Solve this composite function:

The value of the function (f+g)(x) = x² + 4x - 4.

An output variable and one or more input variables are at least two of the variables that make up a function. A mathematical equation may have any number of variables and says that two expressions are equivalent (none, one, or more). A function is frequently expressed as an equation, however not all equations are functions.

Given that,

f(x) = 4x + 2

g(x) = x² - 6

(f+g)(x) = f(x) + g(x) = 4x + 2 + x² - 6

(f+g)(x) = x² + 4x - 4

Hence, the value of the function (f+g)(x) = x² + 4x - 4.

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The total amount that Rahul will have is 108,006.20.

Compound interest is a type of interest where the interest earned on a principal amount is added to the principal, and the new total amount becomes the basis for calculating interest in the next period.

In other words, the interest is earned not only on the principal amount but also on the accumulated interest.

The formula for compound interest is:

Here we have, Rahul's plans to invest $25,000 in a retirement account that compounds 6% monthly.

From the data,

The principal amount, P = 25000

Rate of interest, r = 6% = 6/100 = 0.06

Time period, t = 25 years  

Number of compounds, n = 12  [ Since compounded annually ]

By using the formula, A = P (1 + r/n)^(n×t)  

A = 25000 [ 1 + 0.6/12]⁽¹²ˣ²⁵⁾

A = 25000 [ 1 + 0.005]⁽³⁰⁰⁾

A = 25000 [1.005]⁽³⁰⁰⁾  

A = 108,006.20 (rounded to the nearest cent)  

Therefore,

The total amount that Rahul will have is 108,006.20.

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Answer: Your welcome!

Step-by-step explanation:

N′(−11, −2), M′(−8, −1), O′ (−11, −5)

The image coordinates of N′M′O′ if the preimage is translated 7 units to the left are N′(−11, −2), M′(−8, −1), O′ (−11, −5). This is calculated by subtracting 7 from the x-coordinate of each point in the original triangle NMO. For example, the x-coordinate of point N in the original triangle is -4, so the x-coordinate of point N′ in the translated triangle is -4 - 7 = -11. The y-coordinate of point N does not change, so the y-coordinate of point N′ is also -2.

Answer:

To translate the triangle 7 units to the left, we need to subtract 7 from the x-coordinates of each vertex:

N' = (N_x - 7, N_y) = (-4 - 7, -2) = (-11, -2)

M' = (M_x - 7, M_y) = (-1 - 7, -1) = (-8, -1)

O' = (O_x - 7, O_y) = (-4 - 7, -5) = (-11, -5)

Therefore, the image coordinates of N'M'O' are (-11, -2), (-8, -1), and (-11, -5).

So the answer is N′(−11, −2), M′(−8, −1), O′ (−11, −5).

The volume of the top part of the pyramid is 13.4% of the total volume.

The amount of mass that a material has in relation to its volume is measured by its density. By dividing the substance's mass by volume, it is determined. Density is calculated as follows: density = mass/volume

A fundamental idea in physics, density is utilised in many branches of research and engineering, including the construction of effective engines and turbines, calculating the buoyancy of objects in fluids, and forecasting the behaviour of materials under stress.

Given that, average density of the entire pyramid is 4.7g/cm3 and that the bottom part has a mass of 972.8g.

The density is given as:

density = mass/volume

Substituting the value we have:

4.7g/cm3 = 972.8g/volume

volume = 207.23 cubic cm.

For the top part, density of 2.9g/cm3 and a mass of 92.8g. :

density = mass/volume

2.9g/cm3 = 92.8g/volume

volume = 32 cubic cm.

The percent of the top part with respect to total volume is:

percentage = (volume of top part / total volume) x 100

total volume = volume of top part + volume of bottom part

total volume = 32 cm3 + 207.23 cm3

total volume = 239.23 cm3

percentage = (32 cm3 / 239.23 cm3) x 100

percentage = 13.4%

Therefore, the volume of the top part of the pyramid is 13.4% of the total volume.

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Answer:

[tex]x^4-3x^2-x^2-4[/tex]

Step-by-step explanation:

Given information.

P(x) = R(x) - C(x)

[tex]R(x) = 2x^4-3x^3+2x-1[/tex]  and [tex]C(x) = 2x^4-x^2+2x+3[/tex]

[tex](2x^4-3x^3+2x-1) - (x^4-x^2+2x+3)[/tex]

Distribute the negative then solve by simplying either add or subtracting.

[tex](2x^4-3x^3+2x-1) +(-x^4+x^2-2x-3)\\[/tex]

[tex](2x^4-x^4)-3x^3-x^2+(2x-2x)+(-1-3)\\\\(x^4) -3x^3-x^2+(0x)-4\\\\x^4 -3x^3-x^2-4[/tex]

The growth rate is - 0.17

a. Growth rate =  (38-55)/100 = -0.17

This shows that it is decreasing

ii. Groth rate = 38-12.5)/(100-250)

= -0.17

This shows that it is decreasing as well

b. The relationship is a linear function. This is because rate of change of price and the number of days are equal

c. formula for game price in terms of days would be:

Price = -0.17*d + 55.

d = days

d. when price is 48.20

48.20 = -0.17d + 55

48.20 - 55 = -0.17d

d = 40

40 days after game was released

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cot (-859°) can be expressed as cot 41° an acute angle which is less than 45°

Trigonometry is used in navigation directions. Estimate the direction you need to place your compass to get a straight line. With the help of a compass and navigation trigonometric functions, it's easy to find a place or find the distance to see the horizon. 

A  Mathematical Statement which contains numbers and variables.

Angle: The two straight lines meeting at the vertex(a common point)

According to the question:

cot (-859) can be expressed as:

cot (-859 + 360x2)= cot (-859 +720)= cot (139)= cot (180 -139)= cot 41°(or)cot(-859) = cot(-859 + 180°x5)= cot (859 +900)= cot (41)°

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Answer:

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where:

A = the final amount

P = the principal (initial amount)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time (in years)

In this case, we have:

P = $200.00

r = 0.09 (9% expressed as a decimal)

n = 1 (compounded annually)

t = 5 years

Plugging these values into the formula, we get:

A = $200.00(1 + 0.09/1)^(1*5)

A = $200.00(1.09)^5

A = $200.00(1.538624)

A = $307.72

Therefore, after 5 years, Megan will have $307.72 in her account.

Step-by-step explanation:

Answer:

See below.

Step-by-step explanation:

We are asked for the diameter, radius, and area of a circle.

We are given the Circumference.

We should know that;

[tex]Circumference = (diameter)\pi[/tex]

[tex]Circumference = 24\pi[/tex] (Exact)

This means that the Diameter is 24.

The Radius is [tex]\frac{1}{2}[/tex] of the Diameter.

This means that the Radius is 12.

The area of a circle is represented as;

[tex]Area = \pi(radius)^2[/tex]

We have the requirements to find the area, with the value of the radius.

Solve for the area;

[tex]Area = \pi(12)^2[/tex]

[tex]Area = 144 \pi[/tex] (Exact)

[tex]Area = about \ 452.39.[/tex] (Approx.)

The area of a rhombus is 399 in².

What is the area of a rhombus?

A rhombus is a quadrilateral whose four sides all have the same length. Another term for this shape is an equilateral quadrilateral since all of its sides are equal in length.

Here, we have

Given: A rhombus with a base of 21 inches and a height of 19 inches.

We have to find the area of a rhombus.

As per the given rhombus,

Base = 21 inches

Height = 19 inches

The area of the rhombus = base ×  height

⇒ 21 × 19 = 399 in²

Hence, the area of a rhombus is 399 in².

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Answer:

to simplify the other dude, its 399 in2

Step-by-step explanation:

hope this helps your day :P

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The median value is 26.5, the first quartile is 24, the third quartile is 35.5, and the highest value is 38. The lowest value is thus 20.

We can plot the data on a number line to determine the data's least value, first quartile, median, third quartile, and greatest value:

20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38\s| | | |

The leftmost number on the number line and the lowest value is 20.

We can split the data into four equal sections to determine the quartiles. The data's middle value is known as the median. We choose the average of the two middle values because there are an even number of data points. The midpoint is:

(26 + 27)/2 = 26.5 is the median.

We calculate the median of the lower half of the data to determine the first quartile:

(23 + 25)/2 = 24 for the first quartile.

We determine the median of the upper half of the data to determine the third quartile:

Third quartile: (34.5) ((34 + 37)/2)

The rightmost number on the number line, 38, has the highest value.

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66640 divided by 31 is approximately equal to 2149.68.

Division is a basic arithmetic operation that is used to split a quantity into equal parts or to find out how many times one quantity is contained within another quantity.

When 66640 is divided by 31, the result is:

66640 ÷ 31 =2149.68 (rounded to two decimal places)

Therefore, 66640 divided by 31 is approximately equal to 2149.68.

In general, when we perform division, we are asking the question "how many times does the divisor fit into the dividend?" The dividend is the number being divided, the divisor is the number we are dividing by, and the result is the quotient.,

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Answer:

One solution at (2, -1)

Step-by-step explanation:

You will want to write the equations for both pairs of points:

(-2,-3) and (0,-2)

The slope is the change in y over the change in x.  The first number of the ordered pairs is the x value and the second number in the ordered pair is the y values.  Find the change by subtraction

[tex]\frac{-2 - -3}{0 - -2}[/tex] = [tex]\frac{-2+ 3}{0 + 2}[/tex] = [tex]\frac{1}{2}[/tex]

The slope (m) is 1/2.

The y intercept is when x = 0.  In the point (0,-2) x is 0, so the y-intercept is -2.

The y-intercept (b) is -2.

y = mx + b  Substitute 1/2 for m and -2 for b

y = [tex]\frac{1}{2}[/tex]x - 2

(0,3) and (1,1)

The slope is

[tex]\frac{1-3}{1-0}[/tex] = [tex]\frac{-2}{1}[/tex] = -2

The slope is --2.

The y intercept is 3.

y = mx + b  Substitutes -2 for m and 3 for b.

y = -2x + 3

Set the 2 equation equal to each other and solve for x.

-2x + 3 = 1/2 x -2   Multiply all the way through by 2 to clear the fraction.

-4x + 6 = x - 4   Add 4x to both sides

-4x + 4x + 6 = x + 4x -4

6 = 5x -4  Add 4 to both sides

6 + 4 = 5x - 4 + 4

10 = 5x  Divide both sides by 5

2 = x

Take either of the two original equations and substitute 2 for x and solve for y

y = -2x + 3

y = -2(2) + 3

y = -4 + 3

y = -1

The solution is (2,-1)

Helping in the name of Jesus.

The result of simplifying this answer is (x - 1)2 = 16(y - 7) (y - 7) The equation for the parabola is presented here in vertex form.

A parabola is a U-shaped curve in mathematics that is produced by the graph of a quadratic function. It is a particular kind of conic section, which is a circle made when a plane and a cone cross each other. A quadratic function with the following standard form can depict a parabola: Y = ax2+bx+c where are constants a, b, and c. Which way the parabola expands depends on the sign of the coefficient a.

given

We can use the following formula to express the equation of a parabola given a focus and a directrix:

where (h,k) is the parabola's vertex, p is the separation between it and the centre, and the directrix is represented by the horizontal line y = k - p.

The centre in this instance is (1,11), and the directrix is y=3.

We also understand that p is the distance, in this instance 4 units, between the vertex and the focus (since the focus is 4 units above the vertex). Therefore, we can enter the numbers into the formula to obtain:

(x - 1)^2 = 4(4)(y - 7) (y - 7)

The result of simplifying this answer is (x - 1)2 = 16(y - 7) (y - 7) The equation for the parabola is presented here in vertex form.

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Answer: b-8

Step-by-step explanation:

b-9=b-9

b-9+1=b-8

The equation can be written as:

(2 + 1/3) + 3*(1/3)

And the solution, writen as a mixed number, is 3 + 1/3.

Here we have a diagram where we can see an addition (its an addition because of the direction of the arrow).

On the leftside we can see two whole squares and a one thid strip.

Then the number is:

2 + 1/3

And to that, we are adding 3 one third strips, then we are adding:

(2 + 1/3) + 3*(1/3)

That should be the equation

We can solve that equation to get:

2 + 1/3 + 3/3

= 2 + 1/3 + 1

= 3 + 1/3

That is the solution written as a mixed number.

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0% would indicate that the kids have not gathered any leaves for the scientific project, and 100% would indicate that they have succeeded in collecting 200 leaves.

In mathematics, a percentage is a quantity or a ratio that is expressed as a fraction of 100. Calculating a percentage involves multiplying a quantity by 100 and dividing it by the total.

To determine "how much" or "how many," utilise the percentage. Calculating the precise quantity or figure that is being discussed is made easier with the use of a percentage. We compare fractions. determining a percentage rise or fall aids in calculating profit and loss margins.

In this case, 0% would indicate that the kids have not gathered any leaves for the scientific project, and 100% would indicate that they have succeeded in collecting 200 leaves for the project.

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True; the point (-1/5, -3/2) does lie on the graph of f(x) = 7.5x.

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

f(x) = 7.5x

The point is given as

(x, y) = (-1/5, -3/2)

To determine whether the point (-1/5, -3/2) lies on the graph of f(x) = 7.5x, we can substitute x = -1/5 into the equation and see if it gives us y = -3/2.

f(x) = 7.5x

By substitution, we have

f(-1/5) = 7.5(-1/5)

Evaluate

f(-1/5) = -1.5

Express as fraction

f(-1/5) = -3/2

So, the point (-1/5, -3/2) does lie on the graph of f(x) = 7.5x.

Hence, the statement is false.

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Complete question

True or False. The point (-1/5, -3/2) lies on the graph of f(x).

Where f(x) = 7.5x

Answer:

y = 3/5x - 3

Step-by-step explanation:

slope (m) of line perpendicular to y = -5/3x is 3/5, the negative reciprocal of -5/3

use the point (5, 0) and the point-slope form to find b, the y-intercept:  

y - 0 = 3/5(x - 5)

y = 3/5x - 15/5

y = 3/5x - 3   equation is now in the slope-intercept form

a. The amplitude of the function y = 4 sin [(2π / 365)(x - 79)] + 12 is 4.

b. The period of the function y = 4 sin [(2π / 365)(x - 79)] + 12 is 365 days.

c. There are approximately 16 hours of daylight on the longest day of the year.

d. There are approximately 8 hours of daylight on the shortest day of the year.

e. The graph for the function is obtained.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The function is given as y = 4 sin [(2π / 365)(x - 79)] + 12.

a. The amplitude of the function is the coefficient of the sine function, which is 4.

Therefore, the amplitude of the function is 4.

b. The period of the function is given by the formula: period = (2π/b), where b is the coefficient of x in the sine function.

In this case, b = (2π/365), so the period is -

period = (2π / (2π/365)) = 365

Therefore, the period value is 365 days.

c. The longest day of the year occurs on the summer solstice, which is around June 21.

On this day, x = 171 (assuming January 1 is x = 1). Plugging x = 171 into the function gives -

y = 4 sin [(2π/365)(171 - 79)] + 12 = 15.998 hours

Therefore, the number of hours for daylight is 16 hours.

d. The shortest day of the year occurs on the winter solstice, which is around December 21.

On this day, x = 355. Plugging x = 355 into the function gives -

y = 4 sin [(2π/365)(355 - 79)] + 12 = 8.002 hours

Therefore, the number of hours for daylight is 8 hours.

e. To graph the function for one period, we need to find the values of y for x ranging from 1 to 365.

We can use a graphing tool or software to plot the function.

The graph is plotted.

The x-axis represents the number of days after January 1, and the y-axis represents the number of hours of daylight.

The function oscillates between 8 and 16 hours of daylight over the course of one year, with the maximum occurring around day 171 and the minimum occurring around day 355.

The graph shows that the function is periodic, with a period of 365 days, as expected.

Therefore, the function is plotted.

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The ratio for the area and the ratio for the circumferences of the circles are 9 : 1 and 6 : 1 respectively.

What is a circle?

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the centre.

If the radius of one circle is three times the radius of another circle, then we can use this information to determine the ratio of the areas of the circles and the ratio of the circumferences of the circles without knowing their actual measurements.

Let's call the radius of the smaller circle "r" and the radius of the larger circle "3r".

Ratio of areas -

The area of a circle is proportional to the square of its radius, so the ratio of the areas of the two circles is -

= (area of larger circle) / (area of smaller circle)

= (π(3r)²) / (πr²)

= 9r²/r²

= 9/1

Therefore, the ratio of the areas of the two circles is 9:1.

Ratio of circumferences -

The circumference of a circle is proportional to its radius, so the ratio of the circumferences of the two circles is -

= (circumference of larger circle) / (circumference of smaller circle)

= 2π(3r) / 2πr

= 6r/r

= 6/1

Therefore, the ratio of the circumferences of the two circles is 6:1.

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The area of the composite figure is 14.71 square units

The area of the composite figure is found by calculating the sum of the areas of the various parts.

The area of the figure = area of sector + area of triangle + area of trapezium

Area of sector = 135/360 * π * 2²

Area of sector = 4.71 square units

Area of triangle = ¹/₂ * 2 * 1

Area of triangle = 1 square unit

Area of trapezium = ¹/₂ (3 + 6) * 2

Area of trapezium = 9 square units

Therefore, area of composite figure =  (4.71 + 1 + 9) square units

The area of the composite figure = 14.71 square units

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(x+4), (3x-1) are the required factors in the given trinomial solution.

The solution provided below has been developed in a clear step by step manner.

Step: 1

Given polynomial is 3x²2² +11x-4

=3x(x+4)-1(x+4)

=(x+4)(3x-1)

Explanation: Please refer to solution in this step.

Step: 2

(x+4), (3x-1) are the required factors

A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them. Factors can be found using either division or multiplication.

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One identity that we can write here is:

cos²(θ/2) = - sin²(θ/2) + 1

Here we want to find something that is equal to cos²(θ/2) for every value of theta, that will be an identity.

The general identity for trigonometric functions is:

cos²(θ) + sin²(θ) = 1

So we can rewrite this as:

cos²(θ) = - sin²(θ) + 1

If instead of theta, the argument is theta over two, we could rewrite this as:

cos²(θ/2) = - sin²(θ/2) + 1

That is the identity.

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Triangle LMO is congruent to NMO because they are reflections of eachother.

The price of Apples are $1.13 per pound and peaches are $0.63 per pound Option B

If pears cost $3 for a 4 pound bag, then the price per pound of pears is:

3/4 = $0.75 per pound

Since pears cost less per pound than apples but more per pound than peaches, we can set up the following inequality:

peaches < pears < apples

Substituting the known price per pound of pears, we get:

peaches < $0.75 < apples

Now, we can check each option to see which satisfies the inequality:

Apples are $1.13 per pound and peaches are $1.04 per pound:

$1.04 < $0.75 < $1.13

This option does not satisfy the inequality.

Apples are $1.13 per pound and peaches are $0.63 per pound:

$0.63 < $0.75 < $1.13

This option satisfies the inequality.

Apples are $1.13 per pound and peaches are $0.75 per pound:

$0.75 < $0.75 < $1.13

This option does not satisfy the inequality.

Apples are $0.63 per pound and peaches are $1.13 per pound:

$1.13 < $0.75 < $0.63

This option does not satisfy the inequality.

Therefore, the price per pound of apples and peaches that could be consistent with the given information is: apples are $1.13 per pound and peaches are $0.63 per pound.

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The comparisons of the fractions given above is enumerated below.

1) To compare 1/8 and 1/9, I can find a common denominator by multiplying the denominators together. The common denominator is 8 x 9 = 72.

Then, I can convert each fraction to have a denominator of 72 by multiplying the numerator and denominator of each fraction by the appropriate factor. The result is 9/72 and 8/72. Since 9/72 is bigger than 8/72, I know that 1/8 is smaller than 1/9.

2) To compare 7/8 and 8/9, I can find a common numerator by multiplying the numerators together. The common numerator is 56. Then, I can convert each fraction to have a numerator of 56 by multiplying the numerator and denominator of each fraction by the appropriate factor. The result is 49/56 and 64/72. Since 64/72 is bigger than 49/56, I know that 8/9 is bigger than 7/8.

3) To compare 15/38 and 5/13, I can find a common numerator by multiplying the numerators together.

The common numerator is 195. Then, I can convert each fraction to have a numerator of 195 by multiplying the numerator and denominator of each fraction by the appropriate factor.

The result is 75/195 and 75/195. Since the numerators are the same, I can compare the denominators. Since 195 is bigger than 169, I know that 15/38 is smaller than 5/13.

4) To compare 5/9 + 7/12 and 1/2, I can compare each fraction to 1/2 separately.

First, 5/9 is smaller than 1/2 because 9 is bigger than 18, so each ninth is smaller than each half.

Next, 7/12 is also smaller than 1/2 because 12 is bigger than 6, so each twelfth is smaller than each half.

Therefore, both fractions added together (without actually adding them) will be smaller than 1/2.

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By answering the above question, we may infer that We may reduce this equation to: Applying the rule that log base an of ab = b 4 = x Hence, x = 4.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

The equation may be changed to read:

x = log base 3 of 81.

81 being equivalent to 3 to the power of 4, we get the following:

x Equals log base 3 of 34.

We may reduce this to: Applying the rule that log base an of ab = b

4 = x

Hence, x = 4.

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Answer:

Reflection in the x-axis

Step-by-step explanation:

f(x) = √x

Shift left 3 units:

f(x + 3) = √(x + 3)

Reflection in x-axis:

-f(x + 3) = -√(x + 3)

Vertical stretch:

-3.f(x + 3) = -3√(x + 3) = g(x)

g(1) = -3√((1) + 3)

g(1) = -6