What is the radius of the circle that is centered at (2, −3) and passes through the point (−1, −6)?

Answer:

3x-7

Step-by-step explanation:

A square’s area represents (ax+b)^2. Let’s expand that. [tex]a^2x^2+2abx+b^2[/tex] now, we can notice this fits perfectly when a=3 and b=-7. Therefore one side length of the square is 3x-7.

Answer:

As a co-worker, you should support your colleague by offering to address the question. Here are some steps to consider:

Acknowledge the concern: Begin by thanking the person for their comment and acknowledging their concern about the data system. This will help to show that you are open to feedback and willing to listen.

Provide context: If appropriate, offer some context about the data system that was used. For instance, if the system was chosen due to budget or resource constraints, you can explain why that decision was made.

Offer a solution: Explain what steps were taken to ensure the accuracy of the data, despite the known issues with the system. If there were steps taken, share those with the audience. Alternatively, offer to follow up with the audience member after the presentation with more information on how the team plans to address the issue.

Stay professional: Be calm, professional, and open-minded throughout the conversation. Avoid getting defensive or argumentative. Instead, focus on addressing the issue in a constructive manner.

By following these steps, you can help to address the concern in a professional and effective manner.

Answer:

21

Step-by-step explanation:

2 1/3 ×9=7/3  × 9=21

The number 3 in the equation h(t) = -16t² + 6t+ 3 represents the initial height from which the ball is thrown.

The equation h(t) = -16t² + 6t+ 3 models the height of the ball thrown in the air, with h(t) measured in feet and time, t, measured in seconds. The number 3 in this equation refers to the height from which the ball is thrown. This is represented by the constant term 3, which is added to the equation after the sum of the variables. The formula h(t) = -16t² + 6t+ 3 can be broken down into three parts. The first part is the constant term, 3, which denotes the initial height of the ball. The second part is the linear term, 6t, which represents the acceleration of the ball due to gravity. Lastly, the quadratic term, -16t², is used to describe the rate at which the ball’s acceleration slows down due to air resistance. Therefore the number 3 in the equation h(t) = -16t² + 6t+ 3 represents the initial height from which the ball is thrown.

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The linear equation that can be given for squirrel y is the value of 12x.

According to the question,

Animal            Mouse       Squirrel

Speed(mph)         8                12

SInce "x" the time goes along with x-axis and "y" is  the distance covered by the animal.

The mouse time and distance would plot the graph (1,8)(2,16)(3,24)....

The squirrel time and distance would plot the graph (1,12)(2,24)(3,36)....

Let us consider the track is a straight line and the shorter distance is 50 meters.

The formula for straight line equation y = mx + b  where 'b' is the base value, 'x' is the time and 'y' is the distance.

The linear equation for squirrel y = 12x+b and the squirrel starts at 0 meters per hour. so the equation becomes y = 12x.

The linear equation for mouse y = 8x + b  and the mouse starts at 0 meters.  so the equation becomes y = 8x.

Distance covered by the mouse and the squirrel at time x = 3 we can find the distance covered by the mouse and the squirrel.

y =12x

y = 12(3)

y = 36.

The distance covered by the squirrel is 36km at time 3hours.

For mouse, at time x = 3 hours.

y = 8(3)

y=24.

The distance covered by the squirrel is 24km at time 3hours.

Hence, The linear equation for squirrel y = 12x.

The linear equation for mouse  y = 8x

The distance covered by the squirrel is 36km at time 3hours.

The distance covered by the squirrel is 24km at time 3hours.

Thus:

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Bobbi owes a total of $10,455.75 in taxes.

Taxes are compulsory financial charges imposed by governments on individuals or entities based on income, property, or goods/services.

To compute the tax owed by Bobbi, we can use the following steps:

Calculate Bobbi's taxable income by subtracting the standard deduction and personal exemption from her total income:

Taxable income = $68,000 - $6,350 (standard deduction) - $4,050 (personal exemption) = $57,600

Determine the tax bracket in which Bobbi's taxable income falls:

Bobbi's taxable income of $57,600 falls in the 25% tax bracket.

Calculate the tax owed by Bobbi by applying the marginal tax rates to her taxable income. We can use the following formula:

Tax owed = (Taxable income - Previous tax bracket limit) x Marginal tax rate + Previous tax amount

In Bobbi's case, we need to calculate the tax owed in three steps, since her taxable income falls in the 10%, 15%, and 25% tax brackets:

For the first $9,325 of her taxable income, Bobbi owes 10% in taxes:

Tax owed = ($9,325 - $0) x 0.10 + $0 = $932.50

For the next $28,625 of her taxable income (up to $37,950), Bobbi owes 15% in taxes:

Tax owed = ($37,950 - $9,325) x 0.15 + $932.50 = $3,825.75

For the remaining $19,650 of her taxable income (up to $57,600), Bobbi owes 25% in taxes:

Tax owed = ($57,600 - $37,950) x 0.25 + $3,825.75 = $5,697.50

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Answer:

3 * 10^8 m/s.

Step-by-step explanation:

The given number is close to 300 million so an approximate speed is

3 * 10^8.

Answer:

The y-intercept represents a starting salary of $32,500.

The slope represents an additional $2,500 in salary for each additional year of employment.

If the starting salary for a new employee is changed to $35,000 and the yearly salary increase is unchanged, the new equation would be
[tex]y=2500x+35000[/tex].

If the yearly salary increase is changed to $3,000 and the starting salary remains the same, the new equation would be
[tex]y = 3000x + 32500[/tex].

Step-by-step explanation:

Answer:

The y-intercept represents a starting salary of $32,500.

The slope represents an additional $2,500 in salary for each additional year of employment.

If the starting salary for a new employee is changed to $35,000 and the yearly salary increase is unchanged, the new equation would be

y=2500x+35000y=2500x+35000 .

If the yearly salary increase is changed to $3,000 and the starting salary remains the same, the new equation would be

y = 3000x + 32500y=3000x+32500 .

Answer:

None of it.

Step-by-step explanation:

Notice the slope is 2.75 this means for EVERY X the graph goes up by 2.75 in the Y axis. For example.
If at                 X=1     y=0
Then for         X=2   y=2.75

and for            X=3  y=2.75+2.75=5.5
also the graph must pass thought point (0,0), the origin, and none of the graph follow this.  

You can also compare the slopes of each equations
for graph A, from x=1 to x=2 the height Y goes from 3 to 3.5, this is a slope of 0.5 (not the 2.75 we are looking for)

for graph A, from x=1 to x=2 the height Y goes from 1 to 2.5, this is a slope of 1.5 (not the 2.75 we are looking for)

for graph A, from x=1 to x=2 the height Y goes from 1 to 2.75 this is a slope of 1.75 (not the 2.75 we are looking for)

notice the last is similar to equation y=1.75X+b, just in case.

Answer:

none

Step-by-step explanation:

Using the multiplication operation, the total quantity that the 27 horses consume in 8 weeks is 1,944 pounds.

The multiplication operation is one of the four basic mathematical operations, including addition, subtraction, and division.

Multiplication operation involves the multiplicand (the number multiplied), the multiplier (the number multiplying), and the product (the result).

The number of horses in a stable = 27

The quantity of food eaten per horse per week = 9 pounds.

The number of weeks involved = 8 weeks.

The total quantity eaten by the 27 horses in 8 weeks = 1,944 pounds (27 x 9 x 8)

With multiplication, we can conclude that the total quantity is 1,944 pounds.

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A stable has 27 horses. Each one eats 9 pounds per week.  How many pounds will the horses eat in 8 weeks?

The area of the shaded portion is solved to be

The area of the shaded portion is solved by finding the whole area  of the triangle and subtracting the area of the circle

Area of the whole shape

The shape is a triangle and the area of the triangle is

= 0.5 * base * height

where

base = 40 km

height = 27 km

plugging in the values

Area = 0.5 * 40 * 27

Area = 540 square km

Area of the circle

= π * radius^2

= 3.142 * 6^2

= 113.112 square km

Area of the shaded portion is

= 540 - 113.112

= 426.888

= 426.89 km²

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Answer:

the answer is 1/3*9/4

Answer:  1/3*9/4

Step-by-step explanation: I did a test.

In the rectangle , the cοοrdinate οf b is (0,2).

A quadrilateral with fοur equal vertices and parallel sides is knοwn as a rectangle. Because οf this, it is alsο knοwn as an equiangular quadrilateral.

The term "parallelοgram" can alsο be used tο describe a rectangle because the οppοsing sides are equal and parallel.

Here In the given rectange abcd,  Let cοοrdinates οf b be (x, y)

then, ac and bd are diagοnals οf the rectangle.

Coordinates of midpoints of ac and bd must be same.

Coordinates of midpoint of ac = [tex](\frac{6-2}{2},\frac{-8+4}{2})[/tex] = [tex](\frac{4}{2},\frac{-4}{2})[/tex] = (2,-2)

Coordinates of midpoint of bd = [tex](\frac{x+4}{2},\frac{y-6}{2}) = (2,-2)[/tex]

=> [tex]\frac{x+4}{2}=2 , \frac{y-6}{2}=-2[/tex]

=> x+4=4 , y-6=-4

=> x=4-4, y=-4+6

=> x=0,y=2

Hence the coordinate of b is (0,2).

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Answer:

Step-by-step explanation:kk

The constant of proportionality that relates the number of milliliters of coffee made y to the number of teaspoons of sugar used x is 12.

When two variables are directly or indirectly proportional to one another, their relationship can be represented as y = kx or y = k/x, where k denotes the direction of the relationship between the two variables. It is known as the proportionality constant, or k.

We must determine the ratio of the two amounts in order to determine the constant of proportionality that connects the number of teaspoons of sugar used x to the number of millilitres of coffee brewed y.

Considering the information provided, we understand that:

168 millilitres of coffee require 14 tablespoons of sugar.

As a result, the following is the relationship between the quantity of coffee prepared and the quantity of sugar used in teaspoons:

y/x = 168/14

Reducing the ratio:

y/x = 12

This indicates that 1 teaspoon of sugar is needed to make every 12 millilitres of coffee.

As a result, 12 is the constant of proportionality that links the quantity of coffee created (y) to the quantity of sugar utilised (x).

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Answer:

2.5

Step-by-step explanation:

If the areas stay the same, then 10*5=20*h

So, 20h=50

h=2.5

Answer: B: y=5x-5

Step-by-step explanation:

Answer: x< 4.5

Step-by-step explanation:

-8x+6>-30

-8x>-36

x<4.5

Answer:

3/4 miles

Step-by-step explanation:

Parameters

Total distance = 3 1/2 miles

Covered distance = 2 3/4 miles

To make things easier let's convert our parameters from fraction to decimal,

Therefore,

Total distance= 3.5 miles

Covered distance = 2.75 miles

Remaining distance = Total distance - Covered distance

Remaining distance = 3.5 miles - 2.75 miles

Remaining distance= 0.75 miles

Converting back to fraction,

Remaining distance = 3/4 miles

Therefore,

Lisa has 3/4 miles left to hike.

Please mark brainliest.

Thanks.

Answer:

Step-by-step explanation:

Ok so basically, what I would do is make note of each of the points of the triangle, and them multiply them by four, or the scale factor.

The probability of selecting the committee in the order of man, man, man, woman, woman, without replacement is; 5/133

The probability of an event is the ratio of the number of desired outcome to the number of possible outcome.

The number of men in the board = 12

The number of women in the board = 10

The probability of selecting a man in the first position = 12/22

The number of men remaining is 11 and the number of women remaining is 10.

The probability of selecting a man in the second position is therefore = 11/21

In the same order, the probability of selecting a man in the third position = 10/20

The probability of selecting a woman next = 10/19

The probability of selecting another woman = 9/18

The probability of selecting the committee of five members in the specified order is therefore;

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To solve this problem, we need to first determine how long it will take for Justin's money to triple in value. We can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where:

A = the final amount

P = the principal (initial amount)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

For Justin, we have:

P = $940

r = 0.07625

n = 12 (monthly compounding)

t = unknown

We want to solve for t when A = 3P = $2820. We can rearrange the formula and plug in the values:

A = P(1 + r/n)^(nt)

3P = P(1 + r/n)^(nt)

3 = (1 + 0.07625/12)^(12t)

ln(3) = 12t * ln(1 + 0.07625/12)

t = ln(3) / (12 * ln(1 + 0.07625/12))

t ≈ 15.8 years

So it will take Justin about 15.8 years for his money to triple in value.

Now we can use the same formula to find how much money Hailey will have in her account after 15.8 years:

P = $940

r = 0.0825

n = 4 (quarterly compounding)

t = 15.8

A = P(1 + r/n)^(nt)

A = $940(1 + 0.0825/4)^(4*15.8)

A ≈ $3501

Therefore, Hailey will have about $3,501 in her account when Justin's money has tripled in value

The expression that does not belong with the other three is B. x ² - 8 ˣ because C. The different expression is the one that is not a polynomial.

Expression 2 is not a polynomial because it contains a term (8^x) with a variable in the exponent, which is not allowed in a polynomial. All the other expressions are polynomials.  This expression therefore does not belong.

Polynomials are mathematical expressions that consist of variables and coefficients, where the variables are raised to non-negative integer powers and the coefficients are constants.

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The area of the forest will be approximately 1396 km sq. after 10 years.

Given that, a forest covers an area of 2100 km sq and that each year this area decreases by 4%..

If the area of the forest decreases by 4% each year, then after one year it will be 96% of the original size.

After two years, it will be 96% of 96% of the original size, or 0.96² of the original size.

After ten years, it will be 96% of itself ten times, or 0.96¹⁰ of the original size.

So the area of the forest after 10 years will be:

Area = Initial area × 0.96¹⁰

Area = 2100 km sq × 0.96¹⁰

Area = 1396 km sq

Therefore, the area of the forest cover in 10 years will be 1396 km sq.

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Her sample is in fact biased, as the sampling method used was voluntary sampling, which results in self-selection bias.

Voluntary sampling is a type of sampling method in which individuals are invited to participate in a study or survey based on their willingness or availability to do so. In other words, individuals choose to participate in the study, rather than being selected randomly by the researcher.

Voluntary sampling is chosen for this problem as the students had the option to answer the e-mail or not.

A limitation of voluntary sampling is that the individuals who choose to participate in the study may not be representative of the larger population from which they were drawn, leading to biased results.

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Answer:

If leg a is the missing side, then transform the equation to the form where a is on one side and take a square root: a = √(c² - b²)

If leg b is unknown, then: b = √(c² - a²)

For hypotenuse c missing, the formula is: c = √(a² + b²)

Step-by-step explanation:

Answer:

[tex]\huge\boxed{\sf P= 9 \ in. }[/tex]

Step-by-step explanation:

Given is a right-angled triangle.

So, we can use Pythagorean Theorem to find the missing length.

It is:

[tex](Hypotenuse)^2=(Base)^2+(Perpendicular)^2[/tex]

Here,

Hypotenuse = 41 in.

Base = 40 in.

Perpendicular = P

[tex](41)^2=(40)^2+P^2\\\\1681 = 1600 + P^2\\\\Subtract \ 1600 \ from \ both \ sides\\\\1681-1600=P^2\\\\81 = P^2\\\\Take \ square \ root \ on \ both \ sides\\\\\sqrt{81} = \sqrt{P^2} \\\\P= 9 \ in. \\\\\rule[225]{225}{2}[/tex]

Answer:

B

Step-by-step explanation:

assuming DF is the diameter of the circle , then

the angle in a semicircle is 90° , that is

∠ DCF = 90° and Δ CDF is a right triangle

using Pythagoras' identity in the right triangle

CD² + CF² = DF²

CD² + 60²  65²

CD² + 3600 = 4225 ( subtract 3600 from both sides )

CD² = 625 ( take square root of both sides )

CD = [tex]\sqrt{625}[/tex] = 25

The expressions are simplified to give;

15xyz + 12

4ab + 10

Algebraic expressions are simply defined as mathematical expressions that are known to contain variables, constants, coefficient, factors and terms.

These algebraic expressions are also known to be made up of mathematical operations, such as;

From the information given, we have that;

13xyz +9 +2xyz + 3

Now, collect the like terms, we have;

13xyz + 2xyz + 9 + 3

Add the values

15xyz + 12

6ab + (-2ab) + 4 + 6​

expand the bracket and collect like terms

4ab + 10

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