write 820.341 in scientific notation​

Answer:

( f + g )( x ) = 8x - 3

Step-by-step explanation:

What this is saying is to add the two functions together.

( 5x+1 ) + ( 3x - 4 )

( f + g )( x ) = 8x - 3 is the simplified version.

Answer:

(f∘g)(x)=25x-1

(g∘f)(x)=25x+19

Step-by-step explanation:

To find (f∘g)(x), use the definition of (f∘g)(x),

(f∘g)(x)=f(g(x))

Substituting 5x−1 for g(x) gives

(f∘g)(x)=f(5x−1)

Find f(5x−1), where f(x)=5x+4, and simplify to get

(f∘g)(x)(f∘g)(x)(f∘g)(x)=5(5x−1)+4=25x−5+4=25x−1

To find (g∘f)(x), use the definition of (g∘f)(x),

(g∘f)(x)=g(f(x))

Substituting 5x+4 for f(x) gives

(g∘f)(x)=g(5x+4)

Find g(5x+4), where g(x)=5x−1, and simplify to get

(g∘f)(x)=5(5x+4)−1

(g∘f)(x)=25x+20−1

(g∘f)(x)=25x+19

The final expression is

sqrt (39y9) = y4 • sqrt(39y) assuming y as positive.

Rewrite

39 y ^9 as ((y^2)^2)^2 . 39 y

Factor out y^8.

√39(y^8 . y).

Rewrite   \(y^8 as (y^4)^2\)

 √39(y^4)^2 . y).

Rules for simplifying variables which may be raised to a power:

  (1) variables with no exponent stay inside the radical

  (2) variables raised to power 1 or (-1) stay inside the radical

  (3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples:

    sqrt(x8)=x4

    sqrt(x-6)=x-3

  (4) variables raised to an odd exponent which is  >2  or  <(-2) , examples:

     sqrt(x5)=x2•sqrt(x)

     sqrt(x-7)=x-3•sqrt(x-1)

Applying these rules to our case we find out that

SQRT(y9) = y4 • SQRT(y)

Therefore, sqrt (39y9) = y4 • sqrt(39y)

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By using the rules:

\(cos(-x) = cos(x)\\\\sec(x) = \frac{1}{cos(x)}\)

We have proven the identity. Below you can follow the demonstration.

Here you need to remember two things:

\(cos(-x) = cos(x)\\\\sec(x) = \frac{1}{cos(x)}\)

Here we have the expression:

\(\frac{1 - cos(-x)}{sec(-x) - 1}\)

By using the first rule, we can rewrite:

\(\frac{1 - cos(-x)}{sec(-x) - 1} = \frac{1 - cos(x)}{sec(x) - 1}\)

By using the second rule, we can rewrite:

\(\frac{1 - cos(x)}{sec(x) - 1} = \frac{1 - cos(x)}{\frac{1}{cos(x)} - 1}\)

Now if we multiply and divide by cos(x), we get:

\(\frac{1 - cos(x)}{\frac{1}{cos(x)} - 1} = \frac{1 - cos(x)}{\frac{1}{cos(x)} - 1} *\frac{cos(x)}{cos(x) } = \frac{(1- cos(x))*cos(x)}{1 - cos(x)} = cos(x)\)

In this way, the identity was proven.

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Answer:

Step-by-step explanation:

\(x + 3 = 6\)

Move constant to R.H.S and change its sign:

\(x = 6 - 3\)

Calculate the difference

\(x = 3\)

Hope this helps...

Good luck on your assignment..

The vertex of point A' in the dilated triangle A'B'C' is (6, 4.5).

1. Start by calculating the distance between the vertices of the original triangle ABC:

  - Distance between A(4, 3) and B(3, -2):

    Δx = 3 - 4 = -1

    Δy = -2 - 3 = -5

    Distance = √((-\(1)^2\) + (-\(5)^2\)) = √26

  - Distance between B(3, -2) and C(-3, 1):

    Δx = -3 - 3 = -6

    Δy = 1 - (-2) = 3

    Distance = √((-6)² + 3²) = √45 = 3√5

  - Distance between C(-3, 1) and A(4, 3):

    Δx = 4 - (-3) = 7

    Δy = 3 - 1 = 2

    Distance = √(7² + 2²) = √53

2. Apply the scale factor of 1.5 to the distances calculated above:

  - Distance between A' and B' = 1.5 * √26

  - Distance between B' and C' = 1.5 * 3√5

  - Distance between C' and A' = 1.5 * √53

3. Determine the coordinates of A' by using the distance formula and the given coordinates of A(4, 3):

  - A' is located Δx units horizontally and Δy units vertically from A.

  - Δx = 1.5 * (-1) = -1.5

  - Δy = 1.5 * (-5) = -7.5

  - Coordinates of A':

    x-coordinate: 4 + (-1.5) = 2.5

    y-coordinate: 3 + (-7.5) = -4.5

4. Thus, the vertex of point A' in the dilated triangle A'B'C' is (2.5, -4.5).

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Answer:

let  f(x)=2,  

•In this function there is no x therefore it's a constant function represent as y=2 at x=0

• Therefore at f(0)=2  and even at x=2 it will be the same

• at  f(2)=2 , coordinate will be (2,2)

•• at  f(0)=2 , coordinate will be (0,2)

Step-by-step explanation:

Answer:

8>_x>4

>_ this is greater than equal to symbol eight is greater than or equal to x is greater than 4

Answer:

Please help me answer this problem

Answer:

14 : 18

Step-by-step explanation:

Any ratio whose parts are multiples of 7 and 9 are equivalent , so

7 : 9

= 7(2) : 9(2)

= 14 : 18

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

7(3) : 9(3)

= 21 : 27

etc

Jenny's Average swimming speed is 1.5 km/h.

Jenny's average swimming speed as S (in km/h). We can then use the given information to set up equations and solve for S.

We know that Jenny swam for 1 hour, so the distance she swam is given by the formula: Distance = Speed * Time.

Thus, the distance she swam is S * 1 = S km.

Next, we know that her average running speed is 8 times her average swimming speed. Therefore, her average running speed is 8S km/h.

Since she ran for 1 hour, the distance she ran is 8S * 1 = 8S km.

Furthermore, we are given that her average bicycling speed is 2 times her average running speed. Therefore, her average bicycling speed is 2 * 8S = 16S km/h.

She biked for 1.75 hours, so the distance she biked is 16S * 1.75 = 28S km.

The total distance of the triathlon is the sum of the distances for each segment: Distance(swimming) + Distance(running) + Distance(biking) = 55.5 km.

Therefore, we can write the equation:

S + 8S + 28S = 55.5.

Simplifying the equation, we get:

37S = 55.5.

To solve for S, we divide both sides of the equation by 37:

S = 55.5 / 37 = 1.5.

Thus, Jenny's average swimming speed is 1.5 km/h.

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Answer:

first draw the line edges and vertical

second put the dot every no.

And put the y=2000×+4000

a. The slopes of the lines are:

Slope of line 1 = 1/4

Slope of line 2 = -4

Slope of line 3 = -1/3

b.

Line 1 and Line 2 : Perpendicular

Line 1 and Line 3 : Neither

Line 2 and Line 3 : Neither

From the question, we are to determine the slope of each of the given lines:

Using the formula,

m = (y₂ - y₁) / (x₂ - x₁)

Where m is the slope

m = (-3 - 0) / (-4 - 8)

m = (-3) / (-12)

m = 1/4

m = (2 - 6) / (0 - (-1))

m = (-4) / (1)

m = -4

m = (-7 - (-4)) / (6 - (-3))

m = (-3) / (9)

m = -1/3

b.

NOTE: Two lines are said to be parallel if they have equal slopes; and they are said to be perpendicular if the slope of one is the negative reciprocal of the other.

Thus,

Line 1 and Line 2 : Perpendicular

Line 1 and Line 3 : Neither

Line 2 and Line 3 : Neither

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Answer:

D.

Step-by-step explanation:

3x + 4 is another way of writing 2 + 3x + 2, if you add the 2's together you get a four (3x + 4).

The height of the sand in the display container is 12 inches when the display container is right triangular prism.

What is right triangular prism ?

A right triangular prism is a three-dimensional geometric shape with two parallel triangular bases and three rectangular faces. The rectangular faces connect the corresponding vertices of the triangular bases.

To find the height of the sand in the display container, we need to use the fact that the volume of sand in the storage container is equal to the volume of sand in the display container.

The storage container has a length, width, and height of 6 inch, 6 inch, and 6inche, respectively. Then, the volume of the storage container is:

\(V_{storage} = L * W * H = 6 * 6 * 6 = 216 inch^3\)

Similarly, let's assume that the display container has a base of length 4 inch and height 9 inches and height of sand be H.

Then, the volume of the display container is:

\(V_{display} = (1/2) * b * h * H = (1/2) * 4 * 9 * H = 18H\)

where (1/2) is the area of the triangle base of the display container.

Since the volumes of sand in both containers are equal, we can set these expressions equal to each other and solve for h:

216 = 18H

H = 12 inches

Therefore, the height of the sand in the display container is 12 inches.

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The disadvantage of piece rate pay is that the cost of producing higher quantities of a product can be a reduction in the quality of the items produced.

Piece rate is any type of job in which a worker is paid a set amount for each unit produced or action performed, regardless of time. Some employees may be paid on a piece rate or on a commission basis.

Employees are paid on a piece rate, and commission payments are based on results rather than an hourly or weekly pay rate. This means that the employee's weekly pay will vary depending on how much work they do. One of the drawbacks of piece rate pay is that the cost of producing larger quantities of a product may result in a decrease in the quality of the items produced.

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Answer: switch sides and theres your answer

Step-by-step explanation:

good luck

The range of the given equation is [-1, infinity).

We are given that;

Equation  y= underroot(x+5​)

Now,

The domain of this equation is the set of x values that make the expression under the square root non-negative.

That is, x+5 >= 0, or x >= -5. So the domain is [-5, infinity).

The range of this equation is the set of y values that are obtained by plugging in the domain values into the equation. Since the square root function is always non-negative, and we are subtracting 1 from it, the smallest possible value of y is -1, when x = -5. As x increases, y also increases, and there is no upper bound for y.

Therefore, by the range the answer will be [-1, infinity).

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(c) is correct option as it is forming an arithmetic sequence with a common difference of -2.

There are two definitions for an arithmetic sequence. It is a "series where the differences between every two succeeding terms are the same" or "each term in an arithmetic sequence is formed by adding a fixed number (positive, negative, or zero) to its preceding term." The following is an arithmetic sequence where each term is created by adding 4 to the one before it.

An arithmetic sequence's first term is 'a', its common difference is 'd', and n is the total number of terms. The AP has the following general forms: a, a+d, a+2d, a+3d, etc., up to n words.

(a) 1,2,3,5,7,9 is not an arithmetic sequence as 2-1=1 and 5-3=2. That shows common difference is not constant.

(b) 1,10,20,30 is not an arithmetic sequence as 10-1=9 and 20-10=10. That shows common difference is not constant.

(c) 1,-1,-3,-5 is an arithmetic sequence as (-1)-1=-2 and -3-(-1)=-2. That shows common difference is constant.

(d) 7,-7,7,-7 is not forming an arithmetic sequence because common difference is not constant.

Option (c) is correct option.

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The expression 1 2/5 + 2 2/3 using fifteenths is 3 + 6/15 + 10/15

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

1 2/5 + 2 2/3

3 + 2/5 + 2/3

To rewrite the expression using fifteenths, we multiply the numerator and the denominator of the fractions by the same number

In this case, we use 3 and 5

So, we have

3 + 2/5 * 3/3 + 2/3 * 5/5

Evaluate the products

3 + 6/15 + 10/15

Hence, the expression using fifteenths is 3 + 6/15 + 10/15

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Using the ratio of the sides, we have:$x\sqrt{3} = 12\sqrt{3}$ (opposite the $60^{\circ}$ angle is 12$\sqrt{3}$)$x = 2\sqrt{3}\cdot6$ (the hypotenuse is $2x = 12\sqrt{3}$)Simplifying, we have:$x = 12\sqrt{3}$. Therefore $x=y=12\sqrt{3}$, which is our answer

In a 30-60-90 triangle, the sides have the ratio of $1: \sqrt{3}: 2$. Let's apply this to solve for the variables in the given problem.

Instructions: Use the ratio of a 30-60-90 triangle to solve for the variables. Leave your answers as radicals in simplest form. x=y=Let's first find the ratio of the sides in a 30-60-90 triangle.

Since the hypotenuse is always twice as long as the shorter leg, we can let $x$ be the shorter leg and $2x$ be the hypotenuse.

Thus, we have: Shorter leg: $x$Opposite the $60^{\circ}$ angle: $x\sqrt{3}$ Hypotenuse: $2x$

Now, let's apply this ratio to solve for the variables in the given problem. We know that $x = y$ since they are equal in the problem.

Using the ratio of the sides, we have:$x\sqrt{3} = 12\sqrt{3}$ (opposite the $60^{\circ}$ angle is 12$\sqrt{3}$)$x = 2\sqrt{3}\cdot6$ (the hypotenuse is $2x = 12\sqrt{3}$)Simplifying, we have:$x = 12\sqrt{3}$

Therefore, $x=y=12\sqrt{3}$, which is our answer.

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Answer:

(- 3, 1.5)

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

Given system:

The first expression is ready to be substituted as no further operation is required to simplify it.

Find x:

It is true that the integers (-4, -2,0, 2, 4) form the set of even integers.

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

Set = (-4, -2,0, 2, 4)

In the above set, we can see that all numbers in the set do not have decimal point

This means that the set of numbers are integers

Also, we can see that the integers are integers that are divisible by 2

This means that the set of integers are set of even integers

Hence, the statement is true

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Complete question

As a integers are integers divisible by 2. The integers (-4, -2,0, 2, 4) form the set of even integers.

True or false

The interval of the graph at which Susan is running fastest is from point A ( 0 , 0 ) to B ( 10 , 3 )

Given data ,

Susan is running a 5k race. The graph of distance vs. time is shown

So , the slope of the first line is m₁

And , the slope of the second line is m₂

where the points are A ( 0 , 0 ) , B ( 10 , 3 ) , C ( 20 , 4 )

Now , slope of AB is

m₁ = ( 3/10 ) = 0.3

And , m₁ = 0.3 kilometers per minute

And , slope of BC is

m₂ = ( 4 - 3 ) / ( 20 - 10 )

m₂ = 1/10

m₂ = 0.1 kilometers per minute

Therefore , the interval is fastest at second line from B ( 10 , 3 ) , C ( 20 , 4 )

Hence , Susan is running fastest is from point A ( 0 , 0 ) to B ( 10 , 3 )

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The simplified form of the expression 4x(x + 1) − (3x − 8)(x + 4) is -3x^2 - 4x - 32.

To simplify the expression 4x(x + 1) − (3x − 8)(x + 4), we can expand the parentheses and combine like terms.

Expanding the first term, we get 4x^2 + 4x.

Expanding the second term, we have -(3x)(x) - (3x)(4) - (-8)(x) - (-8)(4), which simplifies to -3x^2 - 12x - (-8x) - (-32), further simplifying to -3x^2 - 12x + 8x - 32.

Combining like terms, we obtain -3x^2 - 4x - 32.

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Answer:

3/2

Step-by-step explanation:

Simplify the following:

((4 + 1/5)×5)/14

((4 + 1/5)×5)/14 = ((4 + 1/5)×5)/14:

((4 + 1/5)×5)/14

Put 4 + 1/5 over the common denominator 5. 4 + 1/5 = (5×4)/5 + 1/5:

(((5×4)/5 + 1/5) 5)/14

5×4 = 20:

((20/5 + 1/5)×5)/14

20/5 + 1/5 = (20 + 1)/5:

(((20 + 1)/5)×5)/14

20 + 1 = 21:

(21/5×5)/14

21/5×5 = (21×5)/5:

((21×5)/5)/14

((21×5)/5)/14 = (21×5)/(5×14):

(21×5)/(5×14)

(21×5)/(5×14) = 5/5×21/14 = 21/14:

21/14

The gcd of 21 and 14 is 7, so 21/14 = (7×3)/(7×2) = 7/7×3/2 = 3/2:

Answer:  3/2

Answer:

5

Step-by-step explanation:

According to the given question, the calculation of number is shown below:-

Let the number be x.

\(\frac{1}{10}\) of x will be added to the number of 2, so that the result is half of x.

\(2 + \frac{1}{10} x = \frac{1}{2} x\)

Now we will solve the above equation

\(2=\frac{1}{2} x-\frac{1}{10} x\\\\2=\frac{2x}{5}\\\\10=2x\\\\\frac{10}{2} =x\\\\\)

x = 5

Therefore the correct answer is 5

Hence, the number based on the given information provided in the question is 5

Answer:

A & B

Step-by-step explanation: