Determine the factor

The results of composition between two functions are listed below:

A: f(g(x)) = 3 · x - 5, Domain: All real numbers.

g(f(x)) = 3 · x - 5 / 2, Domain: All real numbers.

f(f(x)) = 36 · x - 35, Domain: All real numbers.

B: f(g(x)) = x - 3, Domain: All real numbers.

g(f(x)) = √(x² - 3), Domain: x ≤ - √3 and x ≥ √3.

f(f(x)) = x⁴, Domain: All real numbers.

And the components of the composition are listed below:

A: f(x) = x⁵, g(x) = x - 9

B: f(x) = √x, g(x) = 5 - x

In this problem we shall use a special operations between two functions known as composition, consisting in substituting the indepedent variable of the first function (f (x)) for the entire second function (g (x)):

f ° g (x) = f[g(x)]  

Part 3 - Now we proceed to determine a composition between two functions and its domain, that is, the set of x-values such that function exists:

Case A: f(x) = 6 · x - 5, g(x) = x / 2

f(g(x)) = 6 · (x / 2) - 5

f(g(x)) = 3 · x - 5

Domain: All real numbers.

g(f(x)) = (6 · x - 5) / 2

g(f(x)) = 3 · x - 5 / 2

Domain: All real numbers.

f(f(x)) = 6 · (6 · x - 5) - 5

f(f(x)) = 36 · x - 35

Domain: All real numbers.

Case B: f(x) = x², g(x) = √(x - 3)

f(g(x)) = x - 3

Domain: All real numbers.

g(f(x)) = √(x² - 3)

Domain: x ≤ - √3 and x ≥ √3.

f(f(x)) = (x²)²

f(f(x)) = x⁴

Domain: All real numbers.

Part 4 - Now we proceed to separate each function as parts of a composition:

Case A: h(x) = (x - 9)⁵

f(x) = x⁵, g(x) = x - 9

Case B: H(x) = √(5 - x)

f(x) = √x, g(x) = 5 - x

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A polynomial of degree 3 with real coefficients can be written in the form f(x) = a(x - r1)(x - r2)(x - r3), where r1, r2, and r3 are the roots of the polynomial. Since the given zeros are -4 and 2 + i, we can write the polynomial as follows: f(x) = a(x + 4)(x - (2 + i))(x - (2 - i)).

What is polynomial of degree?

A polynomial is a mathematical expression consisting of variables and coefficients, which are combined using only the operations of addition, subtraction, and multiplication. The degree of a polynomial is defined as the highest power of the variable in the polynomial. For example, the polynomial 3x^2 + 2x + 1 has a degree of 2, since the highest power of x is 2. A polynomial of degree 0 is a constant, a polynomial of degree 1 is a linear function, a polynomial of degree 2 is a quadratic function, and so on.

A polynomial of degree 3 with real coefficients can be written in the form f(x) = a(x - r1)(x - r2)(x - r3), where r1, r2, and r3 are the roots of the polynomial. Since the given zeros are -4 and 2 + i, we can write the polynomial as follows:

f(x) = a(x + 4)(x - (2 + i))(x - (2 - i))

The third root is the complex conjugate of the second root, and since the coefficients of the polynomial are real, the conjugate must also be included.

To determine the value of the coefficient a, we can use synthetic division or long division to divide (x + 4) into (x^3 + bx^2 + cx + d). To get the cubic polynomial:

x^3 + bx^2 + cx + d = (x + 4)(x - (2 + i))(x - (2 - i))

Expanding the right side of the equation, we get:

x^3 + bx^2 + cx + d = x^3 - 4x^2 + (4 + 4i)x^2 - (4 - 4i)x + 16

Comparing the coefficients of like terms on both sides of the equation, we get:

b = -4

c = 4 + 4i

d = -16

So the polynomial is:

f(x) = a(x + 4)(x - (2 + i))(x - (2 - i)) = a(x^3 - 4x^2 + (4 + 4i)x^2 - (4 - 4i)x + 16)

Since the coefficient a is arbitrary, we can set it to 1 for convenience:

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

= x^3 - 4x^2 + (4 + 4i)x^2 - (4 - 4i)x + 16

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For a given polynomial 45x+7, x will be -7/45.

What are polynomials?

Polynomials are algebraic expressions that consist of variables and coefficients. Variables are also sometimes called indeterminates. We can perform arithmetic operations such as addition, subtraction, multiplication, and also positive integer exponents for polynomial expressions but not division by variable. An example of a polynomial with one variable is x^2+x-12. In this example, there are three terms: x^2, x and -12.

Based on the number of terms present in the expression, it is classified as

Monomial:-A monomial is an expression which contains only one term. For an expression to be a monomial, the single term should be a non-zero term. A Examples of monomials are: 5x,3.

Binomial:-A binomial is a polynomial expression which contains exactly two terms. A binomial can be considered as a sum or difference between two or more monomials.  Examples of binomials are:

– 5x+3, 6a^4 + 17x.

Trinomial:-A trinomial is an expression which is composed of exactly three terms. A Examples of trinomial expressions are:

– 8a^4+2x+7, 4x^2 + 9x + 7.

Now,

Given polynomial is is in form of a linear equation i.e. 45x+7

To find value of x, put 45x+7=0

45=-7

x=-7/45

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Answer: 10 7/12 or if you don't want a mixed number 127/12

Step-by-step explanation: use 10 7/12 just realized it said used a mixed number so the answer is 10 7/12

Answer:

The slope of the line through the points (12, 10) and (24, 20) is 0.5

Step-by-step explanation:

To graph the line, use the slope-intercept form of the equation of a line, which is y = mx + b, where m is the slope and b is the y-intercept. For this particular line, the equation would be y = 0.5x + b. To find the y-intercept, use one of the given points, (12, 10) in this case, to solve for b. So, 10 = 0.5(12) + b, thus b = 0. So, the equation of the line is y = 0.5x + 0. If graphed, the line should go through the points (12, 10) and (24, 20).

The output voltage of an amplifier is 1350mV.

The voltage that a machine, like a voltage regulator or a generator, releases into the air is known as the output voltage. Voltage regulators keep voltage levels steady.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the output voltage of an amplifier is calculated by multiplying the input voltage by the voltage gain of the amplifier.

The output voltage will be calculated as:-

Output voltage = 45 x 30

Output voltage = 1350 mV

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Answer:

The equation |z + 3| = |z - 2| can be solved by first considering two cases:

z + 3 = z - 2

Adding 3 to both sides and subtracting z from both sides gives:

6 = -2

This is a contradiction, so this case has no solution.

z + 3 = - (z - 2)

Adding 3 to both sides and subtracting z from both sides gives:

1 = -2z

z = -1/2

So the only solution to the equation |z + 3| = |z - 2| is z = -1/2.

The required interval notation of the given inequality is (-∞, 2). A graph of the given inequality has been shown.

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,
Given inequality x < 2
Since the above inequality shows that the value of x is all real numbers less than 2. A Set of all real numbers less than 2 is given as (-∞, 2)

Thus, the required interval notation of the given inequality is (-∞, 2). A graph of the given inequality has been shown.

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It will take 27.8 hours for all beetles to embark onto the ark.

Speed is measured as the ratio of distance to the time in which the distance was covered.

Given,

There are 1/4 million beetles

250,000 beetles

they move side by side in pairs

250,000 /2 = 125,000 pairs form a line.

Length of each beetle 1 cm

space of 7cm between them

total distance = 8cm.

125,000 form a line

so total length = 125,000 * 8 = 1000,000 cm is the length of the line.

the length of the plank = 500 cm

so the distance covered = 1000,000+500 = 1000,500 meters

distance = 1000,500 cm

speed = 10 cm/s

Time = distance / speed

Time = 1000,500/10

Time = 100050 seconds

         = 100050/3600 hours

         = 27.8 hours

Hence, all 1/4 million species will take 27.8 hours to embark onto the ark.

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Answer:

i don't know

Step-by-step explanation:

Answer:aw dawd

Step-by-step explanation:awd awdkakwd

[tex]\texttt{speed} = {\dfrac{d}{t}[/tex]

distance = 30 km

t = 3 hr

[tex]\texttt{speed}=\dfrac{30}{3}[/tex]

[tex]\fbox{\texttt{speed} = 10 km/hr}[/tex]

The cost of seed for one acre of land is $79.68

A rate is a special ratio in which the two terms are in different units. For example, if a 12-ounce can of corn costs 69¢, the rate is 69¢ for 12 ounces.

The cost of 80,000 kernel bag of seed is $255.60

He will plant 25,000 kernels of corn per acre

Therefore the cost of one seed = 255/80,000

. This means the cost of seed corn per acre = 255/80,000 × 25000

= $79.68

Therefore the cost of seed for 1 acre is $79.68

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The coordinates of its P-intercept is -18.

The coordinate points give values of dependent and independent variables.

Coordinates on graphs, it is typically represented by a pair of numbers: the first number indicates the length along, while the second number indicates the length up or down. The point (12,5), for instance, is 12 units down and 5 units up.

The coordinates of its P-intercept is the value of the P intercept is the value of P(x) when t = 0.

The given function is as follows:

Given the function P(x) = -(x-1) (x+3) (x-6)

when x = 0

P(0) = -(0 - 1) (0 + 3) (0 - 6)

P(0) = -(-1) (3) (-6)

P(0) = -18

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Answer:

Step-by-step explanation:

slope intercept form is

y=mx+b

where m is the slope and b is the y-intercept.

In your equation m = 5/4 so this is your answer.

The value of 96.1% of 146 is 140.31

percentage, a relative value indicating hundredth parts of any quantity.

We have to find the value of 96.1% of 146.

Convert 96.1% to the decimal value by dividing with 100

96.1/100=0.961

Now multiply 0.961 with the 146 to find the value.

0.961×146

140.306

Hence, the value of 96.1% of 146 is 140.31

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Answer:

x = 34°

Step-by-step explanation:

The angle x and 146° are complementary angles, meaning that they form a 180° angle when combined. This is known because they share a straight line.

Because they are complementary, the sum of the angles is 180°:

x + 146° = 180°

Now we have a one-step equation! Solve by subtracting 146 from both sides:

x = 34°

Mosaic Tile Company produces two kinds of tiles, that:

We will solve this problem using the linear programming concept.

From the given case, we know that:

x --> larger tiles

y --> smaller tiles

molding: 0.45x + 0.30y ≤ 75

baking: 0.40x +0.60y ≤ 105

glazing: 0.15x + 0.25y ≤ 60

materials: 30x + 20y ≤ 6,000

Profit: 190x + 240y

We need to find each functions respective constraints and construct a graph containing all of these function constraints.

0.45x + 0.30y = 75

(x = 0)

0.45(0) + 0.30y = 75

y = 250

(y = 0)

0.45x + 0.30(0) = 75

x = 166

0.4x + 0.6y = 105

(x = 0)

0.4(0) + 0.6y = 105

y = 175

(y = 0)

0.4x + 0.6(0) = 105

x = 262

0.15x + 0.25y = 60

(x = 0)

0.15(0) + 0.25y = 60

y = 240

(y = 0)

0.15x + 0.25(0) = 60

x = 400

30x + 20y = 6000

(x = 0)

30(0) + 20y = 6000

y = 300

(y = 0)

30x + 20(0) = 6000

x = 200

We can construct the graph of these constraints such as the attached graph below. From the graph we know that the contraints of molding and baking are intersecting with each other under all of the given constraints. We need to find the intersection point:

0.4x + 0.6y = 105 | x 1| 0.4x + 0.6y = 105

0.45x + 0.3y = 75 | x 2| 0.9x + 0.6y = 150

                                       -0.5x          = -45

                                              x   = 90

0.45(90) + 0.3y = 75

40.5 + 0.3y = 75

0.3y = 34.5

y = 115

The intersection point is (90,115)

We have 3 possible scenario points, their position and each possible profit are:

(0, 175) --> P = 190(0) +240(175) = $42,000

(90, 115) --> P = 190(90) + 240(115) = $44,700

(166,0) --> P = 190(166) + 240(0) = $31,540

The optimum scenario is producing 90 larger tiles and 115 smaller tiles.

By producing the optimum scenario tiles, the baking resources will have:

Baking: 0.40x + 0.6y ... 105

              0.40(90) + 0.6(115) = 105 --> no left over resources

If Mosaic add another hour for Molding, there will be some additional profit, which is can be calculated by trying to create a new equation:

0.45x + 0.30y =< 75+1

0.45x + 0.30y =< 76

0.45x + 0.30y = 76

(y = 0)

0.45x + 0.30(0) = 76

x = 168

We can compare with the initial condition of available molding resources of 75 by producing 166 larger tiles:

Additional profit = (168 x 190) - (166 x 190)

Additional profit = $31,920 - $31,540

Additional profit = $380

Mosaic Tile should not accept the supplier offer because the most critical bottleneck at the time is the molding and baking capacities. Both lines are below the other resources lines and acting as the direct constraint on deciding the optimum possible output. If Mosaic wants to increase its profit, it should look for a solution to increase either or both molding and baking capacities.

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Answer: 36 problems

Step-by-step explanation:

40% is nothing but 40/100, which is just 4/10. To start, multiply 60 by the fraction 4/10. Cancel out the 10 from the denominator of the fraction to get 4 x 6 = 24. Now, we just found the number of problems that the student solved, but we need to find how many problems still need to be solved. To do that, do 60 - 24 = 36. The student needs to solve 36 more problems.

I hope this helps!

We are 95% confident that the true population proportion is between 71.6% and 80.4%

The 95% confidence interval for the proportion of all U.S. grown people who would include those  on their list of 10 historic events can be constructed using the formula:

Where:

[tex]pi[/tex] = sample proportion (76%)

SE = standard error (square root of [tex]pi(1-pi)/n[/tex])

z = the critical value for a 95% confidence level (1.96)

n = sample size (2025)

Plugging in the values, we get:

[tex]SE =\sqrt{(0.76(1-0.76)/2025)} = 0.0240\\CI = 0.76 ± (1.96)(0.0240) = (0.716, 0.804)[/tex]

The 95% confidence interval can be interpreted as follows: If we repeated this study many times, 95% of the intervals constructed would contain the true population proportion of all U.S. grown persons who would include on their list of 10 historic events. Based on this sample, we are 95% confident that the true population proportion is between 71.6% and 80.4%.

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Answer:

Answer B

Step-by-step explanation:

See graph below

1,-1    and    1,1   are both on Andres' graph....which shows TWO y values for ONE x value....does not pass the 'vertical line test' <====it is not a function

For any value of k and h = -18, the system will have infinitely many solutions.

Hence, option (b) is the correct choice.

A coefficient matrix in linear algebra is a matrix made up of the coefficients of the variables in a group of linear equations. In order to solve systems of linear equations, the matrix is employed.

The system will have infinitely many solutions when the determinant of the coefficient matrix is equal to 0.

The determinant can be calculated from the upper triangular matrix as the product of the diagonal elements, which is 0 * (-20) * (h + 18) = 0.

Therefore, the system will have infinitely many solutions when h + 18 = 0,

or h = -18.

This means the answer is (b) any value of k and h = -18.

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The length of side PT by using the ratio of similar triangles is 49/3 or 16 1/3. Option A is correct.

Triangles that are similar to one another in terms of shape but not necessarily size are called similar triangles. In simple words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are also equivalent.

In the event that two triangles are similar with sides P, Q, R and p, q, r, then the pair of their matching sides is also proportional.

From the given figure, using the ratios of similar triangles;

QP/QS = RP/RT

(12+28)/12 = (7 + x)/7

40/12 = (7 +x)/ 7

7(40/12) = 7 + x

70/3 = 7 + x

x = 49/3 o 16 1/3

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Answer:

[tex]n \leqslant 312[/tex]

Step-by-step explanation:

[tex]45 + 7 \geqslant \frac{1}{6}n - 7 + 7 [/tex]

[tex]52 \times 6\geqslant \frac{1}{6} n \times 6[/tex]

[tex]312 \geqslant n[/tex]

You can multiply by 6 without changing the sign as 6 > 0

The required number of flour cups does he need to make the muffins are 7.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.

We have,

Ratio of 3.5 cups of flour for every 1.75 cups of sugar.

cups of flour/ cups of sugar = 3.5/1.75

= 2:1

So, for every two cups of flour, there is one cups of sugar.

The number of cups of flour for 3.5 cups of sugar.

= 2(3.5)

= 7 cups.

Thus, there are 7 cups of flour required.

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Answer:

1) It's a slope

2) It's the x-intercept

3) It's the y- intercept