Find the length of the following curve. If you have a​ grapher, you may want to graph the curve to see what it looks like.
y=1/27((9x^2)+(6))^3/2 ,from x=3 to x=6

The equation written in slope-intercept form is y = (1/3)x -9

A linear equation is that which can be represented in the form of y =mx +c , m is the slope and c is the intercept.

The given equation is

y+6 = 1/3(x-9)

To determine the slope and the intercept this equation needs to be solved

y+6 = (1/3)x - 3

y = (1/3)x -9

Therefore this is the slope intercept format , here

the slope = 1/3

intercept = -9

To know more about Linear Equation

https://brainly.com/question/11897796

#SPJ1

Answer:

3

Step-by-step explanation:

pls mark brainliest

Answer:

i hope this will help you

Tess and Jack are both correct with their claims

The attached image completes the question

From the complete question, we have the following highlights

The above properties represent a square

A rhombus can also have the above properties when the vertices are at 90 degrees

Hence, Tess and Jack are both correct with their claims

Read more about squares and rhombus at:

https://brainly.com/question/20627264

#SPJ1

Answer:

13/32 Susan

5/16 Enrique

9/32 Martin

Step-by-step explanation:

26+20+18=64

26/64=13/32

20/64=5/16

18/64=9/32

Step-by-step explanation:

Vertical asymptote can be Identites if there is a factor only in the denominator. This means that the function will be infinitely discounted at that point.

For example,

[tex] \frac{1}{x - 5} [/tex]

Set the expression in the denominator equal to 0, because you can't divide by 0.

[tex]x - 5 = 0[/tex]

[tex]x = 5[/tex]

So the vertical asymptote is x=5.

Disclaimer if you see something like this

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

x=5 won't be a vertical asymptote, it will be a hole because it in the numerator and denominator.

Horizontal:

If we have a function like this

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

We can determine what happens to the y values as x gets bigger, as x gets bigger, we will get smaller answers for y values. The y values will get closer to 0 but never reach it.

Remember a constant can be represent by

[tex]a \times {x}^{0} [/tex]

For example,

[tex]1 = 1 \times {x}^{0} [/tex]

[tex]2 = 2 \times {x}^{0} [/tex]

And so on,

and

[tex]x = {x}^{1} [/tex]

So our equation is basically

[tex] \frac{1 \times {x}^{0} }{ {x}^{1} } [/tex]

Look at the degrees, since the numerator has a smaller degree than the denominator, the denominator will grow larger than the numerator as x gets larger, so since the larger number is the denominator, our y values will approach 0.

So anytime, the degree of the numerator < denominator, the horizontal asymptote is x=0.

Consider the function

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

As x get larger, the only thing that will matter will be the leading coefficient of the leading degree term. So as x approach infinity and negative infinity, the horizontal asymptote will the numerator of the leading coefficient/ the leading coefficient of the denominator

So in this case,

[tex]x = \frac{3}{1} [/tex]

Finally, if the numerator has a greater degree than denominator, the value of horizontal asymptote will be larger and larger such there would be no horizontal asymptote instead of a oblique asymptote.

Answer:

Its Option C.

Step-by-step explanation:

I took this quiz and got this correct, atleast I think...??

Answer:

ok umm this looks hard can u give mor info?

Step-by-step explanation:

Answer:84

Step-by-step explanation:

Okay. Are you taking calc? Dv/dt =d/dt(L(t)^3)=d/dt[(sqrt(14)+2t)^3]= 6(Sqrt(14)+2t)^2)=44. We defined t=0 to be time at which length is sqrt(14). Does that work?

Answer:

E. 38°

Explanation:

A rhombus has 360° interior angle.

Half of the other side has 180° angle.

Solve for x:

sum of interior angles = 180°

x + 14 + x + 14 + x + x = 180°

4x + 28° = 180°

4x = 180° - 28°

4x = 152°

x = 152°/4 = 38°

Sum of half interior angles=180°

So

Option E

Assets are the goods you possess that can generate future economic advantage. The correct option is D.

