Simplify the following expression and write
in scientific notation.
(0.00045)(500,000)
0.0015

Function transformation involves changing the position of a function.

The graph of g(x) is the graph of f(x) translated 2 units right, and [tex]\mathbf{g(x) = 3(x -2) + 1}[/tex]

The function is given as:

[tex]\mathbf{f(x)=3x + 1}[/tex]

The graph of g(x) passes through (2,1) and (0,-5).

Start by calculating the slope (m)

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

So, we have:

[tex]\mathbf{m = \frac{-5-1}{0-2}}[/tex]

[tex]\mathbf{m = \frac{-6}{-2}}[/tex]

[tex]\mathbf{m = 3}[/tex]

The equation is then calculated as:

[tex]\mathbf{g(x) = m(x -x_1) + y_1}[/tex]

So, we have:

[tex]\mathbf{g(x) = 3(x -2) + 1}[/tex]

By comparing [tex]\mathbf{f(x)=3x + 1}[/tex] and [tex]\mathbf{g(x) = 3(x -2) + 1}[/tex]

The graph of f(x) is shifted 2 units to the right

Read more about function transformation at:

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Answer:

Step-by-step explanation:

Problem 14: Mean 5.5, Range: 5.8

Problem 15: question #1 4, mode: 63

Probelm 16: Median 63, Range:  8.3

Answer:

14: Mean is 5.5 Hours

Range is 7.9 Hours

15: 4 Numbers

Mode is 6.3

16: Median is 6.3

Range is 8.3

Step-by-step explanation:

(I'll edit in the explanations momentarily)

Answer:

b.$3170

Step-by-step explanation:

43,000-35,000=8,000

SO you would find 9% commission on 8,000

8,000x.09=720

then, you would find his normal commission if he only made 35,000

so you would do 35,000x.07=2450

you would, then, add the two together to get his entire commission, which is $3170

Answer:

b

Step-by-step explanation:

Answer:

Triangle

Step-by-step explanation:

Has 120° degrees of rotation and measure of the central angle and has 3-fold rotational symmetry

Answer:

1) [tex]DIAGRAM \mapsto B[/tex]  

2) DEFINITION [tex]\mapsto A[/tex]

3) THEOREM [tex]\mapsto C[/tex]

4) POSTULATE [tex]\mapsto D[/tex]

Step-by-step explanation:

1) DIAGRAM  B) A visual tool representing mathematical ideas to be interpreted

A diagram is the depiction or representation of information using symbols

2) DEFINITION A) A formal statement declaring the meaning of a word

A definition is a statement that outlines the meaning of a word or a group of words or a diagram, or a symbol or sign

3) THEOREM C) A mathematical statement proven using postulates and definitions

A general statement of a proposition that is by itself not evident, but given proof by a combination of postulates

4) POSTULATE D) A mathematical statement taken as a fact

An assumed truth taken as the foundation for further reasoning

Answer:

f = - [tex]\frac{19}{7}[/tex]

Step-by-step explanation:

Given f varies directly with m then the equation relating them is

f = km ← k is the constant of variation

To find k use the condition f = - 19 when m = 14, thus

- 19 = 14k ( divide both sides by 14 )

- [tex]\frac{19}{14}[/tex] = k

f = - [tex]\frac{19}{14}[/tex] m ← equation of variation

When m = 2, then

f = - [tex]\frac{19}{14}[/tex] × 2 = - [tex]\frac{19}{7}[/tex]

Answer:

a. 126 pie cm^3

Step-by-step explanation:

Area of a circle = pi*r²

Volume = area*height

(pi*r²)*14

Since your answers are with Pi omit the Pi and times 3² * 14 = 126 pie cm³

Answer:

A. 126pi cm^3

Step-by-step explanation:

The volume of a cylinder can be found using the following formula.

[tex]v=\pi r^2 h[/tex]

First, we must find the radius. The radius is half of the diameter.

[tex]r=\frac{d}{2}[/tex]

The diameter of the cylinder is 6 cm.

[tex]r=\frac{6cm}{2}[/tex]

[tex]r= 3cm[/tex]

The radius is 3 cm.

Now, we can substitute values into the formula.

[tex]v=\pi r^2 h[/tex]

[tex]r= 3cm\\h=14 cm[/tex]

[tex]v=\pi (3cm)^2*14 cm[/tex]

Evaluate the exponent.

[tex](3cm)^2=3cm*3cm=9cm^2[/tex]

[tex]v=\pi*9cm^2*14cm[/tex]

Multiply 9 cm^2 and 14 cm

[tex]9 cm^2*14cm=126cm^3[/tex]

[tex]v=\pi*126cm^3[/tex]

The answer choices are in terms of pi, so we can simply rearrange our answer:

[tex]v=126\pi cm^3[/tex]

The volume of the cylinder is 126pi cubic centimeters and A is the correct answer.

Answer:

91

Step-by-step explanation:

Look at multiples of 7 and you’ll find 91.

91 dived by 3 is 30 with a remainder of 1.

91 divided by 5 is 18 with a remainder of 1.

91 divid by 7 is 13 with no remainder.

91 is the number between 1 and 100 satisfies the above conditions

A number system is defined as a system of writing to express numbers.

Given that a number is divided by 3 or 5, the remainder is 1.

If it is divided by 7, there is no remainder

We need to find the number between 1 and 100 which satisfies the given conditions.

Let us consider 91.

When 91 is divided by 3 we get 30 and 1 as remainder.

91 divided by 5 is 18 with a remainder of 1.

91 divided by 7 is 13 it does not have any remainder or remainder is zero.

Hence, 91 is the number between 1 and 100 satisfies the above conditions

To learn more on Number system click:

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Answer:

Step-by-step explanation:

x^2 - 9x - 70

we need to find two numbers whose sum is -9 and product id -17

The numbers are -14 and 5

By splitting the middle term,

x^2 - 14x + 5x - 70

= x ( x - 14 ) + 5 ( x - 14 )

( x + 5 ) ( x - 14 )

Hope this helps

Plz mark as brainliest!!!!!

Answer:

Step-by-step explanation:

Sum = -9

Product = -70

Factors = -14 , 5

x² - 9x - 70 = x² + 5x - 14x + (-14) * 5

                  =x(x + 5) - 14(x + 5)

                  = (x + 5)(x - 14)

Answer:

n=3s-2

Step-by-step explanation:

Step 1: Remove unnecessary parentheses (2s-1)

Step 2: Collect "Like Terms" (2s+s= 3s)

Last Step: Put them all together (n=3s - 2)

Answer:

(p^2) + 3p - 18

Step-by-step explanation:

Have a nice day!

Answer:

2p+3

Step-by-step explanation:

(p+6)(p-3)

you have to open the brackets i.e

p+p+6-3

add p+p and you get 2p then you  subtract positive 6 from 3 and you get 3

so your answer will be 2p+3

Answer:

same day = 25

advanced = 40

Step-by-step explanation:

Let a = advanced tickets

s = same day tickets

s+a = 65

25a+35s = 1875

Multiply the first equation by -25

-25s -25a = -1625

Add this to the second equation

25a+35s = 1875

-25a -25s= -1625

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

     10s = 250

Divide each side by 10

10s/10 = 250/10

s =25

Now find a

s+a = 65

25+a = 65

a = 40

Answer: same day = 25

advanced = 40

Answer:

El móvil B necesita 60 segundos para alcanzar al móvil A y le alcanza una distancia de 2400 metros con respecto al punto de referencia.

Step-by-step explanation:

Supóngase que cada movil viaja en el mismo plano y que el móvil B se localiza inicialmente en la posición [tex]x = 0\,m[/tex], mientras que el móvil A se encuentra en la posición [tex]x = 1200\,m[/tex]. Ambos móviles viajan a rapidez constante. Si el móvil B alcanza al móvil A después de cierto tiempo, el sistema de ecuaciones cinemáticas es el siguiente:

Móvil A

[tex]x_{A} = 1200\,m+\left(20\,\frac{m}{s} \right)\cdot t[/tex]

Móvil B

[tex]x_{B} = \left(40\,\frac{m}{s} \right)\cdot t[/tex]

Donde:

[tex]x_{A}[/tex], [tex]x_{B}[/tex] - Posiciones finales de cada móvil, medidas en metros.

[tex]t[/tex] - Tiempo, medido en segundos.

Si [tex]x_{A} = x_{B}[/tex], el tiempo requerido por el móvil B para alcanzar al móvil A es:

[tex]1200\,m+\left(20\,\frac{m}{s} \right)\cdot t = \left(40\,\frac{m}{s} \right)t[/tex]

[tex]1200\,m = \left(20\,\frac{m}{s} \right)\cdot t[/tex]

[tex]t = \frac{1200\,m}{20\,\frac{m}{s} }[/tex]

[tex]t = 60\,s[/tex]

El móvil B necesita 60 segundos para alcanzar al móvil A.

