Select the correct answer from each drop-down menu. The general form of the equation of a circle is 7x2 + 7y2 − 28x + 42y − 35 = 0. The equation of this circle in standard form is . The center of the circle is at the point , and its radius is units.

Answers

Answer 1

[tex]7x^2+7y^2-28x+42y-35=0 \\ \\ x^2 +y^2-4x+6y-5=0 \\ \\ x^2+y^2-4x+6y=5 \\ \\ x^2-4x+4+y^2+6y+9=18 \\ \\ \boxed{(x-2)^2+(y+3)^2=18}[/tex]

So, the center is [tex](2,-3)[/tex] and the radius is [tex]3\sqrt{2}[/tex].


Related Questions

what fraction of the numbers from 1 to 20 contain the digit 7

Answers

Answer:

2/20

Step-by-step explanation:

Only 7 and 17 contain the number 7

5 Math on the Spot Robin says, "I can find 6 × 9 by
multiplying 4 X 9 and doubling it." Does her statement
make sense? Justify your answer.

Answers

If Robin says, "I can find 6 × 9 by multiplying 4 X 9 and doubling it, her statement didn't make any sense because it is not possible.

What is distributive property?

The same outcome will be obtained by multiplying the sum of two or more addends by a number as it is by multiplying each addend separately by the number and then adding the resulting products.

A × (B + C) = AB + AC

A (B - C) = AB - AC

Here,

we can write 6 × 9 as,

           =  6 × 9 = 6 × (6 + 3) = (6 × 6) + (6 × 3), by applying distributive property

Hence, If Robin says, "I can find 6 × 9 by multiplying 4 X 9 and doubling it, her statement didn't make any sense because it is not possible.

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A study was commissioned to find the mean weight of the residents in certain town. The study found the mean weight to be 193 pounds with a margin of error of 9 pounds. Which of the following is not a reasonable value for the true mean weight of the residents of the town?

Answers

Considering the confidence interval, the non-reasonable value for the true mean weight of the residents of the town is:

A value that is less than 184 or more than 202.

How to obtain the confidence interval?

The confidence interval for a population mean is given by the point estimate of this mean, which is the sample mean, plus/minus the margin of error.

For the context of this problem, these parameters are given as follows:

Point estimate: 193 pounds.Margin of error: 9 pounds.

Hence the lower bound of the interval is:

193 pounds - 9 pounds = 174 pounds.

The upper bound of the interval is:

193 pounds + 9 pounds = 202 pounds.

All the values that are in the interval are reasonable values for the population mean, hence, in the context of this problem, the not reasonable values are given as follows:

A value that is less than 184 or more than 202.

(as they would be outside the confidence interval).

Missing Information

The options are not given, hence the answer was given in general terms.

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lamp post tilts
toward the Sun at a 2° angle from
the vertical and casts a 25-foot shadow.
The angle from the tip of the shadow
to the top of the lamp post is 45°.
Find the length of the lamp post.

Answers

Answer:

the lamp of post is 24 of the same

The Fitness Studio, Inc.’s, 2021 income statement lists the following income and expenses: EBITDA = $686,000, EBIT = $547,000, interest expense = $94,000, and net income = $426,000.

Answers

Based on the data on the income statement, the amount of the tax equals to $27,000.

What is a taxes?

Generally, a taxes refers to those mandatory contributions levied on individuals or corporations by a government entity either from local, regional, or national government.

Given that: EBIT = $547,000 Interest expense = $94,000 Net income = $426,000

EBT = EBIT - Interest expense

EBT = $547,000 - $94,000

EBT = $453,000

The tax reported in Income statement:

= EBT - Net income

= $453,000 - $426,000

= $27,000

In conclusion, the 2021 taxes reported on the income statement equals to $27,000.

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what is the expected value of x? where x/p equals 0/.15, 4/.05, 8/.25, 12/.05, 16/.5

Answers

The expected value of x is 10.8

How calculate the expected value of x?

Expected value is defined as the predicted value of a variable, calculated as the sum of all possible values each multiplied by the probability of its occurrence.

Given :

x|  0       4       8       12     16

p| 0.15 0.05 0.25  0.05  0.5

The expected value of x, E(x) =Σ xp

E(x) = (0×0.15) + (4×0.05) + (8×0.25) + (12×0.05) + (16×0.5)

E(x) = 0 + 0.2 + 2 + 0.6 + 8

E(x) = 10.8

Therefore, the expected value of x is 10.8

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Select the correct answer. What is this equation rewritten in logarithmic form? 9x = 3
A. log9 3 = x
B. logx 3 = 9
C. log3 9 = x
D. log3 x = 9

Answers

Answer:

A. [tex]\log_9{3}=x[/tex]

Step-by-step explanation:

[tex]y=e^x\rightarrow\log_e{y}=x[/tex]

Therefore,

[tex]3=9^x\rightarrow\log_9{3}=x[/tex]

what is meter × meter

Answers

metre squared or m^2

[tex]meter^{1`} *meter^{1} \\=meter^{1+1} \\=meter^{2}[/tex]

Mote I used the laws of exponents    : [tex]=x^{m} *x^{n} \\=x^{m+n}[/tex]

Function Notation - Function Machines
#1. Find the following...
f(1) =
f(0) =
f(-3)=
f(8)=
x - input
?
4x + 1
f(x) - output

Answers

The function notation of the following are:

f(1) = 5

f(0) = 1

f(-3) = -11

f(8) = 33

Given:

x is the input.

the function is 4x+1

f(x) is the output.

we are asked to determine the values of the following :

a. f(1)

x = 1

so f(x) = 4x+1

f(1) = 4(1)+1

f(1) = 4+1

f(1)=5

b. f(0)

x = 0

so f(x) = 4x+1

f(0) = 4(0)+1

f(0) = 0+1

f(0)=1

c. f(-3)

x = -3

so f(x) = 4x+1

f(-3) = 4(-3)+1

f(1) = -12+1

f(1)= -11

d. f(8)

x = 8

so f(x) = 4x+1

f(8) = 4(8)+1

f(8) = 32+1

f(1)=33

Hence we get the required values.

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In a class of 152 ​students, 100 are taking math​ (M), 77 are taking science​ (S), and 55 are taking both math and science. One student is picked at random. Find the probability.

​P(taking math or science or​ both)

Answers

The probability of taking math or science or both is 123/152

The total number of students = 152 students

Number of students who take math = 100 students

Number of student who take science = 77 students

Number of students who take both math and science = 55 students

The probability = Number of favorable outcomes /  Total number of outcomes

We have to find each term

The number of favorable outcomes =55+45+23

= 123

Total number of outcomes = 152

Substitute the values in the equation

​Probability of taking math or science or​ both = 123/152

Hence, the probability of taking math or science or both is 123/152

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K
Choose the measurement closest to 30 km: 10 mi, 20 mi or 30 mi.
Choose the correct answer below.
20 mi
30 mi
10 Ini
O
O
O 10

Answers

Answer:

20 miles

Step-by-step explanation:

1.6km is equivalent to 1 mile

so 30km / 1.6 = 18.75 miles

therefore 20 miles is the closest to 30km

Whats ?? Also right an addition expression to get the same answer Answer ASAP

Answers

Answer:

p=-10

Step-by-step explanation:

-10-20=-30

Subtracting a negative from a negative will result in a higher negative, the same can be said for -10-20. Removing 10 from -20 will result in a lower answer. This is 20.

It takes 36 pounds of seed to completely plant a 6 acre field. How many acres can be planted per pound of seed?

Answers

Answer: 6 lbs per acre

Step-by-step explanation: just divide 36 by 6 and you get 6. To check your answer multiply 6 and 6. Then you get 36 and know your answer is right.

The diameter of the circle is 10 centimeters and the measure of is 72º. Find the length of.

Round your calculations to the nearest tenth. Complete your work in the space provided.

Answers

The arc length of the segment it 6.28 meters

How to calculate the arc length using?

From the question, we have the following parameters:

Central angle, x = 72 degrees

Diameter, d = 10 centimeters

The radius of the circle can be calculated using

r = d/2

So, we have

r = 10/2

Evaluate

r = 5 cm

The exact arc length using the central angle measure is calculated as:

Arc length = x/360 * 2πr

Substitute the known values in the above equation

Arc length = 72/360 * 2π * 5

Evaluate

Arc length = 6.28

Hence, the exact arc length using the central angle measure is 6.28 meters

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Possible question

The diameter of the circle is 10 centimeters and the measure of is 72º. Find the length of arc

Round your calculations to the nearest tenth. Complete your work in the space provided.

Need help please is do tomorrow

Answers

Answer: 39

Step-by-step explanation:

it starts at 11 and adds 7 everytime, assuming its linear (meaning it has a constant rate of change) u would add 7 to 32 to get your 5th value

Answer: y = 39

Step-by-step explanation:

Since the line is linear, the y increases 7 every time x increases 1

Add 7 to 32 and it equals 39

O Points: 0 of
A medical research study on a new medicine for multiple sclerosis is being conducted with 24 patients. After the study was concluded, it
medicine, 7 reacted unfavorably, and 2 were unaffected. If three of the patients are randomly selected, determine the probability that nor

Answers

If three of the patients are randomly selected, then the probability that none of the patients reacted favorable is 21/506.

In the given question,

A medical research study on a new medicine for multiple sclerosis is being conducted with 24 patients.

After the study was concluded, it was concluded it was determined that 15 patients reacted favorably to the medicine, 7 reacted unfavorably, and 2 were unaffected.

If three of the patients are randomly selected, then we have to determine the probability that none of the patients reacted favorable.

Total patient are 24.

The patients reacted favorably to the medicine is 15.

The patients reacted unfavorably to the medicine is 7.

The patients unaffected to the medicine is 2.

Randomly selected patients are 3.

So the probability that none of the patients reacted favorable

P(E) = 9/24 × 8/23 × 7/22

Simplifying

P(E) = 9/3 × 1/23 × 7/22

P(E) = 3 × 1/23 × 7/22

P(E) = 21/506

Hence, if three of the patients are randomly selected, then the probability that none of the patients reacted favorable is 21/506.

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The right question is

"A medical research study on a new medicine for multiple sclerosis is being conducted with 24 patients. After the study was concluded, it was concluded it was determined that 15 patients reacted favorably to the medicine, 7 reacted unfavorably, and 2 were unaffected. If three of the patients are randomly selected, then we have to determine the probability that none of the patients reacted favorable."

Ten men working 6 hours a day takes 12 days to complete a job.How long will it take 8 men working 12 hours a day to complete the same job

Answers

Answer:

It will take 7.5 days to complete the job.

Step-by-step explanation:

First, find how many total hours the ten men worked to complete the job

10 x 6 = 60 hours a day

12 x 60 = 720 hours total

Now compare that with the 8 men's hours

8 x 12 = 96 hours a day

720 / 96 = 7.5 days

ABC has a right angle at C, BC=6.8 centimeters, and m

Answers

Answer:

your question is cutoff, cant read it


216. Разложите на множители, а затем вычислите значение выражения
a) a² + ab при а = 6,6, b = 3,4;

б) x2 - ху при х = 0,5, у = 2,5;


в) —5а² — 5ах при а = 4, x = -3

Answers

Answer:

Doesn't make a lot of sense. Can you be more specific.

Step-by-step explanation:

A group of 3 students plants 141 seeds. Each student plants the same number of seeds.
How many seeds does each student plant?
Write an expression you can use to solve
the problem.

Answers

Answer:

to find the answer you just need to divide 3 out of 141

141÷3=47seeds per each student

3x=141

x=141÷3

x=47

The equation is represented as A = S/3 , where S is the total number of seeds and A is the number of seeds planted by each student and the value of A = 47 seeds

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total number of seeds by each student be A

Now , the equation will be

The total number of seeds be S = 141 seeds

The number of students be n = 3 students

So , the total number of seeds planted by each student A = total number of seeds S / number of students n

A = S / n

Substituting the values in the equation , we get

Total number of seeds planted by each student A = 141 / 3

Total number of seeds planted by each student A = 47 seeds

Therefore , the value of A is 47 seeds

Hence , the number of seeds is 47 seeds

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Simplify 5^3 x 5 please

Answers

Answer:

5^4

Step-by-step explanation:

5^3x5

5x5x5x5

5^4

Hopes this helps please mark brainliest

The simplified form of the expression, 5³.5 will be 625.

What is an integer exponent?

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

It is given that the expression is, 5³.5

=5³.5

The base should remain constant and the exponents added when multiplying like bases. Keep the base constant when raising a base with power to another power, and multiply the exponents instead. Keep the base constant and deduct the exponents in the denominator and numerator when dividing like bases.

Apply the law of exponent as

xᵃ × xᵇ = xᵃ⁺ᵇ

=5³⁺¹

=5⁴

=5x5x5x5

=625

Thus, the simplified form of the expression, 5³.5 will be 625.

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5k+(2k)-(-1)……………..
……………………

Answers

5k+(2k)-(-1) = 7k+1





:p

Select all of the following that are ordered pairs of the given function.
h(x) = 3x²
(1, 3)
(-1, -3)
(-1,3)
(1, -3)

Answers

The ordered pairs of the function, h(x) = 3x², are (1,3) and (-1,3).

According to the question,

We have the following information:

h(x) = 3x²

Now, we will look at the options to know the correct option of ordered pairs.

Now, in the options, there are only two values of x (1 and -1). So, we will solve the given function using these two values and we will find the value of h(x).

h(x) = 3x²

h(1) = 3*1*1

h(1) = 3

So, the first ordered pair is (1,3).

When x = -1:

h(x) = 3x²

h(-1) = 3*-1*-1

h(-1) = 3

Now, the second ordered pair of the function is (-1,3).

