If g (x) = one-third x and 3 x (StartFraction x Over 3 EndFraction), which expression could be used to verify that (one-third x) (3 x) is the inverse of One-third (3 x)?

Here the set given is

So the set should be

The set elements are

{..,1,2,3}

Answer:

{ ..., 0, 1, 2, 3}

Step-by-step explanation:

Set notation is used in math to list numbers, objects or outcomes.

It uses curly brackets called "braces". Objects placed within the braces are the elements of the set.

Given set notation:   { x | x ∈ I, x ≤ 3 }

The ∈ symbol means "is an element of".

Therefore, x ∈ I means that x is an element of the set of integers. (Integers are whole numbers that can be positive, negative, or zero).

The ≤ symbol means "less than or equal to".

Therefore, x ≤ 3 means that x is less than or equal to 3.

Therefore, the given set notation means:

x is an element of the set of integers less than or equal to 3

The listing method of set notation simply lists the numbers in the set.

The three dots "..." means it is infinite (goes on forever).

Therefore:

{ x | x ∈ I, x ≤ 3 } = { ..., 0, 1, 2, 3}

Step-by-step explanation:

v = Victor's age

m = Maria's age

v = 3m

v - 10 = 7(m - 10)

3m - 10 = 7m - 70

60 = 4m

m = 15

v = 3m = 3×15 = 45

Victor is 45 years old. Maria is 15 years old.

Answer:

>

Step-by-step explanation:

Cause 750 was the least they could raise

Answer:

>=

Step-by-step explanation:

>= because the teacher wants AT LEAST 750. at least meaning you can raise 750 or MORE

Answer:

The slope of the line is:  

              [tex]-\frac{3}{4}[/tex]

Slope of a parallel line is the same:

             [tex]-\frac{3}{4}[/tex]

Slope of a perpendicular line, invert the sign and fraction:

              [tex]\frac{4}{3}[/tex]

Hope this helps

Answer:

3 1/2 or said as 3.5 cups is equal to 1 pound

Step-by-step explanation:

1 Pound brown sugar is equivalent to ___3 1/2 or 3.5 __ cups

Hope This Helped

Answer:

A. (AAA)

Step-by-step explanation:

.....(AAA) "does not work because it can produce similar but not congruent triangles"

.....(AAS) "If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent."

.....(ASA)"triangles are congruent if any two angles and their included side are equal in the triangles."

Hope This Helped

Answer:

Girls = 16

Total students = 40

Step-by-step explanation:

40% of the students are girls, this means 60% of the students are boys.

To find the number of girls, setup a proportion using the percentages and actual number of students in the class. I am going to make the numerator the numbers that go with the girls and the denominator will be the numbers that go with the boys.

Also let's convert the percentages to decimals by moving the decimal two places left.

40% = 0.4 and 60% = 0.6

[tex]\frac{.4}{.6} =\frac{g}{24} \\.6g=9.6\\\frac{.6g}{.6} =\frac{9.6}{.6} \\g=16[/tex]

Now let's find the total number of students by adding the number of girls to the number of boys.

16 + 24 = 40

Answer:

[tex]y=\frac{1}{2} x[/tex]

Step-by-step explanation:

The equation of a line through two points can usually (except when the line is a vertical line) be written in slope intercept form,  [tex]y=mx+b[/tex] , where "m" is the slope of the line, and "b" is the y-intercept of the line.

To find "m", use the formula for slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\dfrac{(3)-(-2)}{(6)-(-4)}[/tex]

[tex]m=\dfrac{3+2}{6+4}[/tex]

[tex]m=\dfrac{5}{10}[/tex]

[tex]m=\dfrac{1}{2}[/tex]

So, the slope is 1/2 and we know that the equation for the line that passes through these two points should look like: [tex]y=\frac{1}{2} x+b[/tex]

To find "b", substitute one of the known points, and solve for "b":

[tex]y=\frac{1}{2} x+b[/tex]

[tex](3)=\frac{1}{2} (6)+b[/tex]

[tex]3=3+b[/tex]

Subtracting 3 from both sides to isolate the "b"...

