Find the domain and range of the function:
--√√5-x-3

The sequence is an arithmetic sequence and the expression used to find the nth term would be 3n option fourth I and II is correct.

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

We have a sequence:

3, 6, 9, 12…

First term a  = 3

Common difference d = 6 - 3 = 3

This is an arithmetic sequence.

nth term of the arithmetic sequence:

a(n) = 3 + (n-1)(3)

a(n) = 3n

Plug n = 5

a(5) = 3(5) = 15

Thus, the sequence is an arithmetic sequence and the expression used to find the nth term would be 3n option fourth I and II is correct.

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The solution to the Raoul's equation x² - 6x - 27 = 0 is x = 9; or x = -3

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the equation:

x² - 6x - 27 = 0

Adding 27 to both sides:

x² - 6x - 27 + 27 = 0 + 27

x² - 6x = 27

Adding to both sides the square of half the coefficient of x, that is 9:

x² - 6x + 9 = 27 + 9

(x - 3)² = 36

taking square root of both sides:

√(x - 3)² = √36

x - 3 = ±6

x = 3 ± 6

x = 3 + 6 or; x = 3 - 6

x = 9; or x = -3

The solution to the Raoul's equation x² - 6x - 27 = 0 is x = 9; or x = -3

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Answer:

q→p

Step-by-step explanation:

The converse of p→q is q→p.

which means If q ,then p.

Answer:

[tex]\boxed{ \rm \: Volume_{(Cylinder)} \approx \: 461.6 \: {m}^{3} } \rm (rounded \: to \: nearest \: tenth)[/tex]

Step-by-step explanation:

Given dimensions:

Given value of π :

To find:

Solution:

Here, we'll need to use the formulae of the volume of cylinder,to find it's volume.Its actually like a savior while solving these type of questions.

[tex] \pink{\star}\boxed{\rm \: Volume_{(Cylinder)} = \pi{r} {}^{2} h}\pink{\star}[/tex]

where,

Plug/substitute them onto the formulae,then simplify it using PEMDAS.

[tex] \rm \: Volume_{(Cylinder)} = \pi(7) {}^{2} \times 3[/tex]

[tex] \rm \: Volume_{(Cylinder)} = \pi(49)(3)[/tex]

[tex] \rm \: Volume_{(Cylinder)} = 147\pi \: [/tex]

[tex] \rm \: Volume_{(Cylinder)} = 147 \times 3.14[/tex]

[tex] \rm \: Volume_{(Cylinder)} = 461.58 \: {m}^{3} [/tex]

[tex] \boxed{\rm \: Volume_{(Cylinder)} \approx \: 461.6 \: {m}^{3}} \rm (rounded \: to \: nearest \: tenth) \: [/tex]

Hence, we can conclude that:

The volume of the cylinder is approximately

461.6 m³.

[tex] \rule{225pt}{2pt}[/tex]

The simplified expression is [tex]\frac{-1}{9x} -9x - 10[/tex].

An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.).

Here, the given expression

           [tex]\frac{1}{x}+\frac{-10x/9}{x^2}-9x-10[/tex]

            [tex]\frac{1}{x}+\frac{-10}{9x}-9x-10[/tex]

             [tex]\frac{9-10}{9x} -9x -10[/tex]

                 [tex]\frac{-1}{9x} -9x - 10[/tex]

Thus, the simplified expression is [tex]\frac{-1}{9x} -9x - 10[/tex].

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Answer:

-50

Step-by-step explanation:

1 - 2 + 3 - 4 + 5 - 6 + 7 - 8...99 - 100

just means,

1 - 2 = -1

3 - 4 = -1

5 - 6 = - 1

7 - 8 = - 1

99 - 100 = -1

basically, -1 + -1 + -1 + -1 + ....+ -1 or -1 - 1 - 1 - 1 - ... - 1

[tex](-1)^{n}[/tex]

Treating Grandi's series as a divergent geometric series we may use the same algebraic methods that evaluate convergent geometric series to obtain a third value:

S = 1 − 1 − 1 + ..., so

1 − S = 1 − (1 − 1 − 1 ...) = 1 − 1 − 1 ... = S

1 - S = S

1 = 2*S

resulting in S = 1/2. The same conclusion results from calculating −S, subtracting the result from S, and solving 2S = 1

1/2 of the last term is 100 x 1/2 = 50

This because you are using 2 numbers per -1

example: 1 - 2 = -1 or 3 - 4 = -1 resulting in 50 of the -1 being subtracted

[tex]\begin{cases} u=6i-2j\\\\ v=-3i+7j \end{cases}\qquad \begin{cases} < 6~~,~~-2 > \\\\ < -3~~,~~7 > \end{cases} \\\\[-0.35em] ~\dotfill\\\\ u-v\implies < 6~~,~~-2 > ~~ - ~~ < -3~~,~~7 > \\\\\\ < 6-(-3)~~,~~-2-7 > \implies < 6+3,-9 > \implies < 9,-9 > \implies 9i-9j[/tex]

Answer:

[tex]\frac{1}{13}[/tex]

Step-by-step explanation:

Probability is the number of favorable outcomes divided by the number of total outcomes. The total outcomes are all the situations that could possibly happen. There are 52 cards in the deck, so there are 52 total outcomes. Next, the favorable outcomes are the outcomes we want. In this case it is drawing a 6. There are four 6's in a deck of cards: 6 of hearts, 6 of spades, 6 of diamonds, and 6 of clubs. This means there are 4 favorable outcomes.

We can write the probability as a fraction: [tex]\frac{favorable-outcomes}{total-outcomes}[/tex], so we can get [tex]\frac{4}{52}[/tex]. Since both 4 and 52 are divisible by 4, the fraction can be simplified to [tex]\frac{1}{13}[/tex].

Answer:

1/13

Step-by-step explanation:

that's the answer to the question

Let's first consider: the fact that a new computer loses 1/2 of its value

 ⇒ third choice and fourth choice are eliminated

    ⇒ because of the graph project the computer's value as growing over  

         years

Now let's try to set up an equation:

After 1st year ⇒ Computer's value = [tex]total_.value*\frac{1}{2}[/tex]

After 2nd year ⇒ Computer's value = [tex]total_.value*\frac{1}{2}*\frac{1}{2}=total_.value*(\frac{1}{2} )^2[/tex]

After 3rd year ⇒ Computer's value =[tex]total_.value*\frac{1}{2}*\frac{1}{2}* \frac{1}{2}=total_.value*(\frac{1}{2})^3[/tex]

 ..... (Hopefully you see a pattern)

After x year ⇒ Computer's value = [tex]total_.value*(\frac{1}{2})^x[/tex]

Therefore, the equation is: [tex]total_.value*(\frac{1}{2})^x[/tex]

  ⇒that means the graph has to exponentially decreasing as it has

     an exponent (meaning the function is exponential) and a base less

     than 1 (meaning that the function is decreasing)

Answer: Choice (1)

Hope that helps!

Answer:

A

Step-by-step explanation:

After x year, computer's value will be (1/2)^x

So the graph has to exponentially decreasing.

Both A and B show decreasing value but B is linear. So B is incorrect

C and D show increasing value so they are both incorrect.

Answer:

  (1/4, 5 7/8)

Step-by-step explanation:

The vertex is the extreme point of the graph. Here, it is a minimum.

For this quadratic function, a graphing calculator can tell you exactly what the vertex is. (No approximation is required.)

__

The graphing calculator in the attachment shows the vertex is ...

  (0.25, 5.875) = (1/4, 5 7/8)

Answer:

381

Step-by-step explanation:

232 + 88 = 320

320 + 61 = 381

Hope this helped and brainliest please

Answer:

The bottom right line plot.

Step-by-step explanation:

In the table, 9 1/4 shows up twice. This can be represented in the line plot by putting 2 x's over the 9 1/4 point.

Answer:

I think the letter B is a good idea for me to do the same as oneroure and I have a module that I can use to make sure that I have the right to use the periodic table to find the element name and its symbol then calculate the total amount of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between thank you

a. A critical point at x = 25 would mean f'(25) = 0 or doesn't exist. We have derivative

[tex]f(x) = x - k \sqrt x \implies f'(x) = 1 - \dfrac k{2\sqrt x}[/tex]

so that

[tex]f'(25) = 1 - \dfrac k{2\sqrt{25}} = 1 - \dfrac k{10} = 0 \implies \boxed{k=10}[/tex]

b. Taking the second derivative, we get

[tex]f''(x) = \dfrac k{4 x^{3/2}} = \dfrac5{2 x^{3/2}}[/tex]

At x = 25, the second derivative has a positive sign,

[tex]f''(25) = \dfrac 5{2 \times 25^{3/2}} = \dfrac 5{2\times5^3} = \dfrac1{50} > 0[/tex]

which means f(x) is concave upward around x = 25, so this critical point is a local minimum.

Answer:

b ≈ 7.8

Step-by-step explanation:

using the law of sines

∠ A = 180° - 105° - 40° = 180° - 145° = 35° , then

[tex]\frac{b}{sin40}[/tex] = [tex]\frac{7}{sin35}[/tex] ( cross- multiply )

b × sin35° = 7 × sin40° ( divide both sides by sin35° )

b = [tex]\frac{7sin40}{sin35}[/tex] ≈ 7.8 ( to the nearest tenth )

The function g(x) = √(x - 8) represents a horizontal shift of the square root parent function f(x) = √x, to the right by eight units. Option B.

To horizontally shift the square root parent function, f(x) = √x, right eight units, we need to replace x with (x - 8) in the function. This shift will move the entire graph eight units to the right.

So, the equation of the new function, let's call it g(x), will be:

g(x) = √(x - 8)

Therefore, the correct choice is  g(x) = √(x - 8).

This means that for any given value of x, we substitute (x - 8) in the original square root function. The effect of this shift is that all x-values on the graph of g(x) will be eight units greater than their corresponding x-values on the graph of f(x).

For example, if we consider the point (8, 2) on the graph of f(x), after the horizontal shift, it will be located at (16, 2) on the graph of g(x). Similarly, the point (0, 0) on the graph of f(x) will shift to (8, 0) on the graph of g(x).

The function g(x) = √(x - 8) represents a horizontal shift of the square root parent function f(x) = √x, to the right by eight units. This transformation allows us to analyze and understand how the graph of the square root function is affected by horizontal shifts. SO Option B is correct.

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Answer:

4 radians

Step-by-step explanation:

[tex]s = \theta r[/tex]

[tex]20 = 5 \theta[/tex]

[tex] \theta = 4[/tex]

△STU is mapped to △PQR with center of dilation (-1.5, -1.5) and a scale factor of 2 and reflected about the x-axis.

From the given graph, we can see that;

SU is 1.5 units and the corresponding side of the dilated figure is 3 units. Thus, the scale factor of dilation is; 3/1.5 = 2

Now, we can see clearly that it is reflected about the x-axis as the x-values remain negative in △STU while the y-values are now positive in △PQR.

Lastly, we can see the dilation was with center (-1.5, -1.5)

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Answer:

i think the answer is 278.75

Answer: not a triangle

Step-by-step explanation:

If this were to be a triangle, the shorter sides would be 11 and 4 and the longest side would be 16.

First, we should determine if it is a triangle.

The quotient of 552/58 is 276/29.

The quotient of a number is the result or the outcome when you divide two numbers together.

From the given information, the quotient of [tex]\mathbf{\dfrac{552}{58}}[/tex] is can be determined by dividing both the numerator and the denominator by (2):

i.e.

[tex]\mathbf{=\dfrac{276}{29}}[/tex]

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Answer:

26x^6 sqrt 23x

Step-by-step explanation:

Answer:

The answer is origin

Answer: orgin

Step-by-step explanation:  orgin

The graphed cosine function can either be:

cos(x + pi) or cos(x - pi).

