c² - 5c + 3 - c² - 4c + 7

collect like terms

7c²- c² - 5c - 4c + 3 - 7

Add or substract the like terms

6c² - 9c -4

Thus, subtracting (c ^ 2 - 4c + 7) from (7c ^ 2 - 5c + 3) would give 6c² - 9c -4

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Answer:6c^2-c-4

Step-by-step explanation:

(7c^2-5+3)-(c^2-4c+7)

7c^2-5c+3-c^2+4c-7

Rearrange the terms

7c^2-c^2-5c+4c+3-7

Combine like terms

6c^2-c-4

Bernice estimated that 69% of 242 is 168. Is her estimate reasonable?
No, because her calculation should be 60% of 250.
No, because her calculation should be 70% of 250.
Yes, because her calculation should be 60% of 240.
Yes, because her calculation should be 70% of 240.

Answers

Answer:

Yes, because her calculation should be 70% of 240.

Step-by-step explanation:

69% can be estimated to 70% and

242 can be rounded off to 240.

70% of 240 = 0.7 * 240

                   = 168

which of these is most likely to weigh 2 kilograms car roast chicken horse egg tea bag

Answers

The item most likely to weigh 2 kilograms is a roast chicken.

Which of them would weight 2 kilograms?

The size, breed, and any other ingredients or stuffing used can all affect the weight of a roast chicken. Weights of roast chickens can range from petite ones weighing less than 1 kilogram to larger ones weighing more than 2 kilograms.

The other things that we have there would either weigh less than 2 Kg such as a tea bag or much more than 2 Kg such as a horse. The egg and the tea a very light and would be less than 2 Kg in weight while the bag and the horse would be above 2 Kg in weight.

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Help me plsssssss 2 1/2 x 3

Answers

exact form: 15/2
decimal form: 7.5
mixed number form: 7 1/2

Please answer correctly Free brainliest

Please answer correctly Free brainliest
Please answer correctly Free brainliest
Please answer correctly Free brainliest

Answers

1) Simplify : - 4x + 3(2x + 5) - 3x + 12

breaking 3(2x + 5) we get,

- 4x + 6x + 15 - 3x + 12

Now, as per the PEMDAS rule let's shorten the like terms

2x - 3x + 27

- x + 27

Correct option is C i.e. - x + 27

2) Simplify : 3x + 3(x + 6) - 4 - 5x

breaking 3(x + 6) we get,

3x + 3x + 18 - 4 - 5x

Again using the same rule we see,

6x + 14 - 5x

x + 14

Correct answer is option C i.e. x + 14

3) Expression : y[x² - 2(1 + 2)] ÷ y + 5²

In this case we are given that x = 3 whereas y = 7

Putting the values of x and y we see,

7[(3)² - 2(3)] ÷ 7 + 25

7[9 - 6] ÷ 7 + 25

7[3] ÷ 7 + 25

21 ÷ 7 + 25

3 + 25

28

Henceforth, the final answer is 28

How to solve your problem

-4x+3(2x+5)-3x+12

Simplify

1

Distribute

-4x+{\color{#c92786}{3(2x+5)}}-3x+12

-4x+{\color{#c92786}{6x+15}}-3x+12

2

Add the numbers

3

Combine like terms

Solution

ANSWER:-x+27

6. -2.5(-3 + 4 + 8) oh god please help​

Answers

-16.5 hope this helped :)

If someone can pls give the answer with steps that would be greatly appreciated :)

If someone can pls give the answer with steps that would be greatly appreciated :)

Answers

hope it helps.

stay safe healthy and happy..
If someone can pls give the answer with steps that would be greatly appreciated :)

Answer: look below

Step-by-step explanation:

A straight angle is 180

180-50=130

the opposite is also the same angle which is the same

180-50-50=80 and 80 + 2x =180

x=50

the angles are 50, 50, 50, 50, 80, 130 and 130 degrees respectively

Question 3
A group of 5 people went to the movies and spent $44 on food and drink. The total amount spent, including
tickets, was $98.50.
What was the price, in dollars, of one ticket?

Answers

Answer:

One ticket cost $10.90.