[tex](3)-3=(3+b)-3[/tex]

[tex]0=b[/tex]

So, the y-intercept is 0.  Substituting into our line equation, [tex]y=\frac{1}{2} x+(0)[/tex] which simplifies to [tex]y=\frac{1}{2} x[/tex]  

Answer:

C

Step-by-step explanation:

equate d to 4 and solve for t , that is

- 9x² + 40 = 4 ( subtract 40 from both sides )

- 9x² = - 36 ( divide both sides by - 9 )

x² = 4 ( take square root of both sides )

x = [tex]\sqrt{4}[/tex] = 2

It takes 2 seconds for the skateboarder to be 4m from bottom of hill

Answer:

b = 40 and -40

General form of Perfect square trinomial is

a

2

+

2

a

b

+

b

2

Therefore from

16

x

2

−

b

x

+

25

a

2

=

√

16

x

2

,

b

2

=

25

, then

a

=

±

4

x

,

b

=

±

5

take consideration a=4x and b=-5 (different sign), then

−

b

x

=

2

(

4

x

)

(

−

5

)

−

b

x

=

−

40

x

b

=

40

The perfect square is

(

4

x

−

5

)

2

=

16

x

2

−

40

x

+

25

.

if we consider a=4x and b=5 (same sign), then

−

b

x

=

2

(

4

x

)

(

5

)

−

b

x

=

40

x

b

=

−

40

The perfect square is

(

4

x

+

5

)

2

=

16

x

2

+

40

x

+

25

.

The first solution

(

4

x

−

5

)

2

is the best solution after comparing the expression given.

Step-by-step explanation:

y + 4 = -4(x - 2) = -4x + 8

y - 4 = -4x

-4x - y = -4

4x + y = 4

Answer:

42.25π m²

Step-by-step explanation:

Let's solve!

⇒ Take the radius of the lawn to be 'r'

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

Then, area of the path equals :

⇒ Area of (lawn + path) - Area of lawn

⇒ π (r + 2)² - πr² = 30π

⇒ πr² - πr² + 4πr + 4π = 30π

⇒ 4πr = 26π

⇒ r = 6.5 m

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

Area of the lawn :

⇒ Area = πr²

⇒ Area = π × (6.5)²

⇒ Area = 42.25π m²

Answer:

198 cm^3

Step-by-step explanation:

volume = 22/7 * 3^2 * 7

volume = 22/7 * 7 * 3^2

volume = 22 * 3^2

volume = 22 * 9

volume = 198

You did not provide any question. I will give general advice.

Pythagorean Theorem: a² + b² = c²

If you know two sides, you know ll three sides.

A house sits in the shade.

The house is 18 feet tall. The shadow is 24 feet long. What is the hypotenuse of this triangle?

We know a and b here! a=18, b=24.

18 * 18 = 324.

24 * 24 = 576.
324+576 = 900

The square root of 900 is what will be your answer:

18*18 + 24*24 = 30*30.

I hope this helps!

Answer:

A standard form of a linear equation would look like this Ax+ By = C A x + B y = C

Step-by-step explanation:

Using translation concepts, it is found that function g(x) is given by:

g(x) = x + 8.

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, function g(x) is a translation 8 units left of f(x) = x, hence x -> x + 8 and:

g(x) = f(x +8) = x + 8.

More can be learned about translation concepts at https://brainly.com/question/4521517

#SPJ1

Answer:

16in x 22in

Step-by-step explanation:
8in = 100%
x = 200%
(200*8) / 100 = 16

11in = 100%
X = 200%
(200*11) / 200 = 22

The trick is to cross multiply (without multiplying the X) and then divide by the number that was not multiplied :)

Answer:

  16 in by 22 in

Step-by-step explanation:

Each dimension is multiplied by the scale factor when a photo is enlarged or reduced.

__

The enlarged photo will have dimensions ...

  (200% × 8 in) by (200% × 11 in) = 16 in by 22 in

_____

Additional comment

The factor 200% is equal to 200/100 = 2. (% and /100 are interchangeable)

Answer:

A , C , E , F

Step-by-step explanation:

If you have to write the solution, just tell me.

The equation for the trigonometric graph given above is:

y = 4sin(2x + (π/2))

y = 4 cos 2x

It is to be noted that the domain value of θ  is displayed on the horizontal x-axis and the range value is depicted on the vertical y-axis in the graphs of trigonometric functions.

Note that

y = A Sin (Bx - C) + D

The vertical shift → D

Horizontal [Phase] shift → C/B

Wavelength [Period] →  (2/B) π

Amplitude → | A |

Vertical Shift → 0
Horizontal | Phase | Shift → C/B → [- (π/4)] → (-π/2/2)

Wavelength | Period | → (2/B)π → π → (2/2)π

Amplitude → 4

Hence, working the above further we get:

y = 4sin(2x + (π/2))

y = 4 cos 2x

Learn more about Trigonometric Graphs at:
https://brainly.com/question/22068269
#SPJ1

Answer(s):

[tex]\displaystyle y = 4sin\:(2x + \frac{\pi}{2}) \\ y = -4cos\:(2x \pm \pi) \\ y = 4cos\:2x[/tex]

Step-by-step explanation:

[tex]\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{\pi}{4}} \hookrightarrow \frac{-\frac{\pi}{2}}{2} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 4[/tex]

OR

[tex]\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 4[/tex]

