Write the equation of the circle in general form.

if anyone can explain this that would be great, if not it's okay, just a little lost on how to do all of this haha

The answer is:

The correct option is:

c) [tex]f^{-1}(x)=\frac{e^{x}}{10}[/tex]

Inversing a function means switching the range and domain of the function. To inverse a function we need to rewrite the variable (x) with the function (f(x) or y), and rewrite the function (f(x) or y) with the variable (x), and then, isolate "y" or "f(x)".

Also, we need to remember how to isolate the variable from a logarithmic function.

[tex]ln(x)=a\\\\e^{a}=e^{ln(x)}\\\\e^{a}=x[/tex]

So, we are given the function:

[tex]f(x)=ln(10x)[/tex]

Which it's equal to write:

[tex]y=ln(10x)[/tex]

Then, inversing the function we have:

[tex]y=ln(10x)[/tex]

[tex]x=ln(10y)[/tex]

[tex]x=ln(10y)\\\\e^{x}=e^{ln(10y)} \\e^{x}=10y\\\\y=\frac{e^{x}}{10}[/tex]

Hence, we have that the correct answer is the option:

c) [tex]f^{-1}(x)=\frac{e^{x}}{10}[/tex]

Have a nice day!

[tex]f(x) = \ln(10x)\\ \\ f^{-1}\Big(f(x)\Big) =x \\ \\ f^{-1}\Big(\ln(10x)\Big) = x\\ \\ \ln(10x) = t \Rightarrow 10x = e^t \Rightarrow x = \dfrac{e^t}{10} \\ \\ \Rightarrow f^{-1}(t) = \dfrac{e^t}{10} \Rightarrow \boxed{f^{-1}(x) = \dfrac{e^x}{10}}[/tex]

Answer:true

Step-by-step explanation:

The statement given is true , Option A is the correct answer.

A cylinder is a three dimensional figure which has two parallel circular bases joint by a curved surface of fixed length.

A statement related to Cylinder is given and asked if it is true

Yes , the statement that a cylinder is made up of discs of same radius , this can be very well understood from the figure itself as the cylinder definition says that it has a curved surface of same radius and fixed height.

Therefore Option A is the correct answer.

To know more about Cylinder

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This is a quadratic equation. You have to factor it.

You have to find two numbers that meet the following requirement:

-When multiplied, is equal to -18.

-When added, is equal to 3.

The two numbers are 6 and -3.

Now factor it:

(x + 6)(x - 3)

So x = -6 or x = 3

Answer:75

Step-by-step explanation:3/5x=45

X=45÷3/5

×=45×5/3

×=75

For this case we must find the value of the variable "x" of the following equation:

[tex]\frac {3} {5} x = -45[/tex]

We multiply by 5 on both sides of the equation:

[tex]3x = -45 * 5\\3x = -225[/tex]

We divide between 3 on both sides of the equation:

[tex]x = \frac {-225} {3}\\x = -75[/tex]

Answer:

[tex]x = -75[/tex]

Answer:

Angle E = 73 degrees

Step-by-step explanation:

Supplementary means it equals 180 degrees.

So to find x, you add the 2 equations.

2x + 15 + 5x - 38 = 180

which equals 7x + (-23) = 180 = 7x - 23 = 180

7x = 203  You move the -23 to the other side

203/7 = 29  So x = 29 degrees

So to find angle E, you put in 29 degrees for x.

2 x 29 + 15 = 73 degrees

Answer:

Are there answer choices?

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

The coefficient is the number in front of the variable.

The coefficient of the a² term in the expression -2a(a + b - 5) + 3(-5a + 2b) + b(6a + b - 8) is a² -2.

To find the coefficient of the a² term in the expression -2a(a + b - 5) + 3(-5a + 2b) + b(6a + b - 8) we proceed as follows

Since we have that expression  -2a(a + b - 5) + 3(-5a + 2b) + b(6a + b - 8) and we want to find the coeffiecient of the a², we need to determine which of the terms in the brackets would be multiplied to give a term in a².

To have a term in a², there must be at one a term outside the bracket and one a term in side the bracket.

Looking at the expression -2a(a + b - 5) + 3(-5a + 2b) + b(6a + b - 8) , the only bracket that has two a terms is the first bracket -2a(a + b - 5).

So, expanding the bracket, we have that -2a(a + b - 5) = -2a² - 2ab + 10.

Now, the coefficient of the a²,  -2a² is the number in front of the a² which is - 2

So,the coeffieient of the a² is - 2.

Answer:

$1.45-$0.25=x

x=$1.20

Step-by-step explanation:

Answer:

1- exponential

2- constant multiplicative rate of change

Step-by-step explanation:

Answer:

Exponential

Constant multiplicative rate of change

Step-by-step explanation:

It is not a linear function because in order to be linear it should decrease or increase the same amount from one moment to another.

Nor is it a quadratic function, since to be quadratic it should have values that increase and then decrease (a point of return).

So the correct option is that it is an exponential function because the values do not change the same amount each time, they change constantly but by a multiplication factor.

So for the second of the options it will be: constant multiplicative rate of change

In summary:

The data in the table can best be described as exponential because there is a constant multiplicative rate of change.

Answer:

Ryan has 2H + 5 stickers.

Step-by-step explanation:

Let J = Janice

Let M = Melvin

Let R = Ryan

J = 2*M

R = J + 5

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

J = 2*H

R = 2H + 5

Answer:

The coefficient of the squared expression in the parabola equation is [tex]a=4[/tex]

Step-by-step explanation:

The equation of a parabola in its vertex form is:

[tex]y = a(x-h) ^ 2 + k[/tex]

Where the vertex of the parabola is the point (h, k)

a is the ceoficiente of the term to the square.

We need to find the equation of a parabola that has its vertex in the point:

(-5, -2)

So:

[tex]h = -5\\\\k = -2[/tex]

Therefore the equation is:

[tex]y = a(x - (-5)) ^ 2 -2\\\\y = a(x + 5) ^ 2 -2[/tex]

We know that the point (-4, 2) belongs to this parable. Then we can find the value of a by replacing the point in the equation of the parabola

[tex](2) = a((-4) + 5) ^ 2 -2\\\\2 = a(1) ^ 2 -2\\\\2 = a -2\\\\a = 4[/tex]

Finally the coefficient is a = 4

Answer:

The answer is 4

Step-by-step explanation:

This is the correct answer

The answer is the AREA of a figure is a measurement of the space inside it.

Answer:

Step-by-step explanation:

Answer:

x

=

π

3

,

2

π

3

,

4

π

3

,

5

π

3

Explanation:

(

sin

x

)

2

=

3

(

cos

x

)

2

(

sin

x

)

2

=

3

(

1

−

(

sin

x

)

2

)

(

sin

x

)

2

=

3

−

3

(

sin

x

)

2

4

(

sin

x

)

2

=

3

(

sin

x

)

2

=

3

4

sin

x

=

±

(

√

3

2

)

x

=

π

3

,

π

−

π

3

,

π

+

π

3

,

(

2

π

)

−

π

3

x

=

π

3

,

2

π

3

,

4

π

3

,

5

π

3

If this was in the region

0

≤

x

≤

2

π

[tex]\bf \textit{Pythagorean Identities} \\\\ sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sin^2(x)=3cos^2(x)\implies sin^2(x)=3[1-sin^2(x)] \implies sin^2(x)=3-3sin^2(x) \\\\\\ sin^2(x)+3sin^2(x)=3\implies 4sin^2(x)=3\implies sin^2(x)=\cfrac{3}{4}[/tex]

[tex]\bf sin(x)=\pm\sqrt{\cfrac{3}{4}}\implies sin(x)=\pm\cfrac{\sqrt{3}}{\sqrt{4}}\implies sin(x)=\pm\cfrac{\sqrt{3}}{2} \\\\\\ sin^{-1}[sin(x)]=sin^{-1}\left( \pm\cfrac{\sqrt{3}}{2} \right)\implies x= \begin{cases} \frac{\pi }{3}\\\\ \frac{2\pi }{3}\\\\ \frac{4\pi }{3}\\\\ \frac{5\pi }{3} \end{cases}[/tex]

that is, on the interval [0, 2π].