We know that this function is a cosine function with a phase shift, so the general form is:

f(x) = cos(x + P).

Where P is the phase shift.

In the graph we can see that when x = 0, f(0) = -1

And we know that cos(pi) = -1 = cos(-pi)

Then we must have that:

f(0) = cos(P) = -1

By what we wrote above, we know that P can be either -pi or pi (because of the parity of the cosine). Let's say that P = pi, then the cosine function is:

f(x) = cos(x + pi).

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Answer:

y-intercept = 1, x-intercept= -1/4

Step-by-step explanation:

Default equation of line:

y = mx+c , where m is the slope and c is the y-intercept.

So first we will find the slope from the values given in the table.

slope of line  [tex]\frac{y1-y2}{x1-x2}\\= \frac{9-5}{2-1} \\= \frac{4}{1}\\ =4[/tex]

So take 1 random value of x and y from the table,

x =1 , y=5

5 = 4(1)+c

c = 5-4 = 1

so equation of line is y = 4x+1

and y intercept = 1

x intercept is the value of x when y = 0.

so given

y = 4x+1

0 = 4x+1

4x = -1

x = [tex]-\frac{1}{4}[/tex]

therefore x intercept = -1/4

Answer:

The 6 names to circle are:

The underlined letters from those circled names are:

The letters form the phrase [tex]\underline{\text{WR}}\ \underline{\text{ON}} \ \underline{\text{G}} \ \ \ \ \ \ \underline{\text{TU}} \ \underline{\text{RN}}[/tex]  or "wrong turn". The spacing is done like that in the first version to show the various subgroups of letters.

Unfortunately the mentioned riddle at the bottom is cut off, so I don't know what the riddle is.

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

Explanation:

Here's a summary table:

[tex]\begin{array}{|c|c|} \cline{1-2}\text{Student} & \text{Are They Correct?}\\\cline{1-2}\text{Laverna} & \textbf{Yes}\\\cline{1-2}\text{Alfonso} & \textbf{Yes}\\\cline{1-2}\text{Autumn} & \textbf{Yes}\\\cline{1-2}\text{Willa} & \text{No}\\\cline{1-2}\text{Ignacio} & \textbf{Yes}\\\cline{1-2}\text{Napoleon} & \text{No}\\\cline{1-2}\text{Kathyrn} & \textbf{Yes}\\\cline{1-2}\text{Titus} & \text{No}\\\cline{1-2}\text{Lawrence} & \textbf{Yes}\\\cline{1-2}\end{array}[/tex]

Put another way, here are the people to circle (i.e. the people who made true statements):

In the order presented above, the letters underlined are:

Through a bit of trial and error, the letters make the phrase of:

[tex]\underline{\text{WR}}\ \underline{\text{ON}} \ \underline{\text{G}} \ \ \ \ \ \ \underline{\text{TU}} \ \underline{\text{RN}}[/tex]

I'm not sure what to do with the extra "RN". It might be a typo, or it might be the case your teacher wants you to ignore repeats like this.

Answer:

⇒8(x−1)=5x

⇒8x−x=5x

⇒8x−5x=8

⇒3x=8

⇒x=

3

8

Answer:

1218 inches

Step-by-step explanation:

First, let's make our numbers equivalent to a certain unit. Preferably inches, since we can't turn inches into yards or feet, but we can turn yards and feet into inches.

3 yards is 9 feet, which when multiplied by 12 (12 inches in a foot) is 108.

5 feet times 12 is 60 inches.

6 inches is 6 inches.

108+60+6 is 174

Multiply all that by 7 and you get your answer of 1218 inches.

Hope this helps!

Answer:

X=-1

Y=1

Step-by-step explanation:

6x-12y

-18

) 6x + 4y

-

-2

Subtract the two equations

6x - 12y - (6x + 4y) = -18 - (-2)

Determine the sign

6x- 12y - 6x- 4y

=-18 + 2

Simplify

-12y

- Ay

=-18 + 2

Solve the equation

Substitute

6×+4

-2

Solve the equation

X=