In need of help in algebra, 4 questions help please

Given that f(x) = x/(x - 3) and g(x) = 1/x and the application of function operators, f ° g (x) = 1/(1 - 3 · x) and the domain of the resulting function is any real number except x = 1/3.

Let be f and g functions. Composition is a binary function operation where the variable of the former function (f) is substituted by the latter function (g). If we know that f(x) = x/(x - 3) and g(x) = 1/x, then the composed function is:

[tex]f\,\circ\,g \,(x) = \frac{\frac{1}{x} }{\frac{1}{x}-3}[/tex]

[tex]f\,\circ\,g\,(x) = \frac{\frac{1}{x} }{\frac{1-3\cdot x}{x} }[/tex]

[tex]f\,\circ\,g\,(x) = \frac{1}{1-3\cdot x}[/tex]

The domain of the function is the set of x-values such that f ° g (x) exists. In the case of rational functions of the form p(x)/q(x), the domain is the set of x-values such that q(x) ≠ 0. Thus, the domain of f ° g (x) is [tex]\mathbb{R} - \{\frac{1}{3} \}[/tex].

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[tex](10^4)^4[/tex]

[tex]10^8[/tex]

Therefore in simplified form [tex](10^4)^4[/tex] is [tex]10^8[/tex]

The probability of the success will be 0.3826.

Bernoulli's trials are those trials which end up randomly either on success (with probability p) or on failures (with probability 1- p = q (say))

The probability that out of n trials, there'd be x successes is given by

[tex]\rm P(x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]

We have

n = 8

p = 0.1

q = 1 – 0.1 = 0.9

x = 1

Then we have

P(1) = ⁸C₁ x (0.1)¹ x (0.9)⁷

P(1) = 0.3826

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Answer:

y = -5x

Step-by-step explanation:

gradient = delta y / delta x

gradient = -10 / 2

gradient = -5

y = mx + b

5 = -5(-1) + b

5 = 5 + b

b = 0

y = -5x

Using translation concepts, the graph that represents a reflection of [tex]f(x) = \frac{1}{3}(9)^x[/tex] across the x-axis is:

On a coordinate plane, an exponential function approaches y = 0 in quadrant 3 and decreases into quadrant 4. It goes through (1, - 3) and (1.25, -7).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, the function is:

[tex]f(x) = \frac{1}{3}(9)^x[/tex]

Which approaches y = 0 in quadrant 2 and increases into quadrant 1. For the reflection over the x-axis, the function assumes inverse(negative) values, that is, quadrant 2 -> quadrant 3 and then quadrant 1 -> quadrant 4, hence the correct statement is:

On a coordinate plane, an exponential function approaches y = 0 in quadrant 3 and decreases into quadrant 4. It goes through (1, - 3) and (1.25, -7).

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The graph which represents a reflection of f(x) = One-tenth(10)x across the y-axis is:

B. On a coordinate plane, an exponential function decreases from quadrant 2 to quadrant 1 and approaches y = 0 in quadrant 1. It goes through (negative 1, 1).

Coordinate Plane

This refers to the two-dimensional surface which is made up of two number lines, x and y.

With this in mind, we can see that from the complete text, we can see that the given graph on the function of x on the y-axis is on a coordinate plane.

Therefore, the correct answer is option B

The Equation is represented as  [tex]\rm F = \dfrac{9}{5} (K -273.15 ) +32[/tex]

Option B is the answer.

An equation is am mathematical statement formed when an algebraic expression is equated by an equal sign with another algebraic expression or a constant.

A Equation is given in the question

[tex]\rm K = \dfrac{5}{9}(F -32) +273.15[/tex]

where K denotes temperature in Kelvins and F denotes Fahrenheit .

To convert the equation in terms of K it can be rewritten as follows

[tex]\rm K = \dfrac{5}{9}(F -32) +273.15\\\\K -273.15 = \dfrac{5}{9}(F -32) \\\\\dfrac{9}{5} (K -273.15 ) = F - 32\\\\F = \dfrac{9}{5} (K -273.15 ) +32[/tex]

Therefore Option B is the right answer.

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Answer:

-8

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

-8/5=(6-(-2))/(x-(-3))

-8/5=(6+2)/(x+3)

-8/5=8/(x+3)

5=-(x+3)

5=-x-3

-x=5+3

-x=8

x=-8

The concentration could not be 59.

The concentration of a solution is a measure of the amount of solute that has been dissolved in a given amount of solvent or solution.

Given:

solutions one of 45% concentration

other of 55% concentration.

The concentration should lie between 45 % to 55 %.

This is because it is not possible to get a mixture concentration which is lower than the lower concentrated acid or higher than the higher concentration acid.

Hence, Mixture concentration must be between 45% and 55%.

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This graph represents the equation y = -3

Answer:

= -9/15 ÷ 4/3

= -9/15×3/5

= -9/15×3/4

= 36/5

=7⅕

Thus, for drawing the graph for y = 3/4x + 7.

For drawing the graph for y = 3/4x + 7, a person can draw a point at x of 0 and y of __7_, a second point by going over 3 and up __8.25__, and then draw a line through the points.

All the points (and only those points) which lie on the graph of the function satisfy its equation.

Thus, if a point lies on the graph of a function, then it must also satisfy the function.

For this case, the equation given to us is:

y=3/4x+7

Any equation of the form y=mx+c where m and c are constants and x and y are variables is the equation of a straight line.

For a straight line to be characterized, only two points are sufficient.

For x = 0, the y-coordinate would be such that it would satisfy the equation

y=3/4x+7

Putting x = 0, we get:

y=3/4(0)+7

y=7

Thus, the y-coordinate of the point on this line whose x-coordinate is 0 is 7. Thus, (0,7) is one of the point coordinates on the considered line.

Putting x = 3, we get:

y=3/4(3)+7

y=9.25

Thus, the y-coordinate of the point on this line whose x-coordinate is 0 is 9.25. Thus, (0,9.25) is another of the point's coordinates on the considered line.

Thus, for drawing the graph for y = 3/4x + 7, a person can draw a point at x of 0 and y of __7_, a second point by going over 3 and up __8.25__, and then draw a line through the points.

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Answer:

219,221

Step-by-step explanation:

the second number can be represented by the equation n1+2=n2

adding these expressions together you get

(n+2)+n=440

youre going to think of n now as just your first number because the equation solves for n1

with that you will get a number valued at 219

you then solve the first equation n1+2=n2 because we now know the value of n1

219+2=221

so the second numbers value is 221

Answer:

70%

Step-by-step explanation:

If 3 child and 7 adult is in the town, then there are total 10 people. 7 ÷ 10 is equal to 0.7, which is 70%.

The correct option is option D: This is the graph of one to one function.

Function is a relationship between two sets X and Y where set X is domain and set Y is codomain.

If we draw a vertical line and it crosses the graph only once at all locations, the relation is a function and this relation will be one-one.

by checking all the options

Option A: If we draw a vertical line parallel to y-axis in this at any location then it crosses the graph only once. So it is a function with one-one relation. Therefore option A is incorrect.

Option B: Linear function is a function in which highest degree of variable is 1 and it also describes the straight line. From the graph, it is clear that it is not a straight line. Therefore option B is incorrect.

Option C: If we draw a vertical line parallel to y-axis in this at any location then it crosses the graph only once. So, it is surely a function. Therefore option C is incorrect.

Option D: If we draw a vertical line parallel to y-axis in this at any location then it crosses the graph only once. So, it is surely a one-one function. Therefore option D is correct.

The correct option is option D: This is the graph of one-to-one function.

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Answer:

Step-by-step explanation:

Answer:

3059＝6940

Step-by-step explanation:

For the two examples given, we can see a consistency:

1 becomes 8 ; 8 becomes 1

5 becomes 4 ; 4 becomes 5

3 becomes 6 ; 6 becomes 3

2 becomes 7

because they are the only two digits left without a correlated pair, we can assume that 0 and 9 have the same relationship

So,

3 -> 6

0 -> 9

5 -> 4

9 -> 0

Meaning that 3059＝6940

hope this helps!! have a lovely day :)

Answers:

2% bond: $11000

4% bond: $13000

========================================================

Explanation:

x = amount invested in the 4% bond

y = amount invested in the 2% bond

Amounts are in dollars

The two amounts add to $24,000 so

x+y = 24000

y = -x+24000 is one equation to set up

0.04x = interest earned from the 4% bond

0.02y = interest earned from the 2% bond

0.04x+0.02y = total interest earned = $700

0.04x+0.02y = 700 is another equation to set up

------------

The system of equations is

[tex]\begin{cases}y = -x+24000\\0.04x+0.02y = 700\end{cases}[/tex]

Apply substitution. Solve for x.

0.04x+0.02y = 700

0.04x+0.02(-x+24000) = 700

0.04x-0.02x+480 = 700

0.02x= 700-480

0.02x= 220

x= 220/(0.02)

x = 11000

Use this to find y

y = -x+24000

y = -11000+24000

y = 13000

The coordinates of the inverse function f⁻¹(x) will be swapped of the coordinates of the function f(x).

The complete question is attached below.

Let the function will be  

f: X → Y

Then the inverse function will be

f⁻¹: Y → X

If the coordinates of the function f(x) are given.

Then the coordinates of the inverse function f⁻¹(x) will be swapped of the coordinates of the function f(x).

         f(x)                          f⁻¹(x)

     (33, 40)                   (40, 33)

     (-19, -15)                  (-15, -19)

    (-28, 47)                   (47, -28)

    (-15, -34)                  (-34, -15)

      (50, 0)                     (0, 50)

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Answer: -4 pounds

Step-by-step explanation:

       The hibernating animal lost 4 pounds. This means we are 4 below wherever the animal's weight was in the beginning. This can be represented with a negative number;

          -4 pounds

Answer:

460

Step-by-step explanation:

4 tens is equivalent to 40, so 500-40 is = to 460.

Hope this helps! :D

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[tex]\large \bold {ANSWER}[/tex]

[tex]\large \bold {SOLUTION}[/tex]

5 hundreds is 5 multiplied by 100, so it equals 500. 4 tens is 4 times 10, so 40.

So 5 hundreds minus 4 tens is 460.

An expression is defined as a set of numbers, variables, and mathematical operations. The value of (16/81)^(1/2) is 4/9.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The value of the given expression (16/81)^(1/2) can be calculated as shown below,

[tex](\dfrac{16}{81})^{\frac12}\\\\=\sqrt{\dfrac{16}{81}}\\\\= \dfrac49[/tex]

Hence, the value of (16/81)^(1/2) is 4/9.

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Answer:

★The square root of 16/81 = 4/9.

Answer:

B, 54

Step-by-step explanation:

Answer:

C the prove is right there on the graph

Answer:

C

Step-by-step explanation:

The graph clearly shows that all the numbers are greater than -6

Answer:

1. x - 1

2. [tex]\sqrt{x^2-1}[/tex]

Step-by-step explanation:

[tex]f(g(x)) = \sqrt{x+1}^2 - 2\\ = x + 1 - 2\\= x - 1[/tex]

[tex]g(f(x)) =\sqrt{x^2-2+1}\\ = \sqrt{x^2-1}[/tex]

The amount to be repaid by Jim Ryan is $14,891.78.

Given that, Principal (P) =$14,000, the rate of interest (R) =7[tex]\frac{1}{2}[/tex]% and T=310 days.

Ordinary interest is calculated on the basis of a 360-day year or a 30-day month; exact interest is calculated on a 365-day year.

Now, the interest=14,000×7.5 %×[tex]\frac{310}{365}[/tex].

=$891.78

The amount to be repaid=14,000+891.78=$14,891.78

Therefore, the amount to be repaid by Jim Ryan is $14,891.78.

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Answer:

  11, 7, 3, -1, -5

Step-by-step explanation:

The dependent variable y is often used interchangeably with the function value f(x). That is, we can usually presume that ...

  y = f(x)

__

To find f(x), put the value of x everywhere x appears in the function definition, and do the arithmetic. A calculator or spreadsheet can relieve some of the boredom of repetition. Here are a couple of examples.

  f(-2) = -4(-2) +3 = 8 +3 = 11

  f(-1) = -4(-1) +3 = 4 +3 = 7

You may notice that each increase of 1 in the value of x causes a decrease of 4 in the value of y. That means we can simply subtract 4 from the previous value of y to find the next one:

  [tex]\begin{array}{|c|c|}\cline{1-2}x&y\\\cline{1-2}-2&11\\\cline{1-2}-1&7\\\cline{1-2}0&3\\\cline{1-2}1&-1\\\cline{1-2}2&-5\\\cline{1-2}\end{array}[/tex]

__

Attached is an example of this table being filled by a calculator.

Answer:

hczgdjatulsfulsitsfisfula7tl7roa7pts

Answer: 10

Step-by-step explanation:

The slope of the given line is 10, and since parallel lines have equivalent slopes, the slope of a line parallel to the given line is also 10

Arc AB measures 3(16) = 48 degrees.

Arc BC measures 2(16) + 5 = 41 degrees.