Step-by-step explanation:

The total spent was $98.50--food, drinks, admission--everything.

$44.00 was for food and drinks.

We can take the 44 away from the total.

98.50 - 44.00

= 54.50

They spent 54.50 on 5 tickets to get in. Divide to find the cost of one tickets. This assumes that all 5 tickets were the same price.

54.50 ÷ 5 = 10.90



The price of one ticket was $10.90

To make this look like algebra class...

let x = the price of one ticket

5x = the price of 5 tickets

5x + 44 = 98.50

subtract 44

5x = 54.50

divide by 5

x = 10.90

are the following ratios equal. write yes or no. use the theroem that the product of the extremes equals the product means.

Answers

The ratios will be equal if the theorem that the product of the extremes equals the product means follows.

Let us understand the equality of ratios through example. The example ratio will be -

7:10 = 21:30

In this ratio, 7 and 30 are first and last numbers and hence they are extremes. The number 10 and 21 are in middle and hence considered mean. Now, we will perform multiplication to if the ratios are equal or not.

Product of extremes = 7 × 30

Extremes product = 210

Product of means = 21 × 10

Means product = 210

Since the products are equal, the ratios are also equal.

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The complete question is -

Are the following ratios equal? write yes or no. use the theroem that the product of the extremes equals the product means.

Ratio = 7:10 and 21:30.

which table does not show y as a function of x?

Answers

Answer:

I am confident the answer is H.

what is the product of 58 and 1000

Answers

Answer:

58000

Step-by-step explanation:

58×1000=58000

Hope it helps :)

Answer:

58000

Step-by-step explanation:

58 times 1000 is equal to 58000

because 1000 has 3 zeros, you just add them to your number

the word 'product' means to multiply

please give me a brainliest!!<3

Write the equation of the line graphed below in Point-Slope form. Use the point labeled on the graph. State the slope and point.

Answers needed are:
Equation:
Slope:
Point:

Write the equation of the line graphed below in Point-Slope form. Use the point labeled on the graph.

Answers

Answer:

Equation:

y= 3x + 5

Slope:

\( 3 \)

Point:

\(( - 1, \: 2)\)

Ackerman and Goldsmith (2011) found that students who studied text from printed hardcopy had better test scores than students who studied from text presented on a screen. In a related study, a professor noticed that several students in a large class had purchased the e-book version of the course textbook. For the final exam, the overall average for the entire class was � = 81.7, but the n = 9 students who used e-books had a mean of M = 77.2 with a standard deviation of s = 5.7.

Answers

The sample is sufficient to conclude that scores for students using e-books were significantly different from scores for the regular class.

What are the hypothesis tested?

At the null hypothesis, it is tested if the scores are not different from the regular class, that is, if the mean is of 81.7, hence:

\(H_0: \mu = 81.7\)

At the alternative hypothesis, it is tested if the scores are different from the regular class, that is, if the mean is different of 81.7, hence:

\(H_1: \mu \neq 81.7\)

We have a two-tailed test, as we are testing if the mean is different of a value, with a significance level of 0.05 and 9 - 1 = 8 df, hence the critical value is given as follows:

|t| = 2.306.

Thus the decision rule is given as follows:

|t| < 2.306 -> do not reject the null hypothesis -> sample is not sufficient evidence.|t| > 2.306 -> reject the null hypothesis -> sample is sufficient evidence.

What is the test statistic?

The test statistic is given by the equation presented as follows:

\(t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}\)

In which:

\(\overline{x}\) is the sample mean.\(\mu\) is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.

The parameters for this problem are of:

\(\overline{x} = 77.2, \mu = 81.7, s = 5.7, n = 9\)

Hence the test statistic is calculated as follows:

\(t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}\)

\(t = \frac{77.2 - 81.7}{\frac{5.7}{\sqrt{9}}}\)

t = -2.37.

|t| > 2.306, hence the sample is sufficient to conclude that scores for students using e-books were significantly different from scores for the regular class.

Missing Information

The problem asks if the sample is sufficient to conclude that scores for students using e-books were significantly different from scores for the regular class? Use a two-tailed test with α = .05.

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