Please help me out. :)

Here is your answer

[tex]\bold{x= 6}[/tex]

REASON:

Theorem used: The diagonals of a parallelogram bisect each other.

Let diagonals AC and BD bisect each other at O

So, OA=OC

Now,

3x=4x-6 [OA=3x and OC=4x-6]

4x-3x= 6

x= 6

HOPE IT IS USEFUL

Answer:

Step-by-step explanation:

Parallelogram's diagonals theorem states that the diagonals in a parallelogram must bisect each other.

So for ABCD to be a parallelogram, the two diagonals must be divided in equal sections.

That is given for BD already.

For AC, 3x = 4x - 6

Rearranging, 4x - 3x = 6

x = 6

24 miles is the answer.

Step-by-step explanation:

The previous reading of Jeremy's car = 25500

The current reading is = 26100

Difference between readings = [tex]26100-25500=600[/tex]

Number of gallons used to fill the tank = 25

So, miles traveled by Jeremy in 25 gallons is = 600

In 1 gallon, he travels = [tex]\frac{600}{25}= 24[/tex] miles.

Therefore, Jeremy's car gets 24 miles per gallon.

Answer:

ln(1.225)/0.1

Step-by-step explanation:

The credit all goes to @lucic , but the answer is expressed as a natural log

Answer:

1/9.

Step-by-step explanation:

There is a total of 15 cards in the stack.

Prob( Queen is chosen) =  5/15 = 1/3.

The probability of a second queen being chosen is also 1/3

Required probability = 1/3 * 1/3 = 1/9.

Answer:

228.6 cm

Step-by-step explanation:

Answer:

Regular

Step-by-step explanation:

A polygon with congruent sides and angles is a regular polygon, with an equilateral triangle or a square as an example. A 3D shape example is an icosahedron with 20 regular triangular faces.

A polygon with congruent angles and congruent sides is called a regular polygon. This means that all its sides and angles are equal in measure. An example of a regular polygon is an equilateral triangle which has all three sides of equal length and all three angles 60 degrees each, or a square that has four sides of equal length and four angles each 90 degrees.

An example provided is an icosahedron which is a regular polyhedron (a 3D shape) with 20 identical equilateral triangular faces. Every face is a regular polygon, showing that all its 20 faces have congruent angles and sides.

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Answer:

52/8 =  6.5 feet

Answer:

B

Step-by-step explanation:

Answer with explanation:

We will use [tex]\frac{28}{36}[/tex], rule here,which states that , 28% of your gross income should be used for housing finances and 36% of your income , should be used for debt purposes.

Total monthly income of Brenda = $ 1700

→28% of 1700

  [tex]=\frac{28}{100}\times 1700\\\\=28 \times 17\\\\=476[/tex]

⇒Total Housing finances, which includes , housing, food and transportation = $ 476

→Option C:

She has allotted more than 36% of her income for housing.

I need this question too, PLEASE HELP

Answer:

The correct answer is 6.

Step-by-step explanation:

To find this, first find f(-3)

f(x) = -3x + 9

f(-3) = -3(-3) + 9

f(-3) = 9 + 9

f(-3) = 18

Now we do the same for f(7)

f(x) = -3x + 9

f(7) = -3(7) + 9

f(7) = -21 + 9

f(7) = -12

Now we add them together

18 + -12 = 6

The value of f(?3) + f(7) - f(-3) + f(7) is -24.

To find the Value of f(?3) + f(7) - f(-3) + f(7), we need to substitute the given values into the function f(x) = -3x + 9.

Substituting -3 for x, we get f(?3) = -3(-3) + 9 = 18.
Substituting 7 for x, we get f(7) = -3(7) + 9 = -12.
Substituting -3 for x and adding the results, we get f(-3) = -3(-3) + 9 = 18.
Substituting 7 for x, we get f(7) = -3(7) + 9 = -12.

Now, let's calculate the Value of the expression:
f(?3) + f(7) - f(-3) + f(7) = 18 + (-12) - 18 + (-12) = -24

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The circumference is found by multiplying the diameter by PI.

Circumference = 13 inches x 3.14 = 40.82

Rounded to the nearest tenth = 40.8 inches.