Answer:

x=4

Step-by-step explanation:

11x-4=5x+20

4x=16

x=4

Answer:

x = 4

Step-by-step explanation:

Note the equal sign, what you do to one side, you do to the other. Isolate the variable, x. First, subtract 5x and add 4 to both sides.

11x (-5x) - 4 (+4) = 5x (-5x) + 20 (+ 4)

11x - 5x = 20 + 4

Combine like terms. Simplify:

(11x - 5x) = (20 + 4)

6x = 24

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Divide 6 from both sides.

(6x)/6 = (24)/6

x = 24/6

x = 4

x = 4 is your answer.

~

Answer:Classifying Polynomials. Polynomials can be classified two different ways - by the number of terms and by their degree. A monomial has just one term. For example, 4x2 .Remember that a term contains both the variable(s) and its coefficient (the number in front of it.)

Step-by-step explanation:Hope this helps. Please name me brainliest

The answer is:

⇨ look at its highest exponent

Work/explanation:

To classify polynomials by their degree, look at the highest exponent of the polynomial.

For instance, if we have [tex]\rm{x^2+2x}[/tex] then we have a second-degree binomial.

(binomial because we have 2 terms)

Answer:

23

Step-by-step explanation:

Basically, (f o g)(1) is saying f(g(1))

So let's plug in 1 into the g(x) equation.

[tex]g(1)=2(1)-6 \\ \\ g(1)=2-6 \\ \\ g(1)=-4[/tex]

Now we can plug in -4 into the f(x) equation.

[tex]f(-4)=-4(-4)+7 \\ \\ f(-4)=16+7 \\ \\ f(-4)=23[/tex]

23

Step-by-step explanation:

This is a problem of composition of function. We can define this as follows:

[tex]The \ \mathbf{composition} \ of \ the \ function \ f \ with \ the \ function \ g \ is:\\ \\ (f \circ g)(x)=f(g(x)) \\ \\ The \ domain \ of \ (f \circ g) \ is \ the \ set \ of \ all \ x \ in \ the \ domain \ of \ g \\ such \ that \ g(x) \ is \ in \ the \ domain \ of \ f[/tex]

So [tex](f.g)(x)=f(g(x))=h(x)[/tex]:

[tex]h(x)=-4(2x-6)+7 \\ \\ h(x)=-8x+24+7 \\ \\ h(x)=-8x+31[/tex]

Therefore:

[tex]h(x)=f(g(1))=-8(1)+31=23[/tex]

Use sin because in relation to angle F, side 12 is the opposite and side 17 is the hypotenuse (soh-cah-toa) so that's why the answer is 45°

Answer:

A

Step-by-step explanation:

Calculate ∠F using the sine ratio

sinF = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{CF}[/tex] = [tex]\frac{12}{17}[/tex]

F = [tex]sin^{-1}[/tex] ([tex]\frac{12}{17}[/tex] ) ≈ 45° → A

Answer:

hello : x=2 and x = -8 is solution

Step-by-step explanation:

x² +6x -16=0

for : x = 2

2² +6(2) -16 = 4+12-16 = 16-16 = 0

for x = - 8

(-8)² +6(-8) -16 = 64 - 48 -16 = 64 -64 = 0

For this case we must solve the following equation of the second degree:

[tex]x ^ 2 + 6x-16 = 0[/tex]

The solution is given by:

[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}[/tex]

Where:

[tex]a = 1\\b = 6\\c = -16[/tex]

Substituting:[tex]x = \frac {-6\pm \sqrt {6 ^ 2-4 (1) (- 16)}} {2 (1)}[/tex]

[tex]x = \frac{-6\pm\sqrt{36+64}}{2}[/tex]

[tex]x = \frac {-6 \pm \sqrt {100)}} {2}\\x = \frac {-6 \pm10} {2}[/tex]

So:

[tex]x_ {1} = \frac {-6 + 10} {2} = \frac {4} {2} = 2\\x_ {2} = \frac {-6-10} {2} = \frac {-16} {2} = - 8[/tex]

Answer:

[tex]x_ {1} = 2\\x_ {2} = - 8[/tex]

If both machines are working at once, 200 tshirts (100 in each machine) could be made in 100 minutes, if 200 shirts can be made in machine 1 in 50 minutes, it will take 25 minutes to make 100. machine b takes 150 minutes per each 200, 150 divided by two is 75. 75 + 25 = 100 minutes

It would work better just to use machine one and take 50

minutes, but i dont think thats an answer choice.

edit: i think from the choices your answer would be: 37.5 as if both machines run at once more tshirts can be made

I’m assuming you need to find y

So what you would do is

3x + y = 2

Subtract 3x from both sides and get:

y = 2 - 3x

From this, we can see the y-intercept is 2. Therefore, the correct graph is the first one.

The answer is:

The value of "x" is 90.16

To solve the problem we need to use the trigonometric identity of the sine that establish that:

[tex]Sin(\alpha )=\frac{OppositeSide}{Hypotenuse}[/tex]

So, we are given the following information:

[tex]\alpha =48(degrees)\\\\OppositeSide=67[/tex]

Then, applying the trigonometric identity, we have:

[tex]Sin(48)=\frac{67}{Hypotenuse}[/tex]

[tex]Sin(48)=\frac{67}{Hypotenuse}\\\\Hypotenuse=\frac{67}{sin(48)}=90.157=90.16[/tex]

Hence, the value of "x" is (rounded to the nearest hundreth) 90.16.

Have a nice day!

Due To My Calculations, The Answer Is 90.16.

For this case we have that by definition, the volume of a cylinder is given by:

[tex]V = \pi * r ^ 2 * h[/tex]

Where:

A: It's the radio

h: It's the height

We have according to the data:

[tex]r = 4 \ in\\h = 15 \ in[/tex]

Substituting:

[tex]V = \pi * (4) ^ 2 * 15\\V = \pi * 16 * 15\\V = \pi * 240\\V = 753.6 \ in[/tex]

Thus, the volume of the paint can is 753.6 cubic inches.

Answer:

[tex]V = 753.6 \ in^3[/tex]

The answer is 753.6 inches.

Hope this helps!

Answer:

Step-by-step explanation:

We have three triangles with base b = 9yd and height h = 10yd, and one triangle in the base of pyramid with base b = 9yd and height h = 7.8yd.

The formula of an area of a triangle:

[tex]A_\triangle=\dfrac{bh}{2}[/tex]

Substitute:

[tex]LA=4\cdot\dfrac{(9)(10)}{2}=(2)(90)=180\ yd^2\\\\B=\dfrac{(9)(7.8)}{2}=(9)(3.9)=35.1\ yd^2\\\\SA=B+LA\to SA=180+35.1=215.1\ yd^2[/tex]

Answer:

Step-by-step explanation:

Answer:

Stem            Leaf

6                   4 9

7

8                   8 8

9                   1  2 3 4 5 7 7

10                  0

Step-by-step explanation:

The stem-and-leaf plot is a semi-graph that allows presenting the distribution of a quantitative variable. It consists of separating each data in the last digit (which is called a leaf) and the remaining front numbers (which form the stem).

It is especially useful for medium-sized data sets and that your data is not grouped around a single stem. With it we can get the idea of ​​what distribution the data have, the asymmetry, etc.

The name of stem and leaves refers to the branch of a plant, with the front digits marking the stem where the number is located and the final digit of the leaf.

1. First at all, we have to sort the data from lowest to highest

64, 69, 88, 88, 91, 92, 93, 94, 95, 97, 97, and 100

2. Draw a table with two columns, the first column for the stem and the second for the leaves. Arrange all the stems in the first column in descending order. Each stem is written only once.

Stem            Leaf

3.  Record all the leaves in the second column, in increasing order, next to the corresponding stem.

Stem            Leaf

6                   4 9

7

8                   8 8

9                   1  2 3 4 5 7 7

10                  0

Answer:

[tex]\large\boxed{\dfrac{10x^6y^3+20x^3y^2}{5x^3y}=2x^3y^2+4y}[/tex]

Step-by-step explanation:

[tex]\dfrac{10x^6y^3+20x^3y^2}{5x^3y}=\dfrac{(5x^3y)(2x^3y^2)+(5x^3y)(4y)}{5x^3y}\\\\=\dfrac{5x^3y(2x^3y^2+4y)}{5x^3y}\qquad\text{cancel}\ 5x^3y\\\\=2x^3y^2+4y[/tex]

Answer:

a. 18.67 + 3.456 + 0.2 + 3.21

=25.536

b. 3.256 + 4.21 + 3.009 + 0.35

=10.825

c. 7 – 3.06

=3.94

d. 62.98 – 3.555

=59.425

e. 5.3 × 12

=63.6

f. 4.35 × 2.11

=9.1785

g. 56/0.7

= 80

h. 5.6/7

=0.8

Perform addition, subtraction, and multiplication operations with decimal numbers.

a. To perform the addition, we simply add the numbers together:

18.67 + 3.456 + 0.2 + 3.21 = 25.536

b. Add the numbers together:

3.256 + 4.21 + 3.009 + 0.35 = 10.825

c. Subtract 3.06 from 7:

7 - 3.06 = 3.94

d. Subtract 3.555 from 62.98:

62.98 - 3.555 = 59.425

e. Multiply 5.3 by 12:

5.3 × 12 = 63.6

f. Multiply 4.35 by 2.11:

4.35 × 2.11 = 9.1785

g. Divide 56 by 0.7:

56 ÷ 0.7 = 80

h. Divide 5.6 by 7:

5.6 ÷ 7 = 0.8

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Multiply the bracket by 1/2

1/2(2n +6)

cross out 2 and 2n and divide by 2.

cross out 6 and 2 and divide by 2

n+3

Answer is n+3

Distribute 1/2 into (2n+6): 1/2 * 2n + 1/2 * 6. Simplify: n + 3. The equivalent expression is n + 3.

Let's break down the process step by step:

Given expression:[tex]\( \frac{1}{2}(2n+6) \)[/tex]

1. Distribute [tex]\( \frac{1}{2} \)[/tex]into the parentheses:

  We multiply each term inside the parentheses by [tex]\( \frac{1}{2} \):[/tex]

  [tex]\( \frac{1}{2} \times 2n + \frac{1}{2} \times 6 \)[/tex]

2. Simplify each term:

  a. [tex]\( \frac{1}{2} \times 2n \):[/tex]

     The [tex]\( \frac{1}{2} \)[/tex] and the [tex]\( 2 \)[/tex] cancel out, leaving [tex]\( n \).[/tex]

  b. [tex]\( \frac{1}{2} \times 6 \):[/tex]

     Multiply [tex]\( \frac{1}{2} \) by \( 6 \) to get \( 3 \).[/tex]

3. Combine the simplified terms:

  Add the simplified terms together:

  [tex]\( n + 3 \)[/tex]

So, the expression equivalent to [tex]\( \frac{1}{2}(2n+6) \) is \( n + 3 \).[/tex]

Answer:

Step-by-step explanation: first u need to write a division equation 8 ÷ 1/3. Then u have to solve. Well first u have to probably turn the whole number 8 into a fraction 1/8. Then u have to multiply 1/8 times 1/3 equals to?

1/24 as ur answer

Answer: 13°

Step-by-step explanation: The correct answer is 13°. Since you know the opposite and adjacent you will use tangent tan x= 12/50

Final answer:

To find the angle of elevation between the diver and the diving board, we use the tangent function of a right triangle, which results in an angle of approximately 13 degrees. Thus, option B (13 degrees) is the correct answer.

Explanation:

The question is asking for the measure of the angle of elevation from the diver looking up to the top of the diving board. To calculate this, we can use trigonometry, specifically the tangent function, which relates the opposite side to the adjacent side of a right-angled triangle. We have a right triangle where the height of the diving board is the opposite side (12 feet), and the distance from the diver to the base of the diving board is the adjacent side (50 feet).

The tangent of the angle \heta is the ratio of the opposite side to the adjacent side:

tan(\ heta) = opposite / adjacent = 12/50

To find \ heta, we take the inverse tangent (arctan) of the ratio:

\heta = arctan(12/50)

Using a calculator, we find that:

\heta\approx 13.4\extdegree

Finally, we round to the nearest whole number:

\heta\approx 13\extdegree

Therefore, the angle of elevation is approximately 13 degrees, which corresponds to option B.

Answer:

A

Step-by-step explanation: