Which is a rational function? Need help on the question I be stuck on it for the last 20 minutes

A statement that is true about the points and planes include the following: B. The line that can be drawn through points D and E is contained in plane Y.

In Mathematics and Geometry, a plane is sometimes referred to as a two-dimensional surface and it can be defined as a flat, two-dimensional surface with zero curvature and zero thickness, that extends indefinitely (infinitely).

If point C lies outside plane Y and point D lies on plane Y, the line that is drawn through the points C and D is not contained in plane Y. Therefore, answer option (A) is incorrect.

If points D and E, both lie in plane Y, the line that is drawn through the points C and D is contained in plane Y. Therefore, answer option (B) is correct.

Since plane X has infinitely many points, point F isn't the only point that lies in plane X. Therefore, answer option (C) is incorrect.

In conclusion, there are infinitely many points in plane Y, which implies that points D and E aren't the only points that would lie in plane Y. Therefore, answer option (D) is incorrect.

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Complete Question;

Planes X and Y and points C, D, E, and F are shown.

Which statement is true about the points and planes?

The line that can be drawn through points C and D is contained in plane Y.

The line that can be drawn through points D and E is contained in plane Y.

The only point that can lie in plane X is point F.

The only points that can lie in plane Y are points D and E.

The increasing trend of part-time college enrollment Reflects the changing needs and priorities of today's students. As the higher education landscape continues to evolve, it is important for institutions to adapt and provide opportunities that meet the diverse needs of their student populations.

In recent years, the percentage of part-time college students has been increasing. According to the National Center for Education Statistics, 41% of all college students were enrolled part-time in 2021. This represents a significant shift in the traditional model of full-time college attendance.

There are several reasons why students may choose to enroll part-time. For example, some students may have work or family commitments that make it difficult to attend classes on a full-time basis. Others may be pursuing additional education while working in their chosen field. Still, others may simply prefer the flexibility that part-time enrollment offers.

Despite the benefits of part-time enrollment, there are also some potential drawbacks. For example, part-time students may not be eligible for the same financial aid or scholarship opportunities as full-time students. Additionally, part-time students may take longer to complete their degree programs, which can result in higher overall costs.

It is important for colleges and universities to recognize the needs of part-time students and provide appropriate resources and support. This may include offering evening or weekend classes, providing online coursework options, and offering flexible scheduling to accommodate work and family obligations.

Overall, the increasing trend of part-time college enrollment reflects the changing needs and priorities of today's students. As the higher education landscape continues to evolve, it is important for institutions to adapt and provide opportunities that meet the diverse needs of their student populations.

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The value of the expressions are,

⇒ (q ο r ) (7) = 22

⇒ (r ο q ) (7) = 8

We have to given that,

Functions are defined as,

⇒ q (x) = x² + 6

⇒ r (x) = √x + 9

Now, We can formulate all the values as,

⇒ (q ο r ) (7)

⇒ q (r (7))

⇒ q (√7 + 9)

⇒ q (√16)

⇒ q (4)

⇒ (4² + 6)

⇒ 22

⇒ (r ο q ) (7)

⇒ r (q (7))

⇒ r (7² + 6)

⇒ r (55)

⇒ √55 + 9

⇒ √64

⇒ 8

Thus, The value of the expressions are,

⇒ (q ο r ) (7) = 22

⇒ (r ο q ) (7) = 8

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Based on the above, the probability that a randomly chosen senior student played football is: 13 / 53

For one to calculate the probability, we need to know the total number of students in the senior group that has played football and so later on, we  divide it by the total number of students in the senior group.

Based on the table,

So, the total number of seniors will be:

26 + 13 + 14

= 53

Hence, the probability that a randomly chosen senior student played football is:

13 / 53

Therefore, The the probability is 13/53.

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All the polygons are,

1) Rectangle

2) Parallelogram

3) Trapezoid

4) Square

For condition, both quadrilateral and a parallelogram. and opposite sides are equal, NOT all of them and my diagonals are congruent.

