The payoff table may be huge, and it would be helpful if we could simplify it. One way is to reject dominated or inadmissible actions. These are choices that should not be made because there are other choices that are always better. More accurately, q, is dominated by 2. if, for all j 1, ...,S, Cij is less than or equal to Caj, and there is at least one value of j such that Cij <0. [...]

The total yards gained by Jordan's team is 4.

What is Expression ?

Mathematical statements called expressions must contain a minimum of two terms with either numbers, variables, or both, joined by an operator. The four different types of mathematical operators are addition, subtraction, multiplication, and division. For instance, the expression x + y is an expression where x and y are terms with an addition operator between them. Mathematical expressions can be divided into two categories: algebraic expressions, which include both numbers and variables, and numerical expressions, which solely contain numbers.

On first day, Jordan's football team gained 12 yards.

On second day, Jordan's football team lost 8 yards.

So, The total yards(net) would be :

= total yards gained by team - total yards lost by team

=  12 - 8

= 4 yards.

Here, total yards gained by team is the first expression while total yards lost by team is the second expression.

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Answer:

Step-by-step explanation: First lets multiply the numerators, so 3*3 is 9, then we multiply the denominators, so 4*5 is 20. 9/20 or 0.45 will be your answer.

Area of circle A is 113.04 in²

Area of circle B is 200.96  in²

Area of circle C is 452.16  in²

Area of circle B is 254.34  in²

The number of times that the area of Circle D greater than Circle A is 2.25

A circle is a bounded figure which points from its center to its circumference is equidistant.

Area of a circle = πr²

Where :

π = pi = 3.14

R = radius

here, we have,

Area of circle A = 3.14 x 6² = 113.04 in²

Area of circle B = 3.14 x (6 + 2)² = 200.96  in²

Area of circle C = 3.14 x (8 + 4)² = 452.16  in²

Area of circle B = 3.14 x (12 - 3)² = 254.34  in²

Number of time that is the area of Circle D greater than Circle A = 254.34  in² / 113.04 in² = 2.25

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Complete question:

The radius of Circle A is 6 in. The radius of Circle B is 2 in. greater than the radius of Circle A. The radius of Circle C is 4 in. greater than the radius of Circle B. The radius of Circle D is 3 in. less than the radius of Circle C. What is the area of each​ circle? How many times greater than the area of Circle A is the area of Circle D​?

To add or subtract the given expressions, we need to combine like terms. Like terms are terms that have the same variable and exponent.

Step 1: Combine like terms for a^(2):
6.9a^(2) + 0 = 6.9a^(2)
Step 2: Combine like terms for b^(2):
-2.3b^(2) + (-2.5b^(2)) = -4.8b^(2)
Step 3: Combine like terms for ab:
2ab + 0 = 2ab
Step 4: Combine like terms for a:
0 + 3.1a = 3.1a
Step 5: Combine like terms for b:
0 + b = b
Step 6: Put all the combined terms together:
6.9a^(2) + (-4.8b^(2)) + 2ab + 3.1a + b
Step 7: Simplify the expression:
6.9a^(2) - 4.8b^(2) + 2ab + 3.1a + b

So the final answer is 6.9a^(2) - 4.8b^(2) + 2ab + 3.1a + b.

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Answer: 12 [tex]m^{3}[/tex]

Step-by-step explanation:

Volume = length x width x height

Volume = 4 m x 1.5 m x 2 m

Volume = 12 cubic meters

The answer of function can be written as [tex]y=(x-3)^4(x+1)^2[/tex].

A 6th degree polynomial with a root of multiplicity 4 at x=3, and a root of multiplicity 2 at x=-1, can be written as the function[tex]y=(x-3)^4(x+1)^2[/tex].

This is because the root of multiplicity 4 at x=3 means that (x-3) is a factor of the polynomial 4 times, and the root of multiplicity 2 at x=-1 means that (x+1) is a factor of the polynomial 2 times.

Therefore, the values of a, b, and c in the function y=(x-3)^(a)(x-b)^(c) are:

a = 4, because the root of multiplicity 4 at x=3 means that (x-3) is a factor of the polynomial 4 times.

b = -1, because the root of multiplicity 2 at x=-1 means that (x+1) is a factor of the polynomial 2 times.

c = 2, because the root of multiplicity 2 at x=-1 means that (x+1) is a factor of the polynomial 2 times.

