Suppose f(x)=√x+1 and g(x)=x² + n. If f(g(7)) = 9, what is the value of g(n)?
..

We will see that the functions are inverses by proving that the composition is equal to the identity.

Two functions are inverses if their composition is equal to the identity, this means that if h(t) and k(t) are inverses, then we can write:

h(k(t)) = t

and

k(h(t)) = t

Proving one of these will be enough.

Here the functions are:

h(t) = (3t + 5)/t

k(t) = 5/(t - 3)

Let's find h(k(t))

We will get:

h(k(t)) = (3*k(t) + 5)/k(t)

Now we can replace the function k(t) there.

h(k(t)) = (3*5/(t - 3) + 5)/(5/(t - 3))

Now we can simplify this using algebra.

h(k(t)) = ( 15/(t - 3) + 5)*(t - 3)/5

h(k(t)) = (15/(t - 3))*(t - 3)/5 + 5*(t - 3)/5

h(k(t)) = 3 + (t - 3) = t

h(k(t)) = t

So yes, the two functions are inverses.

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Answer:

[tex]x \geqslant 360[/tex]

Answer:

page 1=45 points

page 2

1=30

2=10

3=56

page 3

$1000

Step-by-step explanation:

Answer:

The distance between these two points with coordinates (-1, -4) and (-9, -8) is 8.94 unites

Loudness, pitch, and timbre are the three psychological aspects of sound that are influenced by the physical properties of sound waves.

When energy moves through a medium (such as air, water, or any other liquid or solid matter), it creates a pattern of disturbance known as a sound wave that propagates away from the sound source.

When an object vibrates, sound waves are produced that are similar to pressure waves, like when a phone rings.

Pitch, intensity, and timbre are three key components of the field of sound psychology or psychoacoustics. People can distinguish the harmonics of a complex periodic sound wave under certain conditions thanks to the way that humans perceive sound and music.

Thus, loudness, pitch, and timbre are the three psychological aspects of sound that are influenced by the physical properties of sound waves.

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Answer:

the answer is 12

explanation 12x12= 144

Answer:

Step-by-step explanation:

well, you have to determine what the variables are first. this question cannot be answered unless the variables are defined. If x=3 then it is 3(3) +5 which is 9 + 5. Then you add the numbers together which equals 14.

Answer:

[tex]r=12, y=12x[/tex]

Step-by-step explanation:

[tex]\frac{y}{x}=\frac{48}{4}=12 \\ \\ \therefore r=12 \implies y=12x[/tex]

Answer:

12

Step-by-step explanation:

y=rx

For me it will be easier to use y=xr

So let’s fill in one of the points

48=4r

Now solve for r

48=4r

/4.  /4

12=r

Now let’s try another point to see if we get the same thing

60=5r

/5.  /5

12=r

We get the same thing so the constant of proportionality is 12

Hopes this helps please mark brainliest

Yes, the selling price of an item is a function of the cost of making the item.

A function connects an input with an output. It is analogous to a machine with an input and an output. And the outcome is somehow connected to the input.

Cost is often the expenditure incurred for producing a product or service that a firm sells. The selling price is the amount paid by the buyer to purchase a product or products.

The selling price of an item is a function of the cost of creating the item since the manufacturer must sell at a price higher than the cost of making the item in order to recoup his investment and make a profit.

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Line A:

1. The points are (4,5) and (2,3)

2. The slope is 1

3. Unit for slope is inch/week

Line B:

1. The points are (4,4) and (2,3)

2. The slope is 1/2

3. Unit for slope is inch/week

What is slope ?

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

Line A:

1. The points are (4,5) and (2,3) ( write in (x,y) form )

2. slope = (5-3)/(4-2) = 2/2 = 1

( slope= change in y values/  change in x values )

3 . mark the slope as 1 inch/week

Line B:

1. The points are (4,4) and (2,3)

2. slope = (4-3)/(4-2) = 1/2

3 . mark the slope as 1/2  inch/week

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Answer:

the son age is 13band Evans age is 52 years old at present day

Dan is 12 years old.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

let the Age of Dan is x years

Mr. Evans Age = 4x

If Mr. Evans was 46 years old 2 years ago

The, Present age of Mr. Evans = 48 years

So, Dan's Age = 48/4

                        = 12 years.

Hence, Dan is 12 years old.

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Answer:  19/21

Step-by-step explanation:  Find the least common denominator of the two which is 21 the first fraction since 3 X 7=21

For the first fraction since 3X7=21, 1/3=1X7=7/3X7=7/21

For the second fraction since 7X3=21, 4/7=4X3/7X3=12/21

Add the two like fractions 7/21+12/21=7+12/21=19/21

The answer is 1/3+4/7=19/21

The number of Kid's Launches that are possible is 128. This is solved using Combination Principle.

A combination in mathematics is a selection of elements from a set with distinct members, where the order of selection is irrelevant.

Hence,

The number of possible "Sizes" from the specified 4 sizes are ⁴C₁

The number of sorts of bun that is possible from the specified two bun types is:  ²C₁

From the four sides, the number of possible side purchases is:  ⁴C₁

Of the available four drinks, the number of the possible drinks is: ⁴C₁

Now the possible number of all lunches are:

⁴C₁ x  ²C₁ x  ⁴C₁ x  ⁴C₁

= 4 x 2 x 4 x 4

= 128

Hence the number of Kid's Lunches that are possible are 128.

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sin(x+5pi/4) sin(x+5pi/4) in terms of sin(x) and cos(x) can be rewritten as cos (x) . sin [tex](\frac{x + 5\pi }{4} )[/tex] .sin (x)

Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles

Let find the common multiplier of sin

[tex](\frac{x + 5\pi }{4} )[/tex]sin (x), cos(x); cos (x) sin[tex](\frac{x + 5\pi }{4} )\\[/tex] sin (x)

Find the least common Multiplier of sin [tex](\frac{x + 5\pi }{4} )[/tex] sin (x) , cos (x)

Lowest common multiplier (LCM)

The LCM of a, b is the smallest multiplier that is divisible by both a and b

Factor sin [tex](\frac{x + 5\pi }{4 } )[/tex]sin ( x)

sin[tex]( \frac{x + 5\pi }{4} )[/tex]. sin(x)

Multiplier each factor with the highest power;

cos (x) .sin [tex](\frac{x + 5\pi }{4} )[/tex].sin (x)

Therefore, the trigonometry sin(x+5pi/4) in terms of sin(x) and cos(x) can be rewritten as cos (x) . sin [tex](\frac{x + 5\pi }{4} )[/tex] .sin (x)

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The diagram of the parabolic graph in the question indicates that responses are;

Vertex; (1, -9)

Axis of symmetry; x = 1

Y-intercept; (0, -8)

X-intercept(s); (-2, 0), (4, 0)

Concavity; opens up

A graph is a pictorial representation of the variation of one variable with respect to other variables.

Vertex

The vertex point of a parabolic graph represents the point where the parabola intersects the axis of symmetry

The vertex point of the parabolic graph in the question is; (1, -9)

Axis of symmetry

The axis of symmetry divides the graph of the parabola into two halves of the same dimensions, such that each side is a mirror reflection of the other.

The axis of symmetry is the line represented by the x-coordinate of the vertex, which is x = 1.

Y-intercept

The y-intercept is the point where the graph intersects the y-axis.

The y-intercept in the parabolic graph in the question is (0, -8)

X-intercept

The x-intercept is the location or point where the graph intersects the x-axis. The x-intercept of the graph in the question are (-2, 0) and (4, 0)

Concavity

The concavity of a graph is the rate of change of the derivative of the function.

If the derivative is increasing, the graph is concave upwards, and has a U-shape

The graph in the question is concave upwards

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The number of men and women that work at the company are;

Number of men = 36

Number of women = 18

Let the total number of employees in the company be x.

Now, we are told that 75% of the employees were men. Thus;

Number of men = 75% * x = 0.75x

Number of women = 0.25x

Now, we are told that after 6 women joined, the ratio of men to women became 2: 1.

Thus;

New total employees = x + 6

New total number of women = 0.25x + 6

Thus;

0.75x/(0.25x + 6) = 2/1

Cross multiply to get;

0.75x = 2(0.25x + 6)

0.75x = 0.5x + 12

0.75x - 0.5x = 12

0.25x = 12

x = 12/0.25

x = 48

Number of women = 0.25(48) + 6 = 18

Number of men = (48 + 6) - 18 = 36

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The solution for the given expression is 14∛x. The correct option is (C).

An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.

The variable part of an algebraic expression can never be added or subtracted from the constant part.

The given expression is as below,

5∛x + 9∛x

The given expression can be simplified as follows,

5∛x + 9∛x

Here, both the terms have equivalent variables. So, both are like terms.

As per the rules like terms can be added or subtracted keeping the variable as the same.

Thus, 5∛x + 9∛x = 14∛x

Hence, the given expression can be evaluated as 5∛x + 9∛x = 14∛x.

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The graph of y=1.4log (x) is black, graph of y=1.2ln(x) is green, graph of y=log(2.25-x) is blue, graph of y=log(0.75-x) is red.

A graph is a diagram that depicts the relationship between two variables, usually measured along opposite axes in a pair, is used.

To determine the color of each function, plot the graph of each function,

The graph of y=1.4log (x) is black.

The graph of y=1.2ln(x) is green.

The graph of y=log(2.25-x) is blue.

The graph of y=log(0.75-x) is red.

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Answer:

7a-7b

Step-by-step explanation:

we distribute the 7 by multiplying it to each term

7(a)-7(b)

7a-7b

Hopes this helps please mark brainliest

Answer:

7a - 7b

Step-by-step explanation:

Given expression,

→ 7(a - b)

Let's simplify the expression,

→ 7(a - b)

→ (7 × a) - (7 × b)

→ 7a - 7b

Hence, the answer is 7a - 7b.

Answer: [tex]7.39466666[/tex]

Step-by-step explanation:

Setting [tex]x=2.2[/tex] and [tex]n=3[/tex],

[tex]e^{2.2} \approx \sum^{3}_{k=0} \frac{2.2^{k}}{k!}=\frac{2.2^0}{0!}+\frac{2.2^1}{1!}+\frac{2.2^2}{2!}+\frac{2.2^3}{3!} \approx 7.39466666[/tex]

Answer:

7.39466667 (8 d.p.)

Step-by-step explanation:

We can approximate the value of eˣ for any x using the following sum formula:

[tex]\boxed{e^{x} \approx \displaystyle \sum^n_{k=0}\dfrac{x^k}{k!}}[/tex]

To approximate [tex]e^{2.2}[/tex] with n = 3, substitute x = 2.2 and n = 3 into the given sum formula:

[tex]e^{2.2} \approx \displaystyle \sum^3_{k=0}\dfrac{2.2^k}{k!}[/tex]

To calculate the sum, substitute k with each value from 0 to 3 and add the results together:

[tex]\begin{aligned}e^{2.2} &\approx \displaystyle \sum^3_{k=0}\dfrac{2.2^k}{k!}\\\\&= \dfrac{2.2^0}{0!}+\dfrac{2.2^1}{1!}+\dfrac{2.2^2}{2!}+\dfrac{2.2^3}{3!}\\\\&= \dfrac{1}{1}+\dfrac{2.2}{1}+\dfrac{4.84}{2}+\dfrac{10.648}{6}\\\\&= 1+2.2+2.42+1.774666666...\\\\&=7.39466667\; \sf (8\;d.p.)\end{aligned}[/tex]

Therefore, the approximate value of [tex]e^{2.2}[/tex] is:

[tex]\large \textsf{$e^{2.2}$}=\boxed{7.39466667}\; \sf (8\;d.p.)}[/tex]

Note: To obtain a more accurate approximate value, increase the value of n.

Answer:

8p^6q^4

6qp-7

Step-by-step explanation:

The percentage change in GDP is 2.04%

Percentage Change is the difference coming after subtracting the old value from the new value and then divide by the old value and the final answer will be multiplied by 100 to show it as a percentage. Generally, to convert a fraction into a percent, we multiply it by 100.

The formula of percentage change is given as

Percentage change =[ (New increase - old value) / old value] * 100

Percentage change = [(14.72 - 14.42) / 14.72] * 100

Percentage change = 2.04%

In this case, there is a percentage decrease of 2.04%

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Answer: Answer below

Step-by-step explanation: So you would simply have to divide 8 into 72 which would be 9.

we can verify our answer by doing 9x8 which equals 72.

Answer: 9

Step-by-step explanation:

bears divided by shelves = number of bears per shelf

72 bears divided by 8 shelves= 9 bears per shelf

Option D. The statement that is true from the equations that we have here is D. The equation x3 - x2 - x + 1 = 0 is equivalent to the equation x2(x - 1)-(x-1)=0.

I will have to start for the equation D, because at close glance we can easily see that the powers would be equal

The equation x3 - x2 - x + 1 = 0 is equivalent to the equation x2(x - 1)-(x-1)=0.

We are to simplify x²(x - 1)-(x-1)

we would have to open the brackets from the above

 x² * x +  x² * (-1) - x - (-1) = 0

It would be important to pay attention at the signs

such that we would have

x³ -  x² - x + 1 = 0

Therefore the equation  x^3 - x^2 - x + 1 = 0 is equivalent or equal to  x³ -  x² - x + 1 = 0 because they have the same solution

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Answer:

(2,-1)

Step-by-step explanation:

Given system of equations:

We are going to use the substitution method.

Step 1: Solve for x = y + 3 for x:
(Substitute y + 3 for x in 3x + 2y = 4)

3x+2y=4

3(y+3)+2y=4

5y + 9 = 4 ----> Simplify both sides of the equation

5y+9+−9=4+−9  -------> Add -9 to both sides

5y=−5

5y5 = -5/5  ------> Divide both sides by 5

y = −1

Step 1: Substitute -1 for y in x = y + 3:

x = y + 3

x = -1 + 3

x = 2 --------> (Simplify both sides of the equation)

Answer:

(2,-1)

Answer:

HNO3. AND H3O

Step-by-step explanation:

BECAUSE THE TWO OF THEN GIVE AN (H) to the base

The equation that represent the proportional relationship is t = 2 / 5 H.

Proportional relationships are relationships between two variables where their ratios are equivalent.

A proportional relationship is one in which two quantities vary directly with each other.

We say the variable y varies directly as x if:  

y = kx

for some constant k , called the constant of proportionality .

The equation that represent the proportional relationship can be represented as follows:

t = KH

using

t = 2

H = 5

Hence,

2 = 5k

k = 2 / 5

Therefore,

t = 2 / 5 H

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See the graph. It shows the sketch.

The expression of 602.16 dam in decimeters can be written as 60216 decimeter.

The concept that will be used in the calculation is conversion. to perform this conversion, it is important to note that 1 Decimeter (dm) is equal to 0.01 dekameter (dam).

Then, if 1dm = 0.01 dam

               Xdm     = 602.16 dam

Where x is the value in decimeter.

Then we can cross multiply as :

X= (602.16 dam * 1dm)/ 0.01 dam

= 60216 decimeter.

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