Type of quadrilateral:

⇒ Rectangle

2-1 have 2 pairs of parallel sides. All of my sides are congruent and my diagonals are perpendicular, but my angles are NOT congruent.

Type of quadrilateral:

⇒ Parallelogram

3-1 have 2 pairs of parallel sides. My opposite sides are congruent, my diagonals bisect each other and my angles are NOT all equal.

Type of quadrilateral:

⇒ Trapezoid

4- I am both quadrilateral and a parallelogram. All of my sides are congruent and All my angles are congruent.

Type of quadrilateral:

⇒ Square

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The TRUE statement about the data set that has 10 values with a mean of 12 and a mean absolute deviation of 4 is C) No values in the data set are less than 8 or greater than 16.

The mean absolute deviation (MAD) measures the variability in the average distance between the observed data and their mean.

We can find the MAD by calculating the absolute deviations of each data value from the mean, and then find the average of those deviations.

On the other hand, the mean is the average value of the data set, which is computed by dividing the total value by the number of items in the data set.

Thus, whereas, the mean is the quotient of the total value and the number of items in the data set, the mean absolute deviation checks for variability from the mean.

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The value of x in the figure that shows two similar tringles is calculated to the nearest tenth as: x = 47.9.

If two triangles have the same shape but different sizes, then they are similar to each pother and their corresponding pair of sides will have lengths that are proportional to each other.

The triangles are similar because they have the same shape but different sizes, therefore:

HF/CE = GF/CD

Given the following:

HF = x

CE = 87

GF = 33

CD = 60

Substitute the values:

x/87 = 33/60

Cross multiply:

60x = 87 * 33

x = 87 * 33 / 60

x = 47.9 [to nearest tenth]

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The particle travels approximately 45.63 units along the path. The displacement is the straight-line distance between the initial and final positions of the particle is 2781.

To find the distance the particle travels along the path, we can integrate the speed over the interval of time. The speed of the particle is given by the magnitude of its velocity vector.

The velocity vector is the derivative of the position function r(t):

[tex]v(t) = (d/dt)(t^3/3, t^2, 2t)[/tex]

[tex]= (t^2, 2t, 2)[/tex]

The speed of the particle at any given time t is:

|v(t)| = √((t^2)^2 + (2t)^2 + 2^2)

= √(t^4 + 4t^2 + 4)

= √((t^2 + 2)^2)

To find the distance traveled along the path, we integrate the speed function over the given interval of time. The particle travels from t = -1/3 to t = 9.

distance = ∫[from -1/3 to 9] |v(t)| dt

= ∫[from -1/3 to 9] |t^2 + 2| dt

= ∫[from -1/3 to 0] -(t^2 + 2) dt + ∫[from 0 to 9] (t^2 + 2) dt

= [-1/3 * t^3 - 2t] (from -1/3 to 0) + [1/3 * t^3 + 2t] (from 0 to 9)

Evaluating the definite integrals:

distance = [-1/3 * 0^3 - 2 * 0 - (-1/3 * (-1/3)^3 - 2 * (-1/3))] + [1/3 * 9^3 + 2 * 9 - (1/3 * 0^3 + 2 * 0)]

= [0 - (1/3 * (-1/27) + 2/3)] + [1/3 * 729 + 18]

= [1/27 + 2/3] + [729/3 + 18]

= 1/27 + 2/3 + 729/3 + 18

= 1/27 + 18/27 + 729/3 + 18

= (1 + 18 + 729)/27 + 18

= 748/27 + 18

= 27.63 + 18

= 45.63 units (approximately)

Therefore, the particle travels approximately 45.63 units along the path.

To find the average speed, we divide the distance traveled by the time taken. The time taken is 9 - (-1/3) = 9 1/3 = 28/3.

average speed = distance / time

= 45.63 / (28/3)

= 45.63 * (3/28)

= 4.9179 units per unit time (approximately)

The displacement is the straight-line distance between the initial and final positions of the particle.

displacement = |r(9) - r(-1/3)|

= |(9^3/3, 9^2, 2 * 9) - ((-1/3)^3/3, (-1/3)^2, 2 * (-1/3))|

= |(27, 81, 18) - (-1/27, 1/9, -2/3)|

= |(27 + 1/27, 81

= 2781.

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Horizontal changes are often the opposite of what you'd expect to see in the formula.

12:

To shrink/compress horizontally by a factor of 2/3, you need [tex]g(x) = f(\frac{3}{2}x)[/tex].

Notice we have the reciprocal inside of the function notation.

13:

To translate left 5 units, you have [tex]g(x) = f( x+5 )[/tex].

Notice we have the opposite sign inside of the function notation.

The exponential function that passes through the points (-1,-y) and (1,20) is f(x) = -20eˣ.

We need to use the given points to form two equations and solve for the constants in the exponential function.

For the first problem:

Let (0,4) and (2,16) be the given points.

Since the function is of the form f(x) = Ca², we have:

f(0) = C(0)² = 4

f(2) = C(2)² = 16

Simplifying each equation:

C = 4

4a² = 16

a² = 4

a = ±2

Therefore, the exponential function that passes through the points (0,4) and (2,16) is f(x) = 4(2)² = 16 or f(x) = 4(-2)² = 16.

For the second problem:

Let (-1,y₁) and (1,y₂) be the given points.

Since the function is of the form f(x) = Ca, we have:

f(-1) = Ca = y₁

f(1) = Ca = y₂

Simplifying each equation:

C =y₁/a

C =y₂/a

Equating both expressions for C, we have:

y₁/a = y₂/a

y₁=y₂

Therefore, the exponential function that passes through the points (-1,-y) and (1,20) is f(x) = -20eˣ.

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Answer:
Marcus is correct

Step-by-step explanation:

If x=3 then 3x3=9 and 9+2=11
and 4x3=12 12-1=11. Both are equivalent
so Marcus is correct.

A) The absolute value equation that represents the situation is |x - $175| = $6.50

B) The maximum amount Shawn might have made last month is $181.50, and the minimum amount Shawn might have made is $168.50.

Part A: The absolute value equation that represents the situation is:

|x - $175| = $6.50

Part B: To find the maximum and minimum amounts Shawn might have made last month, we can set up two equations based on the absolute value equation.

Solve for x when x - 175 = 6.50:

x - 175 = 6.50

x = 6.50 + 175

x = 181.50

Solve for x when x - 175 = -6.50:

x - 175 = -6.50

x = -6.50 + 175

x = 168.50

Therefore, the maximum amount Shawn might have made last month is $181.50, and the minimum amount Shawn might have made is $168.50.

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Probability that jakes throw will earn at least 30 points is 33.5% .

Now,

Area of whole dartboard

Radius = 3 (4 x 4) = 19

⇒ Total area of dartboard = π19² = 361π in²

Area of 30, 40, 50 points zone

Radius = 3 + (2 x 4) = 11

⇒ Area of at least 30 points = π11² = 121 π in²

Probability,

probability = (121π ÷ 361π) x 100 = 33.5%

Jake can accept the tie because the probability of winning is just 33.5 % and if chooses to play one more team the chances of winning are just 33.5%.

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The values of the variables in the expression are as follows:

a = 3

b = 4

c = 3

d = -4

Here, we have,

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Let's find the value of the variables in the expression.

(ax + b)(cx - d) = 9x² - 16

acx² - adx + bcx - bd = 9x² - 16

Therefore,

9x² - 16 = (3x + 4) (3x - 4)

Hence,

(ax + b) = (3x + 4)

Therefore,

a = 3

b = 4

(cx - d) = (3x - 4)

cx = 3x

d = -4

Therefore,

c = 3

d = -4

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cmplete question:

What is the value of a ?

What is the value of b ?

What is the value of c ?

What is the value of d ?

Answer: a , c , D

Step-by-step explanation:

i took the test

Rational numbers can be represented in decimal form and will fit properly in a number line.

Representing rational numbers on a number line helps us visualize their relative positions and understand their magnitudes. Decimals are often used to represent rational numbers on a number line, providing a clear depiction of their location between other numbers.

To represent a rational number as a decimal on a number line, we can convert it from a fraction to a decimal form. For example, the rational number 3/4 can be represented as the decimal 0.75. Placing 0.75 on the number line would show its position between 0 and 1, closer to 1 but not quite reaching it.

Real-world situations can also be used to represent rational numbers. Let's consider a scenario where you have a pizza that is divided into 8 equal slices. If you have eaten 3 slices, the rational number representing the portion you consumed is 3/8. In this real-world situation, you can imagine a pizza with 8 slices, and mentally mark off 3 slices as consumed, giving a visual representation of the fraction.

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The possibility diagram representing all the possible outcomes is as follows:

The probability that the customer selects a small bottle of apple juice is 1/6

The probability that the customer selects a small bottle of apple juice is calculated as follows:

number of expected outcomes = 3

number of  possible outcomes = 18

P(selecting a small bottle of apple juice) = 3/18

P(selecting a small bottle of apple juice) = 1/6

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Answer:

The sum of two number is 40 would be :

x + y = 40

The second number is 5 less than twice the first number would be :

y = 2x - 5

We can find the value by solving this system of equations, we will isolate x in the first equation, then we replace it in the second equation :

x = 40 - y

y = 2(40 - y ) - 5

y = 80 - 2y -5

y + 2y = 75

3y = 75

y = 75/3 = 25

We then replace this value in one equation of find the other variable :

x + 25 = 40

x = 40 -25

x = 15

Therefore the value of the first number is 15 and the second number is 25.

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The domain of the piecewise function is [-3, ∞)and the value of f(2) is 0.

A piecewise function represents a numerous pieces of curves in its graph. A piecewise function contains different functions for different inputs at different intervals.

From the given information, we are given f(x) = 5 if -3 ≤ x < 2 and -2x + 4   if x. Using the graphing tools, the piecewise function can be seen in the image attached below.

The domain of the piecewise function is an area where the function is defined and it is [-3, ∞).  The when x is 2, f(2)  lies in -2x + 4.

f(2) = -2x + 4

f(2) = -2(2) + 4

f(2) = 0

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When evaluating ∫sec^m x tan^n x dx, if the power of sec x is even, we can substitute u = sec x + tan x.

We have,

Here's the reasoning behind this substitution:

If m is an even number,

Then we can rewrite sec^m x as (1 + tan^2 x)^(m/2) using the Pythagorean identity sec^2 x = 1 + tan^2 x.

So we have:

∫sec^m x tan^n x dx = ∫(1 + tan^2 x)^(m/2) tan^n x dx

Now

We can make the substitution u = sec x + tan x,

so,

du/dx = sec x tan x + sec^2 x, and we can rewrite tan x dx as:

(du/dx - sec^2 x) dx:

∫(1 + tan^2 x)^(m/2) tan^n x dx

= ∫(1 + u^2)^(m/2) ((du/dx - u^2 + 1)/u) dx

The term (du/dx - u^2 + 1)/u can be simplified to 1/u, so we have:

∫(1 + tan^2 x)^(m/2) tan^n x dx

= ∫(1 + u^2)^(m/2) (1/u) du

Now we can integrate with respect to u, and then substitute back in for x at the end.

Thus,

When evaluating ∫sec^m x tan^n x dx, if the power of sec x is even, we can substitute u = sec x + tan x.

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Answer:

A ≈ 904.8 cm²

Step-by-step explanation:

the area of a circle is calculated as πr² ( r is the radius )

the area (A) of the semicircle , that is half of the circle is

A = [tex]\frac{1}{2}[/tex] πr²

the diameter of the semicircle is 48 cm then r = 48÷ 2 = 24 cm , so

A = 0.5 × π × 24²

   = 0.5 ×π × 576

  = 288 × π

  ≈ 904.8 cm² ( to 1 decimal place )

Answer: c

Step-by-step explanation:

Answer:

Option D

Step-by-step explanation:

The highest number represents the length of the hypotenuse

The remaining two numbers represent the opposite and adjacent.

Using [tex]hyp^{2} = opp^{2} + adj^{2}[/tex]

Check to see if the numbers satisfy the equation

Hence, [tex]9^{2} +12^{2} = 15^{2}[/tex]

Answer:

The area of the trapezoid is 3(8 + √3) square units, which is about 29.196 square units.

Step-by-step explanation:

In each 30°-60°-90° triangle, h = 3 since the length of the shorter side is one-half the length of the hypotenuse. So the length of the longer side of each of these triangles is 3√3 since the length of the longer side is √3 times the length of the shorter side.

Now we compute the area of the trapezoid:

A = (1/2)(3)(8 + √3 + 8 + √3)

= (1/2)(3)(16 + 2√3)

= 3(8 + √3) = about 29.196

The solids have the following surface areas:

Case 1: A = 708.4 in²

Case 2: A = 89.4 yd²

Case 3: A = 537.841 mm²

Case 4: A = 73.6 m²

Case 5: A = 311.4 ft²

Case 6: A = 857.184 km²

In this problem we must determine the surface area of six solids, that is, the sum of the areas of all faces. The area of each face can be found by using any of the following formulas:

Triangle

A = 0.5 · b · h

Square

A = l²

Circle

A = π · r²

Where:

And the surface area of each solid is:

Case 1

A = (11 in)² + 4 · 0.5 · (11 in) · (26.7 in)

A = 708.4 in²

Case 2

A = 0.5 · (6 yd) · (5.2 yd) + 3 · 0.5 · (6 yd) · (8.2 yd)

A = 89.4 yd²

Case 3

A = π · (8 mm)² + π · (13.4 mm) · (8 mm)

A = 537.841 mm²

Case 4

A = 0.5 · (4 m) · (3.5 m) + 3 · 0.5 · (4 m) · (11.1 m)

A = 73.6 m²

Case 5

A = (9 ft)² + 4 · 0.5 · (9 ft) · (12.8 ft)

A = 311.4 ft²

Case 6

A = π · (8.5 km)² + π · (8.5 km) · (23.6 km)

A = 857.184 km²

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Step-by-step explanation:

Understand

Gary owns a farm and he sent 35 of his cows to the market. He assumed he would have around 1100 cows left.

plan

we need to calculate the total amount of cows Gary owns and subtract the amount he sent to the market to find out the actual amount of cows left.

Carry out

total number of cattles = 305 + 530 + 320 + 130 = 1285

cattles left = 1250

Check

Gary assumed he had 1100 cattles left but he has 1250 left.

Q2

It was a good guess since the amount Gary guessed is close enough to the actual amount he has.

The actual amount left is greater than that Gary assumed.

The amount Gary guessed to have is reasonable since the amount is close to the actual amount.

The first option is the correct one for the line y = x - 2:

" coordinate plane with a line starting at (negative 2, negative 4), passing through (0, negative 2)"

Here we want to identify the graph of the linear equation:

y = x - 2

First, notice that when we evaluate this in x = 0 we get the y-intercept:

y = 0 - 2

y = -2

Then the y-intercept there is (0, -2)

Also, evaluating the linear equation in x = -2, then we will get:

y = -2 - 2

y = -4

So we have the point (-2, -4)

Then the correct option is the first one:

" coordinate plane with a line starting at (negative 2, negative 4), passing through (0, negative 2)"

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The way we calculate the measures of Variability are:

Range is difference between largest and smallest value.

Interquartile range is is the range of the middle half of a distribution.

Standard deviation is is the average distance from the mean.

Variability is defined as the most commonly measured with the following descriptive statistics:

Range: The way this is calculated is that it is the difference between the highest and lowest values in a given set of data.

Interquartile range: This way that this is calculated is that it is the range of the middle half of a distribution.

Standard deviation: The way that this is calculated is that it is the average distance from the mean.

Variance: The way that this is calculated is that it is the average of squared distances from the mean.

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