So, the function can be written as [tex]y=(x-3)^4(x+1)^2[/tex].

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The quotient and remainder using (x^(5)-x^(4)+9x^(3)-9x^(2)+9x-12)/(x-1) are 1x^(4)-2x^(3)+11x^(2)-20x+29 and -41, respectively.

To find the quotient and remainder using (x^(5)-x^(4)+9x^(3)-9x^(2)+9x-12)/(x-1), we will use synthetic division.

Write down the coefficients of the dividend polynomial in descending order of the exponent of x. In this case, the coefficients are 1, -1, 9, -9, 9, -12.

Write down the constant term of the divisor polynomial. In this case, the constant term is -1.

Bring down the first coefficient of the dividend polynomial.

Multiply the constant term of the divisor polynomial by the first coefficient of the dividend polynomial and write the result under the second coefficient of the dividend polynomial.

Add the second coefficient of the dividend polynomial and the result from step 4.

Repeat steps 4 and 5 until all the coefficients of the dividend polynomial have been used.

The last result from step 5 is the remainder. The other results are the coefficients of the quotient polynomial.

The synthetic division is shown below:

-1 | 1 -1 9 -9 9 -12
 | -1 2 -11 20 -29
 ---------------------
   1 -2 11 -20 29 -41
 
The quotient is 1x^(4)-2x^(3)+11x^(2)-20x+29 and the remainder is -41.

Therefore, the quotient and remainder using (x^(5)-x^(4)+9x^(3)-9x^(2)+9x-12)/(x-1) are 1x^(4)-2x^(3)+11x^(2)-20x+29 and -41, respectively.

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Answer: A) -4.2, B) -3.8 C) -9/2 (-4.5)

Step-by-step explanation: Think of a number line, you have 0-10, and -10-0, as you keep going down the number like, the numbers become less and less, just like how -4.2 is less than -3.5, because it is further to the left of the number line, meaning it is less than. Hope this helps!

For the trapezoid given the value for x is obtained as 6.

A polygon with only one set of parallel sides is called a trapezoid. The parallel bases of a trapezoid are another name for these parallel sides. Trapezoids have two additional sides that are not parallel and are referred to as their legs.

The value for parallel sides of a trapezoid is given as 3x + 2 and 2x - 2.

A line segment divides the trapezoid in half.

The line segment dividing the trapezoid in half measures 15 units.

We know that the line segment dividing the trapezoid in half is also the average of the parallel sides.

So we can set up an equation -

(3x + 2 + 2x - 2) / 2 = 15

Simplifying the left side, we get -

(5x) / 2 = 15

Multiplying both sides by 2/5, we get -

x = 6

Therefore, the value of x is 6.

We can check that this value works by plugging it into the expressions for the parallel sides -

3x + 2 = 20

2x - 2 = 10

So the lengths of the parallel sides are 20 and 10.

Therefore, the average of these is indeed 15, and so the line segment dividing the trapezoid in half has length 15, as given.

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Answer: A. Segment CD only

Step-by-step explanation:

Perpendicular lines form 90 degree angles. The only segment that creates a 90 degree angle is CD. And we know this due to the little box that represents 90 degrees.

1. The probability of getting a z-score of 0.189 or less is 0.5753.  

2. The probability of getting a z-score of 1.13 or less is 0.8708.

3. The probability of getting a z-score of 3.02 or less is 0.9982.

Normally distributed data refers to data that follows a normal distribution, also known as a Gaussian distribution or bell curve.

In a normal distribution, the data is symmetric around the mean and the majority of the data is clustered around the mean with decreasing density as the data moves further away from the mean.

Here we have

The mean price for liquid crystal display (LCD) computer monitors is $ 170  and the standard deviation is $ 53.  

Find the z-score associated with $ 180 using the formula:

z = (x - μ) / σ

where x is the value we need to find the probability, μ is the mean, and σ is the standard deviation.

z = (180 - 170) / 53

z = 0.189

Hence, using a standard normal distribution table or calculator, we can find that the probability of getting a z-score of 0.189 or less is 0.5753.  

To find the probability that the mean cost of 9 randomly selected LCD computer monitors is less than $ 180, find the standard deviation σ/√n.

The standard deviation of the sample means is σ/√n = $53/√9 = $17.67.

