What is the solution to the inequality x-41 <3?

To find the value of r that makes the statement an identity, we need to set the two sides of the equation equal to each other and solve for r.

First, let's multiply both sides of the equation by (x-10) to eliminate the denominator:

(x^(2)-x-8) = (x-10)(x+9) + r

Next, let's expand the right side of the equation:

x^(2)-x-8 = x^(2) + 9x - 10x - 90 + r

Now, let's rearrange the equation and solve for r:

r = x^(2)-x-8 - x^(2) - 9x + 10x + 90

r = 90

Therefore, the value of r that makes the statement an identity is 90.

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The image of the figure under a dilation with scale factor 3/2 is attached

From the question, we have the following parameters that can be used in our computation:

Center = (0, 0).

Point = (6, 12), (8, 12) and (8, 8)

Scale factor = 3

A dilation with center (0, 0) and scale factor k multiplies the coordinates of a point by k.

So, to find the image of the point under the dilation with scale factor 3/2, we multiply each coordinate by 3/2:

Image = [(6, 12), (8, 12) and (8, 8)] * 3/2

Image = [(9, 18), (12, 18) and (12, 12)]

Hence, the image of the figure is attached

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AB is parallel to DC because they are equal and corresponding sides of similar triangles.

The reflexive property of equality is a basic principle in mathematics that states that any quantity is equal to itself. In other words, if we have a variable, say "a", then a is always equal to a. Similarly, if we have an equation such as 2 + 3 = 5, we can use the reflexive property of equality to say that 5 = 5, since any quantity is equal to itself. The reflexive property is used frequently in mathematical proofs to simplify expressions and make them easier to work with.

AD || BC, AD = CB - Reflexive Property of Equality

Explanation: This reason uses the reflexive property of equality, which states that a quantity is equal to itself. In this case, the reason is stating that the given information is true and using the reflexive property of equality to restate it in a different way.

2 = 3 - If Alternate Interior Angles are Congruent, then Lines are Parallel.

Explanation: This reason uses the angle congruence property that if the alternate interior angles are congruent, then the lines are parallel. This property is used to show that angles ACD and CAB are congruent because they are alternate interior angles.

ACD = CAB - If Lines are Parallel, then Alternate Interior Angles are Equal.

Explanation: This reason uses the angle equality property that if the lines are parallel, then the alternate interior angles are equal. This property is used to show that lines AD and BC are parallel because they are given to be parallel, and therefore the alternate interior angles ACD and CAB are equal.

1 = 4 - SAS (Side-Angle-Side)

Explanation: This reason uses the similarity property that if two triangles have the same side-angle-side, then they are similar. This property is used to show that triangles ABD and CBD are similar because they have the same side AD = CB and the same angles ABD and CBD.

AB || DC - CPCTE (Corresponding Parts of Congruent Triangles are Equal)

This reason uses the CPCTE property that the corresponding parts of congruent triangles are equal. This property is used to show that sides AB and DC are equal because they are corresponding sides of similar triangles ABD and CBD. Therefore, AB is parallel to DC because they are equal and corresponding sides of similar triangles.

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Answer:

0

Step-by-step explanation:

y = 1x + b

-3 = 1(-3) + b

-3 = -3 + b
+3   +3

0 = b

The discussion-based assessment is meant to provide you with an opportunity to reflect on the topics and skills you have learned, as well as identify any areas you may need additional support in.

The conversation should be guided by your instructor, who will ask questions to ensure you understand the material, as well as provide feedback and advice on how to improve your understanding and performance.

At the end of the assessment, you and your instructor should have a clear understanding of your progress and where you need to focus your efforts moving forward.

The instructor should also provide feedback on your performance and suggest strategies for improvement. Additionally, you should have an understanding of the topics you need to work on and the resources available to you to help you improve.

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The complete question is:

Discussion-based Assessment

A student using a computer to study once you have completed the lesson and assignments, please contact your instructor to complete your discussion-based assessment. You and your instructor will discuss what you have learned up to this point in the course to make sure you're ready to move on to the next lesson. What does it mean?