Ahora, la distancia se obtiene por sustitución directa en cualquiera de las ecuaciones cinemáticas:

[tex]x_{B} = \left(40\,\frac{m}{s} \right)\cdot (60\,s)[/tex]

[tex]x_{B} = 2400\,m[/tex]

El móvil B alcanza al móvil A a una distancia de 2400 metros con respecto al punto de referencia.

Answer:

17.2a+14.6

Step-by-step explanation:

Answer:

x=9

Step-by-step explanation:

<B = <E  from the concurrency statement

5x = 45

Divide by 5

5x/5 = 45/5

x = 9

Answer:

Hey there!

These are similar triangles, and similar triangles have congruent angles.

Thus, we have 5x=45

Simplifying, we have x=9

Let me know if this helps :)

Answer:

61 cm^2.

See below.

Step-by-step explanation:

Answer:

y = 9x - 59

Step-by-step explanation:

y - 4= 9(x-7)

y - 4 = 9x - 63

y - 4 + 4 = 9x - 63 + 4

y = 9x - 59

Answer:

Below

Step-by-step explanation:

● y-4 = 9(x-7)

Multiply 9 by (x-7)

● y-4 = 9x - 63

Add 4 to both sides

● y-4+4 = 9x-63 +4

● y = 9x - 59

Answer:

The graph representing the above equation is attached below.

Step-by-step explanation:

The equation that modeled the average number of non-defective refrigerators produced per hour in terms of x, the number of hours of production per day is:

[tex]y=\frac{196-3x}{x}[/tex]

Simplify the expression as follows:

[tex]y=\frac{196-3x}{x}[/tex]

[tex]y=\frac{196}{x}-3[/tex]

The graph representing the above equation is attached below.

On moving the pointer to y = 15, it was determined that the value of x was 10.89.

The point is also plotted on the graph

Answer:

There would be 11 hours of production in a day.

Step-by-step explanation:

Answer:

The correct option is;

C. Transformation

Step-by-step explanation:

In mathematics, transformation refers to the relocation of an object called the pre-image from initial position to another new location at which point the object will be known as the image whereby there is a one to one mapping from each point on the pre-image to the image

The types of transformation includes reflection, rotation, and translation which involve changes in position and dilation, which involves changes in the size of the pre-image.

Answer:

100 pages

Step-by-step explanation:

Yesterday, there were 400 pages left unread so you read 1/4 * 400 = 100 pages yesterday. Today, there are 400 - 100 = 300 pages left unread so today, you read 2/3 * 300 = 200 pages. This means that there are 300 - 200 =   100 pages left in the book.

Answer:

14

Step-by-step explanation:

Using the sine ratio in the right triangle and the exact value

sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] , thus

sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{7\sqrt{2} }{x}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )

x = 7[tex]\sqrt{2}[/tex] × [tex]\sqrt{2}[/tex] = 7 × 2 = 14

Answer:

Step-by-step explanation:

[tex]Hypotenuse = x \\Opposite = 7\sqrt{2} \\\alpha = 45\\\\\Using \: SOHCAHTOA\\Sin \alpha = \frac{Opposite}{Hypotenuse}\\ \\Sin 45 = \frac{7\sqrt{2} }{x} \\\\\frac{\sqrt{2} }{2} = \frac{7\sqrt{2} }{x} \\\\\sqrt{2x} = 14\sqrt{2} \\\\\frac{\sqrt{2x} }{2} = \frac{14\sqrt{2} }{2} \\x = 14[/tex]

Answer:

(3, 2) and (1, 4)

Step-by-step explanation:

Plot the two points on a graph.

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

To do this with algebra, it takes a few steps.

The diagonals of a square are perpendicular and bisect each other. You are given opposite vertices, so first, find the midpoint of that diagonal.

((1 + 3)/2, (2 + 4)/2) = (2, 3)

The midpoint of the diagonal is (2, 3).

This diagonal has slope 1 and y-intercept 1, so its equation is

y = x + 1

The perpendicular bisector has equation

y = -x + 5

The two vertices we are looking for, lie in a circle whose center is the midpoint of the diagonals, (2, 3), and whose radius is half of the diagonal.

Use Pythagoras to find the diagonal's length.

