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The single transformation that transforms ∆RST to ∆R'S'T' is a reflection.

Part A:

For the first figure it is visible that the orientation of the pre-image (∆RST) is similar to that of the image (∆R'S'T').The image is received from the pre-image through moving the pre-image a few units down. Therefore, the single transformation that transforms ∆RST to ∆R'S'T' is a translation.

Part B:

For the second figure ,it is visible that the orientation of the pre-image (∆RST) is similar to that of the image (∆R'S'T').The image is received from the pre-image through moving the pre-image a few units down and a few units to the right. Therefore, the single transformation that transforms ∆RST to ∆R'S'T' is a translation.

Part C:

For the third figure it is visible that the orientation of the pre-image (∆RST) isn't similar to that of the image (∆R'S'T').The image is received from the pre-image through rotating the pre-image a few 180 degrees. Therefore, the single transformation that transforms ∆RST to ∆R'S'T' is a rotation.

Part D:

For the fourth figure it is  visible that the orientation of the pre-image (∆RST) isn't similar to that of the photograph (∆R'S'T').The image is received from the pre-image through reflecting the pre-image.

Therefore, the single transformation that transforms ∆RST to ∆R'S'T' is a reflection.

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The vector that represents the resultant velocity of the plane will be V = 30.72 i + 135.89 j + 53.46 k.

The quantity which has magnitude, and direction, and follows the law of vector addition is called a vector.

An airplane is taking off headed due north with an air speed of 173 miles per hour at an angle of 18° relative to the horizontal. The wind is blowing with a velocity of 42 miles per hour at an angle of  S 47° E.

Let north be the y-axis and east be the x-axis. Then the vector equation will be given as,

V = (42 sin 47°) i + (173 cos 18° - 42 cos 47°) j + (173 sin 18°) k

V = 30.72 i + 135.89 j + 53.46 k

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The difference in the elevation between the canyon and the bird's nest is 737. 3 feet

From the information given, we have that;

Let's convert the mixed fractions to improper fraction;

= - 263/ 5 = - 52. 6 feet

789 3/ 10 = 7893/ 10 = 789. 3 feet

The difference in the elevation between the canyon and the bird's nest ;

= -52. 6 + 789. 9

= 737. 3 feet

Thus, the difference in the elevation between the canyon and the bird's nest is 737. 3 feet

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Answer:

i think the answer is 0.3 but im not sure i just used a calculator

From the result you can see that the result must have a significant figure of 2 since that is the lowest significant figure in question

The standard scientific notations is expressed according to the expression A * 10^n

where

A is any value from 1 to 10

Given the following quotient

4.0286 × 10^9/3.1 × 10^−4

This can also be expressed as:

4.0286 × 10^9/3.1 × 10^−4 = (4.0286/3.1) × 10^9+4
4.0286 × 10^9/3.1 × 10^−4 = 1.2995 × 10^13

From the result you can see that the result must have a significant figure of 2 since that is the lowest significant figure in question

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Answer: The answer is 2

Step-by-step explanation: Hope this helps :)

Based on the calculation done below, the number of lower level tickets sold is 750.

Let:

L = number of lower-level tickets sold = 5U

M = number of mezzanine tickets sold

U = number of upper balcony tickets sold

We therefore have:

35L + 25M + 15U = 37,500 ...................... (1)

25M = 4 * 15U = 60U

Substituting L = 5U and 25M = 60U into equation (1) and solve for U, we have:

35(5U) + 60U + 15U = 37,500

175U + 60U + 15U = 37,500

250U = 37,500

U = 37,500 / 250

U = 150

Susbstituting U = 150 into L = 5U, we have:

L = 5 * 150

L = 750

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The value of the expression (n+8)(n-4) - (n+3)(n-2) + 27 is not divisible by 3 for any whole number n

The expression is given as

(n+8)(n-4) - (n+3)(n-2) + 27

Open the brackets

So, we have

n^2 + 8n - 4n - 32 - n^2 - 3n + 2n - 6 + 27

Collect the like terms

So, we have

n^2 - n^2 - 3n + 8n - 4n  + 2n - 32  - 6 + 27

Evaluate the like terms

So, we have

3n - 11

The above expression cannot be expressed as a factor of 3

Hence, the value of the expression (n+8)(n-4) - (n+3)(n-2) + 27 is not divisible by 3 for any whole number n

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A 25% rate of interest is required for Rupees 4000 amount to Rupees 6000 in 2 years.

Here we are given the following-

Principal amount = Rs 4000

Amount received after 2 years = Rs 6000

Time period = 2 years

Let the rate of interest = r%

Then, according to the simple interest formula-

Simple interest = Principal × time period × rate/100

and Simple interest = Final amount - principal amount

Here, simple interest = 6000 - 4000 = Rs 2000

Thus,

2000 = 4000 × 2 × r/100

2000/4000 = 2 × r/100

1/2 = 2 × r/100

1/4 = r/100

r = 100/4

r = 25

Thus, the rate of interest is 25%.

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a) 3 - 8 + 2i - (-5i) = -5 + 2i +5i = -5 + 7i

b) 4 - 20i - 2i + 10i² = 4 - 22i + 10([tex]\sqrt{-1}[/tex])² = 4 - 22i + 10(-1) = 4 - 10 -22i

= -6 -22i

c) Multiply both numerator and denominator by i

[tex]\frac{i(-2-4i)}{i^{2} }[/tex] = [tex]\frac{-2i - 4i^{2} }{i^{2} }[/tex] = [tex]\frac{-2i - 4(\sqrt{-1})^{2} }{(\sqrt{-1})^{2}}[/tex] = [tex]\frac{-2i - 4(-1)}{-1}[/tex] = [tex]\frac{-2i+4}{-1}[/tex] = 2i - 4 = -4 + 2i

d) Multiply both numerator and denominator by (3+6i)

[tex]\frac{(3+6i)(-3+2i)}{(3+6i)(3-6i)}[/tex] = [tex]\frac{-9+6i-18i+12i^{2} }{9-36i^{2} }[/tex] = [tex]\frac{-9-12i+12(\sqrt{-1} )^{2} }{9-36(\sqrt{-1} )^{2} }[/tex] = [tex]\frac{-9-12i+12(-1)}{9-36(-1)}[/tex] = [tex]\frac{-9-12-12i}{9+36}[/tex]

= [tex]\frac{-21-12i}{45}[/tex] = [tex]-\frac{21}{45} - \frac{12}{45}i[/tex]

Answer:b. the salt and sugar will disappear and the oil will float on the surface of water

Step-by-step explanation: If you stir salt and sugar it will dissapear but oil in thick and if you know it will float to the surface

The difference between the highest recorded temperature on Earth of 134 degrees Fahrenheit and the lowest recorded temperature of -128.6 is equal to 262.6 degrees Fahrenheit.

In mathematics, the difference can be described as the result of the subtraction of one numeral or value to another.

Hence the difference between the highest recorded temperature and the lowest recorded temperature on Earth can be found by the subtraction of the highest and lowest recorded temperatures.

The difference in the two temperatures = highest recorded temperature - lowest recorded temperature

Difference in Farenheit = 134 - ( -128.6)

Difference in Farenheit  = 134 + 128.6

Difference in Farenheit  = 262.6

Hence, the difference between the highest recorded temperature and the lowest recorded temperature is calculated to be 262.6 degrees fahrenheit.

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The answer is 60%

According to the original information given, the estimated average number of shoppers in the original store at any time(x) is 45.

In the question, it states that, in the new store, the manager estimates that an average of 90 shoppers per hour(60 minutes) enter the store, which is equivalent to 1.5 shoppers per minute(s).

The manager also estimates that each shoppers stays in the store for an average of 12 minute (t). Thus, by Little's law there are, on average,

x = s x t

=> x = 1.5 x 12

=> x = 18

Hence, there are 18 shoppers at any time in the new store.

Now, Percentage of shoppers

[tex]\frac{45-18}{45}[/tex] x 100 = 27/45 x 100 = 2700/45 = 60%

Therefore, the answer is 60%

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Answer:

525

Step-by-step explanation:

f(x)=(x)(2x+5)

f(x)=2x^2+5x

f(15)=2*(15)^2 + 5*15

= 2*225 + 75

=450 + 75

=525

Evaluation of the equation is [tex]\frac{y^{-14} }{6718464}[/tex]

Here from the question, we get the evaluation

                     [tex][(2y)^{-3} (3y)^{-2} (6y)^{-2}]^{2}[/tex]

Now evaluate it in the simple form we have

                   [tex][(\frac{1}{2y} )^{3} (\frac{1}{3y} )^{2} (\frac{1}{6y} )^{2} ]^{2}[/tex]

                   [tex][\frac{1}{8y^{3} } \frac{1}{9y^{2} } \frac{1}{36y^{2} } ]^{2}[/tex]

                  [tex][\frac{1}{2592y^{7} } ]^{2}[/tex]

                  [tex]\frac{1}{6718464y^{14} }[/tex]

                   [tex]\frac{y^{-14} }{6718464}[/tex]

Therefore we get the simplest form of the evaluation.

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if the given graph is f(x)= [tex]x^{2}[/tex], then the new graph is y= [tex]2x^{2}[/tex] and we have drawn the graph

Given,

The graph of the function y =f(x)

From the graph we can say that

f(1)=1

f(2)=4

f(-1)=1

f(-2)=4

So,

f(x)= [tex]x^{2}[/tex]

Then,

y= 2f(x)

y= [tex]2x^{2}[/tex]

draw the graph

Hence, if the given graph is f(x)= [tex]x^{2}[/tex], then the new graph is y= [tex]2x^{2}[/tex]

and we have drawn the graph

The complete question is:

The graph of y = f(x) is shown. Draw the graph of y = 2f(x) .

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For the given quadratic function we have that:

For a function h(x), we define the domain as the set of the inputs (values of x) and the range is the set of the outputs (values of y).

Generally, for all quadratic functions, the domain is the set of all real numbers, so we already know the domain.

Now let's look at the range.

The given function is:

h(x) = -12*(x - 4)^2 + 3

Remember that if a quadratic function has a vertex (h, k), then the vertex form is:

f(x) = A*(x - h)^2 + k

So the vertex here is (4, 3)

And we also can see that the leading coefficient of the quadratic function is negative. This means that the function opens downwards, so the vertex is the maximum.

Then the range is the set of all real values smaller than or equal to 3, then the range is:

R: y ≤ 3.

Concluding:

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In a list of measurements in increasing order: 4, 5, 6, 8, 10, and x, the value of x is 16.

To get the value of x, we will use algebraic expressions to demonstrate the given relationships.

If the median of these measurements is ​six sevenths​ times their arithmetic mean, then:

median = 6/7 x mean

Median (Md), is a single value at the middle of the data values arranged in increasing or decreasing order. On the other hand, arithmetic mean (μ) is the sum of the data values divided by its total number.

For the list of measurements in increasing order is 4, 5, 6, 8, 10, and x,

The median is between 6 and 8.

Md = 6+8/2

Md = 7

Evaluating the first equation using Md = 7:

median = 6/7 x mean

7 = 6/7 x mean

mean = 49/6

By definition,

mean = (4 + 5 + 6 + 8 + 10 + x)/6

Equating both equations for the mean:

49/6 = (4 + 5 + 6 + 8 + 10 + x)/6

49 = 33 + x

x = 16

Hence, the value of x is 16.

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b r = 17 - b

when it is 8 inches tall after 9 inches have burned from the candle.

A formula in mathematics is an assertion of a fact, rule, or principle using mathematical symbols. Equations, equalities, identities, inequalities, and asymptotic expressions are a few examples of formulae.

In the theory of logic, the word "formula" is also frequently used to refer to a sentential formula, also known as a propositional formula, or a formula in propositional calculus.

A 17 inch candle is lit and steadily burns until it is burned out.

Let b represent the burned length of the candle (in inches ) and let r represent the remaining length of the candle (in inches) .

Write a formula that expresses r in terms of b r = 17 - b  

Preview b. When 6.8 inches have burned from the candle, the remaining length of the candle is 10.2 inches.

Therefore the point should be on the graph of r in terms of b. c. On the graph below:

i, represent the linear relationship between l and b ii. plot the point that represents the candle when it is 8 inches tall after 9 inches have burned from the candle.

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Answer:

it shows that the answer is (-2,8(

the brackets are the symbols of inequality

Answer:

2b² + 2b

Step-by-step explanation:

b + 3b² + b - b²

= 3b² - b² + b + b

= 2b² + 2b

Answer:

[tex] \sf \: {2b}^{2} + 2b [/tex]

Step-by-step explanation:

Given expression,

→ b + 3b² + b - b²

Let's simplify the expression,

→ b + 3b² + b - b²

→ (3b² - b²) + (b + b)

→ (2b²) + (2b)

→ 2b² + 2b

→ 2b(b + 1)

Hence, answer is 2b² + 2b.

The real world situation will be , Ram buys y pens and each pen costs $10 . How much he need to pay if he has already paid $3.

It is given that an equation is 10y - 3.

We have to write a real world situation representing above equation.

What is algebra ?

Algebra is the branch that deals with various symbols and the arithmetic operations such as addition , division , etc.

As per the question ;

The expression given is 10y - 3.

Let's write a real world situation representing the above equation.

Ram buys y pens and each pen costs $10 . How much he need to pay more if he has already paid $3.

Let's assume no. of pens be 4 i.e., y = 4.

So ;

He need to pay more ;

= 10 × 4 - 3

= 40 - 3

= $ 37

Thus , the real world situation will be , Ram buys y pens and each pen costs $10 . How much he need to pay if he has already paid $3.

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An expression that has a value of less than 3 when x = 6 is; 20 - 3•x

An expression is a symbol collection that together expresses a quantity.

An expression consists of variables, numbers and operators placed together to express a quantity.

A possible expression that have a value of less than 3 when x = 6, is presented as follows;

The above expression satisfies the given condition (have a quantity less than 3), given that we have;

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Answer: He can play 6 games

Step-by-step explanation:

40-10 = 30

30- 12 = 18

18- 8.50 = 9.50

9.50 divided by 1.50 = 6.3

Your cars average acceleration in that time is 12.21m/s^2

The given parameters are

Initial velocity, u = 8.9 m/s

Final velocity, v = 35.76 m/s

Time, t - 2.2 seconds

The average acceleration is calculated using

v = u + at

So, we have

35.76 = 8.9 + 2.2a

Evaluate the like terms

26.86 = 2.2a

Divide by 2.2

a = 12.21

Hence, your cars average acceleration in that time is 12.21m/s^2

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Lee jogged a total of 5 3/22 laps

Lee jogged 3 1/11 laps in the morning

He then jumped 2 3/22 laps in the evening

Therefore the total laps jogged can be calculated by adding both values together

3 1/11 + 2 3/22

34/11 + 47/22

= 113/22

= 5 3/22

Hence the total laps jogged is 5 3/22 laps

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Hence , on solving the given expression , we get values of h(1) = 58/35 ,    h(2) = 86 /35 and  h(-1/2) =26 /35.

We have given an expression h(x)=-4/5x+6/7 .

Putting x = 1 in h(x) , we get

   h(1) = 4/5(1) +6/7

          = 4/5 +6/7

          = 28 + 30 /35

          = 58 /35

Putting x = 2 in h(x) , we get          

   h(2) = 4/5(2) +6/7

          = 8/5 + 6/7

          = 56 + 30 /35

          = 86 /35

Putting x = -1/2 in h(x) , we get      

  h(-1/2) =  4/5(-1/2) +6/7

             = -2/5 + 6/7

             = -14 + 30 /35

             = 26 /35

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