Now we need to find the z-score associated with $ 180 using the formula:

z = (x - μ) / σ/√n

where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

z = (180 - 170) / (53 / √9)

z = 1.13

Hence, using a standard normal distribution table or calculator, we can find that the probability of getting a z-score of 1.13 or less is 0.8708.  

To find the probability that the mean cost of 36 randomly selected LCD computer monitors is less than $ 180, we can use the same formula as in part 2, with n = 36:

z = (x - μ) / σ/√n

z = (180 - 170) / (53 / √36)

z = 3.02

Hence, using a standard normal distribution table or calculator, we can find that the probability of getting a z-score of 3.02 or less is 0.9982.

Therefore,

1. The probability of getting a z-score of 0.189 or less is 0.5753.  

2. The probability of getting a z-score of 1.13 or less is 0.8708.

3. The probability of getting a z-score of 3.02 or less is 0.9982.

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The missing side lengths are computed below

Triangle 22

The side length x can be calculated using

sin(30) = 9/x

So, we have

x = 9/sin(30)

Evaluate

x = 18

For length y, we have

y = √(18² - 9²)

Evaluate

y = 9√3

Triangle 23

The side length y can be calculated using

sin(30) = y/√3

So, we have

y = √3 * sin(30)

Evaluate

y = 1/2√3

For length x, we have

x = √(√3² + (1/2√3)²)

Evaluate

x = √(15/4)

x = 1/2√15

Triangle 24

The side length y can be calculated using

cos(60) = y/2√3

So, we have

y = 2√3 * cos(60)

y = √3

For x, we have

x = √((2√3)² - (√3)²)

x = √9

x = 3

Triangle 25

The side length x can be calculated using

cos(60) = 5/x

So, we have

x = 5/cos(60)

x = 10

For y, we have

y = √(10² - 5²)

y = 5√3

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The linear equation in the given graph is.

y = 40x

We know that the general linear equation is:

y = a*x + b

Where a is the slope and b is the y-intercept, these two values are constants, and the variables are x and y.

First, notice that the line intercepts the y-axis at the point (0, 0), then b = 0.

So we can write:

y = a*x

Also notice that the line passes through the point (1, 40), then:

40 = a*1

40/1 = a

The linear equation is.

y = 40x

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The total number of hours Eric worked is 7 3/4 hours.

What is addition in mathematics?

Addition is one of the four basic arithmetic operations in mathematics, along with subtraction, multiplication, and division. Addition is the process of combining two or more quantities or numbers to find their sum, or total. The symbol used to represent addition is the plus sign (+).

For example, if we want to find the sum of 3 and 4, we would write:

3 + 4 = 7

The number 3 and the number 4 are called addends, and the result of the addition operation is called the sum. Addition can involve whole numbers, fractions, decimals, and even negative numbers.

Addition has many applications in mathematics, science, and everyday life. It is used to calculate simple arithmetic problems, such as adding up the cost of items in a shopping cart, as well as more complex calculations, such as adding up the values in a data set or solving equations in algebra.

To find the total number of hours Eric worked in the neighborhood garden, we need to add the number of hours he worked on Monday and Wednesday.

Eric worked 3 1/2 hours on Monday, which can also be written as 7/2 hours.

Eric worked 4 1/4 hours on Wednesday, which can also be written as 17/4 hours.

To add these two amounts, we need to find a common denominator. The smallest number that both 2 and 4 divide into is 4. So we can convert 7/2 to 14/4 by multiplying the numerator and denominator by 2:

7/2 = 14/4

Now we can add the two fractions:

14/4 + 17/4 = 31/4

This is the total number of hours Eric worked in the neighborhood garden, in fraction form. To write it as a mixed number, we can divide the numerator by the denominator:

31 ÷ 4 = 7 with a remainder of 3

So the total number of hours Eric worked is 7 3/4 hours.

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heres the answer:

8x10=80

2x1=2/100= 0.02

9x1=9/1000= 0.002

0.002+0.02+80=

80.002!!

Renee's monthly payment will be $504.46. The closest answer choice is d. $504.46.

To calculate Renee's monthly payment, we need to first determine the total cost of the new car after taxes and fees and subtract the trade-in value of her old car. Then, we can use the loan information to calculate the monthly payment.

Total cost of the new car:

List price: $19,675

Vehicle registration fees: $1,420

Documentation fees: $85

Sales tax: 8.92% of ($19,675 + $1,420 + $85) = $1,894.51

Total cost = $19,675 + $1,420 + $85 + $1,894.51 = $22,074.51

Trade-in value of the old car:

2002 Buick LeSabre in good condition: $3,374 (from the table)

85% of trade-in value: 0.85 x $3,374 = $2,867.90

Net cost of the new car:

$22,074.51 - $2,867.90 = $19,206.61

To calculate the monthly payment, we can use the formula for the present value of an annuity:

PV = PMT x (1 - (1 + r)^(-n)) / r

where PV is the present value of the loan, PMT is the monthly payment, r is the monthly interest rate (11.34%/12), and n is the number of payments (4 years x 12 months/year = 48).

Solving for PMT:

PMT = PV x r / (1 - (1 + r)^(-n))

PMT = $19,206.61 x 0.1134/12 / (1 - (1 + 0.1134/12)^(-48))

PMT = $504.46

Therefore, Renee's monthly payment will be $504.46. The closest answer choice is d. $504.46.

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Therefore, the expected typing speed of a student who is 17 years old is 94 words per minute.

It functions by dividing distance by speed. The time can also be calculated by dividing the distance traveled by the speed. You can determine the third input if you know the first two. For instance, we may get the speed as 120 x 2 = 60 miles per hour if a car travels 120 miles in two hours.

The equation of the line of best fit is:

y = -1.4x + 117.8

where x is the age in years and y is the typing speed in words per minute. To find the expected typing speed of a 17-year-old student, we can substitute x = 17 into the equation:

y = -1.4(17) + 117.8

y = -23.8 + 117.8

y = 94

Therefore, the expected typing speed of a student who is 17 years old is 94 words per minute.

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The direction the plane flew is 14.6 degrees North of East.

So, the final answer is:

Distance = 342 miles

Direction = 14.6 degrees North of East

The distance the plane flew can be found using the Pythagorean Theorem, which states that for a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b): c^2 = a^2 + b^2. In this case, the distance east (331 miles) is one side of the triangle and the distance north (86 miles) is the other side.

So, we can plug in the values and solve for c:

c^2 = 331^2 + 86^2

c^2 = 109561 + 7396

c^2 = 116957

c = √116957

c = 342 miles

Therefore, the distance the plane flew is 342 miles.

To find the direction, we can use trigonometry. The direction is the angle between the east-west line and the line connecting the starting point and the landing point. We can use the tangent function to find this angle:

tan θ = opposite/adjacent

tan θ = 86/331

θ = tan^-1(86/331)

θ = 14.6 degrees

Therefore, the direction the plane flew is 14.6 degrees North of East.

So, the final answer is:

Distance = 342 miles

Direction = 14.6 degrees North of East

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Answer:

x3

Step-by-step explanation:

To make equivalent rational expressions, we need to multiply the numerator and denominator of the left-hand side of the equation by the same value.

In this case, we can multiply both the numerator and denominator by (5x^(3))/(5x^(3)) to get the equivalent expression on the right-hand side. (3)/(x^(6)) * (5x^(3))/(5x^(3)) = (15x^(3))/(5x^(9))

Therefore, the value that we need to fill in the blank is (15x^(3)). So the equivalent rational expression is:

(3)/(x^(6))=(15x^(3))/(5x^(9))

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The answer of -x+3y=20; 7y=x will be x = -[tex]\frac{7}{2\\}[/tex] and y = - [tex]\frac{1}{2}[/tex].

Given,

-x+3y=20 .... (1)

7y=x .... (2)

By using the method of substitution.

We will use equation (2) as

7y=x

=>y= [tex]\frac{x}{7}[/tex] ....(3)

Putting equation (3) in (1)

We have, -x+3([tex]\frac{x}{7}[/tex])=20

Taking L.CM.

[tex]\frac{-7x+3x}{7}[/tex] = 20

-7x +3x = 140

-4x = 140

0r, x = - [tex]\frac{140}{4}[/tex]

x = - [tex]\frac{7}{2}[/tex]

Now by putting value of x in equation (2),  we get

7y = x

7y = -[tex]\frac{7}{2}[/tex]

0r, y = -[tex]\frac{1}{2}[/tex]

Thus, x = -[tex]\frac{7}{2\\}[/tex] and y = - [tex]\frac{1}{2}[/tex]

This code use to measures may be equivalent after some transformation.