83/17 = 4.88235294118

Answer:

4.88, and 4.9 rounded to the nearest 10th and 5 round to the nearest whole number.

Step-by-step explanation:

The answer to this question is as follows e. Untrue. It is not possible to equation predict how many of the 200 clients will buy roasted turkey as an entrée using the information in the table.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

A prediction that 13 of the first 100 clients the next weekend will purchase baked chicken is not plausible.

b. Untrue. This weekend, 20% of consumers didn't purchase eggplant parmesan,

c. Untrue. Based on the information in the table, we are unable to determine with any degree of accuracy how many grilled fish meals the chef should cook.

d. True. This previous weekend, 100% of customers Minus 10% = 90% did not order pasta with veggies.

e. Untrue. It is not possible to predict how many of the 200 clients will buy roasted turkey as an entrée using the information in the table.

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Using the values given in the table to evaluate each expression, the value of each expression is (a) 5, (b) 8, (c) -7, (d) -3, (e) 1, and (f) 3.

To evaluate the expressions, we need to use the values given in the table for f(x) and g(x). The composition of functions (f∘g)(x) means that we plug the value of g(x) into the function f(x).

a. (f∘g)(1) = f(g(1)) = f(0) = 5

b. (f∘g)(2) = f(g(2)) = f(-3) = 8

c. (g∘f)(2) = g(f(2)) = g(3) = -7

d. (g∘f)(3) = g(f(3)) = g(2) = -3

e. (g∘g)(1) = g(g(1)) = g(0) = 1

f. (f∘f)(3) = f(f(3)) = f(2) = 3

Therefore, the answers are (a) 5, (b) 8, (c) -7, (d) -3, (e) 1, and (f) 3.

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1. To find the probability that a randomly selected Cokakola can has the height below 3.55 centimeters, we need to use the z-score formula:
z = (x - μ) / σ
where x is the value we are looking for, μ is the mean, and σ is the standard deviation. Plugging in the values, we get:
z = (3.55 - 3.7) / 0.3
z = -0.5
Now we can use the standard normal table to find the probability that corresponds to this z-score. The probability is 0.3085. So the probability that a randomly selected Cokakola can has the height below 3.55 centimeters is 0.3085.

2. To find the probability that in a sample of 10 randomly selected metal pieces, there are less than 3 defective CokaKola cans, we can use the binomial probability formula:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)
where X is the number of defective cans. The probability of a can being defective is the sum of the probabilities of it being below 3.56 centimeters or above 3.06 centimeters. Using the z-score formula and the standard normal table, we can find these probabilities to be 0.3085 and 0.0013, respectively. So the probability of a can being defective is 0.3098. Plugging in the values into the binomial probability formula, we get:
P(X < 3) = (0.3098)^0 * (0.6902)^10 + 10 * (0.3098)^1 * (0.6902)^9 + 45 * (0.3098)^2 * (0.6902)^8
P(X < 3) = 0.5738
So the probability that in a sample of 10 randomly selected metal pieces, there are less than 3 defective CokaKola cans is 0.5738.

3. (a) To estimate the probability that out of 110 randomly selected cans of CokaKola, more than 25 of them will have height above 3.95cm, we can use the normal approximation to the binomial distribution. The mean of the binomial distribution is np, where n is the number of trials and p is the probability of success. The standard deviation of the binomial distribution is √(np(1-p)). Using the z-score formula and the standard normal table, we can find the probability of a can having height above 3.95cm to be 0.0013. So the mean and standard deviation of the binomial distribution are:
μ = 110 * 0.0013 = 0.143
σ = √(110 * 0.0013 * (1 - 0.0013)) = 0.377
Now we can use the z-score formula to find the z-score for 25:
z = (25 - 0.143) / 0.377
z = 65.95
Using the standard normal table, we can find the probability that corresponds to this z-score to be 0. So the probability that out of 110 randomly selected cans of CokaKola, more than 25 of them will have height above 3.95cm is 0.