Hence, the correct options are A and C.

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If a plant grows 15 cm in 3 hrs. Determine which expression correctly represents a unit rate for the situation.

Answers

The unit rate of the plant growth is 5cm per hour

How to calculate the unit

The unit rate refers to amount the plant will grow 1 hour

from the relationship

15 cm = 3 hours

? cm = 1 hour

cross multiplying

3 * ? = 15 * 1

? = 15 / 3

? = 5 cm

The plant's unit rate of growth is 5cm per hour

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Using the graph below, determine the employee's hourly wage.

Answers

Using the graph, the hourly wage of the employees is: $8 per hour.

How to Determine Hourly Wage From a Graph?

Slope of a proportional graph is the unit rate between two variables, x and y, and it is calculated as: k = y/x.

To find the unit rate or slope of the graph, use any point on the graph (x, y).

The unit rate of the graph in the image above is the hourly wage of the employees.

Using any point on the line, say, (13, 104), we can find the slope/unit rate. Therefore:

Unit rate/slope, k = 104/13

Unit rate/slope, k = 8

Therefore, the hourly wage is: $8 per hour.

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In your lab, a substance's temperature has been observed to follow the function T(x) = (x − 5)3 + 9. The turning point of the graph is where the substance changes from a liquid to a gas. Using complete sentences in your written answer, explain to your fellow scientists how to find the turning point of this function. Hint: The turning point of the graph is similar to the vertex of a quadratic function.

Answers

The turning point is at x = 5, and this means that the substance changes from liquid to gas when x = 5.

How to find the turning point?

Here we have the temperature function:

T(x) = (x - 5)^3 + 9

The turning point is the point where the curvature of the function changes,  by differentiating the function two times and finding the zero, we can get the turning points.

T'(x) = 3*(x - 5)^2

T''(x) = 3*2*(x - 5) = 6*(x - 5)

This is zero when x = 5, then:

T''(5) = 6*(5 - 5) = 0

So the turning point is there.

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a piece of pipe is 40in. long. It is cut in to 3 pieces. the longest piece is 3 times as long as the middle sized piece and the shortest piece is 23 in. shorter than the longest piece. Find the lengths of all 3 pieces of pipe.​

Answers

The length of shortest piece is 4 inches, middle sized piece is 9 inches and that of longest piece is 27 inches.

According to the question,

We have the following information:

A piece of pipe is 40in. long. It is cut in to 3 pieces. The longest piece is 3 times as long as the middle sized piece and the shortest piece is 23 in. shorter than the longest piece.

Let's take the length of middle sized piece to be x inches.

Length of longest piece = 3x inches

Length of shortest piece = (3x-23) inches

Now, we have the following expression:

x+3x+3x-23 = 40

7x-23 = 40

Adding 23 on both the sides:

7x = 40+23

7x = 63

Dividing by 7 on both the sides:

x = 63/7

x = 9 inches

Length of longest piece = 3*9 inches

Length of longest piece = 27 inches

Length of shortest piece = (27-23) inches

Length of shortest piece = 4 inches

Hence, the length of shortest piece is 4 inches, middle sized piece is 9 inches and that of longest piece is 27 inches.

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work out the size of angle x 24

Answers

The size of angle x in the isosceles triangle is:78°.

What is an Isosceles Triangle?

A triangle that has two sides that have congruent lengths is called an isosceles triangle. The base angles of the isosceles triangle are the angles that are opposite the congruent lengths, they are also equal to each other.

The triangle in the image below has two congruent sides, therefore, it is an isosceles triangle and the angles opposite its congruent sides will also be equal to each other.

Therefore:

x = 1/2(180 - 24)

x = 1/2(156)

x = 78°

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a certain washing machine uses 29 gallons of water for each load of laundry washed. How many gallons of water would the washing machine use for 156 loads of laundry?

Answers

Answer:156

Step-by-step explanation:

Ryan is going to spin the spinner 80 times.
(b)
Work out an estimate for the number of times he should expect the spinner to land on 2

Answers

The estimate for the number of times Ryan should expect the spinner to land on 2 is 13.

How to calculate the number of times?

From the information, the spanner has numbers labeled 1 - 6 and Ryan is going to spin the spinner 80 times.

It should be noted that the fraction for getting a 2 is 1 out of 6. This will be 1/6.

Therefore, when it's spinned 80 times, the expected number will be:

= 1/6 × 80

= 13

The number of times is 13.

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Complete question

A spanner has numbers labeled 1 - 6. Ryan is going to spin the spinner 80 times. Work out an estimate for the number of times he should expect the spinner to land on 2

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