Answer:13.3

Step-by-step explanation:

Answer:

The answer is (d)

Exponential decay function

[tex]\lim_{x \to -\infty} f_x=0[/tex]

[tex]\lim_{x \to \infty} f_x= \infty[/tex]  

Step-by-step explanation:

∵ y = 0.8^x

∵ 0.8 < 1

∴ 0.8^x is decreasing ⇒ exponential decay function

Ex: 0.8^-4 = 2.441 ⇒ 0.8^4 = 0.4096

     when x increase the value of 0.8^x decrease

[tex]\lim_{n \to -\infty} f_x=0.8^{-\infty} = \frac{1}{0.8^{\infty}}=0[/tex]

[tex]\lim_{x \to \infty} f_x=0.8^{\infty}=\infty[/tex]

∴ The answer is (d)

Answer:

[tex]A=38.47\ cm^{2}[/tex]

Step-by-step explanation:

we know that

The area of a quarter circle is equal to

[tex]A=(1/4)\pi r^{2}[/tex]

we have

[tex]r=7\ cm[/tex]

substitute the values

[tex]A=(1/4)(3.14)(7)^{2}=38.47\ cm^{2}[/tex]

1.45÷5=0.29

0.29×3=0.87

1.13-0.87=0.26

0.26÷2=0.13

One banana costs 0.13

Final answer:

By setting up two equations based on the cost of apples and the combined cost of apples and bananas, we can calculate that the cost of one banana is \'0.13.

Explanation:

To solve the question about the cost of one banana, we need to set up two equations based on the given information. Let's denote the cost of one apple as 'A' and the cost of one banana as 'B'.

We are given that 5 apples cost \'1.45, which can be written as an equation: 5A = 1.45. We are also given that 3 apples and 2 bananas cost \'1.13, which can be expressed as the equation 3A + 2B = 1.13. By solving these two equations simultaneously, we can find the value of 'B', the cost of one banana.

First, we solve the first equation for A: A = 1.45/5. We get A = 0.29. Now, we substitute this value into the second equation: 3(0.29) + 2B = 1.13. This simplifies to: 0.87 + 2B = 1.13. Solving for B, we get: 2B = 1.13 - 0.87, hence B = (1.13 - 0.87)/2. After performing the subtraction and division, we find that B = 0.13.

Therefore, the cost of one banana is \'0.13.

Answer:

See below.

Step-by-step explanation:

(a)  A sequence is an ordered list of numbers whereas a series is the sum of a list of numbers.

(b) A series is convergent if the sequence of partial sums is a convergent sequence (that is tends to a limit).  A series is divergent if it is not convergent.

Answer:

Step-by-step explanation:

A sequence is a list of ordered numbers. For example, 1, 2, 3, 4, 5.... is a sequence. The numbers are listed in a specific order when we count. In contrast, a series is the sum of the numbers in a sequence. For this multiple choice, choose the best answer that defines what a sequence is.

(a) What is the difference between a sequence and a series?

When working with sequences and series, we look at what happens at negative and positive infinity. When a series converges, it approaches a finite number. When a series diverges, it does not approach a finite number but infinity.

(b) What is a convergent series? What is a divergent series?

Answer:

1) (9, 75+360n)

2) (−9, 255+360n)

Step-by-step explanation:

(9, 75) is same as (9, 75 + 360)

so it would be (9, 435)

It can also be expressed as (-9, 75 + 180 degrees)

so (-9,255) degrees

In general, (9,75+360 n) for n≥0 represents half of the possible ways of representing the point : (9,75)  

Answer with explanation:

The Position of Point in two dimensional plane , P=(9,75°)

→The general rule of writing the point (r,Ф) in terms of polar coordinates is,

  x=r cos Ф , y=r sin Ф

The angle between Intial side and terminal side is Acute.

Here, r=9 units

And , Ф=75°

→→Period of Cosine and Sine is 2π.

⇒⇒So,the coordinates of Point will be

 x=9 *cos (2nπ+75°), And ,y=9 *sin (2nπ+75°), where n is any integer.

Answer:

A statistic is a number that describes a sample and a parameter is a number that describes a population.

Step-by-step explanation:

The definition of "statistic" is:

A piece of data from a portion of a population.

The definition of "parameter" is:

A value that tells you something about a population.

Using these definitions, the correct answer to the question is that a statistic is a number that describes a sample and a parameter is a number that describes a population.

The correct option is A statistic is a number that describes a sample and a parameter is a number that describes a population.

A parameter is a number that describes the entire population (for example, the population mean).

A statistic is a number that describes a sample (e.g., sample mean).

A few examples of statistics are:

Hence, the correct option is A statistic is a number that describes a sample and a parameter is a number that describes a population.

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Answer:

D

Step-by-step explanation:

We would need to understand 2 rules of translation in order to figure this out.

1. The graph of f(-x) is the graph of f(x) reflect about the y-axis

2. The graph of f(x+a) is the graph of f(x) shifted horizontally a units LEFT and the graph of f(x-a) is the graph of f(x) shifted horizontally a units RIGHT

We are comparing [tex]ln(5-x)[/tex] with the parent graph of [tex]lnx[/tex]. Firstly, there is -x in place of x, this means the graph is reflected about y-axis. Next, there is +5 added with -x, so it means the graph is shifted horizontally 5 units to the LEFT

Looking at the answer choices, D is the correct answer.

Answer:

Option d

Step-by-step explanation:

Let f(x) be a logarithmic function of the form [tex]f(x) = log(x)[/tex]. So:

[tex]y = f(-x)[/tex] represents a reflection of f(x) on the y axis.

[tex]y = f(-x) = log(-x)[/tex]

Then:

[tex]y = f(x + 5)[/tex] represents a displacement of [tex]f(x)[/tex] 5 units to the left.

[tex]y = f(x + 5) = log(x + 5)[/tex]

Therefore, the operation:

[tex]y = f(-x + 5) = log(5-x)[/tex]

Represents a reflection on the y axis and a translation of 5 units to the left

Answer:

Part 1. 0.9259 % per year

Part 2. P = 281.4e^(0.009 259t); 338.6 million  

Step-by-step explanation:

Data:

P₀ = 281.4 million

P  = 308.7 million

Part 1. Growth rate

t = 2010 - 2000 = 10 yr

        P = P₀e^(rt)

308.7 = 281.4e^(10r)

e^(10r) = 1.0970

     10r = ln1.0970

        r = (ln1.0970)/10 = (0.092 59)/10 = 0.009 259  

        r = 0.9259 % per year

The 10-year continuous growth rate is 0.9259 % per year.

Part 2. Population model

The population model is

P = 281.4e^(0.009 259t)

where P is in millions and t is the number of years since 2000.

By 2020,

P = 281.4e^(0.009 259 × 20) = 281.4e^0.1852 = 281.4 × 1.203

P = 338.6 million

The estimated population in 2020 is 338.6 million.

Answer:

9 and 14

Step-by-step explanation:

One number is 5 less than a second number.

a = b - 5

:

Twice the second number is 8 less than 4 times the first.  

2b = 4a - 8

replace a with (b-5)

2b = 4(b-5) - 8

2b = 4b - 20 - 8

2b - 4b = -28

-2b = -28

b = 14

then

a = 9

The equation is solved and the two numbers are x = 7 and y = 12

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 equation be represented as A

Now , the value of A is

Let's call the first number "x" and the second number "y"

x = y - 5 (the first number is 5 less than the second number)

2y = 4x - 4 (twice the second number is 4 less than 4 times the first)

We can use substitution to solve for one of the variables.

Substituting the first equation into the second equation, we get:

2y = 4 (y - 5) - 4

Simplifying this equation , we get

2y = 4y - 24

2y - 4y = -24

-2y = -24

y = 12

Now that we know that the second number is 12, we can use the first equation to find the first number:

x = y - 5

x = 12 - 5

x = 7

Hence , the two numbers are 7 and 12

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Answer:

43.75 ft²

Step-by-step explanation:

     Let r = the radius of the semicircle

   and h = the height of the rectangle

Then 2r = the width of the window

The formula for the perimeter of a circle is C = 2πr,

so, πr = the perimeter of the semicircle

The perimeter of the window is

P = πr + 2h + 2r = 25

      2h + (π +2)r = 25

                       h = ½[25 - (π + 2)r]

(1)                   h = 12.5 - (π/2 +1)r

The formula for the area of a circle is A= πr²,  so

½πr² = the perimeter of the semicircle

The area of the window is

(2) A = ½πr² + 2rh

Substitute (1) into (2).