You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of sine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = 4sin\:2x,[/tex]in which you need to replase "cosine" with "sine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the sine graph [photograph on the right] is shifted [tex]\displaystyle \frac{\pi}{4}\:unit[/tex]to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACKWARD [tex]\displaystyle \frac{\pi}{4}\:unit,[/tex]which means the C-term will be negative, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-\frac{\pi}{4}} = \frac{-\frac{\pi}{2}}{2}.[/tex]So, the sine graph of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 4sin\:(2x + \frac{\pi}{2}).[/tex]Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph WILL hit [tex]\displaystyle [-1\frac{1}{4}\pi, 0],[/tex]from there to [tex]\displaystyle [-\frac{\pi}{4}, 0],[/tex]they are obviously [tex]\displaystyle \pi\:units[/tex]apart, telling you that the period of the graph is [tex]\displaystyle \pi.[/tex]Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 0,[/tex]in which each crest is extended four units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

I am delighted to assist you at any time.

Answer:

B. Square

Step-by-step explanation:

Finding the side lengths :

Side 1

⇒ d₁ = √(-4 - 0)² + (8 - 8)²

⇒ d₁ = √16

⇒ d₁ = 4

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

Side 2

⇒ d₂ = √(-4 + 4)² + (8 - 4)²

⇒ d₂ = √16

⇒ d₂ = 4

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

Side 3

⇒ d₃ = √(-4 - 0)² + (4 - 4)²

⇒ d₃ = √16

⇒ d₃ = 4

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

Side 4

⇒ d₄ = √(0 - 0)² + (8 - 4)²

⇒ d₄ = √16

⇒ d₄ = 4

As all sides of the figure are equal, and it creates 4 right angles, it is a square.

Answer: move up or add 7 in positive direction

Answer:

1 and 4

Step-by-step explanation:

(x²+1)(x²-4)  = x^4 -3x²-4

The green blank is 1 and the blue/purple is 4.

Hope this helped and brainliest please

Answer:

see explanation

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k )² = r²

where (h, k ) are the coordinates of the centre and r is the radius

given

x² + y² - 8x + 8y + 23 = 0

collect the x and y terms together and subtract 23 from both sides

x² - 8x + y² + 8y = - 23

using the method of completing the square

add ( half the coefficient of the x / y terms )² to both sides

x² + 2(- 4)x + 16 + y² + 2(4)y + 16 = - 23 + 16 + 16

(x - 4)² + (y + 4)² = 9 ← in standard form

with centre = (4, - 4 ) and r = [tex]\sqrt{9}[/tex] = 3

this is shown in graph b

Answer:one pen = $1.50

Step-by-step explanation:

See picture for the math if that helps

Using p for pens, h for highlighter,

A for first equation

B for second equation

I used equation A to reduce to a usable substitute by dividing all by 3

And then isolating “h”.

Now substitute the value of “h” into equation B and solve for “p”

P=$1.50

To check your work, substitute p ($1.50) into equation B and solve for “h”

h=$4.00

Now substitute the p and h values into either equation A or B and solve, they equal the numbers given

The value of "x" and "y".

Let's solve "x" first.

Given is a supplementary angle so it should add up to 180°

[tex]x=180-123[/tex]

[tex]\large\boxed{x=57°}[/tex]

Now, we can solve "y"

Given is an isosceles triangle so the opposite sides will be equal.

[tex]57+57[/tex]

[tex]114°[/tex]

Angle sum of triangle is 180° so, it should add up to 180°

[tex]y=180-114[/tex]

[tex]\large\boxed{y=66°}[/tex]

Therefore, the correct answer is option C

Answer:

50.27

Step-by-step explanation:

area for a circle is (pie)r^2

r^2=16

16xpie=50.27

The correct function that matches the data in the graph is  a(n) = 46-(n-1)-4 (option C)

The only way is to verify the function matches the data by replacing n.

For example, we know at 5 seconds the temperature is 30. Let's use 5 (n) to verify the function.

This option matches the value of the temperature.

Learn more about function in: https://brainly.com/question/12431044

#SPJ1

Answer:

4/25

Step-by-step explanation:

Let's make the units the same :

2 kg = 2000 g

Now lets simplify this fraction :

Divide top and bottom by 2 until you can't :

320/2000 = 160/1000

160/1000 = 80/500

80/500 = 40/250

40/250 = 20/125

Now we divide top and bottom by 5 as 2 is not a factor of 125 :

20/125 = 4/25

This is our final answer

Hope this helped and brainliest please

Answer:

1150.35 ft^3

Step-by-step explanation:

4/3πr^3 is the equation to find the volume of a sphere.

we know the radius is 6.5 feet so all we have to do is input it and calculate.

please give brainliest!

hope this helps