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.

In conclusion, the integer solutions of the given system of equations are [tex]$(x, y, z) = (1, 2, 0)$ and $(x, y, z) = (-1, 4, 0)$.[/tex]

An integer is a positive, negative, or zero-valued whole number. It is a number without a fractional or decimal component.

To find all integer solutions of the given system of equations:

[tex]x + y &= 3 \[/tex]

[tex]3xy - z^2 &= 9[/tex]

We can start by solving the first equation for one of the variables. Let's solve for y in terms of x:

[tex]x + y &= 3 \[/tex]

[tex]y &= 3 - x[/tex]

Now we substitute this expression for y into the second equation:

[tex]3xy - z^2 &= 9 \[/tex]

[tex]3x(3-x) - z^2 &= 9 \quad \text{Substituting } y = 3-x \[/tex]

[tex]9x - 3x^2 - z^2 &= 9 \[/tex]

[tex]3x^2 + z^2 &= 9x - 9 \[/tex]

[tex]3x^2 - 9x + z^2 &= -9 \quad \text{(1)}[/tex]

Now we will examine equation (1) for integer solutions.

Case 1: [tex]z= 0[/tex]

If  then equation (1) becomes:

[tex]3x^2 - 9x &= -9 \quad \text{(1a)} \[/tex]

[tex]3x(x-3) &= -9[/tex]

Since we are looking for integer solutions, 3x and x-3 must have opposite signs. The possible pairs of factors of -9 with opposite signs are (3,-3) and (-3,3). So we have two possible sets of equations to solve:

The discriminant is negative, there are no integer solutions. Therefore, there are no integer solutions for the original system of equations when [tex]z \neq 0.[/tex]

In conclusion, the integer solutions of the given system of equations are [tex]$(x, y, z) = (1, 2, 0)$ and $(x, y, z) = (-1, 4, 0)$.[/tex]

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Answer:108 degrees

Step-by-step explanation:easy

Answer: The commission rate for the real estate agency is 7.5% of the sale price, which is:

0.075 x 343000 = $25,725

The agent's commission is 30% of the amount the agency gets, which is:

0.3 x 25725 = $7,717.50

Therefore, the real estate agency made $25,725 on the house and the agent earned a commission of $7,717.50.

Step-by-step explanation:

Answer:

what is 5+17894874298748

Answer:

Therefore, the total amount the Bells will pay for their house is $344,520.

Step-by-step explanation:

We can start by using the information about the monthly mortgage payment to calculate the total number of payments they will make over the 30-year term:

30 years × 12 months/year = 360 months

So the Bells will make 360 monthly payments of $957. To find the total amount they will pay for the house, we need to multiply the monthly payment by the number of payments:

$957/month × 360 months = $344,520

Therefore, the total amount the Bells will pay for their house is $344,520.

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The area of the ripple at t=2 is 32π square inches.

What is area ?

Area is the measure of the size of a two-dimensional surface enclosed by a closed boundary, such as a polygon or a circle. It is typically measured in square units such as square meters, square feet, or square inches.

The equation for the radius of the circular ripple is given by r(t) = √(15t+2). The equation for the area of a circle with radius r is A(r) = πr².

Therefore, the area of the ripple as a function of time is given by:

A(t) = π[r(t)]²

Substituting the expression for r(t), we get:

A(t) = π[(√(15t+2))²]

A(t) = π(15t+2)

A(t) = 15πt + 2π

To find the area of the ripple at t=2, we substitute t=2 into the expression for A(t):

A(2) = 15π(2) + 2π

A(2) = 30π + 2π

A(2) = 32π

Therefore, the area of the ripple at t=2 is 32π square inches.

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Scarcity principle: Resources are limited and choices must be made, b. Rational person: Makes decisions based on logical thinking and self-interest, c. Economic surplus: Net gain to society from producing and consuming a good, d. Marginal benefit: Additional benefit from consuming one more unit of a good or service.

A statement is a declarative sentence that expresses a fact, opinion, or idea. It is a sentence that makes a claim or assertion that can be true or false, and it can be either affirmative (positive) or negative. A statement can be a simple sentence, or it can be a complex sentence that includes multiple clauses

a. The scarcity principle is the economic principle that states that resources are limited and cannot satisfy all human wants and needs. This principle recognizes that we live in a world of limited resources, and therefore, we must make choices about how to allocate those resources to satisfy our wants and needs. For example, a farmer may have limited land and water resources to cultivate crops, and he must choose which crops to grow based on their profitability, water requirements, and market demand.

b. A rational person is an individual who uses logical thinking and makes decisions based on self-interest to achieve the best possible outcome. A rational person weighs the pros and cons of each option and selects the alternative that maximizes their satisfaction or utility. For example, a consumer may compare prices and quality of different brands before purchasing a product to get the best value for their money.

c. Economic surplus is the difference between the total value that consumers place on a good or service and the total cost of producing it. It represents the net gain to society from producing and consuming the good or service. For example, if a firm produces 100 units of a product at a total cost of $500 and sells them for a total of $700, then the economic surplus is $200.

d. Marginal benefit is the additional benefit that a person receives from consuming one more unit of a good or service. It is the change in total benefit divided by the change in the quantity consumed. For example, if a consumer derives 10 units of satisfaction from consuming the first slice of pizza and 8 units of satisfaction from consuming the second slice, then the marginal benefit of the second slice is 8-10=-2 units of satisfaction.

Therefore, a. Scarcity principle: Resources are limited and choices must be made, b. Rational person: Makes decisions based on logical thinking and self-interest, c. Economic surplus: Net gain to society from producing and consuming a good, d. Marginal benefit: Additional benefit from consuming one more unit of a good or service.

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Answer:

1 ⅓

Step-by-step explanation:

there 4 glasses and you put ⅓ in each one therefore 4 x ⅓ = 1 ⅓

As a result, the original figure's corresponding sides and those of its enlarged image are parallel.

A quadrilateral is a closed, two-dimensional form in geometry that has four straight sides. Four sides, four edges, and four angles make up the polygonal shape. The total of a quadrilateral's internal angles is 360 degrees. Kites, squares, rectangles, parallelograms, and trapezoids are examples of quadrilaterals.

given

Each side of the original figure is expanded to meet the dilation scale factor when a quadrilateral is dilated from an outer centre of dilation, and the sides of the dilated image are parallel.

Parallel lines continue to be parallel after scaling because dilatation scales each side of the quadrilateral by a constant factor.

As a result, the original figure's corresponding sides and those of its enlarged image are parallel.

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By adding  the monthly finance charge to the unpaid balance, the new account balance is $4,056.91.

What is addition?

Addition is a mathematical operation that involves combining two or more numbers to produce a sum or total. It is commonly denoted by the plus sign (+) and is one of the four basic arithmetic operations.

To find the new account balance, we need to add the monthly finance charge to the unpaid balance.

First, we need to calculate the monthly finance charge:

Monthly finance charge = 1.75% of unpaid balance

= 0.0175 * $3,987.11

= $69.80

Next, we add the monthly finance charge to the unpaid balance:

New account balance = Unpaid balance + Monthly finance charge

= $3,987.11 + $69.80

= $4,056.91

Therefore, the new account balance is $4,056.91.

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Answer: (-2,-3)

Step-by-step explanation:

Cheryl ran a total of 8 miles in five days.

1 + 1 + 1 + 2 + 3 = 8

Written as a decimal, this is 8.0 miles.

On a number line graph, the inequality X > 12 would be represented as follows:

A number line is a mathematical tool used to represent and visualize numbers, particularly real numbers, in a linear manner.

On a number line graph, the inequality X > 12 would be represented as follows(check attachment)

The line represents all real numbers, with the arrow pointing towards the right indicating that any number greater than 12 is a solution to the inequality. The circle at the end of the line is an open circle, indicating that 12 is not included in the solution set because the inequality is strict, i.e., X is strictly greater than 12.

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pi x 2r = circ

2r = circ/pi

r = circ /(2 x pi) =  65.94/(2 x 3.14) = 10.5 feet

Function[tex]y = arcsin(x)[/tex]is symmetric with respect to the origin, while function [tex]y = arccos(x)[/tex] is not. This is as inverse sine function is an odd function, while inverse cosine function is an even function.

If [tex]f(-x) = -f(x)[/tex] for all values of x in the function's domain, then the function is symmetric with regard to the origin. In other words, a function is said to be symmetric with regard to the origin if it passes through the origin and has the same shape on each side of the y-axis.

We must substitute -x for x in each function and simplify to find out if the functions [tex]y = arcsin(x)[/tex] and [tex]y = arccos(x)[/tex] are symmetric with respect to the origin.

According to the equation [tex]y = arcsin(x)[/tex], we get:

[tex]-arcsin = arcsin(-x) (x)[/tex]

Because it is odd, the function[tex]y = arcsin(x)[/tex] is symmetric with respect to the origin.

According to the equation [tex]y = arccos(x)[/tex]:

[tex]x(-arccos) = -arccos (x)[/tex]

Because it is not odd, the function[tex]y = arccos(x)[/tex] is not symmetric with respect to the origin.

In conclusion, [tex]y = arccos(x)[/tex]is not symmetric with regard to the origin, but [tex]y = arcsin(x[/tex] is. Due to the fact that the inverse cosine function is an even function, whereas the inverse sine function is an odd function, this is the case.

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By answering the presented question, we may conclude that Therefore, the solution set to the equation f(x) = 0 is {0}.

In mathematics, a function seems to be a link between two sets of numbers in which each member of the first set (known as the domain) corresponds to a specific member of the second set (called the range). In other words, a function takes input from one collection and creates output from another. The variable x has frequently been used to represent inputs, whereas the variable y has been used to represent outputs. A formula or a graph can be used to represent a function. For example, the formula y = 2x + 1 depicts a functional form in which each value of x generates a unique value of y.

the equation:

[tex]3x^2 + x^2 = 0\\4x^2 = 0\\x^2 = 0\\x = 0[/tex]

Therefore, the solution set to the equation f(x) = 0 is {0}.

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Answer:
8. A) 3.75

9. B) 5.00

Answer: -31x

Step-by-step explanation:

|x|31 becomes -x31 which is -31x

The value of the equation are 1. (-2√3 + 2)(√3 - 5) = -16 + 8√3 2. (5 - 4√5)(-2 + √5) = -30 + 21√. 3. (-2 - 3√5)(5 - √5) = -5 - 17√5. 4. (√5 - √3)(√5 + √3) = 2.

An expression is a mathematical sentence without the equal sign that can include variables, operators, and integers. Although it can be appraised or simplified, there isn't a single perfect answer. An expression is, for instance, 3x + 2y.

A mathematical statement that has an equal sign and expresses the equivalence of two expressions is called an equation, on the other hand. To determine the values of variables that meet an equality, equations can be solved. One equation is 3x + 2y = 7, for instance.

1. Multiplying (-2√3 + 2)(√3 - 5), we get:

= -2√3 × √3 + (-2√3 × -5) + (2 × √3) + (2 × -5)

= -2√(3 × 3) + 10√3 - 2√3 - 10

= -2(3) + 8√3 - 10

= -16 + 8√3

Therefore, (-2√3 + 2)(√3 - 5) = -16 + 8√3.

2. Multiplying (5 - 4√5)(-2 + √5), we get:

= 5(-2) + 5√5 + (-4√5)(-2) + (-4√5)(√5)

= -10 + 13√5 + 8√5 - 4(5)

= -30 + 21√5

Therefore, (5 - 4√5)(-2 + √5) = -30 + 21√5.

3. Multiplying (-2 - 3√5)(5 - √5), we get:

= (-2 × 5) + (-2 × √5) + (-3√5 × 5) + (-3√5 × -√5)

= -10 - 2√5 - 15√5 + 3(5)

= -5 - 17√5

Therefore, (-2 - 3√5)(5 - √5) = -5 - 17√5.

4. Multiplying (√5 - √3)(√5 + √3), we get:

= (√5 × √5) - (√3 × √3)

= 5 - 3

= 2

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Without the specific details or an image of the line segment on the coordinate grid, I'm unable to provide you with the specific numbers included in the range.

To help you generally, a line segment is a part of a line with two endpoints, and it is located on a coordinate grid, which is a two-dimensional plane formed by the intersection of horizontal and vertical lines (x and y axes).

To determine the range of the line segment, you need to identify the y-coordinates of the two endpoints.

The range includes all the y-coordinates between those two points, inclusive of the endpoints. To find the range, observe the line segment and note the y-coordinates of both endpoints. Then, list all the numbers (whole or fractional) between those values, including the endpoints themselves.

Once you have the necessary details or an image of the line segment, feel free to ask again, and I'll be happy to help you identify the numbers within the range.

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The value of X when <1 = 3x+15 = 25. Then the value of the missing part of the sides of the kite (KITE) is given as follows;

X = 25

a.) ET = 60

b.) KE = 20

One of the properties of a kite is that it has two pairs of adjacent equal sides and the longer diagonal bisects the shorter one with the formation of angle 90°.

Therefore to calculate for X when <1 = 3x+15 is as follows;

<1 = 90°

90= 3x+15

3x = 90-15

3x = 75

X = 75/3

X = 25

But IT = ET

Given IT = 2x +20

X = 25

IT = ET = 2(20)+20

= 40+20 = 60

But KI = KE

Given that KI = 2x-30

X = 25

KI= KE = 2(25)-30

= 50-30 = 20

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Answer:

I think a

good luck

have a good day

Answer:

Length ≥ 40

Width ≥ 5

Perimeter = 2 × (Length + Width)

2 × (Length + Width) ≤ 150

Step-by-step explanation:

To create a graph showing the possible dimensions of the garden, we need to plot the length and width of the rectangular area on the x and y axes, respectively. Since we want the length to be at least 40 feet and the width to be at least 5 feet, we can represent these constraints by the following inequalities:

Length ≥ 40

Width ≥ 5

We also know that the total length of fencing available is 150 feet, which means that the perimeter of the rectangular area must be less than or equal to 150 feet. The perimeter of a rectangle is given by:

Perimeter = 2 × (Length + Width)

So, we can write the inequality representing the perimeter as:

2 × (Length + Width) ≤ 150

To graph the possible dimensions of the garden, we can plot the points that satisfy all three inequalities on the x-y plane.

Regarding the vegetables, it is not clear what vegetables the user would like to plant in the garden. As such, we cannot provide a specific answer to this question.

In summary, we need to write three inequalities to represent the constraints in the problem, and we can graph the solution space using these inequalities.

(a) The right distributive law is proven for S.For S, this is expressed as (a,b)·(c,d)=(a,b)·(c,d)=(a·c,a·d+b·c).

(a,b)·(c,d)=(bd−ad−bc,ac−ad−bc)=(a·c,a·d+b·c).

(b) we can deduce that x=1 and y=0. Hence, the multiplicative identity element for S is (1,0).

(c) For S, this is expressed as (a,b)·(1,0)=(a,b). Let (a,b) be an arbitrary element in S. The multiplicative identity law is proven for S.

The right distributive law states that the product of a scalar and a vector is equal to the sum of the products of the scalar with each component of the vector.

(a) For S, this is expressed as (a,b)·(c,d)=(a,b)·(c,d)=(a·c,a·d+b·c).

To prove this, we need to show that (a,b)·(c,d)=(a·c,a·d+b·c).

Let (a,b) and (c,d) be two arbitrary elements in S. Then,

(a,b)·(c,d)=(bd−ad−bc,ac−ad−bc)

=(a·c,a·d+b·c).

Therefore, the right distributive law is proven for S.

(b) The multiplicative identity element for S is (1,0). To find this, we need to find a pair of elements (x,y) such that (a,b)·(x,y)=(a,b).

Let (x,y) be an arbitrary pair of elements in S. Then,

(a,b)·(x,y)=(ax−by,ay+bx)

=(a,b).

From this, we can deduce that x=1 and y=0. Hence, the multiplicative identity element for S is (1,0).

(c) The multiplicative identity law states that the product of a scalar and the multiplicative identity element is equal to the scalar itself. For S, this is expressed as (a,b)·(1,0)=(a,b).

To prove this, we need to show that (a,b)·(1,0)=(a,b).

Let (a,b) be an arbitrary element in S. Then,

(a,b)·(1,0)=(a·1−b·0,a·0+b·1)

=(a,b).

Therefore, the multiplicative identity law is proven for S.

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Answer:

 y = 7x + 10

Step-by-step explanation:

Use your point-slope form: y- y1 = m (x - x1) to substitute the given information.

    y - 6 = 7(x - (-4))

Then simplify.

     y - 6 = 7(x + 4)

Next, distribute the 7 into the parenthesis which will give you the point-slope form.

     y - 6 = 7x + 28

In order to write it in slope-intercept form, add 6 to both sides.

    y - 6 + 6 = 7x + 4 + 6

Then simplify to write the equation in slope-intercept form.

    y = 7x + 10

Answer:

1 shorter than 2 longer than 3 short

Answer:

4

Step-by-step explanation:

The product of eight and two is 8 x 2 = 16.

The product of three and four is 3 x 4 = 12.

So, the expression "the product of eight and two, minus the product of three and four" can be written as:

16 - 12 = 4

Therefore, the answer is 4.

Answer:

k+5

Step-by-step explanation:

k= Elliot

Victoria is 5 years older than Elliot

=k+5