Write in slope intercept form.

For the given function f(x) = x²-16 , the inverse of the function if the domain f(x) is x> 0 is equal to f⁻¹(x) = √x+16.

As given in the question,

Given function is equal to:

f(x) = x²-16

To calculate the inverse of the function if the domain f(x) is x> 0,

Let us consider f(x) = y

y = x²-16

⇒ x² = y + 16

⇒ x = √y + 16

Now, replace x by f⁻¹(x) and y by x we get,

f⁻¹(x) = √x+16

Therefore, for the given function f(x) = x²-16 , the inverse of the function if the domain f(x) is x> 0 is equal to f⁻¹(x) = √x+16.

The complete question is:

Which function is the inverse of f(x)=x²-16 if the domain of f(x) is x> 0?

a. f⁻¹(x) = √x+16

b.  f⁻¹(x) = √x + 4

c.  f⁻¹(x) =  √x -16

d.  f⁻¹(x) =  √x - 4

Learn more about function here

brainly.com/question/5975436

#SPJ9

Answer:

y - 2 = 3(x + 1)

Step-by-step explanation:

The slope is 3 and the point is (-1,2)

From the plot pointed, you go up three unit and 1 unit to the right to get back on the line.  This is 3/1 or 3.

y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex])  

Replace m =3

Replace [tex]y_{1}[/tex] = 2

Replace [tex]x_{1}[/tex] = -1

y - 2 = 3(x - -1)

y - 2 = 3(x +1)

Answer:

x = y + 5

Step-by-step explanation:

The difference is 5, while x is the bigger number and y the smaller number. So you have to add 5 to y to get x.

Step-by-step explanation:

a line with undefined slope is a vertical line, because x does not change on this line at all, and therefore the shoe is y/0.

a vertical line is parallel to the y-axis.

and to go through the given point, it has to use the x- coordinate.

so, the equation is

x = -5

that's really it.

this is the line of all points with the x-coordinate = -5. any value for y is valid.

The range of the function is:  (- ∞,3) or - ∞ < x < 3

Range (statistics), is the difference between the highest and the lowest values in a set. Interval (mathematics), also called range, is a set of real numbers that includes all numbers between any two numbers in the set.

Given that

U (x) =  -2x² +  3

V(x) = 1/x

(u-v)(x)  can be represented as

U(x) – v(x)

So, we have:

-2x²+ 3 - 1/x

= (-2x³ + 3x -1)/ x

Therefore, the range of the function is (- ∞,3) or -∞ < x < 3

To learn more about range visit

https://brainly.com/question/28135761

#SPJ13

let's say "x" is the original price, now let's reduce it by 25%

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{25\% of x}}{\left( \cfrac{25}{100} \right)x}\implies \cfrac{1}{4}x\hspace{5em}x-\stackrel{25\%}{\cfrac{1}{4}x}\implies \stackrel{new~price}{\cfrac{3}{4}x}[/tex]

so the new price after applying a 25% or namely 1/4 of "x" is just 3/4 of "x".

if we apply the same reduction again, we'll  be left with only 3/4 of ( (3/4)x ) and so on, check the picture below which shows the value once we apply the 1/4 four times, we end up with the new price being to 3/4 of whatever it was before, so

[tex]\cfrac{3}{4}\cdot \cfrac{3}{4}\cdot \cfrac{3}{4}\cdot \cfrac{3}{4}x\implies \cfrac{81}{256}x\hspace{5em}\cfrac{81}{256}\cdot 37\implies \cfrac{2997}{256}[/tex]

now, since we know the 100% or original price was 37, what's the new reduced price of 2997/256 off of it in percentage?

[tex]\begin{array}{ccll} amount\%\\ \cline{1-2} 37&100\\[1em] \frac{2997}{256}&p \end{array}\implies \cfrac{37}{~~ \frac{2997 }{256 } ~~}=\cfrac{100}{p}\implies \cfrac{(37)(256)}{2997}=\cfrac{100}{p} \\\\\\ (37)(256)p=299700\implies p=\cfrac{299700}{(37)(256)}\implies p\approx \stackrel{\%}{31.64}~\hfill \underset{savings}{\stackrel{100\%~~ - ~~31.64\%}{\approx\text{\LARGE 68.36\%}}}[/tex]

To see the graph in the below attachment. The graph of inequality is      x > -6 .

Given,

In the question:

The inequality is given as:

-4(x + 3) ≤ -2x

What is inequality?

An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.

Now, According to the question:

Solution set of inequality -4(x + 3) ≤ -2x

-4(x + 3) ≤ -2x

Apply the Distributive property :

-4x - 12 < -2x

Rearrange the variables:

-4x + 2x < 12

Combine like terms:

-2x  < 12

Divide both sides:

x > -12/2

Cross out the common factor:

x > -6

Hence, To see the graph in the below attachment. The graph of inequality is x > -6 .

Learn more about Inequality at:

https://brainly.com/question/20383699

#SPJ9

The vertical line intercept the the graph more than once, the graph is of a relation but it is not a function

Hence, the vertical line intercept the the graph more than once, the graph is of a relation but it is not a function.

To know more about function check the below link:

https://brainly.com/question/25638609

#SPJ1

Answer:

Step-by-step explanation:

Cube Surface Area = 150 cm2

Cube Volume = ?

Ac = 6 a2

150 = 6a2

150/6 = a2

25 = a2

5 = a

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

Vc = a3

Vc = (5)3

Vc = 125 cm3

Answer:

Step-by-step explanation:

divide 150 by 6 and find the area of ​​one face of the cube, take the square root and find the side, side^3 and find the volume

150 : 6 = 25 cm² (area of ​​one face of the cube)

√25 = 5 (side of the cube)

5³ = 125 cm³ (volume of the cube)

Answer:

C or third option

Step-by-step explanation:

standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

[tex](\stackrel{x_1}{-8}~,~\stackrel{y_1}{0})\hspace{10em} \stackrel{slope}{m} ~=~ - 4 \\\\\\ \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}=\stackrel{m}{- 4}(x-\stackrel{x_1}{(-8)}) \implies y -0= -4 (x +8) \\\\\\ y=-4x-32\implies {\Large \begin{array}{llll} 4x+y=-32 \end{array}}[/tex]

Answer: $0.576

Step-by-step explanation:

The total amount in prizes is $1800.

For there to be 60% profit, the total cost of the tickets need to be [tex]1800(1.6)=\$ 2880[/tex].

Thus, each ticket must sell for [tex]\frac{2880}{5000}=\$ 0.576[/tex]

The constant of proportionality k, of the given equation y = (2/7)x  is 2/7.

Proportionality :

Proportion is a mathematical comparison between two numbers.

here

y=2/7x

y [tex]\ \propto[/tex] 2

shows that y is  directly proportional  to 2.

y [tex]\ \propto[/tex] 1/ 7x

shows that y is inversely proportional  to 7x.

The constant of proportionality is given as:

y = kx or  y = k/x

where k is the proportionality constant

The constant of proportionality k, of the given equation y = (2/7)x  is 2/7.

To know more about proportionality

https://brainly.com/question/8598338

#SPJ1

After solving the expression we get the answer as the equation does not have a solution.

Given, we have:

(x+10)²-7=5

Open the brackets.

⇒ (x²+20x+100)-7=5

⇒ x²+20x+100-7=5

Calculate the difference.

⇒ x²+20x+93=5

Arrange the like terms:

⇒ x²+20x+93-5=0

⇒ x²+20x+88=0

Factorize the a²ove expression.

⇒ x²+20x+88

can't be factorize, as it does not have factors to reduce the expression.

Hence the expression does not have a solution.

Learn more about Linear equations here:

brainly.com/question/4074386

#SPJ1

Answer:

x = -4.5

Step-by-step explanation:

[tex]20 = 2 - 4x[/tex]

[tex]18 = - 4x[/tex]

[tex] - 4.5 = x[/tex]

For x =  12°, line m and line n will be parallel to each other.

Option (C) is correct.

What are angles in a linear pair?

When two lines intersect at a single point, a linear pair of angles is formed. If the angles are adjacent to each other after the two lines intersect, they are said to be linear. The sum of the angles of a linear pair is always 180°. These angles are also referred to as supplementary angles.

In the given figure, the line m and line n will be parallel, if and only if the both angles are in a linear pair,

So by using the property of the angles in a linear pair, we get

             11x° + 4x° = 180°

             15x° = 180°

              x° = 180°/15°

              x = 12°

Hence for x =  12°, line m and line n will be parallel to each other.

Option (C) is correct.

To learn more about angles in a linear pair, visit:

brainly.com/question/1757859

#SPJ1

Answer:

[tex]z \in \left[-\frac{3}{16}, \frac{3}{16} \right][/tex]

Step-by-step explanation:

[tex]-9 \leq 32z-3 \leq 3 \\ \\ -6 \leq 32z \leq 6 \\ \\ -\frac{3}{16} \leq z \leq \frac{3}{16} \\ \\ \therefore z \in \left[-\frac{3}{16}, \frac{3}{16} \right][/tex]

The solution set of the inequalities given in the task content is described as; (-infinity, -17) U [ -9, infinity).

It follows from the task content that the solution set containing values of w which render the pair of inequalities true be determined.

On this note, since the inequalities given are;

-14 > w + 3 or 3w ≥ -27

By solving the inequalities individually; we have;

-14 > w + 3

Subtract 3 from both sides of the equation so that we have;

-14 - 3 > w; Therefore, -17 > w.

Also, 3w ≥ -27

Therefore; w ≥ -9.

On this note, it follows that; w < -17 or w ≥ -9.

Consequently, the solution set of the inequalities can be represented using interval notation as;

(-infinity, -17) U [ -9, infinity)

Read more on solution of inequalities;

https://brainly.com/question/11613554

#SPJ1

Answer: 100 x 1.05^(15x12) = $651739.184097

Step-by-step explanation:

Answer:

This is what I got, hope it helps!

Step-by-step explanation:

There is exactly one solution. The ordered pair for the given set of solutions is (-4,-3). Option A is correct.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, the equation is

x/4 -y/2 =1/2

x+4y=-16

[tex]\begin{bmatrix}\frac{x}{4}-\frac{y}{2}=\frac{1}{2}\\ x+4y=-16\end{bmatrix} \\\\ \begin{bmatrix}2\left(y+1\right)+4y=-16\end{bmatrix} \\\\ \begin{bmatrix}6y+2=-16\end{bmatrix} \\\\ y = -3[/tex]

Substitute the value of y in equation (2)

[tex]x=2\left(-3+1\right) \\\\ x=-4 \\\\ x=-4,\:y=-3[/tex]

Thus, there is exactly one solution. The ordered pair for the given set of solutions is (-4,-3). Option A is correct.

Learn more about the equation here,

https://brainly.com/question/10413253

#SPJ1

Answer: 870

Step-by-step explanation:

The tickets will sell until there is a day when a non-positive number of tickets will be sold.

[tex]\lfloor 133/11 \rfloor=12[/tex], so this will be after 12 days.

Thus, we can interpret this as an arithmetic series with 12 terms, a first term of 133, and a common difference of -11.

The sum of this series is [tex]\frac{12}{2}[2(133)+(12-1)(-11)]=870[/tex].

Answer:

7 yd

It's a 16 by 13 rectangle. Since 6 yd are already showing on the left side, you know 7yd remain to get 13 yd.

Answer:

BGHA

Step-by-step explanation:

Just look at the coordinates.

1 is at x=0 and y=4, so (0, 4), or B

2 is at x=-4 and y=3, so (-4, 3), or G

3 is at x=2 and y=0, so (2, 0), or H

4 is at x=0 and y=-1, so (0, -1), or A

EAnswer:her son is eight

Step-by-step explanation:

The solution to the questions are:

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

Length = 350 - 2x

Width = x

The area of a rectangle is the product of its dimensions

So, we have

Area = Length x Width

Substitute the known values in the above equation, so, we have the following representation

A = (350 - 2x) * x

Evaluate

A = 350x - 2x²

Differentiate and set to 0

350 - 4x = 0

So, we have

4x = 350

Divide by 4

x = 87.5

Recall that

Length = 350 - 2x

So, we have

Length = 350 - 2 x 87.5

Evaluate

Length = 175

The area is then calculated as

Area = Length x Width

So, we have

Area = 175 x 87.5

Evaluate

Area = 15312.5 square meters

Hence, the area is 15312.5 square meters

Read more about rectangles at

brainly.com/question/25292087

#SPJ1