    A = ½πr² + 2r[12.5 - (π/2 +1)r] = ½πr² + 25r - (π +2)r²

    A = 25r - (π + 2 - π/2)r²

(3) A =  -(π/2 + 2)r² + 25r

This is the equation for a downward opening parabola.

One way to find the vertex is to set the first derivative equal to zero.

dA/dr = -2(π/2 + 2)r + 25 = 0

               -(π    + 4)r  + 25 = 0

               -(π     + 4)r        = -25

                                     r = 25/(π + 4)

(4)                                 r ≈ 3.50 ft

The maximum area occurs when r = 3.50 ft.  

Substitute (4) into (1).

h = 12.5 - (π/2 +1)(3.50) = 12.5 - (2.571× 3.50) = 12.5 - 9.00 = 3.50  

(4) h = 3.50 ft

Substitute (4) into (2)

A =  1.571(3.50)² + 2×3.50×3.50 = 19.25 + 24.50

A = 43.75 ft²

The area of the largest possible Norman window with a perimeter of 25 ft is 43.75 ft².

The maximum area of a Norman window with a given perimeter of 25 feet can be found by creating an equation for the area, taking its derivative, setting it equal to zero and solving for the window's dimensions. This involves calculus, namely the method for optimization problems.

The problem involves maximizing the area of a Norman window given a certain perimeter. The Norman window is composed of a rectangle and a semicircle, where the diameter of the semicircle equals the width of the rectangle. First, let's denote the width of the rectangle or the diameter of the semicircle as x. The radius of the semicircle will then be x/2. The height of the rectangle can be represented as 25 - x (since the perimeter of the window should equal 25 feet).

The area of a rectangle is height multiplied by width. The area of a semicircle is (1/2)πr2. So to find the area A of the Norman window, we add the area of the rectangle and the semicircle: A = x(25-x) + (1/2)π*(x/2)2.

To find the maximum area, we need to take the derivative of A with respect to x, set it equal to zero, and solve for x. We find x approximates to around 7.64 feet (after using calculus concepts). Then substitute x = 7.64 into the area function A and solve for A, which gives us the maximum area of the Norman window.

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A kite's symmetrical structure typically forms isosceles triangles due to equal side lengths. Asymmetrical kites generate scalene triangles with varying side lengths, influencing triangle types and angles within based on side intersections.

A kite, with its distinct shape formed by two pairs of adjacent congruent sides, generates triangles within. These triangles can exhibit various properties based on the kite's symmetry. If the kite is symmetrical, the triangles formed tend to be isosceles due to the equal side lengths.

However, asymmetrical kites can yield scalene triangles with sides of varying lengths. The relationship between the kite's structure and the triangle types arises from the lengths and intersections of its sides.

Symmetry tends to create similar or congruent triangles, while asymmetry leads to triangles with differing side lengths. Consequently, the angles within these triangles vary based on the intersection of the kite's sides, resulting in a mix of acute, obtuse, or right angles.

complete the question

What are the possible types of triangles formed within a kite, and how do their properties relate to the structure of the kite? Discuss the potential combinations of isosceles, equilateral, and scalene triangles within a kite, considering the lengths of the sides and the angles formed by the kite's structure."

Answer:B:There is no overlap between the two distributions hope this helps

Answer: There is no overlap between the two distributions

Answer:

D, 60.

Step-by-step explanation:

Well first of all, 30, 20, or 40 isn't even on the graph in the first place, and since the garage opens at 8, and it was 8 exactly and there were 60 cars parked, that means there was 60 parked over night. hope i helped!!

The number of cars parked overnight will be 180.

Option D is the correct answer.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

From the graph,

We have the following coordinates:

(10, 80), (20, 100), (30, 120), (40, 140), (50, 160), and (60, 180)

This means,

(10, 80)

After 10 minutes Past 8 am, the number of cars is 80.

Now,

The number of cars parked overnight will be 180.

From the graph, we have the highest coordinates as (60, 180).

Thus,

The number of cars parked overnight will be 180.

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Answer:

  y = -4

Step-by-step explanation:

Once you recognize the line as being horizontal, you know its equation will be ...

  y = (some constant)

The value of the constant will correspond to the y-coordinate of the points the line goes through. It will also be the value of the y-intercept. Here, that value is -4, so the equation is ...

  y = -4

Answer:

y= -4 since it is on the x-axis but does not have any x coordinates

Answer:

see explanation

Step-by-step explanation:

If (x + 2) is a factor then x = - 2 is a root and p(- 2) = 0

p(- 2) = -4[tex](-2)^{4}[/tex] + 6(- 2)³ + 8(- 2)² + 2(- 2) - 1

         = - 64 - 48 + 32 - 4 - 1 = - 85

Hence remainder R = - 85

Since p(- 2) ≠ 0 then (x + 2) is not a factor of p(x)

Answer:

1) x² + y² - 4x + 12y - 20 = 0 ⇒ (x - 2)² + (y + 6)² = 60

2) x² + y² + 6x - 8y - 10 = 0 ⇒ No choice

3) 3x² + 3y² + 12x + 18y - 15 = 0 ⇒ (x + 2)² + (y + 3)² = 18

4) 5x² + 5y² - 10x + 20y - 30 = 0 ⇒ No choice

5) 2x² + 2y² - 24x - 16y - 8 = 0 ⇒ (x - 6)² + (y - 4)² = 56

6) x² + y² + 2x - 6y - 9 = 0 ⇒ (x + 1)² + (y - 6)² = 46

Step-by-step explanation:

- The general form of the equation of the circle is:

* x² + y² + Dx + Ey + F = 0

 where D , E and F are constant

- The standard form of the equation of the circle is:

* (x - h)² + (y - k)² = r²

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

- To chose the circle equations in general form with their

  corresponding equations in standard form lets do that

1) x² + y² - 4x + 12y - 20 = 0

- we will start to find h and k

∵ h = -coefficient x ÷ 2 coefficient x²

∴ h = -(-4)/2(1) = 2

∵ k = -coefficient y ÷ 2 coefficient y²

∴ k = -(12)/2(1) = -6

∵ r² = h² + k² - F

- where F is the numerical term of the general form

∴ r² = (2)² + (-6)² - (-20) = 4 + 36 + 20 = 60

∴ The equation of the circle in standard form is:

* (x - h)² + (y + k)² = r²

∴ (x - 2)² + (y + 6)² = 60 ⇒ x² + y² - 4x + 12y - 20 = 0

2) x² + y² + 6x - 8y - 10 = 0

- we will start to find h and k

∵ h = -coefficient x ÷ 2 coefficient x²

∴ h = -(6)/2(1) = -3

∵ k = -coefficient y ÷ 2 coefficient y²

∴ k = -(-8)/2(1) = 4

∵ r² = h² + k² - F

- where F is the numerical term of the general form

∴ r² = (-3)² + (4)² - (-10) = 9 + 16 + 10 = 35

∴ The equation of the circle in standard form is:

* (x - h)² + (y + k)² = r²

∴ (x + 3)² + (y - 4)² = 35 ⇒ there is no choice

3) 3x² + 3y² + 12x + 18y - 15 = 0

- we will start to find h and k

∵ h = -coefficient x ÷ 2 coefficient x²

∴ h = -(12)/2(3) = -2

∵ k = -coefficient y ÷ 2 coefficient y²

∴ k = -(18)/2(3) = -3

∵ r² = h² + k² - F

- where F is the numerical term of the general form

∴ r² = (-2)² + (-3)² - (-15/3) = 4 + 9 + 5 = 18

- We divide F by 3 because the coefficient of x² and y²

∴ The equation of the circle in standard form is:

* (x - h)² + (y + k)² = r²

∴ (x + 2)² + (y + 3)² = 18 ⇒ 3x² + 3y² + 12x + 18y - 15 = 0

4) 5x² + 5y² - 10x + 20y - 30 = 0

- we will start to find h and k

∵ h = -coefficient x ÷ 2 coefficient x²

∴ h = -(-10)/2(5) = 1

∵ k = -coefficient y ÷ 2 coefficient y²

∴ k = -(20)/2(5) = -2

∵ r² = h² + k² - F

- where F is the numerical term of the general form

∴ r² = (1)² + (-2)² - (-30/5) = 1 + 4 + 6 = 11

- We divide F by 5 because the coefficient of x² and y²

∴ The equation of the circle in standard form is:

* (x - h)² + (y + k)² = r²

∴ (x - 1)² + (y + 2)² = 11 ⇒ there is no choice

5) 2x² + 2y² - 24x - 16y - 8 = 0

- we will start to find h and k

∵ h = -coefficient x ÷ 2 coefficient x²

∴ h = -(-24)/2(2) = 6

∵ k = -coefficient y ÷ 2 coefficient y²

∴ k = -(-16)/2(2) = 4

∵ r² = h² + k² - F

- where F is the numerical term of the general form

∴ r² = (6)² + (4)² - (-8/2) = 36 + 16 + 4 = 56

- We divide F by 2 because the coefficient of x² and y²

∴ The equation of the circle in standard form is:

* (x - h)² + (y + k)² = r²

∴ (x - 6)² + (y - 4)² = 56 ⇒ 2x² + 2y² - 24x - 16y - 8 = 0

6) x² + y² + 2x - 12y - 9 = 0

- we will start to find h and k

∵ h = -coefficient x ÷ 2 coefficient x²

∴ h = -(2)/2(1) = -1

∵ k = -coefficient y ÷ 2 coefficient y²

∴ k = -(-12)/2(1) = 6

∵ r² = h² + k² - F

- where F is the numerical term of the general form

∴ r² = (-1)² + (6)² - (-9) = 1 + 36 + 9 = 46

∴ The equation of the circle in standard form is:

* (x - h)² + (y + k)² = r²

∴ (x + 1)² + (y - 6)² = 46 ⇒ x² + y² + 2x - 6y - 9 = 0

Answer and Step-by-step explanation:

Answer:

# x² + y² - 4x + 12y - 20 = 0 ⇒ (x - 2)² + (y + 6)² = 60

# 3x² + 3y² + 12x + 18y - 15 = 0 ⇒ (x + 2)² + (y + 3)² = 18

# 2x² + 2y² - 24x - 16y - 8 = 0 ⇒ (x - 6)² + (y - 4)² = 56

# x² + y² + 2x - 12y - 9 = 0 ⇒ (x + 1)² + (y - 6)² = 46

Step-by-step explanation:

* Lets study the problem to solve it

- Use the terms of x and y in the general form to find the standard form

∵ x² + y² - 4x + 12y - 20 = 0

- Use the term x term

∵ -4x ÷ 2 = -2x ⇒ x × -2

∴ (x - 2)²

- Use the term y term

∵ 12y ÷ 2 = 6y ⇒ y × 6

∴ (y + 6)²

∵ (-2)² + (6)² + 20 = 4 + 36 + 20 = 60

∴ x² + y² - 4x + 12y - 20 = 0 ⇒ (x - 2)² + (y + 6)² = 60

∵ x² + y² + 6x - 8y + 10 = 0

- Use the term x term

∵ 6x ÷ 2 = 3x ⇒ x × 3

∴ (x + 3)²

- Use the term y term

∵ -8y ÷ 2 = -4y ⇒ y × -4

∴ (y - 4)²

∵ (3)² + (-4)² - 10 = 9 + 16 - 10 = 5

∴ x² + y² + 6x - 8y + 10 = 0 ⇒ (x + 3)² + (y - 4)² = 5 ⇒ not in answer

∵ 3x² + 3y² + 12x + 18y - 15 = 0 ⇒ divide all terms by 3

∴ x² + y² + 4x + 6y - 5 = 0

- Use the term x term

∵ 4x ÷ 2 = 2x ⇒ x × 2

∴ (x + 2)²

- Use the term y term

∵ 6y ÷ 2 = 3y ⇒ y × 3

∴ (y + 3)²

∵ (2)² + (3)² + 5 = 4 + 9 + 5 = 18

∴ 3x² + 3y² + 12x + 18y - 15 = 0 ⇒ (x + 2)² + (y + 3)² = 18

∵ 5x² + 5y² - 10x + 20y - 30 = 0 ⇒ divide both sides by 5

∴ x² + y² - 2x + 4y - 6 = 0

- Use the term x term

∵ -2x ÷ 2 = -x ⇒ x × -1

∴ (x - 1)²

- Use the term y term

∵ 4y ÷ 2 = 2y ⇒ y × 2

∴ (y + 2)²

∵ (-1)² + (2)² + 6 = 1 + 4 + 6 = 11

∴ 5x² + 5y² - 10x + 20y - 30 = 0 ⇒ (x - 1)² + (y + 2)² = 11 ⇒ not in answer

∵ 2x² + 2y² - 24x - 16y - 8 = 0 ⇒ divide both sides by 2

∴ x² + y² - 12x - 8y - 4 = 0

- Use the term x term

∵ -12x ÷ 2 = -6x ⇒ x × -6

∴ (x - 6)²

- Use the term y term

∵ -8y ÷ 2 = -4y ⇒ y × -4

∴ (y - 4)²

∵ (-6)² + (-4)² + 4 = 36 + 16 + 4 = 56

∴ 2x² + 2y² - 24x - 16y - 8 = 0 ⇒ (x - 6)² + (y - 4)² = 56

∵ x² + y² + 2x - 12y - 9 = 0

- Use the term x term

∵ 2x ÷ 2 = x ⇒ x × 1

∴ (x + 1)²

- Use the term y term

∵ -12y ÷ 2 = -6y ⇒ y × -6

∴ (y - 6)²

∵ (1)² + (-6)² + 9 = 1 + 36 + 9 = 46

∴ x² + y² + 2x - 12y - 9 = 0 ⇒ (x + 1)² + (y - 6)² = 46

The dress will cost $50.40 after a 20% discount from the original price of $63. You calculate this by finding 20% of $63, which is $12.60, and subtracting it from $63.

When a store is having a 20% off sale, it means that the original price of the item is reduced by 20%. In this case, you need to calculate 20% of $63, which is the original price of the dress.

To find 20% of $63, you multiply 63 by 20/100 (because percent means per hundred). That is: 63 * 0.20 = $12.60.

So the amount of the discount is $12.60. Therefore, you subtract this discount from the original price of the dress to find out the new price: 63 - 12.60 = $50.40.

So, after a 20% off sale, the dress will cost $50.40.

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Answer:

Polynomial expression that represents the area of blanket:

[tex]A(x)=(6x^2+5x-21)cm^2[/tex]

If [tex]x=2[/tex]: [tex]A(2)=13cm^2[/tex]  

Step-by-step explanation:

The area of the rectangle can be calculated with the formula:

[tex]A=lw[/tex]

Being l the lenght of the rectangle and w the width of the rectangle.

In this case, the lenght and the width are represented with:

[tex]l=(3x+7)cm[/tex]

[tex]w=(2x-3)cm[/tex]

Substitute them into  [tex]A=lw[/tex]:

 [tex]A(x)=(3x+7)(2x-3)[/tex]

Then:

Use Distributive property (Remember the Product of powers property: [tex]b^a*b^c=b^{(a+c)}[/tex] ):

[tex]A(x)=(3x+7)(2x-3)\\A(x)=6x^2-9x+14x-21[/tex]

Add like terms:

[tex]A(x)=(6x^2+5x-21)cm^2[/tex] (Simplied form)

Evaluate [tex]x=2[/tex]:

[tex]A(2)=(6(2)^2+5(2)-21)cm^2\\A(2)=(6(4)+10-21)cm^2\\A(2)=(24-11)cm^2\\A(2)=13cm^2[/tex]

Answer:

1 hour and 45 mins

Step-by-step explanation:

As mentioned,

Starting time = 2:30 PM

Ending time = 4:15 PM

The given time is in hours and minutes, to calculate the duration of movie, time should be converted into a same unite minutes.

1 hour = 60 minutes

Therefore,

2:30 = 2 hours and 30 mins = 2*60 + 30 mins = 150 mins

4:15 = 4 hours and 15 mins = 4*60 + 15 mins = 255 mins

The duration = Ending time - Starting time

=> 255 - 150

=> 105 mins

or

60 + 45

1 hour and 45 mins