Predict the value of f(x) when x = 6. *

If you apply the changes below to the absolute value parent function, f(x) = |x|, the equation of the new function is option  A. g(x) = |x – 4| + 6

The mathematical function f(x) = |x|, commonly referred to as the absolute value parent function, yields the numerical value of a provided input in an absolute sense.

from the question,

[tex]f(x)= /x/[/tex]

as well as the fact that  It shifted 4 units to the right end 6 units up.

So, we see that:

(0) 4 units to the right

(b) 6 units up

Hence, Equation f(x)= /x/ is one that have moved the vertex of the parabola 4 units to the right as well as 6 units up.

So,

[tex]f(x) = a(x-h)^{2} + k\\\\f(x) = /x/[/tex]

So by moving right it implies one is adding 4 h= 4 and going up implies adding for example. k = 6

So:

[tex]f(x)= |x|\\\\g(x) = /x-4/ + 6[/tex]

So, based on the equation above, the transformation that is correct is option (A).

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See full text below

If you apply the changes below to the absolute value parent function, f(x) = |x|, what is the equation of the new function?Shift 4 units to the right.Shift 6 units up.

A. g(x) = |x – 4| + 6

B. g(x) = |x – 6| + 4

C. g(x) = |x + 6| + 4

D. g(x) = |x + 4| + 6

Answer:

66-26 = 40

Step-by-step explanation:

u = 40 degrees

The graph of Melinda's model for the height of the Ferris wheel using the transformation of y = sin(x) indicates;

The amplitude = 35 feet

The midline is the line; y = 43

The period = 120 seconds

The frequency = 1/120 s

Phase shift = 90°

A transformation of a function is the translation, resizing, rotation, or reflection of a parent function.

The parent function which Melinda transforms to model her height on the Ferris wheel is; y = sin(x)

The peak of the height on the graph = (60, 78)

The trough of the graph = (0, 8), (120, 8)

The amplitude, a = (Peak y-value - Trough y-value)/2 = (78 - 8)/2 = 35

The period = 2·π/b = The distance between two troughs = 120 - 0 = 120

Therefore; 120 = 2·π/b

b = π/60

The y-coordinates of the midline of the graph, D = 8 + a = 8 + 35 = 43

The sine function is; y = a·sin(b·x + c) + d

The coordinates of the trough and peak points, (0, 8), (60, 78), indicates that the phase shift of the midline from the y-axis to the graph is; c = (60 - 0)/2 = 30

However, Δx = 60 is equivalent to a rotation of 180°

Therefore, Δx = 30 is equivalent to a rotation of 90°

90°  = π/2

Therefore, the phase shift = π/2 = 90°

The equation for the Ferris wheel is therefore;

Please find attached the graph of the function showing the amplitude, midline, period, vertical shift and phase shift created with MS Excel

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The volume of cylinder is,

V = 26,940.59 cm³

We have to given that,

The height of a cylinder is 24.8cm

And, the ratio of the diameter of the cylinder to the height of the cylinder is 3:2

Hence, Lenght of height = 2x

And, Diameter of cylinder = 3x

Since, The height of a cylinder is 24.8cm

So,

2x = 24.8

x = 24.8 / 2

x = 12.4 cm

Hence, Diameter of cylinder is,

d = 3x

d = 3 (12.4)

d = 37.2 cm

So, Radius = 37.2 / 2 = 18.6 cm

Thus, Volume of cylinder is,

V = πr²h

V = 3.14 × 18.6² × 24.8

V = 26,940.59 cm³

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There were no fewer than 1 fruit snacks in the bag.

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

x + 3 >= 4

Subtract 3 from both sides of the inequality

So, we have the following representation

x + 3 - 3 >= 4 - 3

When the like terms are evaluated, we have

x >= 1

This means that that were at least 1 fruit snack in the bag.

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

are 2 similar triangles, we solve with a proportion between the corresponding sides, see the figure below

4 : a = 3 : 4

a = 4 × 4 : 3

a = 16 : 3

a = 5.333...

or a = 5 1/3 (your answer)

a.) The two of the graphs given above that displays the same data is graph I and II.

b.) The third graph which is III doesn't match with others because the years where not represented.

A bar chart is defined as a type of data representation that involves the use of rectangular bars that compares two different variables.

In graph I (a bar chart), the county voter turnout was plotted against the various years it was carried out which is the same with the second graph.

But the third graph is different from the first two graphs because the years where removed and a new variable was introduced.

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Fr tho. I'm over here as a freshman answering sophmore-junior year college questions with ease.

The expression simplified is:

[tex]\frac{y^{-5}}{x^{-3}} = \frac{x^3}{y^5}[/tex]

Remember that a negative power just means that we need to take the inverse, such that:

[tex]n^{-m} = (1/n)^m[/tex]

In this case we want to simplify the expression:

[tex]\frac{y^{-5}}{x^{-3}}[/tex]

Using that rule, we can take the two correspondent inverses, then we will have x to the third power on the numerator and y to the fifth power in the denominator, that is:

[tex]\frac{y^{-5}}{x^{-3}} = \frac{x^3}{y^5}[/tex]

That is the only simplification we can do.

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The y-intercept of the equation for the line of best fit would increase while the magnitude of the slope would decrease, if only the data from 2010 to 2016 are considered. Also, there would be a positive correlation because as the independent variable increases, the dependent variable increases.

In Mathematics and Statistics, a trend line is sometimes referred to as a line of best fit and it can be defined as a statistical tool which is commonly used in conjunction with a scatter plot, in order to determine whether or not there's any form of correlation (either positive or negative) between a given data.

Generally speaking, the line of best fit or trend line should be very close to the data points as much as possible.

By critically observing the scatter plot using the data from 2010 to 2016, we can logically deduce that the y-intercept of the equation for the line of best fit would increase while the magnitude of the slope for the line of best fit would decrease.  

Additionally, there would be a positive correlation from 2010 to 2016 because as the independent variable on the x-axis increases, the dependent variable on the y-axis increases simultaneously.

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Subtracting 58 cm from 734 cm will give a perfect square.

To find the value that needs to be subtracted from 734 cm to obtain a perfect square, we can start by finding the largest perfect square that is less than or equal to 734.

The largest perfect square less than 734 is 676, which is equal to 26².

To obtain this perfect square, we subtract 676 from 734:

734 - 676

= 58

Therefore, subtracting 58 cm from 734 cm will give a perfect square.

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We can solve the inequality |x + 3| < 1 by considering two cases:

Case 1: x + 3 ≥ 0

If x + 3 ≥ 0, then the inequality simplifies to:

x + 3 < 1

Subtracting 3 from both sides gives:

x < -2

So the solution set for this case is -3 < x < -2.

Case 2: x + 3 < 0

If x + 3 < 0, then we have:

-(x + 3) < 1

Multiplying both sides by -1 (which reverses the direction of the inequality) gives:

x + 3 > -1

Subtracting 3 from both sides gives:

x > -4

So the solution set for this case is -4 < x < -3.

Combining the solution sets from both cases, we get:

-4 < x < -2

Therefore, the solution to the inequality |x + 3| < 1 is the open interval (-4, -2).

The distance, d, that the ladder goes up the wall (above the fire truck) is approximately 7.76 meters.

1. Convert the angle from degrees and minutes to decimal form.

  47 degrees 44' = 47 + (44/60) = 47.7333 degrees (rounded to four decimal places)

2. Use trigonometric ratios to find the length of the side opposite the angle.

  sin(47.7333) = Opposite / Hypotenuse

3. Rearrange the formula to solve for the Opposite side.

  Opposite = sin(47.7333) * Hypotenuse

4. Substitute the known values into the equation.

  Opposite = sin(47.7333) * 10.5 meters

5. Calculate the value of sin(47.7333) using a calculator.

  sin(47.7333) ≈ 0.7431

6. Substitute the value of sin(47.7333) and the given value of Hypotenuse into the equation.

  Opposite = 0.7431 * 10.5 meters

7. Calculate the value of Opposite.

  Opposite ≈ 7.76 meters

Therefore, the distance, d, that the ladder goes up the wall (above the fire truck) is approximately 7.76 meters.

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The area of a rectangle is calculated by multiplying its length by its width. In this case, the rectangle is 3 inches by 5 inches. Therefore, the area of the rectangle is:

Area = Length × Width

Area = 3 inches × 5 inches

Area = 15 square inches

So, the area of the rectangle is 15 square inches.

Answer:

15 inches

Step-by-step explanation:

We can use the formula Length times Width to find the Area. In this case the Length and Width are 3 inches and 5 inches. 3 times 5 is 15, so that is the answer.

Answer:

In continuous exponential growth, the size of a population can be modeled by the formula:

P = P0 * e^(rt)

where:

P = final amount (1982 bacteria in this case)

P0 = initial amount (1900 bacteria in this case)

r = growth rate (the variable we're trying to find)

t = time (1.5 hours in this case)

First, let's isolate the variable r in the equation:

1982 = 1900 * e^(1.5r)

Dividing both sides by 1900 gives:

1982 / 1900 = e^(1.5r)

Taking the natural logarithm (ln) of both sides (since the natural logarithm is the inverse of the exponential function) gives:

ln(1982 / 1900) = 1.5r

Now, solve for r:

r = ln(1982 / 1900) / 1.5

Using a calculator to evaluate this, we get:

r ≈ 0.0224

Therefore, the hourly growth rate is approximately 0.0224 or about 2.24% per hour. This means the bacteria population is growing at a rate of about 2.24% every hour.

The probability that a randomly chosen musician is a singer is

To find the probability that a randomly chosen musician is a singer, we need to divide the number of singers by the total number of musicians.

Probability of choosing a singer = Number of singers / Total number of musicians

probability of choosing a singer = 35 / 82

simplifying this fraction, we find that the probability is approximately:

probability of choosing a singer ≈ 0.4268

Therefore, the probability that a randomly chosen musician is a singer is 35/82 or approximately 0.4268.

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The scale factor of the dilation is: 3/2

Dilation is a transformation of an object which changes its size. if the dilated image is larger then it is called enlargement. If the dilated image is smaller it is called reduction.

If the dilation has the origin as the center of dilation, we can find points on the image formed by dilation by multiplying the coordinates of the original geometric object like triangle multiplying by the scale factor. For scale factor k, the transformation of the dilation is written as :  (x, y) → (k x, k y).

The scale factor ,k  = coordinate of image / coordinate of original

Given that Triangle ABC is dilated to create triangle A’B’C’ using point O as the center of dilation as shown in the figure

A is two units away from O and A' is 1 unit away from O. You add 1 + 2 to get the total distance and divide that number by 2 to get the scale factor. 3/2

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Answer:

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Probability of drawing a green marble is:

Since marbles are replaced the probability of a second green is same, 1/2.

So the probability of two green marbles is:

The probability of drawing two green marbles in a row is, 1/4

We have to given that,

In a bag with 20 marbles, 10 marbles are white and 10 are green. They are all mixed up.

Since, Each time a marble is pulled from the bag, the color is recorded and the marble is put back into the bag.

Hence, The probability of drawing a green marble on any one draw is,

= 10/20

= 1/2

Thus, The probability of drawing two green marbles in a row is,

= 1/2 x 1/2

= 1/4

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Answer:

x <  4

the 1st number line should be used.

Step-by-step explanation:

3/4(x + 8) > 1/2(2x + 10)

(2)(3)(x + 8) > (4)(1)(2x + 10)

6x + 48 > 8x + 40

6x - 6x + 48 - 40 > 8x - 6x + 40 - 40

8 > 2x

x < 8/2

x < 4

The area of the actual flower bed is 192 square feet.

We are given that;

Scale = 1 in. : 2 ft.

Actual length: 16 ft

Actual width: 12 ft

Now,

To find the length and width of the actual flower bed, we need to use the scale given in the problem. The scale is 1 in. : 2 ft., which means that 1 inch on the drawing represents 2 feet in real life. The length of the flower bed on the drawing is 8 inches, so the actual length is:

8 inches x 2 feet/inch = 16 feet

Similarly, the width of the flower bed on the drawing is 6 inches, so the actual width is:

6 inches x 2 feet/inch = 12 feet

To find the area of the actual flower bed, we can use the formula for area of a rectangle:

area = length x width

Substituting in the values we found above, we get:

area = 16 feet x 12 feet = 192 square feet

Therefore, by area the answer will be 192 square feet.

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The inequality representing the possible distances between a car and Jim for any period of time after he spots it is -1,080 ≤ d ≤ 1,080 and d ≤ 90t.

Let's denote the distance between Jim and the car as "d" (in feet), and the time elapsed after Jim spots the car as "t" (in seconds).

Given that no car travels faster than 90 feet/second on this road, we can establish the following relationship between distance, time, and speed:

d ≤ 90t

However, Jim has a camera that allows him to see up to 1,080 feet in either direction.

This means that the distance between Jim and the car should be within the range of the camera's visibility, which is 1,080 feet.

Therefore, the inequality representing the possible distances between the car and Jim for any period of time after he spots it is:

-1,080 ≤ d ≤ 1,080

Combining both inequalities, we have:

-1,080 ≤ d ≤ 1,080 and d ≤ 90t

Hence the inequality representing the possible distances between a car and Jim for any period of time after he spots it is -1,080 ≤ d ≤ 1,080 and d ≤ 90t.

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The line which is symmetrical to y=10+3x+x^2 is x = 3/2.

We are given that;

The equation y=10+3x+x^2

Now,

The line of symmetry of a parabola is a vertical line that passes through the vertex of the parabola and divides it into two congruent halves. The equation of the line of symmetry is given by the x-coordinate of the vertex 1.

To find the vertex of a parabola that is given in standard form y = ax^2 + bx + c, you can use the formula 2:

x = -b / 2a

This formula gives you the x-coordinate of the vertex. The y-coordinate can be found by plugging this value into the original equation.

We can rewrite it in standard form by rearranging the terms:

y = -x^2 + 3x + 10

Now you can identify the values of a, b and c:

a = -1 b = 3 c = 10

Using the formula for the x-coordinate of the vertex, you get:

x = -b / 2a x = -(3) / (2 * -1) x = 3/2

Therefore, by symmetry the answer will be  x = 3/2.

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The pressure exerted by the cube on the countertop is 23060 Pa.

We are given that;

Side of cube=30cm

Now,

The force is equal to the weight of the cube, which is the product of its mass and the acceleration due to gravity. To find the mass, you need to multiply the volume and the density of iron. The volume of a cube is the cube of its side, and the density of iron is about 7870 kg/m^3. The acceleration due to gravity is about 9.8 m/s^2. Therefore:

F = mass * gravity F = (volume * density) * gravity F = ((side)^3 * density) * gravity F = ((0.3 m)^3 * 7870 kg/m^3) * 9.8 m/s^2 F = 2075.4 N

The area is equal to the area of one face of the cube, which is the square of its side. Therefore:

A = (side)^2 A = (0.3 m)^2 A = 0.09 m^2

Now that you have the force and the area, you can plug them into the formula for pressure:

P = F / A P = 2075.4 N / 0.09 m^2 P = 23060 Pa

Therefore, by algebra the answer will be 23060 Pa.

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The complete question is;

If an iron cube of 30 cm side is resting on a countertop, what pressure does it exert?

Answer:

Its D 1/221

Step-by-step explanation:

The measure of each labeled angles in the rhombus are  ∠1 = 49°, ∠2 = 90°, ∠3 = 49° and ∠4 = 41°

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

The rhombus

By corresponding angles, we have

∠3 = 49°

∠1 = 49°

The diagonals of a rhombus bisect each other at right angles

So, we have

∠2 = 90°

Ths sum of angles in a triangle is 180

So, we have

∠4 = 180 - 90 - 49°

Evaluate

∠4 = 41°

Hence, the measure of the angles in the rhombus are  ∠1 = 49°, ∠2 = 90°, ∠3 = 49° and ∠4 = 41°

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The unknown angle in the cyclic quadrilateral is as follows:

∠R = 86 degrees

The diagram above is cyclic quadrilateral. A cyclic quadrilateral is a four sided shape that can be inscribed into a circle.

The sum of angles in a cyclic quadrilateral is 360 degrees. The opposite angles in a cyclic quadrilateral is supplementary.

Hence, let's find the unknown angle.

∠R = 1 / 2 (92 + 80)

∠R = 1 / 2 (172)

∠R = 86 degrees

Therefore, the unknown angle is 86 degrees.

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The volume of the cylinder rounded to the nearest cm is,

V₁ = 9,646.1 cm³

We know the following:

Cylinder volume: V₁ = π r² h

Ball (sphere) volume: V₂ =4/3 π r³

where:

V - volume

r - radius of base of cylinder and diameter of ball

h - height of cylinder.

Here, We have,

D = 16 cm ⇒ r = 16 ÷ 2 = 8

π = 3.14

a) Since balls touch all sides of cylinder (as shown in image), it can be concluded that height of cylinder is equal to sum of diameters of 3 balls and that radius of base of cylinder is equal to radius of ball:

h = 3 × r = 3 × 16 cm = 48 cm

r = 8 cm

So,

V₁ = π r² h

V₁ = 3.14 × (8 cm)² × 48 cm

V₁ = 9,646.1 cm³

Thus, The volume of the cylinder rounded to the nearest cm is,

V₁ = 9,646.1 cm³

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The answer is written as

Your given expression is "n^3 + 4". However, to solve an equation, you need to have an equals sign, that is, there needs to be something on the other side of the equation.

For example, if you had "n^3 + 4 = 0", then you could solve for n:

n^3 + 4 = 0,

n^3 = -4,

n = ∛(-4).

But with only "n^3 + 4", there isn't anything to solve for because it's not set equal to anything. This is an expression, not an equation.

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