<!DOCTYPE html>

<html lang="en">

<head>

<title>Cat in night</title>

</head>

<body>

<div id="wrapper">

<section class="sky">

<div class="moon"></div>

<ul>

<li class="cloud"></li>

<li class="cloud"></li>

<li class="cloud"></li>

</ul>

</section>

<section class="wall">

<section class="cat">

<div class="cat-head">

<div class="eyes">

<div class="eye"></div>

<div class="eye"></div>

</div>

</div>

<div class="cat-body">

<div class="tail"></div>

</div>

</section>

</section>

</div>

<style>

.sky {

height: 300px;

background: radial-gradient(#112A71, #000A31);

overflow: hidden;

position: relative; }

.sky .moon {

width: 80px;

height: 80px;

border-radius: 50%;

background-color: #FEFF79;

-webkit-box-shadow: 0 0 150px #FEFF79, inset 0 1px 20px rgba(0, 0, 0, 0.3);

box-shadow: 0 0 150px #FEFF79, inset 0 1px 20px rgba(0, 0, 0, 0.3);

position: absolute;

top: 30px;

right: 100px; }

.sky .cloud {

width: 80px;

height: 30px;

background-color: #8D8D8D;

border-radius: 50px;

-webkit-box-shadow: inset 0 -1px 10px rgba(0, 0, 0, 0.3);

box-shadow: inset 0 -1px 10px rgba(0, 0, 0, 0.3);

position: relative;

top: 60px;

left: 30px;

-webkit-animation: shift 100s infinite linear;

animation: shift 100s infinite linear; }

.sky .cloud:nth-child(2) {

-webkit-transform: scale(-1.5, 1.3);

transform: scale(-1.5, 1.3);

top: 100px;

left: 250px;

-webkit-animation-duration: 40s;

animation-duration: 40s; }

.sky .cloud:last-child {

top: 150px;

left: 100px;

Transformation refers to a significant change or shift in an entity, be it a person, organization, system, or society, towards a desired state or outcome. It is a process of evolving, improving, or adapting in response to internal or external pressures or opportunities. Transformation involves a fundamental shift in the way things are done, the mindset, values, and behavior of the entity undergoing the change.

Transformation can occur in various contexts, such as business, technology, education, social and political systems, and personal development. It often requires a clear vision, strategic planning, and effective execution to achieve the desired outcome. The process can be challenging and requires significant effort and resources, but the benefits of transformation can be substantial, leading to increased efficiency, innovation, growth, and social impact.

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Complete Question: -

It is important to define or select similarity measures in data analysis. However, there is no commonly-accepted subjective similarity measure. Results can vary depending on the similarity measures used. Nonetheless, seemingly different similarity measures may be equivalent after some transformation. Suppose we have the following two-dimensional data set:

A1

A2

X1

1.5

1.7

X2

2

1.9

X3

1.6

1.8

X4

1.2

1.5

X5

1.5

1.0

Consider the data as two-dimensional data points. Given a new data point, x = (1.4, 1.6) as a query, rank the database points based on similarity with the query using Euclidean distance, Manhattan distance, supremum distance, and cosine similarity.

The payment (future value), to the nearest rand, which should be made at the end of the seventh year in order to liquidate the debt, is​ R9,338.80.

The future payment to be made at the end of the seventh year is determined by computing the future values in two stages. The first stage computes the future value before the payment at the end of the first year.  The second stage computes the future value for six years.  

here, we know,

The future value is computed by compounding the present value at an interest rate.

Current debt = R6,421,00

Compound interest rate = 11% per year

Compounding period = Quarterly

Future Value in 1 Year:

N (# of periods) = 4 quarters (1 year x 4)

I/Y (Interest per year) = 11%

PV (Present Value) = R6,421.00

PMT (Periodic Payment) = R0

Results:

Future Value (FV) = R7,156.98

Total Interest = R735.98

Future Value (FV) = R7,156.98

Payment in one year's time = R2,287.00

Balance = R4,869.98

Future Value at the end of the 7th Year:

N (# of periods) = 24 quarters (6 years x 4)

I/Y (Interest per year) = 11%

PV (Present Value) = R4,869.98

PMT (Periodic Payment) = R0

Results:

Future Value (FV) = R9,338.80

Total Interest = R4,468.82

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Hence, the amount of glass needed in square feet is 2 × 14.4 = 28.8 sq feet.

A square in geometry is a two-dimensional plane figure with four equal sides and four equal but 90 degree angles. The characteristics of a rectangle and a square are somewhat comparable, but only the opposite sides of a rectangle are equal. So, only if all four of a rectangle's sides are the same length can it be said to be a square.

Only the window of a new house was advertised.

a kite with a height of 3.2 and 4 feet, a width of 2 feet, and a width of 2 feet.

Two panes make up the window.

To determine: How so many sq ft of glass is needed for the window,

Triangle area equals (1/2) base x height.

= (1/2) × 2 × 3.2 + (1/2) ×2 × 3.2 + (1/2) × 2 × 4 + (1/2) × 2 × 4

=2 × 3.2 + 2 × 4

= 2 × (3.2 + 4)

= 2 × 7.2

= 14.4 sq feet

Double-paned glass is a given.

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Answer: stop being a brat

Step-by-step explanation:

The Complete value for the Table is

x               f(x)                   g(x)

1                8                         1.1

5               20                  1.61051

10              35                  2.5937

20             65                   6.7274

The function f(x) grows with faster rate.

A function is an expression, rule, or law in mathematics that describes a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given:

We have f(x) = 3x+ 5 and g(x) = [tex](1.1)^x[/tex]

The Complete value for the Table is

x                   f(x)                                           g(x)

1               3x+ 5 = 3(1) +5= 8                         1.1

5              3x+ 5 = 3(5) +5= 20                      [tex](1.1)^5[/tex]= 1.61051

10             3x+ 5 = 3(10) +5= 35                    [tex](1.1)^{10}[/tex]= 2.5937

20            3x+ 5 = 3(20) +5= 65                    [tex](1.1)^{20}[/tex]= 6.7274

So, the function f(x) grows with faster rate.

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To find the image for each given value of k, we need to multiply the original volume (100 cubic units) by the scale factor (k).

Volume is a measure of the amount of space occupied by an object or substance. It is expressed as a numerical value, usually in cubic units, such as milliliters (mL) or cubic centimeters (cc). It is also used to measure the capacity of a container, such as a bottle, or a tank.

Dilation is a transformation that changes the size of a shape. When a solid is dilated by a scale factor of k, the new solid will be k times larger than the original solid. For example, if a solid has a volume of 100 cubic units and is dilated by a scale factor of 2, the image solid will have a volume of 200 cubic units (2 x 100).

To find the image for each given value of k, we need to multiply the original volume of the solid (100 cubic units) by the scale factor (k). We can use the equation V = kV0, where V0 is the original volume and V is the new volume, to calculate the new volume of the solid.

For example, if k = 3, the new volume will be 3 x 100 = 300 cubic units. If k = 4, the new volume will be 4 x 100 = 400 cubic units. In general, for any given value of k, the new volume will be k times the original volume.

To summarize, when a solid with a volume of 100 cubic units is dilated by a scale factor of k, the image solid will have a volume of k times the original volume (V = kV0). Therefore, to find the image for each given value of k, we need to multiply the original volume (100 cubic units) by the scale factor (k).

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Answer:

x = -8, 8

Step-by-step explanation:

The student did make an error. When factoring [tex]x^2-64[/tex], they used incorrect factors. Using FOIL method, the students factored equation would become [tex]x^2 +32x-32x-1024 = x^2-1024[/tex], which is not [tex]x^2-64[/tex].

Instead, the factors 8 and -8 should be used.

[tex]x^{2} +5x-60=5x+4\\x^2 +5x - 64=5x\\x^2-64=0\\(x+8)(x-8)=0\\x=-8, 8[/tex]

Answer: x = ±8

Step-by-step explanation:

The given equation is:

x² + 5x - 60 = 5x + 4

The student's work shows that they simplified the equation correctly to:

x² - 64 = 0

However, their factorization of the resulting equation is incorrect. Factoring x² - 64 using difference of squares we get:

(x + 8)(x - 8) = 0

So, the solutions for x are x = -8 and x = 8. The student's solutions of x = ±32 are incorrect.

Therefore, the student made an error in factoring the equation, and the correct solutions for x are x = -8 and x = 8.

Given - two tangent lines are drawn from the point B

To find - the value of BC

Explanation - when tangent lines are drawn for outside of the circle then the length of line formed is equal

We get

AB=BC

[tex]x+3 =3x-1\\x-3x=-1-3\\-2x=-4\\x=2[/tex]

BC= [tex]3x-1 =3(2)-1=6-1=5[/tex]

The length of BC = 5

Final answer - The option A is correct, the length is 5