Determine the domain of the quadratic function. f (x) = 7x2 - 10x + 10 Get Hint Enter Your Stop Here 16 8704 МАА 3

The result of the division is a monomial, and it is in standard form: [tex]-0.195b^4[/tex]

The result of the division of the monomials is a monomial. To find the result, we need to divide the coefficients and subtract the exponents of the same variables.

The steps are as follows:

Divide the coefficients: -0.26 ÷ (4(1)/(3)) = -0.26 ÷ (4/3) = -0.26 × (3/4) = -0.195

Subtract the exponents of the same variables: a^(3-3) = a^0 = 1, b^(6-2) = b^4

Multiply the result of step 1 and step 2: -0.195 × 1 × b^4 = -0.195b^4

Therefore, the result of the division is a monomial, and it is in standard form: -0.195b^4.

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The cone is composed of a half sphere and a triangular cone, the total volume would be 301.59 cubic centimeters.

This cone is composed of two shapes, these shapes are:

The volume of the cone can be calculated using the following formula:

V=1/3hπr²

V= 1/3 10 π4²

V= 167.55 cm

The volume of the sphere can be calculated using the following formula:

V = 4/3 π r³ /

V = 4/3 π 4³/ 2  

V = 268.08 / 2 = 134.04 cm

Total volume : 134.04 + 167.55 = 301.59 cubic centimeters

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The values of x that satisfy the equation are (l + sqrt(11)l)/10 and (l - sqrt(11)l)/10.

To find the values of x such that the angle between the vectors < 2, 1, -1 > and < l,x,0 > is 45 degrees, we can use the formula for the dot product of two vectors:

= |u||v|cos(theta)

Where  is the dot product of the vectors u and v, |u| and |v| are the magnitudes of the vectors, and theta is the angle between them. Plugging in the values from the question, we get:

< 2, 1, -1 > . < l,x,0 > = |< 2, 1, -1 >||< l,x,0 >|cos(45)

Simplifying the dot product, we get:

2l + x = sqrt(6)sqrt(l^2 + x^2)/sqrt(2)

Squaring both sides and rearranging, we get:

4l^2 + 4lx + x^2 = 6l^2 + 6x^2

2l^2 + 2lx - 5x^2 = 0

Using the quadratic formula, we can solve for x:

x = (-2l +/- sqrt(4l^2 - 4(2l^2)(-5)))/(2(-5))

x = (-l +/- sqrt(l^2 + 10l^2))/(-10)

x = (-l +/- sqrt(11)l)/(-10)

x = (l +/- sqrt(11)l)/10

Therefore, the values of x that satisfy the equation are (l + sqrt(11)l)/10 and (l - sqrt(11)l)/10.

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The total number of codes possible is 9 × 10 × 10 × 8.

To find the total number of codes possible, we need to multiply the number of choices for each digit.

For the first digit, there are 9 choices (0 is not allowed).

For the second and third digits, there are 10 choices each (0-9).

For the last digit, there are 8 choices (0 and 1 are not allowed).

So the total number of codes possible is 9 × 10 × 10 × 8 = 7200.

Therefore, there are 7200 different codes possible for the lock.

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(a) True

(b) True

(c) False

(d) True

(e) False

(a) True. For any n × n invertible matrix A, the equation Ax = 0 admits only the trivial solution. This is because if A is invertible, then there exists an inverse matrix A^-1 such that A^-1A = I, where I is the identity matrix. Therefore, if Ax = 0, then A^-1Ax = A^-10, or x = 0. This means that the only solution to the equation is the trivial solution x = 0.

(b) True. For any two matrices A and B of size n × n, (AB)^T = (B^T) (A^T). This is a property of matrix multiplication and transposition, and can be easily verified by performing the operations on the matrices.

(c) False. Let A be a matrix of size n × n. If for two vectors y and z of R^n we have Ay = Az, it does not necessarily mean that y = z. It is possible for two different vectors to produce the same result when multiplied by the same matrix. For example, consider the matrix A = [[1, 0], [0, 1]] and the vectors y = [1, 0] and z = [0, 1]. Both Ay and Az will result in the same vector [1, 1], but y and z are clearly not equal.

(d) True. If A is a matrix of size n × n such that A^3 = I(n), then A is invertible. This is because A^3 = I(n) implies that A^2 = A^-1, meaning that the inverse of A exists and A is invertible.

(e) False. For any two matrices A and B of size n×n such that AB = 0, it is not necessarily true that A = 0 or B = 0. It is possible for two non-zero matrices to multiply to produce the zero matrix. For example, consider the matrices A = [[1, -1], [1, -1]] and B = [[1, 1], [1, 1]]. Both A and B are non-zero matrices, but AB = 0.

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[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{"y" varies inversely with "x"}}{y = \cfrac{k}{x}}\hspace{5em}\textit{we also know that} \begin{cases} x=8\\ y=30 \end{cases} \\\\\\ 30=\cfrac{k}{8}\implies 240=k\hspace{9em}\boxed{y=\cfrac{240}{x}} \\\\\\ \textit{when y = 20, what's "x"?}\qquad 20=\cfrac{240}{x}\implies x=\cfrac{240}{20}\implies x=12[/tex]

The surface area of the cylinder with a height of 8 yards and a radius of 82.13 yards is  46,486.93 sq. yards.

What is a cylinder?

One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry. One of the fundamental three-dimensional shapes in geometry is the cylinder, which has two distant, parallel circular bases. At a predetermined distance from the centre, a curved surface connects the two circular bases. The axis of the cylinder is the line segment connecting the centres of two circular bases. The height of the cylinder is defined as the distance between the two circular bases.

Given,

The height of the cylinder = 8 yards

 The circumference of the cylinder = 515.79 yards

We are asked to find the surface area of the cylinder.

Now the formula to find the surface area of a cylinder is:

SA = 2πr( r+h)

where r = radius

      h = height

Radius can be found from the circumference formula

2πr = 515.79

r = 515.79/ 2π = 515.79 / (2*3.14) = 82.13 yards

Then,

SA = 2πr( r+h) = 2*3.14*82.13 ( 82.13+8) = 46,486.93 sq. yards

Therefore the surface area of the cylinder with a height of 8 yards and a radius of 82.13 yards is  46,486.93 sq. yards.

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Therefore, the column space C(A) in the vector space A is the set of all linear combinations of the columns of A

The column space C(A) in the vector space A can be written as the span of the columns of A. In this case, the columns of A are:

This means that any vector in the column space C(A) can be written as a linear combination of the columns of A. For example, the vector [3,2,4,3] can be written as:

Therefore, the column space C(A) in the vector space A is the set of all linear combinations of the columns of A.

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The total amount for an  of $5,000 over 5 years at an annual interest rate of 6% if the interest is compounded quarterly is $5386.42.

Interest is the amount a lender or financial institution receives for lending money. Interest can also refer to a shareholder's ownership interest in a company and is usually expressed as a percentage.

Interest rate indicates the cost of borrowing or the reward for saving. Therefore, if you are a borrower, interest rate is the amount charged to borrow money, expressed as a percentage of the total loan amount.  

Solution according to the information given in the question :

Given, Principal(P) = $5,000

           Compounding per year(n) = 4

          Time(in years)(T) = 5

          Interest rate = 6%

Amount = P× (1 + r/n)^t

             = 5000 × (1 + 6/4×100)⁵

            = 5000 × (1.015)⁵

            = 5000 ×1.07

            = $5286.42

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The multiplication sentence will be: Volume = Length × Width × Height.

Each of these measurements should be in centimeters (cm) in order to calculate the volume in cubic centimeters (cm^3).

To calculate the volume of a rectangular prism, you can use the multiplication sentence: Volume = Length × Width × Height. Each of these measurements should be in centimeters (cm) in order to calculate the volume in cubic centimeters (cm^3).

For example, if the length of the rectangular prism is 5 cm, the width is 3 cm, and the height is 2 cm, the multiplication sentence would be:

Volume = 5 cm × 3 cm × 2 cm

The volume of this rectangular prism would be 30 cm^3.

In general, the multiplication sentence to calculate the volume of a rectangular prism is:

Volume = Length × Width × Height

Make sure to include the units (cm) in your multiplication sentence in order to get the correct answer in cubic centimeters (cm^3).

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The coordinate of D is (0, - 2) if the points A, B and C are 3 corners of a parallelogram the answer would be (0, - 2).

In two-dimensional geometry, it is a plane shape having four sides, in which two pairs of sides are parallel to each other and equal in length. The sum of all angles in a parallelogram is 360°.

It is given that:

the points A, B, and C are 3 corners of a parallelogram what are the coordinates of D.

Let D = (x, y)

Now, We know that;

The midpoint of AC = Mid-point of BD

(-2 + 5)/2 = (x + 3)/2

3 = x + 3

x = 0

(- 3+3)/2 = (y + 2)/2

y = - 2

Thus, the coordinate of D is (0, - 2) if the points A, B and C are 3 corners of a parallelogram the answer would be (0, - 2).

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The nearest 5 integers of 562817​ are:

562815​, 562816​, 562817​, 562818​, 5628179

An integer comprises a whole number which can be positive, negative, and zero and is not a fraction. Integer examples include: -5, 1, 25, 18, 97, as well as 3,043. 1.43, 21 3/4, 3.84, and other numbers that don't constitute integers are some examples.

Thus,

The nearest 5 integers of 562817​ are obtained by subtracting and adding the smallest integer that is 1 from the given number.

562815​, 562816​, 562817​, 562818​, 5628179

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Answer:

6

Step-by-step explanation:

First, we need to calculate the average number of toys produced per hour during the busy season and the regular season.

During the busy season, the factory operates for 2 x 30 = 60 days or 60 x 12 = <<2*30=60>>720 hours.

The average number of toys produced during this time is 528 toys per 12-hour shift, or 528/12 = <<528/12=44>>44 toys per hour.

During the regular season, the factory operates for the rest of the year, which is 12 - 2 = 10 months, or 10 x 4 = 40 weeks, or 40 x 5 = <<1045=200>>200 days, or 200 x 8 = <<200*8=1600>>1600 hours.

The average number of toys produced during this time is 304 toys per 8-hour shift, or 304/8 = <<304/8=38>>38 toys per hour.

The difference between the average number of toys produced per hour during the busy season and the regular season is:

44 - 38 = <<44-38=6>>6 toys per hour.

Therefore, the factory produces 6 more toys per hour during the busy season than during the regular season. Answer: 6.

Answer:

To calculate the number of more toys the factory produces in an hour during the busy season than during the regular season, we can divide the difference between the two shifts by the total hours of each shift:

More toys per hour = (528-304)/(12-8) = 224/4 = 56 toys per hour

a) The critical value of t for this question at the .05 significance level is -2.11.

b) The calculated value of t for this question at the .05 significance level is -1.47, given a standard deviation of 0.63.

c) We can reject the null hypothesis because the calculated t-value (-1.47) is less than the critical t-value (-2.11). This indicates that games are less than 3.50 hours long.

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The Cartesian equation y = 3x^2 as a polar equation can be write as r(θ) = 3 sec(θ) / (1 + tan²(θ)).

To rewrite the Cartesian equation y = 3x² as a polar equation, we need to use the conversion formulas between Cartesian coordinates (x, y) and polar coordinates (r, θ):

x = r cos(θ)
y = r sin(θ)

Substituting these formulas into the Cartesian equation gives us:

r sin(θ) = 3(r cos(θ))²

Dividing both sides by r and rearranging terms gives us:

r = 3 cos²(θ) / sin(θ)

Using the identity 1 + tan²(θ) = sec²(θ), we can rewrite the equation in terms of tan(θ) and sec(θ):

r = 3 (1 / (1 + tan²(θ))) / (1 / sec(θ))

Simplifying gives us the final polar equation:

r(θ) = 3 sec(θ) / (1 + tan²(θ))

Therefore, the Cartesian equation y = 3x²can be rewritten as the polar equation r(θ) = 3 sec(θ) / (1 + tan²(θ)).

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Malcom ate 7/10 of the total chocolates.

Amount is a term used to describe the quantity of something, usually a numerical value. It can refer to money, a number of people or objects, or a measurement such as weight or volume. Amounts can also be used to represent a value of something abstract, such as time, effort, or emotion. Amounts are typically quantified, meaning they can be easily compared to other amounts.

The fraction of chocolates that Malcom ate is 5/7 of the milk chocolates and 2/5 of the dark chocolates, so the total fraction of chocolates that Malcom ate is (5/7) + (2/5) = 7/10. Therefore, Malcom ate 7/10 of the total chocolates.

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Therefore , the solution of the given problem of function comes out to be the function that fits the given graph is f(x) = [x] + 1.

In addition to numbers, symbols, but also their constituent expression parts, anatomy, construction, and both real and fictitious geographic places are all covered in the study of mathematics. A function explains the connections between various variables, which all have a related outcome. A function is composed of a number of unique parts that, when combined, result in particular outputs for each input.

Here,

The largest number that is less than or equal to x is returned by the greatest integer function, denoted by [x]. For instance, [3.4] = 3, [-2.8] = 3, and [5] = 5 are all equal.

The curve of the largest integer function is moved up one unit by the function f(x) = [x] + 1.

The graph of the largest integer function is moved up by zero units by the function f(x) = [x].

The largest integer function's graph is reflected and moved down by one unit by the function f(x) = -[x] - 1.

The curve of the largest integer function is moved down by one unit by the function f(x) = [x] - 1.

Therefore, the function that fits the given graph is f(x) = [x] + 1.

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The expression 0.26 when written as a fraction in its lowest term is 13/50

Based on the question, we have a set of values that can be used in our calculations.

Fraction = 0.26

As a general rule, a fraction can be expressed as a/b

Where

Using the above values as a guide, we have the following expression

Fraction = 0.26

Multiply the fraction by 1

Fraction = 0.26 * 1

Express 1 as 100/100

So, we have

Fraction = 0.26 * 100/100

Evaluate the product of 0.26 and 100

This gives

Fraction = 26/100

Reduce the quotient of 26 and 100 to the lowest terms by dividing by 2

Fraction = 13/50

Hence, the fraction of 0.26 is 13/50

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To find the inverse equation of f(x) = 3x + 5, we first replace f(x) with y:

y = 3x + 5

Next, we switch x and y and solve for y:

x = 3y + 5

x - 5 = 3y

y = (x - 5)/3

Therefore, the inverse of f(x) is f^-1(x) = (x - 5)/3.

To find the inverse equation of g(x) = x^2 - 6, we replace g(x) with y:

y = x^2 - 6

Next, we switch x and y and solve for y:

x = y^2 - 6

x + 6 = y^2

y = ±sqrt(x + 6)

Since we want a function, we take the positive square root:

y = sqrt(x + 6)

Therefore, the inverse of g(x) is g^-1(x) = sqrt(x + 6).

The relationship between a function and its inverse is such that if (a,b) is a point on the graph of f, then (b,a) is a point on the graph of f^-1. In other words, the roles of x and y are reversed in the inverse function. The domain of the function becomes the range of the inverse, and the range of the function becomes the domain of the inverse.

In general, not all functions have inverses. For a function to have an inverse, it must be one-to-one (i.e., each x-value in the domain maps to a unique y-value in the range). If a function is not one-to-one, then it may be possible to restrict the domain to a smaller interval so that the restricted function does have an inverse. When a function has an inverse, the domain and range of the inverse follow a pattern as stated above.

The family uses 68.7 gallons of water every day for all purposes

If 22.9% of the water is used for cleaning, then the remaining 100% - 22.9% = 77.1% of the water is used for other purposes such as drinking and cooking.

To find out how much water the family uses every day, we need to add the amount of water used for cleaning to the amount of water used for other purposes.

Quantity of water used for cleaning = 22.9 percentage of the total amount of water used every day = 0.229 x 68.7 gallons = 15.71 gallons

Quantity of water used for other purposes = 77.1% of the total amount of water used every day = 0.771 x 68.7 gallons = 52.99 gallons

Total quantity of water used every day = amount of water used for cleaning + amount of water used for other purposes = 15.71 gallons + 52.99 gallons = 68.7 gallons

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With speed = 10 m/s, the rope will hit ground after 3.36 seconds.

Speed is a measure of how fast an object is moving, usually measured in units of distance per unit time, such as meters per second (m/s) or kilometers per hour (km/h). It is a scalar quantity, meaning it only has magnitude and no direction.

Mathematically, speed is defined as the distance an object travels per unit time. The formula for calculating speed is:

Speed = Distance / Time

where Distance is the distance traveled by the object, and Time is the time taken to cover that distance.

Now,

To find when the rope will hit the ground, we can use the kinematic equation:

y = vi * t + (1/2) * a * t²

where:

y = 50 m (the height of the cliff)

vi = 10 m/s (the initial velocity of the rope)

a = 9.8 m/s² (the acceleration due to gravity, acting downward)

t = time it takes for the rope to hit the ground

We can solve for t by setting y=50 and solving for t:

50 = 10t + (1/2) * 9.8 * t²

50 = t(10 + 4.9t)

t = 50/14.9=3.36 s

Therefore, the rope will hit the ground after 3.36 seconds.

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Answer:

Step-by-step explanation:

~P is true

q is true

~p v q is true

the hypothesis  (or antecedent)  is true

the conclusion  (or consequent)  is false

R is false and ~q is false

the conditional says if true then false

so the conditional is false

The range for the usual number of correct answers is given as follows:

[7, 16]

The mass probability formula, giving the probability of x successes on n trials, is given by the equation presented as follows:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are listed as follows:

The parameter values for this problem are given as follows:

p = 0.5, n = 23.

The mean and the standard deviation are given as follows:

The usual range of correct answers is within 2.5 standard deviations of the mean, hence:

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No solution is the answer because the equation cannot be solved because both sides of the equation do not have the same denominator. To solve the equation, we can cross-multiply and simplify the terms to get a quadratic equation.

Then we can use the quadratic formula to find the solutions. The denominator of the left side is w, while the denominator of the right side is (w² - 4).

Here are the steps:

1. Cross-multiply to get rid of the fractions: (w)(w² - 4) = (w + 2)(w + 25) - (5)(w + 2)(w - 2)
2. Distribute the terms: w³ - 4w = w² + 27w + 50 - 5w² + 10w
3. Combine like terms and rearrange to get a quadratic equation: w³ - 6w² - 41w - 50 = 0
4. Use the quadratic formula to find the solutions: w = (-(-6) ± √((-6)² - 4(1)(-41)(-50)))/(2(1))
5. Simplify the terms inside the square root: w = (6 ± √(36 - 8200))/2
6. Simplify further: w = (6 ± √(-8164))/2
7. Since the square root of a negative number is not a real number, there are no real solutions to this equation.

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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 transformation of the points and shapes after being transformed are calculated below

The coordinates of B in the figure is

B = (5, 1)

A translation of (x-4, y-3) means

B' = (5 - 4, 1 - 3)

B' = (1, -2)

Here, we have the following corresponding points

Pre = (2, 1)

Image = (-1, 2)

This represents

(x, y) = (-y, x)

This represents (d) 270° clockwise rotation

Given that the smaller figure is gotten from a bigger figure

Then the dilation is a reduction and the scale factor could be 1/2 or 1/4

We have

P = (3, -2) and S = (4, -5)

For the first transformation, we have

(x - 2, y)

P' = (1, -2) and S' = (2, -5)

For the second, we have

P'' = (1, 2) and S'' = (2, 5)

Here, we have

A = (-2, -5)

This means that the new ordered pair of point A is

A' = (-2, -5) * 1/2

A' = (-1, -2.5)

Hence, the new ordered pair of point A is (-1, -2.5)

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1). W is closed under addition.  

  W is not closed under scalar multiplication

2. W is not closed under addition

   W is closed under scalar multiplication

1. Let V be the vector space of all 2x2 matrices with real entries. Consider the subset W of V consisting of matrices of the form:

| a b |

| 0 c |

where a, b, and c are real numbers. Note that W is non-empty, since the matrix |0 0| is in W.

|0 0|

Now, let A and B be any two matrices in W, so that A has the form:

| a1 b1 |

| 0 c1 |

and B has the form:

| a2 b2 |

| 0 c2 |

Then the sum of A and B has the form:

| a1+a2 b1+b2 |

| 0 c1+c2 |

which is clearly also in W. Therefore, W is closed under addition.

However, W is not closed under scalar multiplication. Let A be any matrix in W, so that A has the form:

| a b |

| 0 c |

where a, b, and c are real numbers. Then, if we multiply A by a non-real scalar k = xi (where x is a real number and i is the imaginary unit), we get:

kA = xi * | a b | = | xia xib |

| 0 c | | 0 xc |

which is not in W, since the entry in the (1,2) position is non-zero. Therefore, W is not closed under scalar multiplication.

2. Let V be the vector space of all polynomials with real coefficients. Consider the subset W of V consisting of all polynomials of degree at most 2.

Note that W is non-empty, since the polynomial p(x) = 0 is in W.

Now, let c be any real scalar, and let p(x) be any polynomial in W.

Then cp(x) is a polynomial of degree at most 2, since multiplying a polynomial of degree at most 2 by a scalar does not change its degree. Therefore, W is closed under scalar multiplication.

However, W is not closed under addition. Let p(x) and q(x) be any two polynomials in W of degree at most 2. Then the sum p(x) + q(x) may have degree greater than 2, and hence may not be in W. For example, if p(x) = x^2 + 2x + 1 and q(x) = -x^2 + x - 1, then p(x) + q(x) = 3x, which is not in W. Therefore, W is not closed under addition.

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The coordinates of the triangle A'B'C' are A'(-2, -6), B'(-14, -2) and C'(-2, -2).

Dilation is the process of resizing or transforming an object. It is a transformation that makes the objects smaller or larger with the help of the given scale factor. The new figure obtained after dilation is called the image and the original image is called the pre-image.

here, we have,

From the given graph, triangle ABC have A(1, 3), B(7, 1) and (1, 1).

Triangle ABC is enlarged with a scale factor of -2 and the origin of the Centre to give triangle A'B'C'.

Now, A(1, 3) → -2(1, 3)→A'(-2, -6)

B(7, 1) → -2(7, 1) → B'(-14, -2)

C(1, 1) → -2(1, 1) → C'(-2, -2)

Therefore, the coordinates of the triangle A'B'C' are A'(-2, -6), B'(-14, -2) and C'(-2, -2).

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