Triangle PQR, with vertices P(4,6), Q(8,5), and R(5,9), is drawn inside a rectangle, as shown below.

The slope of the line that passes through (4,1) and (2,5) is -2.The slope of a line can be expressed in many ways, including as a fraction, decimal, or even in terms of the angle of inclination.

The slope or gradient of a line in mathematics is a numerical representation of the steepness and direction of the line.The slope of a line is calculated by finding the difference in the y-values (rise) divided by the difference in the x-values (run).

In this case, the rise is 5 - 1 = 4 and the run is 2 - 4 = -2.

Therefore, the slope of the line is 4/-2 = -2.

In the case of a horizontal line, the slope is 0, and in the case of a vertical line, the slope is undefined. The slope is a useful tool in mathematics as it can be used to determine the equation of a line, the rate of change on a graph, or the amount of change for every unit of time. It can also be used to determine the area between two points on a graph. Slope is an essential concept in mathematics and can be used to solve many types of problems.

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If  equation y = 6200x represents the number of miles, y, that the satellite Space Explorer flies in a hours then 6200 is the rate of change.

Two or more expressions with an Equal sign is called as Equation.

The given equation is y = 6200x

y equal to six thousand two hundred times of x.

y = 6200x represents the number of miles, y, that the satellite Space

Explorer flies in a hours.

We need to find the rate of change.

Rate of change means how quickly something changes over time.

Differentiate the equation with respect to x

dy/dx=6200

Hence, the rate of change is 6200.

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The sum of three integers is greater than 9. Assuming all integers same can show that one of the integers must be greater than 3.

The three elements that make up an integer are zero, the natural numbers, and their additive inverse. It can be shown on a number line, but without the fractional portion. Z stands for it.

Given,

Sum of three integers is greater than 9.

Let all the integer be same, then

x + x + x > 9

3x > 9

x > 3

Let take that the three integers are consecutive, then

x+ x + 1 + x +2> 9

3x + 3>9

3x > 6

x> 2

So, the integer must be 3, 4 and 5

Here we can see that one integer must be greater than 3.

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When the scale factor is greater than one, then the dilation is not a reduction.

What is a dilation?

Dilation is a process of changing a thing. It is a process of transformation that to make the objects smaller or larger, with the use of specific scale factor.

The new figure that is the result of dilation is known as the image. Initial figure is referred to as the pre-image.

What is a center of dilation?  

Center of dilation is the resizing that happens from a point. The objects/figures are expanded or contracted from the center of dilation.

Scale factor is a figure by which the size of any geometrical figure can be resized, with respect to its original size. The scale factor is multiplied to get image.

Figure size increased, when the scale factor is greater than 1.

Thus, the dilation will be a expansion, when the scale factor is a greater than one.

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The standard form of the quadratic equation is x² -17x + 60 =0

What is a quadratic equation?

A quadratic equation is a second-order polynomial equation with a single variable such as x, where ax²+bx+c=0. with a ≠ 0 . Given that it is a second-order polynomial equation, the algebraic fundamental theorem ensures that it has at least one solution. Real or complicated solutions are both possible.

Standard form of a quadratic equation:

ax² + bx + c=0

Given:

x² = 17x - 60

move right side terms to the left

x² -17x + 60 =0

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The appropriate sample size for the 95% confidence interval is given as follows:

139.

To obtain the appropriate sample size for the confidence interval, we need to look at it's equation for the margin of error, which is defined as follows:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which the parameters are listed as follows:

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The margin of error and the population standard deviation have the values given as follows:

[tex]M = 1, \sigma = 6[/tex]

Then the sample size is obtained as follows:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]1 = 1.96\frac{6}{\sqrt{n}}[/tex]

[tex]\sqrt{n} = 1.96 \times 6[/tex]

[tex](\sqrt{n})^2 = (1.96 \times 6)^2[/tex]

n = 139 (rounded up, as for a sample size of 138 the margin of error would be slightly above 1).

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Answer:

Acute angle

Step-by-step explanation:

Any angle less than 90° is acute.

Answer:

Acute.

Step-by-step explanation:

90 degree angle = Right Angle

Greater than 90 degrees = Obtuse Angle

Less than 90 degrees = Acute Angle

Volume of ice cream Cone = 753.6[tex]cm^{3}[/tex]

A three-dimensional space's occupied volume is measured. It is typically quantified using a variety of imperial or US-standard units as well as SI-derived units. The definition of length and volume are connected.

According to the given information

Volume of toy ice cream Cone = Volume of Cone + Volume of Hemisphere

We are given that

Radius of cone = Radius of hemisphere = 6 cm

Height of cone = 8 cm

So

Volume of Sphere = [tex]\frac{1}{2}[/tex] × [tex]\frac{4\pi r^{3} }{3}[/tex]

                               = 1/2 × 4/3 × 3.14 × [tex]6^{3}[/tex]

Volume of sphere = 452.16 [tex]cm^{3}[/tex]

Volume of Cone = [tex]\frac{\pi r^{2}h }{3}[/tex]

                            = 1/3 × 36 ×3.14 ×8

                            = 301.44 [tex]cm^{3}[/tex]

So

The Volume of ice cream cone = 452.16 [tex]cm^{3}[/tex] + 301.44 [tex]cm^{3}[/tex]

                                                     = 753.6[tex]cm^{3}[/tex]

Volume of ice cream Cone = 753.6[tex]cm^{3}[/tex]

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Square 1 is so named because of the shape of the puzzle: it is a cube with four sides, each with nine squares, creating a square shape

The puzzle is also sometimes referred to as a "magic cube" because it can be rearranged into different shapes and configurations.Square 1 is a 3-dimensional puzzle that consists of nine squares on each side of a cube. The puzzle is made up of four layers of nine colored squares that can be rotated around the center axis. This creates a square-like shape, hence the name “Square 1”. The object of the game is to arrange the nine squares on each side so that all of the colors match up. This requires the player to manipulate and rotate the pieces in order to achieve the desired outcome.

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Equation which represents the relationship between the number of soda bottles with winning caps and the total number of soda bottles produced is 7w=20t

Two or more expressions with an Equal sign is called as Equation.

Given that Seven out of every twenty soda bottles produced have caps indicating that the purchaser has won a prize.

We need to find the equation which  represents the relationship between the number of soda bottles with winning caps and the total number of soda bottles produced.

Let w represent the number of bottles with winning caps, and

let t represent the total number of bottles produced.

t=7/20w

7w=20t.

Hence, 7w=20t is the equation represents the relationship between the number of soda bottles with winning caps and the total number of soda bottles produced.

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Answer: 9

Step-by-step explanation:

3x9=27

27-18=9

Answer:

Step-by-step explanation:

dw

The required simplified solution of the given expression is 4√15i.

A simplified solution of the given expression √-240 is to be determined.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,

The square root of the negative value induces the property of the complex number. (a complex number is a number that contains both the real and imaginary parts of the number)

Simplifying,
√-240= √4×4×-15
         = 4 √-15
         = 4√15i   {∵ √-1 = i}

Thus, 4√15i is the required simplified solution to the provided expression.

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The question seems to be incomplete,
The complete question could be as,

Simplify the complex number √-240 ?

The ball' velocity when it left Zoey' hand is 8.85 m/s

What is the principle of conservation of energy?

The word "conservation" in physics describes anything that doesn't change. This indicates that a conserved quantity is represented by a variable in an equation that is constant over time. Its value is the same whether an event occurs before or after it.

In physics, there are a lot of conserved quantities. For making forecasts in what would otherwise be exceedingly complex situations, they are frequently remarkably useful. There are three fundamental quantities in mechanics that are conserved. They are power, forward motion, and angular momentum.

According to question

Mass of the ball = 0.2 kg

Maximum height of the ball = 4 m

Gravity = 9.8 m/s²

Therefore:

Using conservation of energy, we know that P.E. top = K.E. bottom. This tells us that the potential energy at the top is all converted to kinetic energy at the bottom. We can substitute the equations for potential energy and kinetic energy

Initial kinetic energy + Initial potential energy =  Final kinetic energy + Final potential energy

1/2mv² + 0 = mgh + 0

½(0.2)v² = (0.2)(9.8)4

v² = 78.4

v = 8.854377…

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Option c) The centers will roughly be equal, and the variability of simulation A will be less than the variability of simulation B

According to the information given in the question,

A true proportion of 0.325 represents that the two simulations will be conducted for sampling proportions from a population

Simulation A -

Sample size - 100

Trials - 1500

Simulation B -

Sample size - 50

Trials - 2000

Now due to the relation of simulation A and simulation B, they are closely equal-

The total sample size of simulation A= 1500 x 100

= 150000

The total sample size of simulation B = 2000 x 50

= 100000

From the above calculations of simulations A and B, we can see that while comparing the,

Sample Size = Simulation A > Simulation B

Variability = Simulation B < Simulation B

Therefore, option c) The centers will roughly be equal, and the variability of simulation A will be less than the variability of simulation B is correct.

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In a recent survey, the proportion of adults who indicated mystery as their favorite type of book was 0.325. Two simulations will be conducted for the sampling distribution of a sample proportion from a population with a true proportion of 0.325. Simulation A will consist of 1,500 trials with a sample size of 100. Simulation B will consist of 2,000 trials with a sample size of 50. Which of the following describes the center and variability of simulation A and simulation B?

A) The centers will roughly be equal, and the variabilities will roughly be equal.

B) The centers will roughly be equal, and the variability of simulation A will be greater than the variability of simulation B.

C) The centers will roughly be equal, and the variability of simulation A will be less than the variability of simulation B.

D) The center of simulation A will be greater than the center of simulation B, and the variability of simulation A will roughly be equal to the variability of simulation B.

E) The center of simulation A will be less than the center of simulation B, and the variability of simulation A will be greater than the variability of simulation B.

The slope of the line of best fits will be $0.15 per minute. Then the correct option is A.

The slope is the ratio of rising or falling and running. The difference between the ordinate is called rise or fall and the difference between the abscissa is called run.

The slope of the line is given as,

m = (y₂ - y₁) / (x₂ - x₁)

Take two points from the table which are (300, 90) and (100, 60). Then the slope of the line is given as,

m = (90 - 60) / (300 - 100)

m = 30 / 200

m = $0.15 per minute

The slope of the line of best fits will be $0.15 per minute. Then the correct option is A.

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Answer: in image

Step-by-step explanation: j

The solution to the equation -2.5(4x - 4) = -6 is x = 1.6

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

-2.5(4x - 4) = -6

Open the bracket using the Distributive Property

So, we have the following representation

-10x + 10 = -6

Subtract 10 from both sides of the equation

-10x = -16

Divide both sides by -10

x = 1.6

Hence, the solution is x = 1.6

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Answer:

6 plus 10

Step-by-step explanation:

6 beginning number plus 10 repeatedly

Answer:B!!!!

Step-by-step explanation:

HOPE THIS HELPED

The required equation of the line is given as y =3x - 3.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

here,

As given in the question that, the line is passing through the point (2,3), and the slope line is 3, the equation of the line is to be determined.

The standard equation of the line is given as
y=Mx + b
Substitute values of point and slope in the above equation,
3 = 2×3 + b
b = -3
Put this b and M in the standard given equation,
y= 3x - 3

Thus, the required equation of the line is given as y =3x - 3.

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Answer:

Step-by-step explanation:

o find the vertex of f(x)=x2−8x+7 , there are several things you can do. You could complete the square to get the equation into vertex ...

Answer:

Step-by-step explanation:

A Commission

The extra 2% of the sales dollars that Padma receives each month is called a commission.

The commission is a payment made to an employee in addition to their regular salary or wages, based on the number of sales or business they bring in. Another popular definition of commission is the amount of money earned by an employee when they sell something: He receives a 1% commission on each sale in addition to his pay.

As per the question, Padma receives a commission of 2% of the sales dollars she brings in each month. The commission is a common form of compensation in sales and customer service jobs, where employees are often paid a base salary plus a commission based on their sales or performance.

Thus, the required fill-in-the-blank will be "commission".

Hence, the extra 2 percent of the sales dollars that Padma receives each month is called a commission.

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The absolute value function which will be narrower than  the parent function is:

f(x) = 2.9|x|

Given parent function is f(x)=|x|

Now we have to find which function from given choices will be narrower than the parent function.

Notice that adding or subtracting some number from the parenth function only shifts the graph up, down, left of right side.

But that will not make function narrorwer or broader.

So f(x) = |x – 2| and  f(x) = |x| + 3, can't be the answer.

Multiplying by some positive real number which is more than 1, makes function narrower.

Only f(x) = 2.9|x| from remaining choices fits that case.

Hence f(x) = 2.9|x| is the final answer.

f(x) = 1.2|x + 8|  will also make the function narrower but will shift the parent function too.

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The translations performed are

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

f(x) = ln(x)

g(x) = -ln(x + 1) - 3

First, we have the transformation to be:

From f(x) = ln(x) to f(x) = -ln(x)

This means a reflection across the x-axis

Next, we have

From f(x) = -ln(x) to f(x) = -ln(x + 3)

This means the function is translated left by 3 units

Next, we have:

From f(x) = -ln(x + 3) to f(x) = -ln(x + 3) - 3

This means the function is translated down by 3 units

Hence, the translation is 3 units left and 3 units down

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Total 83 numbers that are positive perfect squares less than [tex]10^6[/tex] are multiples of 24.

What is perfect Square?

A perfect square is a number that can be written as the second exponent of an integer or as the product of an integer by itself.

For instance, the number 25 is a perfect square since it is the product of the integer 5 multiplied by itself, 5*5 = 25.

21 cannot be expressed as the product of two identical integers, so it is not a perfect square number.

Prime Factorization of 24 is 2^3*3.

There must be at least 3 factors of number 2 and 1 factor of number 3 in each square.

its square root must have 2 factors of number 2 and 1 factor of number 3.

This means each square should be in the from [tex](12*c)^2[/tex]. where 12 is a positive numbers less than [tex]\sqrt{10^6}[/tex]  = 1000.

So total numbers of positive perfect squares.

= 1000/12 = 83.

Total 83 numbers that are positive perfect squares less than [tex]10^6[/tex] are multiples of 24.

Given question is incomplete Complete Question here

How many perfect squares less than 10^6 are multiples of 24.

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Answer:

28 divided by 66.29 is approximately 0.4223. To find the exact result, you would need to perform long division. The process for doing this is as follows:

Begin by dividing the leftmost digit of the dividend (28 in this case) by the divisor (66.29). In this case, the result is 0 with a remainder of 28.

Bring down the next digit of the dividend (0 in this case), so that the dividend is now 280.

Divide 280 by 66.29. The result is 4 with a remainder of 36.29.

Bring down the next digit of the dividend (0 in this case), so that the dividend is now 36.29.

Divide 36.29 by 66.29. The result is 0.54 with a remainder of 0.29.

Bring down the next digit of the dividend (0 in this case), so that the dividend is now 0.29.

Divide 0.29 by 66.29. The result is 0.004 with a remainder of 0.

The remainder is 0, so the division is complete. The result is 0.004223.

Alternatively, you can use a calculator to perform the division. Just enter "28 / 66.29" and the calculator will give you the result.

Step-by-step explanation:

The vector in component form for an object flying at 235 mph at a bearing of N55°W is given as follows:

(-134.79, 192.5).

The vector is composed by two components, the x-component and the y-component, as follows:

<x,y>.

The components are defined as follows:

In which the variables are defined as follows:

In the context of this problem, the values of these parameters are given as follows:

v = 235, θ = 55º.

The positions are given as follows:

Hence the components of the vector are given as follows:

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45 is the rate does the car use gas, in miles per gallon.

Cameron's car used 15 gallons to travel 675 miles.

Simply dividing the distance driven by the quantity of petrol your car required to fill up is the simplest approach to figure out how much gas you'll need. That is the sum of the miles traveled and the gas consumed.

The car travels 675 miles, which we divide by the 15 gallons in a full tank of gas to determine miles per gallon of fuel.

Rounding to the nearest tenths place, 675/115 equals 45.

45 is the rate does the car use gas, in miles per gallon

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Answer:

Step-by-step explanation:

I think it's B or C because if you look closely u see that the line goes up then straight on 4. Go for an educational guess.