What are two possible transformations that together could have been used to create the red figure from the blue figure?

mc023-1 (see picture for graph )
A. a translation of 2 units up followed by a translation of 4 units right
B. a rotation of 90 degrees counterclockwise about the origin followed by a translation of 2 units up
C. a reflection across the y axis followed by a translation of 2 units up
D. a translation of 2 units up followed by a reflection across the x axis

By analyzing the given graph, we can see that the rate of change of the linear equation is 8.

A general linear equation can be written as:

y = a*x + b

Where a is the slope (also known as the rate of change, this is what we are looking for here) and b is the y-intercept.

If the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope can be written as:

a = (y₂ - y₁)/(x₂ - x₁)

Here we can see the points:

(1, 28) and (2, 36) and we can use these two to find the slope.

a = (36 - 28)/(2 - 1)

a = 8

So the slope (thus, the rate of change) is 8.

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The composition of two functions, g(x) and h(x), is written as (g•h)(x).

Function in math is a relationship between two variables where one variable determines the behavior of the other. It is a mathematical expression that assigns each element in a set to a specific output. Functions can be used to represent things like motion, growth, and decay. They are used to create models that can be used to make predictions and analyze data. Functions are used throughout mathematics and science and can be used to solve real-world problems.

This means that the output of function g(x) is used as the input of function h(x). In this case, (g•h)(x) is equal to h(g(x)). So, (g•h)(x) = h(x-2) = (x-2)^2 - 1.

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To write the point (1, 2) on a graph, you would first locate the point on the x-axis where x = 1, and then go up 2 units on the y-axis.

The point (1, 2) is on the Cartesian plane and it represents the coordinates of a point in the 2-D space. This point is located 1 unit to the right of the y-axis and 2 units above the x-axis.

It can be represented graphically as a point on a coordinate plane where the x-coordinate is 1 and the y-coordinate is 2.

On the graph, you can plot the point by first drawing the x and y axes and their respective scales, then place a dot on the point (1,2) which represents the coordinates of the point.

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The formula to compute the total weekly in cell H2 is H2=D2+G2

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

(a).By using formula we get;

Regular gross pay= Regular Hours x Hourly Rate

D2=B2*C2

(b) By using the formula we get;

Overtime Hours = Hours Worked -Regular Hours

E2=A2-B2

(c) By using the formula we get;

Time-and-a-half overtime

hourly rate = Hourly rate 1.5

F2=C2x1.5

(d) By using the formula we get;

Total overtime pay

=Overtime Hours x Overtime rate

G2=E2 x F2

(e) By using the formula we get;

Total weekly pay =  Regular pay + Overtime pay

H2=D2+G2

Therefore, the unitary answer will be H2=D2+G2

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Answer:C

Step-by-step explanation:

x is [tex]\sqrt{7} \\[/tex]=2.645

which means 2.645²=7

0.1728 suburban park users bike on the park trail.

A mathematical comparison of two numbers is called a proportion.

It is an equation or statement used to depict that two ratios or fractions are equal.

According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

The proportion (p) is calculated as:

p = bike the trail/number of residents

Given that,

The number of users who bike the trail = 42

The number of residents using the park trails = 243

Thus,

p = 42/243 = 0.1728

Therefore, 0.1728 suburban park users bike on the park trail.

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Answer:

2.56% or 2.6% (to nearest 10th of a %)

Step-by-step explanation:

Percent error is determined by the expression

    [(Measured - Actual)/Actual]*100%

 [16" - 15.6"]/(15.6")*100% = 2.56%

The radius of the circle will be [tex]\sqrt{22}[/tex].

In our question, we shall first extend QRS to the circle's point T.

According to the power of a point.

[tex]QP^{2}[/tex]  =  QR*QT

[tex]6^{2}[/tex]  =  3*QT

QT = 12

Since QR = 3, RT = 9.

Since RS = 3, ST = 6.

Draw OT and OR, creating a triangle(TSO) and triangle(RSO).

OT and OR are radii, Let the radius be r.

Use the Law of Cosines on these two triangles.

OT2  =  [tex]r^{2}[/tex]  =  [tex]6^{2}[/tex] + [tex]2^{2}[/tex] - 2*6*2*cos(TSO)

OR2  =  r2  =  [tex]3^{2}[/tex] + [tex]2^{2}[/tex] - 2*3*2*cos(RSO)

Since these are equal:

[tex]6^{2}[/tex] + [tex]2^{2}[/tex] - 2*6*2*cos(TSO)  =  [tex]3^{2}[/tex] + [tex]2^{2}[/tex] - 2*3*2*cos(RSO)

40 - 24*cos(TSO)  =  13 - 12*cos(RSO)

Since angle(RSO) is supplementary to angle(TSO),  cos(RSO) = - cos(TSO)

40 - 24*cos(TSO)  =  13 + 12*cos(TSO)

27  =  36*cos(TSO)

0.75  =  cos(TSO)

Since  [tex]OT^{2}[/tex]  =  [tex]r^{2}[/tex]  =  [tex]6^{2}[/tex] + [tex]2^{2}[/tex] - 2*6*2*cos(TSO)

[tex]r^{2}[/tex]  =  40 - 24*0.75  

[tex]r^{2}[/tex]  =  22

r  =  [tex]\sqrt{22}[/tex]

Hence the radius of the given circle will be [tex]\sqrt{22}[/tex].

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y + 3 = (-4/3)(x - 6) is the equation of the line that passes through the point (-6, 3) and has slope of -4/3.

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Out of 400 band-aids, 200 were used yesterday. Therefore, the percentage of band-aids used yesterday is 50%.

You started with 4 boxes × 100 band-aids per box

= 400 band-aids.

You ended with 2 boxes × 100 band-aids per box

= 200 band-aids

So you used

400 band-aids - 200 band-aids = 200 band-aids yesterday.

To find the percentage of band-aids used, you can divide the number of band-aids used by the total number of band-aids you started with and multiply by 100:

= (200 band-aids / 400 band-aids) × 100

= (1/ 2) × 100

= 50%

Therefore, 50% of the band-aids were used yesterday.

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The graph provided in the exercise must be used in this task, together with our statistical understanding, so that we can state: correct option is A

Statistics is a discipline of applied mathematics concerned with the gathering, description, analysis, and derivation of inferences from quantitative data. Calculus of differential and integrals, linear algebra, and probability theory are key mathematical concepts in statistics.

Statistics provide us the knowledge we need to understand how things operate. To conduct research, assess results, foster critical thinking, and make wise judgements, statistics are utilized. Almost any subject of study may benefit from the application of statistics to explore the causes, timing, and predictability of events.

The maximum points on the graph are at 21 and 31, and the sample ranges appear to be centered below 32, so we may claim so the option A is more appropriate.

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The complete question is as follows:

The ratio of water, sucrose, and saline solution needed is 1000:199:271 in its simplest form.

The amount of water, sucrose, and the saline solution used can be expressed as a ratio in its simplest form by finding the greatest common divisor (GCD) of the three quantities and dividing each by it.

1l of water = 1000 ml of water.

Let's find the GCD of the three quantities:

GCD(199,271,1000) = 1

So we can express the amount of water, sucrose, and saline solution needed as a ratio in its simplest form by dividing each of the three quantities by 1

Water : Sucrose : Saline solution = 1000 : 199/1 : 271/1 = 1000:199:271

Hence, the ratio of water, sucrose, and saline solution needed is 1000:199:271 in its simplest form.

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The anti-derivative of g(x) is G(x) = x3 + 3x2 and the anti-derivative of f(x) is F(x) = x2 + 2x.

Part a:

The value of the integral from 0 to 6 of f(x)dx is 16. This can be calculated using the Fundamental Theorem of Calculus (FTC) which states that the integral of a function is equal to the anti-derivative of that function evaluated at the upper limit minus the anti-derivative of that function evaluated at the lower limit. This can be written as:

∫f(x)dx = F(6) - F(0)

The anti-derivative of f(x) is F(x) = x2 + 2x, so the value of the integral is:

∫f(x)dx = (62 + 2*6) - (02 + 2*0) = 36 - 0 = 16.

Part b:

The value of the integral from 4 to 9 of g(x)dx is 20. This can be calculated using the FTC which states that the integral of a function is equal to the anti-derivative of that function evaluated at the upper limit minus the anti-derivative of that function evaluated at the lower limit. This can be written as:

∫g(x)dx = G(9) - G(4)

The anti-derivative of g(x) is G(x) = x3 + 3x2, so the value of the integral is:

∫g(x)dx = (93 + 3*9) - (43 + 3*4) = 729 - 168 = 20.

Part c:

The value of the integral from 4 to 9 of 2*g(x) - f(x)dx is 68. This can be calculated using the FTC which states that the integral of a function is equal to the anti-derivative of that function evaluated at the upper limit minus the anti-derivative of that function evaluated at the lower limit. This can be written as:

∫(2*g(x) - f(x))dx = 2*G(9) - F(9) - [2*G(4) - F(4)]

The anti-derivative of g(x) is G(x) = x3 + 3x2 and the anti-derivative of f(x) is F(x) = x2 + 2x, so the value of the integral is:

∫(2*g(x) - f(x))dx = (2*(93 + 3*9) - (92 + 2*9)) - [2*(43 + 3*4) - (42 + 2*4)]

= (1854 - 19) - (544 - 16) = 1735 - 528 = 68.

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Answer: half

Step-by-step explanation:

Answer:

12. 12 students scored in the 80-89 range

13. 31 students took the maths test

Answer: A. [tex]4[/tex]

Step-by-step explanation:

Since the points have the same [tex]y[/tex]-coordinate, take the absolute value of the difference of the [tex]x[/tex]-coordinates. Doing so yields [tex]|-4-0|=4[/tex].

The surface area of the box with a height of 8 inches, a length of 12 inches, and a width of 6 inches is 432 square inches.

The surface area of a box with a height of 8 inches, a length of 12 inches, and a width of 6 inches can be calculated using the formula SA = 2lw + 2lh + 2wh. In this case, SA stands for surface area, l stands for length, w stands for width and h stands for height.

To calculate the surface area of the box, substitute the given values for l, w and h into the formula and solve:

SA = 2(12)(6) + 2(12)(8) + 2(6)(8)

SA = 144 + 192 + 96

SA = 432 square inches

Therefore, the surface area of the box with a height of 8 inches, a length of 12 inches, and a width of 6 inches is 432 square inches.

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The maximum deflection of the simply supported beam, given the applied load P, the length of the beam L, the Young's Modulus E of the beam material, and the moment of inertia I, is equal to (5*P*L^3)/1536.3*10^15 m.

The maximum deflection of the simply supported beam is given by:

Maximum deflection = (5PL^3)/(384EI)

where P is the load applied to the beam, L is the length of the beam, E is the Young's Modulus of the beam material, and I is the moment of inertia of the beam.

Substituting the given values into the equation, we get:

Maximum deflection = (5*P*L^3)/(384*200*10^9*39.9*10^6)

= (5*P*L^3)/(1536.3*10^15)

= (5*P*L^3)/1536.3*10^15 m

The maximum deflection of the simply supported beam, given the applied load P, the length of the beam L, the Young's Modulus E of the beam material, and the moment of inertia I, is equal to (5*P*L^3)/1536.3*10^15 m.

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On solving the provided question, we can say that equation let x =amount of copies sold  = > 37,600is = .073  X x = 515,068.4932.

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

let x =amount of copies sold to date.

37,600is = .073  X x

t x = 37,600 / .073

= 515,068.4932.

round to nearest 515,068.

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Answer:

Given: QR = QS (by given)

We are to prove: LS = ZR

Proof:

Since QR = QS, by the SAS (Side-Angle-Side) congruence postulate, we know that triangle QRS is congruent to triangle QSZ (both have two equal sides and included angle).

By the AAS (Angle-Angle-Side) congruence postulate, we know that if two angles of one triangle are congruent to two angles of another triangle, and the included side is congruent, then the two triangles are congruent.

Therefore, by using AAS congruence, we can say that triangle QRS is congruent to triangle QSZ.

By the CPCTC (Corresponding parts of congruent triangles are congruent), we know that if two triangles are congruent, then their corresponding sides are congruent.

Therefore, LS is congruent to ZR.

Therefore, we have proved LS = ZR

Note: The above proof uses the properties of congruence of triangles, if the student is not familiar with this, it might be challenging for them.

The expression describing how many songs are played by the radio station in H hours is 12H

The phrase used to describe how many songs the radio station plays in H hours is Number of songs = 12 xH

288 songs are played in a 24-hour period.

60 nonstop songs are played over the course of 5 hours.

Given

Every hour, a radio station plays 12 songs.

Compose an expression that indicates how many songs the radio station plays in H hours.

There are 12 songs performed throughout an hour.

Then,

Number of songs=  songs played in one-hour x songs played in H hour

Number of songs=12H

The expression describing how many songs are played by the radio station in H hours is 12H

The phrase used to describe how many songs the radio station plays in H hours is 12H

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Answer:

Step-by-step explanation:

The inequality that represents all the solutions of 10(3x + 2) > 7(2x − 4) is 10(3x + 2) > 7(2x − 4). To solve this inequality, first we must combine like terms on each side of the inequality. On the left side, 10(3x + 2) becomes 30x + 20. On the right side, 7(2x − 4) becomes 14x − 28. After combining the like terms, the inequality becomes 30x + 20 > 14x − 28. Next, we must subtract 14x from both sides of the inequality. On the left side, 30x + 20 becomes 16x + 20. On the right side, 14x − 28 becomes −28. After subtracting 14x from both sides, the inequality becomes 16x + 20 > −28. Finally, we must subtract 20 from both sides of the inequality. On the left side, 16x + 20 becomes 16x. On the right side, −28 becomes −48. After subtracting 20 from both sides, the inequality becomes 16x > −48. To solve the inequality, we must divide both sides of the inequality by 16. On the left side, 16x becomes x. On the right side, −48 becomes −3. Therefore, the solution to the inequality is x > −3.

(a) The Population of LaVergne, Tennessee in Standard Form is 33,777.

(b) The combined population of both cities is 147,815

In the given question, according to state census information, the population of LaVergne, Tennessee in 2012 was 33.777 x [tex]10^3[/tex].

The population of Murfreesboro, Tennessee in 2012 was 1.14038 x [tex]10^5[/tex].

(a) We have to write the Population of LaVergne, Tennessee in Standard Form.

The population of LaVergne, Tennessee in 2012 = 33.777 x [tex]10^3[/tex]

The population of LaVergne, Tennessee in 2012 = 33.777 x 1000

Now multiplying

The population of LaVergne, Tennessee in 2012 = 33,777

(b) We have to find the combined population of both cities.

The population of LaVergne, Tennessee in 2012 = 33,777

The population of Murfreesboro, Tennessee in 2012 = 1.14038 x 100,000

The population of Murfreesboro, Tennessee in 2012 = 114038

The combined population of both cities = The population of LaVergne, Tennessee + The population of Murfreesboro, Tennessee

The combined population of both cities = 33,777 + 114038

The combined population of both cities = 147,815

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From the given line equation, the closet point to the origin is (-6/5, 3/5).

Here we have given that the point on the line y=2x+3 that is closest to the origin.

As we all know that the closest point from origin will be the perpendicular distance from origin to the line.

Here we need to find an equation of the perpendicular from (0,0) on y = 2x + 3.

As we all know that the standard form of the equation is in slope-intercept form is written as,

=> y = mx + c

While we comparing this with the given equation, then we get the value of the Slope that is m = 2 and the Slope of the perpendicular is calculated as,

=> - (1/m) = -1/2

Now, we have to write the equation of the perpendicular is found by using the formula,

=> (y - y1) = m (x - x1)

Apply the value on the equation, then we get,

=> y - 0 = (-1/2) (x - 0)

=> y = (-1/2)x

therefore, the resulting perpendicular equation is written as,

=> 2y + x = 0 ----------------(2)

When we solving (1) and (2), then we get,

=> 5y = 3

Therefore, y = 3/5

And the value of x is calculated as

=> x + 2(3/5) = 0

=> x = -6/5

So the point on the line is (-6/5, 3/5).

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Check the picture below.

The position number for term 47 is 269.

This is an arithmetic sequence since each term has a common difference. Let us test it.

The difference between 1st and 2nd terms is

-7 + d = -1

d = -1 + 7

  = 6

Now we check the difference for term

The difference between 3rd and 4th terms is

5 + d = 11

d = 11 – 5

  = 6

So the difference is the same so we can apply a common equation for arithmetic sequence

[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + d ( n - 1 )

Where :

[tex]a_{n}[/tex] = number at term n

[tex]a_{1}[/tex] = first number of sequence

d = difference for each number sequence

n = term

From the question, we need to find the number at position term 47

[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + d ( n - 1 )

[tex]a_{47}[/tex] = -7 + 6 ( 47 - 1 )

    = -7 + 6 ( 46 )

    = -7 + 276

    = 269

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Answer:

Step-by-step explanation:

The length that needs to cover all 3 sides of both book ends will be √208 inches.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

Sylvie realizes the container will be 8 inches long and the level will be 12 inches.

Then the length is given as,

H² = 12² + 8²

H² = 144 + 64

H² = 208

H = √208 inches

Then the length that needs to cover all 3 sides of both book ends will be √208 inches.

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use the 20m/70ft as the next depth and put 27 minutes for the criteria ABT. With the surface interval of 62 mins and G as the new pressure group. Use the 18m/60ft as the final depth, the final ABT will be approximately 34 mins.

If we use the general Dive Planning mode on the eRDPML and insert the option "No" for the Multilevel Dive. Furthermore, insert the option "Yes" for the First Dive. If we use 25m/80ft and click the enter button when the NDL appears. Also put 22 minutes for the criteria ABT. For the surface interval (i.e. 52 mins), E/D is the new pressure group.

i am an advanced open water diver. i plan to do three dives. the first dive is a 25-meter dive for 22 minutes followed by a 52-minute surface interval. the second dive is to 20 meters for 27 minutes followed by a surface interval of 62 minutes. my third dive is to 18 meters.

In addition, use the 20m/70ft as the next depth and put 27 minutes for the criteria ABT. With the surface interval of 62 mins and G as the new pressure group. Use the 18m/60ft as the final depth, the final ABT will be approximately 34 mins.

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