2^2 + 2^2 = c^2

c^2 = 8

c = sqrt(8) = 2sqrt(2)

Half of the diagonal is sqrt(2). This is the radius if the circle.

The equation of the circle is

(x - 2)^2 + (y - 3)^2 = (sqrt(2))^2

(x - 2)^2 + (y - 3)^2 = 2

The points of intersection of this circle and the second diagonal are the two vertices you are looking for.

System of equations:

(x - 2)^2 + (y - 3)^2 = 2

y = -x + 5

Use substitution and substitute y with -x + 5 in the equation of the circle.

(x - 2)^2 + (-x + 5 - 3)^2 = 2

(x - 2)^2 + (-x + 2)^2 - 2 = 0

x^2 - 4x + 4 + x^2 - 4x + 4 - 2= 0

2x^2 - 8x + 6 = 0

x^2 - 4x + 3 = 0

(x - 3)(x - 1) = 0

x - 3 = 0   or x - 1 = 0

x = 3 or x = 1

Now we find corresponding y values.

y = -x + 5

x = 3

y = -3 + 5 = 2

This gives us (3, 2).

y = -x + 5

x = 1

y = -1 + 5 = 4

This gives us (1, 4).

Answer: (1, 4) and (3, 2)

[tex]2\sqrt{28}-3\sqrt{63}=2\sqrt{4\cdot7}-3\sqrt{9\cdot7}=4\sqrt7-9\sqrt7=-5\sqrt7[/tex]

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         Hi my lil bunny!

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[tex]x+\frac{2}{x} -2-x+\frac{3}{x} -1[/tex]

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

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Hope this helped you.

Could you maybe give brainliest..?

❀*May*❀

Answer:

Hey there!

Angles in a triangle add to 180 degrees.

24+134+2x=180

158+2x=180

2x=22

x=11

Let me know if this helps :)

Answer:

$86.40

Step-by-step explanation:

The house Trevor's family lives in has 6 people (including Trevor) and 3 bathrooms. In the past month, each person showered for an average of 480 minutes and used an average 72 liters of shower water (over the

entire month). Water costs 0.20 dollars per liter.

How much did Trevor's family pay per minute on shower water

Average person=72 liters of water

6 people=72*6= 432 liters

Each person = 480 minutes

6 people=480*6= 2,880 minutes

Water=$0.20 per liter

Total cost of water= 432 * 0.20

= $86.40

Answer:

o.o3

Step-by-step explanation:

Answer:

The slope of f(x) is equal to the slope of g(x).

Step-by-step explanation:

The question is incomplete. Here is the complete question.

Compare the slopes of the linear functions f(x) and g(x) and choose the answer that best describes them.

a graph of a line labeled f of x passing through 0, negative 1 and 3, 1

x g(x)

0 2

3 4

6 6

Slope is defined as the change of the y axis to the z axis of a plane.

Slope = ∆y/∆x

Slope = y2-y1/x2-x1

For f(x) with coordinates (0, -1) and (3,1)

x1 = 0, y1 = -1, x2 = 3 and y2 = 1

Slope of f(x) = 1-(-1)/3-0

Slope = 1+1/3

Slope = 2/3

For g(x), we will choose any two of the coordinates from the table. Using the coordinates (3,4) and (6,6)

x1 = 3, y1 = 4, x2 = 6 and y2 = 6

Slope of g(x) = 6-4/6-3

Slope of g(x) = 2/3

It can be seen that the value of both slopes are equal. Hence, the slope of f(x) is equal to the slope of g(x) is the correct option.

Answer:

The answer is C. The slope of f(x) is equal to the slope of g(x).

Step-by-step explanation:

Did the test.

Answer:

0.324m^2 ; 18 ft

Step-by-step explanation:

Given the triangle :

Base (b) of triangle = 54cm

Height (h) of triangle = 1.2m

Area(A) of a triangle is given by:

0.5 * base * height

Base = 54cm = 54/100 = 0.54 m

Therefore,

A = 0.5 * 0.54m * 1.2m

A = 0.324m^2

2.) Average of the two bases in the trapezoid :

From the trapezium Given :

Base 1 = 15 feets

Base 2 = 7 yards

1 yard = 3 Feets

Therefore, base 2 in Feets = 7 * 3 = 21 Feets

Average of the two bases :

(21 Feets + 15 Feets) / 2

= 36 Feets / 2

= 18 Feets

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