Which best represents the change in the vertices of rectangle ABCD to form rectangle A'B'C'D'?
F) (x, y ) → (2x, 2y)
G) (x, y ) → (1. 5x, 1. 5y)
H) (x, y ) → (3x, 3y)
J) (x, y ) → (4x, 4y)

The image of (2, 3) under a dilation with center at the origin and a scale factor of −3 will be (-6, -9).

What is Image of a point ?

Dilation is the process of resizing or altering an object. With the aid of the specified scale factor, it is a transformation that reduces or enlarges the objects. The initial figure is referred to as the pre-image, while the new figure acquired after dilatation is known as the image.

Given point : (2,3)

the scale factor is -3 which means the point should be enlarged by -3 times to get the desired image.

So, we can write as : (a, b) where,

     a = 2 × -3 =  -6

and, b = 3 × -3 = -9

Hence, the coordinates of the image will be (-6, -9).

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Answer:

The length of the unknown side of the triangle is

[tex]5 \sqrt{5} [/tex]

[tex]m=15-0.75g[/tex] is the equation to represent the total amount of money, m, remaining on the gift card after playing g arcade games.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. While the definition of an equation in English is any well-formed formula consisting of two expressions related by an equals sign, the definition of an equation and its cognates in other languages may have subtly different meanings. For instance, an équation is defined as having one or more variables in French.

According to the question,

Total money = $15

The games at the arcade cost $0. 75.

Let total amount of money be 'm' and arcade games played by him be 'g'.

Now,

Equation to represent the remaining money,

[tex]m=15-0.75g[/tex]

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Answer:

Domain is x-value and range is y-values

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

9/10

Answer: I agree with Moriah. If two equations represent the same proportional relationship, then they should have the same constant of proportionality. In this case, the constant of proportionality in p = 1.5 and 2/3p = q is different, so the two equations cannot represent the same proportional relationship.

It's possible that the two equations represent two different proportional relationships, but without more information it's impossible to determine if that is the case.

Step-by-step explanation:

The coordinates of the fourth vertex of the parallelogram are (1, -3).

A parallelogram is defined as a special type of quadrilateral that has both pairs of opposite sides parallel and equal.

Three vertices are located at these coordinates: (-1, 2), (1, 2), and (-1,-3).

we have three points in the coordinate plane, we can use the concept of vector addition to find the fourth point.

The vectors connecting the first and second points, and the first and third points can be determined as follows:

v₁ = (1,2) - (-1,2) = (2,0)

v₂ = (-1,-3) - (-1,2) = (0,-5)

The fourth point will be located at the vector sum of the first point and the vector formed by adding v₁ and v₂.

v₃ = v₁ + v₂ = (2,0) + (0,-5) = (2,-5)

So, the fourth point will be located at:

(-1,2) + (2,-5) = (1,-3)

Thus, the coordinates are (1, -3).

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Answer:

y – 7 = 3(x – 5)

Step-by-step explanation:

[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{7})\hspace{10em} \stackrel{slope}{m} ~=~ 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{ 3}(x-\stackrel{x_1}{5}) \\\\\\ y-7=3x-15\implies {\Large \begin{array}{llll} y=3x-8 \end{array}}[/tex]

By expression, x - y = x' - y' , Distance of 3rd and 4th obstacle is equal to distance of 7th and 9th obstacle.

Distance is a numerical measurement of how far apart objects or points are, it is the length along a line or line segment between two points on the line or line segment.

Given,

The distance between obstacle three and obstacle seven is the same as the distance between obstacle four and obstacle nine.

Distance of 7th obstacle = x

Let,

Distance of 9th obstacle = y

Distance of 3rd obstacle = x'

Distance of 4th obstacle = y'

Distance between obstacle 3 and 7 = x - x'

Distance between obstacle 4 and 9 = y - y'

Distance between obstacle three and obstacle four = x' - y'

Distance between obstacle seven and obstacle nine.= x - y

According to the question

x-x' = y-y'

⇒ x - y = x' - y'

Hence, Distance between third and fourth obstacle is same as distance between 7th and 9th obstacle.

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When the input of the function is -3, the output of the function is -4

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

The graph

On the graph, we have the following reading at x = -3

(x, y) = (-3, -4)

This means that when x = -3, the value of y is -3

So, the conclusion is that

An input of -3, gives an output of the function is -4

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The ordered pairs (21, 0) and (6, -4) are the solutions to the given inequality.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given inequality is y<2/7x-5.

Here,

Put (x, y)=(21, 0) in the given inequality, we get

0<2/7(21)-5

0<1

So, it is solution

Put (x, y)=(6, -4) in the given inequality, we get

-4<2/7(6)-5

-4<12/7-5

-4<1.7-5

-4<-3.3

So, it is solution

Put (x, y)=(0, -5) in the given inequality, we get

-5<2/7(0)-5

-5<-5

Which is not true, it is not a solution

Put (x, y)=(7, -3) in the given inequality, we get

-3<2/7(7)-5

-3<-3

Which is not true, it is not a solution

Therefore, the ordered pairs (21, 0) and (6, -4) are the solutions to the given inequality.

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The rate at which the water level is rising when the water level is 2 cm is 8 cm.

A pyramid's volume is equal to 1/3 of B, where B is the base's area and h is its height. Given that the base is square, B = s2, where s is a base side The volume is therefore 1/3 s2h.

We are aware that the base's side is 8 cm long and the whole pyramid's height is 11 cm. Also, no matter how high the water is, its surface will always form a square with the same proportion to the water's depth as a side of the pyramid's top has to the pyramid's total height. This indicates that s = 8/11 h regardless of the water depth.

So that means that the formula for the volume of the pyramid formed by the water is V = 1/3 (8/11 h)2 h = 64/363 h3.

Separate this as a function of time to get the rate of change of the volume of water :

V = 64/363 h3

dV/dt = 3 (64/363) h2 dh/dt = 192/363 h2 dh/dt

Nonetheless, we are aware that the volume is shifting at a speed of 65 cc every second.  So at any point in time,

65 = 192/363 h2 dh/dt

65 * 363 / 192 = h2 dh/dt

23595 / 192 = h2 dh/dt

(23595 / 192) / h2 = dh/dt

When the level of water (h) is 8, that indicates:

(23595 / 192) / 64 = dh/dt

1.92 = dh/dt

So the water level is rising at the rate of 1.92 cm per second when the water level is 8 cm.

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If two angles and the included side of a triangle are congruent to two angles and the included side of another triangle, the two triangles are congruent by the ASA congruence condition. Hence, option a. is the right answer.

According to the definition, we know that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the two triangles are congruent by the ASA congruence condition.

Let us consider two triangles △ABC and △QRP as shown below -

So, in △ABC and △QRP, we have,

∠B=∠R

∠C=∠P

BC=RP

∴ By ASA congruence test for triangles, we get △ABC ≅ △QRP

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The complete question is -

If two angles and the included side of a triangle are congruent to two angles and the included side of another triangle, the two triangles are congruent by _____ congruence condition.

a. ASA

b. AAA

c. SAS

d. RHS

Answer:

1m/sec

Step-by-step explanation:

Mr. Hall spent 3 seconds to increase his speed to 3m/sec increasing 1m/sec, don't over think it.

Answer:

To convert 6 feet into meters, first create a conversion factor to convert from feet to meters. Make sure the original unit is in the denominator, then cancel feet. Next, multiply the original measure by the conversion factor to get 1.8288 meters, or 1.83 meters if you simplified it.

Step-by-step explanation:

The percentage of the shipping crate when compared to the total weight of the shipment would be = 16%

The weight of two granite specimen = 22 pounds

The weight of the crate = 20 pounds

The weight of shipping crate = 8 pounds

The total weight of the whole shipment = 22+20+8 = 50 pounds.

Therefore the percentage of shipping crate as compared to the total weight;

= 8/50 × 100/1

= 800/50

= 16%

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The number of wires that cut from of 200 meters is 66 meters 66 centimeters.

What are the nearest two places?

The second place to the right of the decimal point, or the hundredth place, is used to round a decimal number to two decimal places. For instance, you can round 2.83620364 to two decimal places as 2.84 and 0.7035 to two decimal places as 0.70.

Given the length of the wire is 200 meters.

Assume that he cuts n pieces of length 3 meters.

The length of n pieces is 3n.

Therefore the equation is

3n = 200

n = 200/3

n= 66.66

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The answers are a) standard deviation ≈  0.02 b) probability ≈ 0.95 c) standard deviation ≈  0.031 d) probability ≈ 0.8098 e) decrease in P = 0.1402

Given: p = 75% or 0.75

n = 450

a) The sampling distribution of the sample proportion is approximately normal with mean = 0.75 and standard deviation is [tex]\sqrt \frac{p(1-p)}{n}[/tex]

= [tex]\sqrt{\frac{0.75(1-0.75)}{450} }[/tex] = 0.02

b) [tex]\^{p} - p[/tex] = 0.04

[tex]z = \frac{\^{p} - p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]

z = ±1.96(approx.)

p(-0.04 <  [tex]\^{p} - p[/tex] < 0.04)

=P(-1.96 < z < 1.96) = 1 - 2P(z < -1.96)

= 1 - 2(0.0250) = 0.95

c) The sampling distribution of the sample proportion is approximately normal with mean = 0.75 and standard deviation [tex]\sqrt \frac{p(1-p)}{n}[/tex]

= [tex]\sqrt{\frac{0.75(1-0.75)}{200} }[/tex] = 0.031

d) [tex]\^{p} - p[/tex] = 0.04

[tex]z = \frac{\^{p} - p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]

z = ±1.31(approx.)

p(-0.04 <  [tex]\^{p} - p[/tex] < 0.04)

=P(-1.31 < z < 1.31) = 1 - 2P(z < -1.31)

= 1 - 2(0.0951) = 0.8098

e) Determine the difference in probabilities (of part b) and part d))

The loss in precision by decreasing the sample size 0.9500 - 0.8098 = 0.1402

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Complete question is:

In 2008 the Better Business Bureau settled 75% of complaints they received. Suppose you have been hired by the Better Business Bureau to investigate the complaints they received this year involving new car dealers. You plan to select a sample of new car dealer complaints to estimate the proportion of complaints the Better Business Bureau is able to settle. Assume the population proportion of complaints settled for new car dealers is 0.75, the same as the overall proportion of complaints settled in 2008. a) Suppose you select a sample of 450 complaints involving new car dealers. Show the sampling distribution of [tex]\overline{p}[/tex].b) Based upon a sample of 450 complaints, what is the probability that the sample proportion will be within .04 of the population proportion? c) Suppose you select a sample of 200 complaints involving new car dealers. Show the sampling distribution of [tex]\overline{p}[/tex] . d) Based upon the smaller sample of only 200 complaints, what is the probability that the sample proportion will be within .04 of the population proportion? e) As measured by the increase in probability, how much do you gain in precision by taking the larger sample in part (b)?

x = k - 2, y = 8 - 2k, z = k is the general solution of the given system, where k is an arbitrary, if k = 1

x = -1, y = 6, z = 1 is the solution.

Ax = [tex]\left[\begin{array}{ccc}1&1&1\\1&2&3\\1&4&7\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x\\y\\z\end{array}\right][/tex]

and b = [tex]\left[\begin{array}{ccc}6\\14\\30\end{array}\right][/tex]

the augmented matrix is [A:B] = [tex]\left[\begin{array}{ccc}1&1&1:6\\1&2&3:14\\1&4&7:30\end{array}\right][/tex]

we need to reduce the augmented matrix [A:B] to row echelon form by applying elementary row transformations only.

operating R₂→R₂-R₁ , R₃→R₃-R₁

[A:B] = [tex]\left[\begin{array}{ccc}1&1&1:6\\0&1&2:8\\0&3&6:24\end{array}\right][/tex]

operating, R₃→R₃-3R₃

~  [tex]\left[\begin{array}{ccc}1&1&1:6\\0&1&2:8\\0&0&0:0\end{array}\right][/tex]

which is the row echelon, form of the matrix [A:B]

we have rank of [A:B] = the number of the non zero rows in echelon form = 2

also by the same elementary transformation we get,

A ~ [tex]\left[\begin{array}{ccc}1&1&1\\0&1&2\\0&0&0\end{array}\right][/tex]

∴ rank of A = 2

since rank A = rank  [A:B] = 2 < number of unknowns

therefore, the given equation are consistent and will have an infinite number of solutions.

We see that the given system of equations is equivalent to the matrix equation

[tex]\left[\begin{array}{ccc}1&1&1\\0&1&2\\0&0&0\end{array}\right][/tex]  [tex]\left[\begin{array}{ccc}x\\y\\z\end{array}\right][/tex]  =  [tex]\left[\begin{array}{ccc}6\\8\\0\end{array}\right][/tex]

which gives the equations x + y + z = 6 ........(1)

and y + 2z = 8 .......(2)

from (2), y = 8 - 2z, putting the value of y in (1) we get,

x = 6 - y - z = 6 (8 - 2z) z = z - 2

taking z = k, we get x = k - 2, y = 8 - 2k, z = k is the general solution of the given system, where k is an arbitrary,

if k = 1

x = -1, y = 6, z = 1 is the solution.

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For the given width length ratio and perimeter of rectangle, the length of rectangle is 80 cm.

The perimeter of a shape is defined as the total length of its boundary. The perimeter of a shape is determined by adding the length of all the sides and edges enclosing the shape.

Let the width of the rectangle be 3x, and the length be 4x (since the ratio of the width to the length is 3:4).

The perimeter of a rectangle is the sum of the lengths of all four sides, so we have:

Perimeter = 2(length + width)

Substituting the expressions for the length and width, we get:

280cm = 2(4x + 3x)

Simplifying the right-hand side, we get:

280cm = 14x

Dividing both sides by 14, we get:

x = 20

Therefore, the length of the rectangle is 4x = 4(20) = 80 cm

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Answer:

Your score as a percent is **92%**. Here is how I calculated it:

To convert a fraction to a percent, you need to divide the numerator by the denominator, multiply the result by 100, and add a "%" sign

In your case, the fraction is 23/25, so you need to divide 23 by 25, multiply by 100, and add a "%".

23 ÷ 25 = 0.92

0.92 × 100 = 92

92 + "%" = 92%

Therefore, your score as a percent is 92%.

Step-by-step explanation:

Answer:

6 students must play both piano and guitar

Answer: To calculate the amount of US dollars you can buy for R12,500 at an exchange rate of 1 US$ = R8.76, you can use the following formula:

US$ = R12,500 / R8.76

Plugging in the values, we get:

US$ = R12,500 / R8.76 = 1,421.51

So, with R12,500, you can buy 1,421.51 US dollars at an exchange rate of 1 US$ = R8.76.

Step-by-step explanation:

For the given equation which shows the relation of temperature in Celsius and Fahrenheit, the correct option is Option D.

What is meant by temperature?

Indicating the direction in which heat energy will naturally flow from a hotter body (one with a higher temperature) to a colder body(one at a lower temperature), the temperature is a measure of hotness or coldness defined in terms of any of several arbitrary scales.

The given equation is:

[tex]C = \frac{5}{9} (F- 32)[/tex]

where C = temperature in Celsius

          F = temperature in Fahrenheit

The above equation can be rewritten as:

C = 5/9F - 160/9

Now, this is an equation of a straight line with a formula,

y = mx + c

Comparing,

m = 5/9 which is the slope of the equation.

This means that for a temperature increase of 1 degree Fahrenheit, the equivalent increase in temperature in Celsius is 5/9.

So the option I is true.

Similarly, an increase in 1 degree Celsius of temperature is equivalent to 9/5 = 1.8 degree increase in Fahrenheit.

So option II is true.

Option III is not true as is discussed above.

Therefore for the given equation of temperature, the correct option is Option D.

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Answer:

D

Step-by-step explanation:

I have nothing else to say- lol

The diameter of the circle with a circumference of 20 ft is 6.37 ft.

The circumference of a circle is the distance around the circle which is 2πr.

The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.

The diameter of the circle can be obtained by the equation of the circumference formula with the given circumference of 20 ft.

Therefore, 2πr = 20.

2r = 20/π.

2r = 6.37 ft.

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The probability that at most four of the M&M are yellow is  0.3357 and the probability that at least two of the four of the M & M are yellow is   0.6622

The probability that at most two of the four M&M's are yellow can be calculated using the cumulative distribution function (CDF) of the binomial distribution. The binomial distribution models the number of successes in a fixed number of independent Bernoulli trials, where each trial has the same probability of success. In this case, the number of trials is 4, and the probability of success (getting a yellow M&M) is 0.13.

The cumulative distribution function of the binomial distribution can be expressed as:

P(X <= k) = SUM[i=0 to k] (n choose i) * p^i * (1-p)^(n-i)

Where n is the number of trials, k is the value we want to find the probability for, p is the probability of success, and (n choose i) is the number of combinations of n items taken i at a time, which can be calculated as n! / (i! * (n-i)!).

For this problem, we want to find the sum of probabilities for X = 0, 1, and 2, so we have:

P(X <= 2) = P(X = 0) + P(X = 1) + P(X = 2)

= (4 C 0) * (0.13)^0 * (0.87)^4 + (4 C 1) * (0.13)^1 * (0.87)^3 + (4 C 2) * (0.13)^2 * (0.87)^2

= 0.3357

NB: "C" represent combination.

So the probability that at most two of the four M&M's are yellow is approximately 0.3357.

b. The probability that at least two of the four M&M's are yellow can be found by subtracting the probability of getting 0 or 1 yellow M&M's from 1. So:

P(X >= 2) = 1 - P(X <= 1)

= 1 - (P(X = 0) + P(X = 1))

= 1 - ((4 C 0) * (0.13)^0 * (0.87)^4 + (4 C1) * (0.13)^1 * (0.87)^3)

= 0.6622

So the probability that at least two of the four M&M's are yellow is approximately 0.6622.

The mean of the distribution is given by n * p = 4 * 0.13 = 0.52, and the standard deviation is given by sqrt(n * p * (1-p)) = sqrt(4 * 0.13 * 0.87) = 0.9304.

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A. 10 cm radius: 2 * pi * 10 cm = 62.83 cm

B. 2.7 cm radius: 2 * pi * 2.7 cm = 16.94 cm

C. 1.2 mm radius: 2 * pi * 1.2 mm = 7.54 mm

D. 9.01 cm radius: 2 * pi * 9.01 cm = 56.76 cm

A. The circumference of a circle with a radius of 10 cm is 62.83 cm.

B. The circumference of a circle with a radius of 2.7 cm is 16.94 cm.

C. The circumference of a circle with a radius of 1.2 mm is 7.54 mm.

D. The circumference of a circle with a radius of 9.01 cm is 56.76 cm.

The circumference of a circle is the distance around its edge. It can be calculated using the formula 2πr, where r is the radius of the circle. The radius is the distance from the center of the circle to any point on its edge. To find the circumference of a circle, we need to multiply the radius by 2 and then by pi (π), which is roughly 3.14.

For example, if the radius of the circle is 10 cm, then the circumference of the circle is 2πr = 2π x 10 cm = 62.83 cm. Similarly, if the radius of the circle is 2.7 cm, then the circumference of the circle is 2π x 2.7 cm = 16.94 cm. If the radius of the circle is 1.2 mm, then the circumference of the circle is 2π x 1.2 mm = 7.54 mm. Finally, if the radius of the circle is 9.01 cm, then the circumference of the circle is 2π x 9.01 cm = 56.76 cm.

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A statement which best describes the graph of y ≥ -x² + 8x - 2 include the following: B. The vertex is at (4, 14). The parabola is a solid line that opens down. Shading is above the parabola.

Generally speaking, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. For this quadratic function, we can logically deduce that the graph is a downward parabola because the coefficient of x² is negative and the value of "a" is less than zero (0).

By critically observing the graph of the given quadratic function, we can logically deduce that the solutions (roots) and vertex are as follows;

x = 0.258, y = 0.

x = 7.742, y = 0.

Vertex = (4, 14).

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Answer:

Step-by-step explanation:

How many pattern block trapezoids would create for hexagons?

2 trapezoids compose a hexagon using equal-size shapes: 2 trapezoids, 6 triangles, or 3 blue rhombuses. compose hexagons using different shapes. So 2 trapezoids create 1 hexagon. This means 6 trapezoids make 3 hexagons.

The exact number of trapezoids needed to create three hexagons depends on the size and shape of the hexagons.

However, in general, you would need at least 18 trapezoids.

An hexagon is a six-sided polygon. It is made up of six equilateral triangles and six trapezoids.

If you are looking to create larger hexagons you will need more trapezoids.

Depending on the size and shape, you could need as many as 24 or more trapezoids.

An hexagon is a six-sided polygon. It is made up of six equilateral triangles and six trapezoids.

Hence, To create an hexagon using pattern blocks, you need 10 equilateral triangles and 20 trapezoids.

Therefore, to create 5 hexagons.

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The probability of the intersection of two events occurring can never be more than the probability of the union of two events occurring.

False.

It should be stated that the likelihood of the intersection of two events occurring is always less than the likelihood of the events occurring together.

It is always less likely than or equal to the likelihood of either event occurring alone for an intersection of two events, which is the chance that both occurrences take place.

In other words, the probability of the intersection and the probability of the union are subsets of one another.

The chance of the intersection of two events occurring can never be greater than the likelihood of the union of two events occurring, hence that is the right statement.

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