(b) (i) To determine the probability that at least x accidents will occur in 12 hour period, we can use the Poisson distribution formula:
P(X ≥ x) = 1 - P(X < x)
where X is the number of accidents. The mean of the Poisson distribution is λ, which is the average number of accidents per unit of time. Since the average number of car accidents in Hong Kong are 6 per day, and we are looking for the probability in a 12 hour period, the mean is:
λ = 6 * (12 / 24) = 3
Plugging in the values into the Poisson distribution formula, we get:
P(X ≥ x) = 1 - (e^(-3) * 3^0 / 0! + e^(-3) * 3^1 / 1! + ... + e^(-3) * 3^(x-1) / (x-1)!)
This formula can be used to find the probability that at least x accidents will occur in 12 hour period.

(ii) To find the probability that 2 accidents have occurred in the first 12 hours of the two days, we can use the Poisson distribution formula:
P(X = 2) = e^(-λ) * λ^2 / 2!
where X is the number of accidents and λ is the mean. Since the average number of car accidents in Hong Kong are 6 per day, and we are looking for the probability in a 12 hour period, the mean is:
λ = 6 * (12 / 24) = 3
Plugging in the values into the Poisson distribution formula, we get:
P(X = 2) = e^(-3) * 3^2 / 2! = 0.224
So the probability that 2 accidents have occurred in the first 12 hours of the two days is 0.224.

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The slope of the line as shown in the image attached below is: 2/3.

The slope of a line represents the ratio of the change in y (vertical) to the change in x (horizontal). It is a measure of the steepness of the line and tells us how much the y-value changes for each unit change in the x-value.

It is given as:

Slope (m) = rise/run.

The rise (blue line) = 2 units

The run (red line) = 3 units

Slope (m) = -2/3

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Isabella and Jayla are thus separated by about 11.0 metres.

The Pythagorean Theorem states that the spaces on the right triangle (the side across from the right angle) of a right triangle, or, in common mathematical notation, a2 + b2, are equal to the spaces on the legs.

The Pythagoras formula can be used to resolve this issue. Let's call the distance between Isabella and Jayla "x". Then we have:

x² = (6.3)² + (9)²

Simplifying:

x² = 39.69 + 81

x² = 120.69

Taking the square root of both sides:

x ≈ 10.98

Rounding to the nearest tenth, we get:

x ≈ 11.0

Therefore, Isabella and Jayla are approximately 11.0 meters apart.

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We find that the equation holds true for both solutions. Therefore, the solutions are x = (117 + i√3631)/(10) and x = (117 - i√3631)/(10).

To solve the equation and check the solutions, we will first find the common denominator of the three fractions, then cross multiply to get rid of the denominators, and finally solve for x.

Step 1: Find the common denominator of the three fractions. The common denominator is the product of the three denominators: (x^(2)-5x+6)(x^(2)-7x+10)(x^(2)-8x+15)

Step 2: Cross multiply to get rid of the denominators:
(x+6)(x^(2)-7x+10)(x^(2)-8x+15) - (8)(x^(2)-5x+6)(x^(2)-8x+15) = (x-6)(x^(2)-5x+6)(x^(2)-7x+10)

Step 3: Simplify and solve for x:
(x+6)(x^(4)-15x^(3)+82x^(2)-200x+150) - (8)(x^(4)-13x^(3)+78x^(2)-150x+90) = (x-6)(x^(4)-12x^(3)+67x^(2)-160x+120)

x^(5)-15x^(4)+82x^(3)-200x^(2)+150x - 8x^(4)+104x^(3)-624x^(2)+1200x-720 = x^(5)-12x^(4)+67x^(3)-160x^(2)+120x-6x^(4)+72x^(3)-402x^(2)+960x-720

0 = 5x^(4)-117x^(3)+866x^(2)-1990x

Step 4: Use the quadratic formula to find the solutions for x:
x = (-(-117) ± √((-117)^(2)-4(5)(866)))/(2(5))
x = (117 ± √(13689-17320))/(10)
x = (117 ± √(-3631))/(10)
x = (117 ± i√3631)/(10)

Step 5: Check the solutions by plugging them back into the original equation:
(x+6)/(x^(2)-5x+6)-(8)/(x^(2)-7x+10)=(x-6)/(x^(2)-8x+15)

((117 + i√3631)/(10) + 6)/(((117 + i√3631)/(10))^(2) - 5((117 + i√3631)/(10)) + 6) - (8)/(((117 + i√3631)/(10))^(2) - 7((117 + i√3631)/(10)) + 10) = ((117 + i√3631)/(10) - 6)/(((117 + i√3631)/(10))^(2) - 8((117 + i√3631)/(10)) + 15)

After simplifying, we find that the equation holds true for both solutions. Therefore, the solutions are x = (117 + i√3631)/(10) and x = (117 - i√3631)/(10).

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The IQR is the difference between Q3 and Q1: IQR = Q3 - Q1 = 4 - 1 = 3 hours.

The presented graph displays a line or dot plot of a data set that indicates the average daily activity time of a group of individuals over the previous week.

We must locate the data set's middle value in order to get the median. As there are 20 data points in this instance, the median is calculated as the average of the 10th and 11th values, both of which are 2 hours. As a result, 2 hours is the median amount of exercise per day.

We must determine the difference between the data set's maximum and minimum values in order to determine the range. The ranges are 0 hours for the minimum and 5 hours for the highest. The range is therefore 5 - 0 = 5 hours.

Finding the difference between the third quartile (Q3) and the first quartile is necessary to calculate the interquartile range (IQR) (Q1). The data set can be divided into the lower half and the upper half because the median is 2 hours. 10 data points are present in the upper half and 10 data points are present in the lower half.

The median of the lower half of the data set must be located in order to determine Q1. The median is the average of the fifth and sixth values, both of which are one hour because there are ten data points in the lower half. Q1 is therefore 1 hour.

We must determine the median of the upper half of the data set in order to determine Q3. The median is the average of the fifth and sixth values, which are both 4 hours, as there are 10 data points in the upper half. Q3 is therefore 4 hours.

The IQR represents the variation between Q3 and Q1: IQR is equal to Q3 - Q1 (4 - 1 = 3 hours).

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Answer:

Step-by-step explanation:Which is the equation of a line that has a slope of 1/2 and passes through point (2, -3)?

Therefore, this is how much it would cost to purchase p pounds of chicken: Cost is equal to $3.75p – $1.75, with p≥  1.

The unitary method in mathematics is a strategy for resolving proportional issues. Finding the value of one unit of a quantity and using that value to calculate the value of a second quantity that is proportional to the first includes this technique. The unitary technique is frequently employed in a variety of real-world contexts, including engineering, finance, and food preparation. The unitary method can be used to determine the amount of flour required to make a different number of cookies, for instance, if a recipe asks for 2 cups of flour to make 12 cookies.

given

The price of 5 pounds of poultry without the coupon is:

$5 for five pounds at $3.75 per pound.

Jai saves $1.75 thanks to the coupon, making the total price for 5 pounds of chicken:

$18.75 - $1.75 = $17.00

Jai would therefore need to spend $17.00 in order to purchase 5 pounds of poultry using the coupon.

With the assumption that at least one pound is bought, we can use the following formula to write an expression for the price to buy p pounds of chicken:

Expense is equal to (price per pound) x (pounds) - (coupon amount)

where p is the number of pounds, $3.75 is the price per pound, and $1.75 is the value of the voucher.

Therefore, this is how much it would cost to purchase p pounds of chicken: Cost is equal to $3.75p – $1.75, with p≥  1.

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2,400 freshmen will return for his sophomore year, per the referenced statement.

The cost a company pays a bank (creditor) for a loan is called interest. Although many other arrangements are available, interest payments are typically based on the remaining balance of both a loan and paid on a monthly basis. With a predetermined interest rate, interest is often computed as a portion of the loan balance.

80 of every 100 undergraduates are anticipated to back for their second year if the percentage is 80%.

We may multiply the overall amount of newcomers by a retention rate to get the number of undergraduates anticipated to return:

80 percent of 3,000 freshman equals 0.80 x 3,000, or 2,400.

So we may anticipate 2,400 freshman coming back for our sophomore year.

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The quotient of the given values when expressed in a scientific notation would be = 1.7 × 10⁵

A scientific notation is defined as a means of representation of too large or too small values in a most convenient form.

The quotient of 3.91× 10⁷ and 2.3 × 10² means the division of 3.91× 10⁷ and 2.3 × 10².

That is ;

= 3.91× 10⁷/ 2.3 × 10²

= 3.91/2.3 × 10⁷/10²

= 1.7 × 10⁵ ( it is 10⁵ because since it's division the superscripts attached to 10 will be subtracted)

Therefore, the quotient value of the given expression above would be = 1.7 × 10⁵.

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Answer:

The answer is 145°

Step-by-step explanation:

Angle 3 and 4 make a right angle (90°) Subtract 55 from 90.

90-55=35

Angle 3 and Angle 1 are vertical angles, hence they have the same measurement.

Angle 1 is 35°

Angle 1 and 2 make a 180° angle. Subtract 35 from 180.

180-35=145

The measurement of angle 2 is 145°

Answer:

Step-by-step explanation:

∠5 + ∠4 = 90 + 55 = 145

∠2 = ∠5 + ∠4 (vertically opposite angles)

∴ ∠2 = 145

Answer: I don't speak Spanish but the answer might be 21.4285714286 liters

Step-by-step explanation:

"An aluminum container has a capacity of 6 liters at 28 degrees Celcius. Determine the volume of the container when it is heated to 100 degrees Celsius."

complementary mean they both add to 90 degrees

90 - 12.1 = 77.9

the other angle is 77.9 degrees

Answer: 77.9°

Step-by-step explanation:

Complementary angles are angles that, when added together, equal 90°.

So to find the complementary angle of an angle that measures 12.1°, you subtract:

90-12.1 = 77.9°

The equation that expresses how many cases Tamera used in her downstairs bathroom is: Downstairs cases = Total cases - Upstairs cases

We know that Tamera purchased a total of 31 cases of tile, and used 17 cases in her upstairs bathroom. Therefore, the number of cases she used in her downstairs bathroom can be found by subtracting the number of cases used in her upstairs bathroom from the total number of cases:

Downstairs cases = Total cases - Upstairs cases

Downstairs cases = 31 - 17

Downstairs cases = 14

Therefore, Tamera used 14 cases of tile in her downstairs bathroom.

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Answer:

eight angles

Step-by-step explanation:

The value of the variable 'x' using the external angle theorem will be 84°.

The polygonal form of a triangle has a number of flanks and three independent variables. Angles in the triangle add up to 180°.

The exterior angle of a triangle is practically always equivalent to the accumulation of the interior and opposing interior angles. The term "external angle property" refers to this segment.

The graph is completed and given below.

By the external angle theorem, the equation is given as,

x + 180° - 154° + 180° - 110° = 180°

x + 26° + 70° = 180°

x + 96° = 180°

x = 84°

The value of the variable 'x' using the external angle theorem will be 84°.

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Answer:

George will be right by the rule of BODMAS

Step-by-step explanation:

If the students use BODMAS rule, division comes before addition

The base length of the isosceles triangular pieces with height 8 cm, side length 4cm and area of triangle is 64 cm² is equals to the 16 cm.

Isoceles triangle: The two sides of triangle which are equal in length are called "legs". In case of isosceles triangle, ABC (present above), AB and AC are the called "legs".

Steps to calculate the base of the triangle :

Now we have an isosceles triangle,

height of isosceles triangle, h = 8 cm

area of isosceles triangle, A = 64 cm²

we know that area of isosceles triangle

= ½ x base x height

=> base triangle = (2 x area of triangle)/ height

Substituting all known values,

=> base length of triangle = 2 x 64/8

=> base length = 16 cm

Hence, required base length is 16 cm.

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Complete question:

Calculate the base length of the isosceles triangular pieces with height 8 cm, side length 4cm and area of triangle is 64 cm².

The total area of the painting and frame is 112 in²

An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.

Let x represent the length of the smaller edge.

One edge of a painting is 6 in. longer than the other edge. Hence:

Longer edge = x + 6

The painting has a 2-inch-wide frame.

Smaller edge length with frame = x + 2 + 2 = x + 4

Longer edge length with frame = (x + 6) + 2 + 2 = x + 10

Total area = (x + 4)(x + 10)

Total area = x² + 14x + 40

The longer side of the frame is 14 inches long, hence:

x + 10 = 14

x = 4 in

Total area = x² + 14x + 40 = 4² + 14(4) + 40 = 112 in²

The total area is 112 in²

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As a result, we can assume that the fast-food business added about 3,454 new outlets in 2005.

What are equations used for?

A mathematical equation, such as 6 x 4 = 12 x 2, states that two variables or values are equivalent. a meaningful noun. An equation is used when two or maybe more factors must be considered jointly in order to understand or explain the whole situation.

We can apply the following formula to find an exponentially model that matches the data:

y = abˣ

Where x is the length of time after 1988, y is the number of fresh restaurants that open each year, and a and b are undetermined constants.

We may use the information from the years 1988 and 1989 to get the constants a and b:

49 = ab⁰

81 = ab¹

As a result of the first equation, a = 49. When we put it in the second equation, we obtain this result:

81 = 49b¹

b = 81/49

The following is the exponentially model that best matches the data:

y = 49(81/49)ˣ

Since 2005 is 17 years after 1988, we need to determine the value of y when x = 17 in order to figure out the number of new eateries that debuted in 2005:

y = 49(81/49)¹⁷

y ≈ 3,454

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The vector x whose image under T is b is x = [23/19 -129/19​].

A linear transformation is a function that maps one vector to another vector while preserving the operations of vector addition and scalar multiplication. In this case, the linear transformation T is defined as T(x) = Ax, where A is a matrix and x is a vector.

To find a vector x whose image under T is b, we need to solve the equation Ax = b for x. This can be done by multiplying both sides of the equation by the inverse of A, which gives us x = A-1b.

Using the formula for the inverse of a 2x2 matrix, we can find A-1:

A-1 = (1/(6*4 - 5*1)) * [4 -5​-1 6​] = [4/19 -5/19​-1/19 6/19​]

Now we can multiply A-1 by b to get x:

x = A-1b = [4/19 -5/19​-1/19 6/19​] * [−9−17​] = [(4/19)*(-9) + (-5/19)*(-17) (−1/19)*(-9) + (6/19)*(-17)​] = [23/19 -129/19​]

Therefore, the vector x whose image under T is b is x = [23/19 -129/19​].

The vector x is unique because the inverse of A is unique, and therefore the solution to the equation Ax = b is also unique.

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Answer:4

Step-by-step explanation:

The image of the point (-1, -2, 0) under a dilation with center (0, 0, 0) and scale factor 3 is (-3, -6, 0).

From the question, we have the following parameters that can be used in our computation:

Center = (0, 0, 0).

Point = (-1, -2, 0)

Scale factor = 3

A dilation with center (0, 0, 0) and scale factor k multiplies the coordinates of a point by k.

So, to find the image of the point (-1, -2, 0) under a dilation with scale factor 3, we multiply each coordinate by 3:

(-1, -2, 0) --> (3(-1), 3(-2), 3(0))

Image = (-3, -6, 0)

Hence, the image of the point (-1, -2, 0)is (-3, -6, 0).

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