Assets are the goods you possess that can generate future economic advantage. Liabilities are amounts owed to other parties. In a nutshell, assets put money in your pocket, while liabilities take money out!

Given Over the period of a year, Julie’s net worth decreased. Therefore, the statement that is true is Julie’s assets decreased by more than her liabilities.

Hence, the correct option is D.

Learn more about Asset and Liabilities:

https://brainly.com/question/14287268

#SPJ1

The perimeter of the base of the right pentagonal prism is 30 units

The given parameters are:

The volume of a right pentagonal prism is:

V = 0.5Pah

Where P represents the perimeter of the base.

So, we have:

0.5 * P * 14 * 4 = 840

Divide both sides by 0.5 * 14 * 4

P = 30

Hence, the perimeter of the base is 30 units

Read more about perimeter at:

https://brainly.com/question/24571594

#SPJ1

Why?

Notice that f(x) is positive when -2 < x < 1. In other words, f(x) is positive when x = -1 and when x = 1.

This interval of -2 < x < 1 translates directly to the interval notation of (-2, 1)

Unfortunately this interval notation looks identical to ordered pair notation. Be sure not to mix the two concepts up.

The parenthesis in interval notation tell the reader "do not include the endpoints". We cannot include x = -2 nor x = 1 because these values make f(x) zero, but we want f(x) > 0.

Something like choice D is a non-answer because the value x = 2 is in the interval (1,4), but f(2) = -8 which isn't positive. We can rule choice D out because of it. Choices A and C are similar situations.

The true statements are; A. Both graphs have exactly one asymptote. C. Both graphs are exponential functions. B. Both graphs have been shifted and flipped.

When the expression of function is such that it involves the input to be present as an exponent (power) of some constant, then such function is called exponential function.

There usual form is specified below. They are written in several such equivalent forms.

For example, y^x

, where a is a constant is an exponential function.

The graphs are exponential functions because as x increases, the y approaches infinity.

Here, the graphs have exactly one asymptote.

we can see that both graphs appear to have been shifted and flipped especially when at their respective coordinates.

The true statements are;

A. Both graphs have exactly one asymptote.

C. Both graphs are exponential functions.

B. Both graphs have been shifted and flipped.

Read more about Function Graphs at;

brainly.com/question/11507546

#SPJ1

The inequality T/5 > 20 represents and T is the total number of points Kylee earned for five games situation option fourth is correct.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

We have:

Kylee is playing a game she has to receive more than 20 points on average of five games to move onto the next level.

T is representing the total number of points Kylee earned for five games

The average is 20.

T/5 is also representing the average points of five games.

She has to receive more than 20 points on average in five games:

T/5 > 20

Thus, the inequality T/5 > 20 represents and T is the total number of points Kylee earned for five games situation option fourth is correct.

Learn more about the inequality here:

brainly.com/question/19491153

#SPJ1

The option (C) f(x) = (x+2)(x-3)²(x+4) is correct because in the graph the minimum value of function is less than 40.

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

We have a graph of a polynomial.

From the graph we can clearly see there is three x-intercept where the value of a polynomial function becomes zero.

The minimum value of function is less than 40

At x = 3, f(3) = 0

At x = -2, f(-2) = 0

At x = -4, f(-4) = 0

Thu graph of a function will be:

[tex]\rm y\ =\ \left(x+2\right)\left(x-3\right)^{2}\left(x+4\right)[/tex]

Thus, the option (C) f(x) = (x+2)(x-3)²(x+4) is correct because in the graph the minimum value of function is less than 40.

Learn more about Polynomial here:

brainly.com/question/17822016

#SPJ1

Step-by-step explanation:

spending 3 parts and saving 2 parts means that there are 3+2 = 5 parts in the whole.

the whole being $100.

one of the 5 parts is then 100/5 = $20.

so, she spent 3×20 = $60 and saved 2×20 = $40.

∠ KGH is equal to 77°. This is arrived at by using the knowledge of the total angles in Parallel Lines.

According to the laws of lines and angles, the total number of angles that can exist on a straight line is 180°.

If ∠CED = 25° and ∠BFL = 78°, then: ∠KGH = 180-(25+78), which is equals 77°. This is because the total angles on a straight-line total 180°

Recall that in angles in parallel lines:

Hence,

We can derive ∠LKJ because it is congruent with ∠BGJ.

To get ∠BGJ, we must get ∠LFH because both of them are interior angles and sum up to 180°.

To get ∠LFH, we must subtract ∠BFL from 180° because they are both angles on a straight line.

Hence ∠LFH = 180 - 78 = 102°

Recall that ∠LFH and ∠BGJ are interior angels. Hence

∠BGJ = 180 - 102 = 78°.

Since ∠BGJ is a corresponding ∠ with ∠LKJ, therefore

∠LKJ = 78°

∠ALM is ∠BFL because they are both corresponding angles and are therefore congruent.

     2. The name given to the triangle mentioned above is Obtuse      

          Triangle. This is because one of the angles exceeds 90°.

Learn more about angles in parallel lines at:
https://brainly.com/question/24607467
#SPJ1

The sentence "Four times the sum of a number and 17 is at least −26" translated to an inequality is 4(x+17) ≥ -26

From the question, we are to translate the given sentence into an equality.

The given sentence is

Four times the sum of a number and 17 is at least −26

Let the unknown number be x

Then,

The sum of a number and 17 will be

x + 17

Then,

Four times the sum of a number and 17 can be written as  

4(x+17)

Now,

"At least -26" means it is greater than or equal to -26

Thus,

Four times the sum of a number and 17 is at least −26 becomes

4(x+17) ≥ -26

Hence, the sentence "Four times the sum of a number and 17 is at least −26" translated to an inequality is 4(x+17) ≥ -26.

Learn more on Translating a sentence here: https://brainly.com/question/12307434

#SPJ1

The perimeter and area of this minor circle are equal to 32.857 units and 88.345 units² respectively.

First of all, we would determine the circumference of this circle by using this formula:

C = πD

C = 22/7 × 14

C = 44 units.

For the length of an arc of the circle:

Arc length/Circumference = 3/7

Arc length = 3/7 × C

Arc length = 3/7 × 44

Arc length = 18.857 units.

Now, we can calculate the perimeter:

Perimeter = 2r + arc length

Perimeter = 2(14/2) + 18.857

Perimeter = 14 + 18.857

Perimeter = 32.857 units.

Mathematically, the area of a minor circle is given by this formula:

Area = θr²/2

But, we would have to find the angle in radians:

18.857/32.857 = θ/360

θ = 3.6059 radians.

Substituting the given parameters into the formula, we have;

Area = (3.6059 × 7²)/2

Area = 88.345 units².

Read more on circumference here: brainly.com/question/14478195

#SPJ1

Answer:

Choice C:   [tex]m=\frac{1}{2}; y=\frac{1}{2} x+4[/tex]

Step-by-step explanation:

To find your slope do:

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

[tex]\frac{3-4}{-2-0}=\frac{-1}{-2} =\frac{1}{2}[/tex]

that's how you get 1/2

4 is just the y-int.

The required equation of line passes through (0, 4) and (-2, 3),  has slope of m = 1/2 , is y = 1/2x + 4. Option C is correct.

The equation is the values of two expressions that are equal.

The slope of the line is the tangent angle made by the line with horizontal. i.e. m =tanx where x in degrees.

The slope of the equation line passing through (0, 4) and (-2, 3)
[tex]m=\frac{y_2-y_1}{x_2-x_1} \\m = (3 - 4) / (-2-0)\\m = -1/-2\\m = 1/2[/tex]

Strand form of the equation of the line,
[tex]y-y_1 = m(x-x_1)[/tex]
Putting values in the standard form of the equation of the line.

y - 4 = 1/2 * (x - 0)
y = 1/2 * x + 4
[tex]y = \frac{1}{2} x + 4[/tex]

Thus, the required equation of line passes through (0, 4) and (-2, 3),  has slope of m = 1/2 , is y = 1/2x + 4. Option C is correct.

Learn more about slopes here:
https://brainly.com/question/3605446

#SPJ5

Answer:

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

Step-by-step explanation:

FOIL what is in the parentheses by multiplying terms by -4.

[tex]-4(3x+\frac{2}{6})[/tex]

-4(3x) = -12x and -4(2/6) = -4/3

now add these products: [tex]-12x-\frac{4}{3}[/tex]

That is the simplified product ^, but assuming you're supposed to set the equation to equal 0...

Set equation to 0 and add the fraction to both sides. Rewrite as [tex]-12x=\frac{4}{3}[/tex]

Divide both sides by -12 to get variable, x, alone. Multiplying 4/3 by -1/12 is the same as dividing 4/3 by -12. The negative sign from the -12 make the quotient negative.

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

Answer:

x = -1/9

Step-by-step explanation:

FOIL what is in the parentheses by multiplying terms by -4.

-4(3x) = -12x and -4(2/6) = -4/3

now add these products:

That is the simplified product ^, but assuming you're supposed to set the equation to equal 0...

Set equation to 0 and add the fraction to both sides. Rewrite as

Divide both sides by -12 to get variable, x, alone. Multiplying 4/3 by -1/12 is the same as dividing 4/3 by -12. The negative sign from the -12 make the quotient negative.

x= 1/9

The correct answer is option B which is u = ( x³ + 1).

The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.

Given expression is as follows:-

16(x³ + 1)² − 22(x³ + 1) − 3 = 0

Put u = ( x³ + 1) the equation will become:-

16u² -22u-3 = 0

Now the above equation has become a quadratic equation.

Therefore the correct answer is option B which is u = ( x³ + 1).

To know more about quadratic equations follow

https://brainly.com/question/1214333

#SPJ1

Answer:

none of the above

Step-by-step explanation:

4x + 7 = x + 2

4x - x + 7 = x - x + 2

3x + 7 = 2

3x + 7 - 7 = 2 - 7

3x = -5

3x / 3 = -5 / 3

x = -5 / 3 = -1.667

5x - 8 = x + 4

5x - x - 8 = x - x + 4

4x - 8 + 8 = 4 + 8

4x = 12

4x / 4 = 12 / 4

x = 3

3x + 2 = 5x + 2

3x - 5x + 2 = 5x - 5x + 2

-2x + 2 = 2

-2x + 2 - 2 = 2 - 2

-2x = 0

x = 0

Integers, As a whole number that can be written without a remainder,

x = 3

x = 0

(Mixed) Fraction

x = -5 / 3 = -1.667

Answer:

12.5

Step-by-step explanation:

divide 43.75 by 3.5 to get your answer

The exterior angles in the given triangle are angles 4 and 5.

The given shape is a triangle. A triangle is a three-sided polygon that has angles that sum up to 180 degrees. The exterior angle is the angle that is formed when a line is extended from the next side and the other side of the triangle. Simply put, it is the angle that is not inside the triangle.

To learn more about angles, please check: https://brainly.com/question/2766460

#SPJ1

Answer:

I guess, A is the wanted answer, but

A and D together are the really correct answer.

Step-by-step explanation:

if I understand this correctly, then

g(x) = sqrt(x - 3)

the domain of a function is the definition of all valid x (input) values.

the range of a function is the definition of all valid y (result) values.

well, the content (the arguments) of a square root cannot be negative (at least not while dealing with real numbers).

so, the answer options B and D are automatically out, because the domain contains values that would make the arguments of the square root negative.

I guess your teacher wants to focus only on the positive results of the square root, so A is the correct number.

BUT formally, without designated restrictions, a square root has always 2 solutions : a positive and a negative one.

because (-x)² = (x)² = x².

so, I would have to say that the really correct answer is

A + D, because the range contains both, the positive and the negative numbers.

Answer:

[tex]2\sqrt{5}[/tex] is an irrational number.

[tex](\sqrt{3} )^2[/tex] is a rational number.

Step-by-step explanation: