How do you solve composite functions examples?

The solution to the pair of simultaneous equations 2x + y = 5 and 3x - 2y = 4 is (2, 1).

A system of linear equations is a set of two or more equations which includes common variables. The solution to a system of equations, is the value of the unknown variables used in the equations that satisfies both equations.

Given two linear equations in x and y,

2x + y = 5     (equation 1)

3x - 2y = 4     (equation 2)

Use substitution method to find its solution. Express the first equation as y in terms of x and substitute the value of y to the second equation.

2x + y = 5     (equation 1)

y = 5 - 2x

3x - 2y = 4     (equation 2)

3x - 2(5 - 2x) = 4

3x - 10 + 4x = 4

Combining all terms containing the variable x on one side and the constants on the other side of the equality, and solve for x.

3x - 10 + 4x = 4

7x = 14

x = 2

Substitute the value of x in the first equation and solve for y.

y = 5 - 2x

y = 5 - 2(2)

y = 5 - 4

y = 1

Hence, the solution of the given system of equations is (2, 1).

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Answer:

2[tex]x^{4}[/tex] + 8[tex]x^{2}[/tex]

Step-by-step explanation:

[tex]x^{2}[/tex](2[tex]x^{2}[/tex] + 8)  When you are multiplying powers that have the same bases, you add the exponents.

Answer:

Step-by-step explanation:

we konw the speed of burn is 1.25 inchs per hour. so, the left candle is

15-1.25t. the answer is L=15-1.25t

Answer:

the 2 positive of number is

Step-by-step explanation:

2_:3+23*3⅔+09=2465

Answer:

[tex]x = \sqrt{87}[/tex]

Step-by-step explanation:

So, we need to use a bit of an unorthodox method here. We will use the Pythagorean theorem to find x. We will first start by finding out what all of our sides are. In the theorem, it's  [tex]a^{2} + b^{2} = c^{2}[/tex] . We know that the b is x, and the c is 16, but we need to know what a is. a is not 18. We need to find the distance starting at the right triangle. To do that, we must subtract 5 from 18, giving us 13. So, we have:

[tex]13^{2} + x^{2} = 16^{2}[/tex]

Now, we will simplify the equations:

[tex]169 + x^{2} = 256[/tex]

Then, we will subtract 169 from both sides, giving us:

[tex]x^{2} = 87[/tex]

Square rooting both sides gives us:

[tex]x = \sqrt{87}[/tex]

And we cannot simplify further because 87's prime factorization doesn't let it have any ways to get out of the square root.  

Hope this helped

Total 56 bags of hardwood and 140 bags of pine bark bags are sold.

In the given question, a local boys club sold 196 bags of mulch and made a total of $357.

It sold two types of mulch: hardwood for $2.00 a bag and pine bark for $1.75 a bag.

We have to find how many bags of each kind of mulch did it sell.

Let total number of x bags of hardwood sell.

Let total number of y bags of pine bark sell.

Now the equation should be

2x + 1.75y = 357............................(1)

Total number of bags sold 196.

So x + y = 196............................(2)

From the equation 2 the value of x = 196-y. Now putting the value of x in equation 1.

2(196 - y) + 1.75y = 357

392 - 2y + 1.75y = 357

392 - 0.25y = 357

Subtract 392 on both side, we get

-0.25y = -35

Divide by -0.25 on both side, we get

y = 140

Now putting the value of y in x = 196-y

x = 196 - 140

x = 56

Hence, 56 bags of hardwood and 140 bags of pine bark bags are sold.

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The sum of 2.3 and 1.94, that is 2.3 + 1.94 is 4 wholes, 2 tenths and 4 hundredths, which can be written in decimal form as 4.24.

Therefore the answer is 4.24.

The first number, 2.3, can be broken down into 2 wholes and 3 tenths.

The second number, 1.94, can be broken down into 1 whole, 9 tenths and 4 hundredths.

To add the two numbers together, we first add the wholes: 2 + 1 = 3.

Next, we add the tenths: 3 + 9 = 12

Since we cannot have more than 9 tenths in a whole, we must regroup 12 tenths as 1 whole and 2 tenths.

We add the regrouped tenths to the number of wholes: 3 + 1 = 4

After regrouping, we have 4 whole and 2 tenths.

Now we add the hundredths: 0 + 4 = 4

Thus the sum is 4 wholes, 2 tenths and 4 hundredths, which can be written in decimal form as 4.24.

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Area = 1/2*base*height = 1/2*9*4 = 18 sq.m

Solution:

We will be using the area of rectangle formula to calculate the areas of the three rectangles given.

(a) Length(l) = 9 m and Breadth(b) = 6 m

Area of rectangle = l × b

= 9 × 6

= 54 m2

(b) Length(l) = 17 m and Breadth(b) = 3 m

Area of rectangle = l × b

= 17 × 3

= 51 m2

(c) Length(l) = 4 m and Breadth(b) = 14 m

Area of rectangle = l × b

= 4 × 14

= 56 m2

Therefore, the area of the rectangle with the dimensions 4m and 14m having an area of 56 m2 that is (c) has the largest area whereas, the area of the rectangle with dimensions 17m and 3m having an area of 51 m2 that is (b) has the smallest area.

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Answer:x=20

Step-by-step explanation:5x+9 and 3x+11 must add to 180, so you can set these equal to 180 and get  8x+20 = 180, this can be simplified to 8x=160 or x = 20

Answer:

x = 20°

Step-by-step explanation:

Given angles,

→ 5x + 9

→ 3x + 11

Forming the equation,

→ (5x + 9) + (3x + 11) = 180°

{Because, sum of two angles in a straight line leads to 180°}

Now the value of x will be,

→ (5x + 9) + (3x + 11) = 180°

→ 5x + 3x + 9 + 11 = 180°

→ 8x + 20 = 180°

→ 8x = 180° - 20

→ x = 160/8

→ [ x = 20° ]

Hence, the value of x is 20°.

The revolution of the Earth and Moon refers to their orbits around the Sun. The Earth's revolution takes time of 365.24 days, and the Moon's revolution takes 27.32 days.

The revolution of the Earth and Moon is the path of the two celestial bodies around the Sun. The Earth takes 365.24 days to complete one revolution, which is also known as one year. The Moon, on the other hand, takes 27.32 days to complete one revolution, which is also known as one lunar month.

The revolution of the Earth and Moon refers to their orbits around the Sun, with the Earth taking 365.24 days and the Moon taking 27.32 days to complete one revolution.The revolution of the Earth and Moon refers to their orbits around the Sun. The Earth's revolution takes 365.24 days, and the Moon's revolution takes time of  27.32 days.

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The answer to all the questions is explained below with justifications.

In statistics, the process of hypothesis testing involves putting an analyst's presumption about a population parameter to the test. The type of data used and the purpose of the study will determine the methodology the analyst uses.

a) The null hypothesis[tex](H_o)[/tex] is that 71.3% or more of American families owned their homes.

The alternative hypothesis[tex](H_1)[/tex]is less than 71.3% of American families owned their homes.

b) The type I error is the null hypothesis is true but we assumed it to be false that is 71.3% or more of American families owned their homes but the council did not provide tax breaks.

The type II error is the null hypothesis is false and we assumed it to be true

that is less than 71.3% of American families owned their homes and the council provides tax breaks.

c) The consequences of the type II error would be the council will provide tax breaks to more people and it would cost them a large amount of money.

d) Type II error is more serious in this context as the council has to lay off a large amount as compared to individual homeowners who already can afford to buy a house.

e) For type I error house owners will be harmed and for type II error counsel will be harmed.

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Using the Central Limit Theorem for proportions, the correct option is:

E. The statistic is biased.

In plain English, what is the central limit theorem?

According to the central limit theorem, even if a population isn't normally distributed, you may still obtain sufficiently big samples from it and have the samples' means be distributed normally.

What is the central limit theorem and why is it significant?

Because of the Central Limit Theorem, we can confidently assume that the sampling distribution of the mean will be normally distributed in most situations.

                  Since a normal distribution is assumed, we can benefit from statistical methods, as we will see in the section after this one.

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The correct statement regarding the comparison of the linear functions f(x) and the graphed function is given as follows:

A. The function ƒ(x) = 4x + 2 has a greater rate of change than the graphed function.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The function f(x) is given as follows:

f(x) = 4x + 2.

The parameters are given as follows:

For the function g(x), we have that:

Hence the correct option is given by option a, as the function f(x) has a greater rate of change, of 4, compared to the graphed function, of 2.

The graphed function is given by the image presented at the end of the answer.

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Therefore , the solution of trigonometry function comes out to be tan x tan(4x+18)

When it comes to trigonometry, the relationship between the rectangular line segment and The field is believed to have originated in the 1770s, most likely beginning in the third century through the fusion of astrophysics and mathematical sciences. Numerous mathematical equations and their possible uses in calculations are covered by precise mathematical techniques. The basis of trigonometry are the six basic trigonometric operations.

Here,

tan x tan 4x=1

cos 4X cos X - sin 4x sin x=0

cos 5x=0

5x=(n+1/2)π,n ∈ Z

x=(2n+1)/10 π,0 <x <π

π/10, 3π/10, 5π/10, 7π/10,9π/10 (5π/10 is not possible)

Thus, there are only four solutions.

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Luc is correct in stating that the line will remain the same with certain dilation centers, such as the origin (0, 0) and the point (3, -4). These centers of dilation will cause a scale factor of 2, but the line will remain the same.

To check if Luc is correct, we can calculate the points of the dilation with scale factor 2.

For the origin (0, 0):

Point A: (x, y) = (0, 3)

Point B: (x, y) = (-4, -3)

Dilated Point A: (x, y) = (0, 6)

Dilated Point B: (x, y) = (-8, -6)

Equation of the dilated line: y = -4x + 6

This shows that the line is dilated with scale factor 2, but is the same line.

For the point (3, -4):

Point A: (x, y) = (3, -1)

Point B: (x, y) = (-1, -7)

Dilated Point A: (x, y) = (6, -2)

Dilated Point B: (x, y) = (-2, -14)

Equation of the dilated line: y = -4x + 3

This shows that the line is dilated with scale factor 2, but is the same line.

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Answer:

the answer us on the attatched documet

Step-by-step explanation:

can u just give me the brainliest

Therefore, K= 66 degrees, LK length = 22 unit, and LK length = 22 unit are the answers to the specific problem of angles.

A geometrical angled construction is constructed from two rays that converge at the summit, or center, of both the angle and are referred to as the face and the vertex, respectively. Guess it depends on how they're situated, it is possible for two rods to create an angle together within plane. When two planes collide, an inclination is also formed. Diahedral angles are the term used to refer to them. Light beams or lines in euclidean geometry can have a wide variety of shapes or angles for the same termination. The phrase "angle" in English is based on the Latin term "angulus," which meaning "horn." the vertex.

Here,

Given: MKL M = 24 degree right triangle

K is 90 degrees, etc.

Thus,

=> ∠L + ∠M +∠K =180

=> 90 + 24 + ∠K = 180

=>∠K =180-114

K equals 66 degrees.

and

The formula for LK length is 22.

The formula for LK length is 22.

In light of this, the answer to the angle problem is

K=66 degrees, and LK length=2 units. LK length equals two units.

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Polynomials form a system like to that of integers hence they are closed under the operations of addition and subtraction.

Exponents of polynomials are whole numbers.

Hence the resultant exponents will be whole numbers , addition is closed for whole numbers. As a result, polynomials are closed under addition.

If an operation results in the production of another polynomial, the resulting polynomials will be closed.

The outcome of subtracting two polynomials is a polynomial. They are also closed under subtraction as a result.

The word polynomial is a Greek word. We can refer to a polynomial as having many terms because poly means many and nominal means terms. This article will teach us about polynomial expressions, polynomial types, polynomial degrees, and polynomial properties.

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the statement that "you walk at a constant rate" tells us that the relationship is indeed proportional, namely, there's a value in the input that's consistent or common yielding the output.

Check the picture below.

to get the equation of any straight line, we simply need two points off of it, for the distance "from school" table, let's use those two points in that table

[tex](\stackrel{x_1}{10}~,~\stackrel{y_1}{0.5})\qquad (\stackrel{x_2}{30}~,~\stackrel{y_2}{1.5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{1.5}-\stackrel{y1}{0.5}}}{\underset{\textit{\large run}} {\underset{x_2}{30}-\underset{x_1}{10}}}\implies \cfrac{1}{20}[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0.5}=\stackrel{m}{\cfrac{1}{20}}(x-\stackrel{x_1}{10})\implies y-0.5=\cfrac{1}{20}x-\cfrac{1}{2} \\\\\\ y=\cfrac{1}{20}x-\cfrac{1}{2}+0.5\implies y=\cfrac{1}{20}x-\cfrac{1}{2}+\cfrac{1}{2}\implies \boxed{y=\cfrac{1}{20}x}[/tex]

If each score is doubled, and then 5 is subtracted from that result, then the mean and standard deviation will be 115 and 36 respectively.

A huge group of test results has a mean of 60 and a standard deviation of 18. If each score is doubled and then 5 is deducted from the result, the mean and standard deviation are “ mean = 115; standard deviation = 36”. Mean = 2 x 60 -5 = 120 -5 = 115

2 x 18 = 36 standard deviation

The mean is the average and is calculated as the sum of all the results from the example divided by the total number of events.

The standard deviation (SD) is a statistic used to assess the degree of variation or dispersion in a set of data values.

A low standard deviation indicates that the information points slant toward being near the mean of the set, whereas an exclusive expectation deviation or a high standard deviation indicates that the information points tilt toward being near the mean of the set.

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The sprinkler should be set to rotate through  the angle 6.42 degrees.

What is an angle?

Two lines intersect at a location, creating an angle. An "angle" is the term used to describe the width of the "opening" between these two rays. Angles are used in the design of buildings, roadways, and sports venues by engineers and architects.

r =  50 yards

Area, A = 140 square yards

Θ = angle

A= (Θ /360) πr²

140 = (Θ /360) * 3.14 * 50*50

Θ = (140*360)/(3.14*25*100) = 6.42 degrees

The sprinkler should be set to rotate through  the angle 6.42 degrees.

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The average tuition for two randomly chosen in-state and out-of-state students is around $1,508 less than the mean of $6,348.75.

Mean Deviation

The average deviation from the mean value of the provided data set is determined using the mean deviation, which is defined as a statistical metric.

Given

μS = $6,348.75

σS = $1508.48

The average sum of the tuition fees is $6348.75

As a result, it follows:

The standard deviation of the tuition for in-state students is measured as a difference from 6348.75.

The standard deviation for out-of-state students gauges how their tuition is different from 1508 in total.

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16<x+y<19,60<xy<84,10/7<y/x<12/6,3<y-x<6

smallest with the smallest biggest with the biggest, biggest with smallest, smallest with biggest

Answer:

x=16/3

Step-by-step explanation:

4=3/4x+0

4=3x/4

4=3x/2square

4times4=16

3x/3=16/3

x=16/3

Inequalities represent Susan's weekly goal of earning money are:

c + e ≤ 20

15c + 10e ≥ 240

The term "inequality" in mathematics refers to a connection between two expressions or values that is not equal to each other. Inequality originates from an imbalance, thus. The majority of the time, size comparisons between two numbers on the number line are made.

The most notable instances of social inequality include those related to health care, social class, gender inequality, and wealth disparity. Comparatively speaking, some people in the healthcare system receive better and more skilled care. For these services, they are also likely to pay more.

Given that,

Susan earns $10 per hour tutoring elementary students in math.

She also earns $15 per hour cleaning in the library.

Her goal each week is to earn at least $240 while working not more than 20 hours.

Thus, the equation of inequality:

c + e ≤ 20

15c + 10e ≥ 240

Here, e represent the number of hours Susan works in one week tutoring elementary students.

c represent the number of hours Susan works in one week cleaning the library.

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