What is the name of a regular polygon with 45 sides?

Answer:

[tex]\dfrac{5}{2}\pi[/tex]

Step-by-step explanation:

Rotation about the y-axis

[tex]\textsf{Volume}=\displaystyle \int^b_a \pi x^2\:\text{d}y[/tex]

where:

Given function of y:  [tex]y = 3x^2[/tex]

Rewrite the given function as a function of y:

[tex]\implies x^2=\dfrac{1}{3}y[/tex]

Substitute the values into the formula:

[tex]\implies \displaystyle \int^4_1 \dfrac{1}{3}\pi y\:\:\text{d}y[/tex]

[tex]\boxed{\begin{minipage}{5 cm}\underline{Terms multiplied by constants}\\\\$\displaystyle \int ay^n\:\text{d}y=a \int y^n \:\text{d}y$\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $y^n$}\\\\$\displaystyle \int y^n\:\text{d}y=\dfrac{y^{n+1}}{n+1}+\text{C}$\end{minipage}}[/tex]

Take out the constant and integrate:

[tex]\begin{aligned}\implies \dfrac{1}{3}\pi\displaystyle \int^4_1 y\:\:\text{d}y & = \dfrac{1}{3}\pi \left[\dfrac{1}{2}y^2\right]^4_1\\\\& =\dfrac{1}{3}\pi \left[\dfrac{1}{2}(4)^2-\dfrac{1}{2}(1)^2\right]\\\\&=\dfrac{1}{3}\pi\left[8-\dfrac{1}{2}\right]\\\\&=\dfrac{5}{2}\pi \end{aligned}[/tex]

Therefore, the exact value of the volume of revolution is:

[tex]\dfrac{5}{2}\pi[/tex]

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The value of x is  2/9

Given equation x +2/3 = 8/9

We need to find the value of x

Simplifying the equation is

x+2/3 = 8/9

x = 8/9 -2/3

Taking L.C.M of the denominators 3 and 9

The L.C.M is 9

So we will multiply the numerator and denominator with 1 in 8/9

And we will multiply the numerator and denominator with 3 in 2/3

Hence the new equation formed = 8/9-6/9

Solving this equation we get

8-6 / 9

= 2 / 9

Hence the value of x is 2/9

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Answer: The fourth choice

Step-by-step explanation:

(f - g)(x) = f(x) - g(x) = 4[tex]x^{2}[/tex] - 5x - (3[tex]x^{2}[/tex] + 6x - 4) = [tex]x^{2}[/tex] - 11x + 4

Answer:

(f • g)(x) = -6x² - 24x

Step-by-step explanation:

The expression (f • g)(x) can be written in an expanded form, f(x) • g(x).

(f • g)(x)                         <----- Original expression

f(x) • g(x)                       <----- Rewritten expression

(- 6 x) • (x + 4)               <----- Insert functions

-6x² - 24x                    <----- Multiply -6x and x, and multiply -6x and 4

Based on the information provided, it can inferred that letter A is equivalent to 4.

The image shows B + B+ A = A. This is only possible if letter adding 2 letters B is equal to 10. Now 10/2 = 5. This means B = 5.

It is known 5 + A + A = A. This is only possible is A is 4. 5 + 4+ 4 + 1 (from the previous addition) = 4 (+2 that is added in the next column).

Note: This question is incomplete below I add the missing image.

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Answer:

B

Step-by-step explanation:

the value of the x should be the same if we want to verify whether x+2 is a factor of f(x)

so if x=-2 ,f(-2) = 29

x+2=0 f(0) = 1

f(0) [tex]\neq[/tex] f(-2) ,so x+2 is not a factor

what it actually means it that if we move the graphic of f(x) to left along to x axis 2 units, the graphic of new one cannot coincide with the original one.

Answer:

? = 3

Step-by-step explanation:

given a line parallel to a side of the triangle and intersecting the other 2 sides, then it divides those sides proportionally , that is

[tex]\frac{?}{6}[/tex] = [tex]\frac{2}{4}[/tex] ( cross- multiply )

4? = 12 ( divide both sides by 4 )

? = 3

Answer:

3

Step-by-step explanation:

Because the triangles are similar

6/4 = (?+6)/(2+4)

6/4 = (?+6)/6

Cross multiply

36 = 4?+24

4?=12

?=3

Answer:

Slope: -1/3

Y-intercept: 0

Step-by-step explanation:

The lines passes the y-axis at 0, and since the line is going downwards, the slope will be negative.

I hope it helps! Have a great day!

bren~

Applying multiplication of functions, the total number of seats in the auditorium is given by:

h(x) = 80x² + 560x.

They are multiplied applying the distributive property, that is, all the terms are multiplied and then the common terms are added.

In this problem, the functions are given as follows:

Then the multiplication is:

h(x) = f(x)g(x) = 80x(x + 7) = 80x² + 560x.

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Answer:

The answer is b

Step-by-step explanation:

:)

Answer:5 million

Step-by-step explanation: Because 300 thousand is below 500 thousand so if its below 500 thousand it cant round up it rounds down.

Answer:

[tex]\huge\boxed{\sf < 2 = 122\°}[/tex]

Step-by-step explanation:

From the figure,

We know that:

So,

Add 22 to both sides

10x + 2 + 22 = 12x

10x + 24 = 12x

Subtract 10x to both sides

24 = 12x - 10x

24 = 2x

Divide 2 to both sides

12 = x

OR

Given that,

∠2 = 12x - 22

Put x = 12

∠2 = 12(12) - 22

∠2 = 144 - 22

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

Answer: 122°

Step-by-step explanation:

∠1 an ∠2 are alternate interior angles, which are angles that are inside both parentheses and are on alternate sides of the transversal. The Alternate Interior Angles Theorem states that if two lines are parallel and cut by a transversal, then the alternate interior angles formed are congruent.

Since the lines are parallel as given in the question, ∠1 and ∠2 are of equal measure. We can solve for ∠2 by first solving for x, then plugging it in ∠2's measure.

[tex]10x+2=12x-22[/tex]

[tex]-2x=-24[/tex]

[tex]x=12[/tex]

Putting x in the expression 12x-22, we get

[tex]12(12)-22\\144-22\\122[/tex]

Hence, the value of ∠2 is 122°.

Using linear function concepts, it is found that the volume of each marble is of 0.05 liters.

A linear function is modeled by:

y = mx + b

In which:

The linear function that gives the volume of water, when n marbles are inserted into the tank, is given by:

w = 32 - 0.05n

The slope of -0.05 means that for each marble inserted, there are 0.05 liters less for water, hence the volume of each marble is of 0.05 liters.

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Answer:

.05 liters

Step-by-step explanation:

Chris and Jim must replace a total quantity of 17 tyres.

In this problem we must use an inequality of the form f(x) ≥ a, where f(x) is the difference between the number of tyres replaced by Jim and the number of tyres replaced by Chris:

(25/20) · x - x ≥ 3

(5/20) · x ≥ 3

x ≥ 12

Then, the minimum number of tyres to be replaced is n = 15 + 12 = 17 tyres.  

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The method that was used to arrive at the approximate population probability is called; a reasonable statistical generalization

Statistical generalization is a concept that involves inferring the results from a sample and applying it to a population. Carrying out this means that the sample must be selected randomly and be representative of the population.

Now, in this case, we see that the sample gave a probability of 68% to represent those were in favor of legalizing recreational marijuana use.

Now, since the conclusion was approximated to 70% to reflect the probability of the population then we can say that a reasonable statistical generalization was utilized.

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The sequence of transformation will be;

Rotate 120 degrees Counterclockwise around B, then Translate B to B' and reflect over segment BA.

We want to find the transformation that maps Quadrilateral ABCD onto Quadrilateral A'B'C'D'.

Looking at the given image, the sequence of transformation will be;

Rotate 120 degrees Counterclockwise around B, then Translate B to B' and reflect over segment BA.

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Answer:

Step-by-step explanation:

hello here is an solution

The domain and range are  (-∞,1/6)∪ (1/6, -∞), {x/x≠1/6} and  (-∞,-7/6)∪ (-7/6, ∞), {y/y≠-7/6} respectively.

A relation is a function if it has only One y-value for each x-value.

The given function is f(x)=(x+1)/6x+7

Let f(x)=y

(x+1)/6x+7=y

x+1=y(6x+7)

x+1=6xy+7y

6xy-x=7y-1

x(6y-1)=7y-1

Divide both sides by 6y-1

x=7y-1/6y-1

So f⁻¹(x)=1-7x/6x-1

The domain is (-∞,1/6)∪ (1/6, -∞), {x/x≠1/6}

The range is (-∞,-7/6)∪ (-7/6, ∞), {y/y≠-7/6}

Hence, the domain and range are  (-∞,1/6)∪ (1/6, -∞), {x/x≠1/6} and  (-∞,-7/6)∪ (-7/6, ∞), {y/y≠-7/6} respectively.

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the translations is,

               C(-5,-1) → (-3,-3)

               D(-4,3) → (-2,1)

               E(-3,2) → (-1,0)

               F(-2,0) → (0,-2)

What is Translation ?

The changes in the value of the x and y  coordinates is known as translation.

Calculation:

The given points are C(-5,-1), E(-4,3), F(-3,2), F(-2,0).

according to the question (x,y)→(x+2,y-2)

 this means x coordinate changes by addition of 2

 And the y coordinate changes by subtraction of 2  

 Addition and Subtraction in the Coordinates,

             C(-5,-1) → (-5+2,-1-2) → (-3,-3)

             D(-4,3) → (-4+2,3-2) → (-2,1)

             E(-3,2) → (-3+2,2-2) → (-1,0)

             F(-2,0) → (-2+2,0-2) → (0,-2)

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The values of 'j' are -11,5.

What is a Quadratic Equation?

Here, the given equation is (2x+7)(x-5) = - 43 + jx

On simplifying the equation we get,

[tex]2x^{2} -10x+7x-35=-43+jx\\2x^{2} -3x-35+43-jx=0\\2x^{2} -3x-jx+8=0\\2x^{2} -(3+j)x+8=0.....(1)\\[/tex]

By comparing the given equation with the standard form of the quadratic equation we get,

a = 2

b = - (3 + j)

c = 8

Therefore,

[tex](-(3+j))^{2} -4\times2\times8=0\\(3+j)^{2} -64=0\\(3+j)^{2} =64\\[/tex]

Take the square root of both sides,

[tex]\sqrt{(3+j)^{2} }=\sqrt{64} \\[/tex]

3 + j = ±8

Therefore,

3 + j = 8

j = 8 - 3        

j = 5

or

3 + j = -8

j = -8 - 3

j = -11

Hence, the possible values of 'j' are -11,5.

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Answer: Option (2)

Step-by-step explanation:

The inverse of a function swaps the domain and range.

The inverse of the function h(x) is

B. h'(x) = ((-5, 3), (-7, 5), (-9, 6), (-12, 10), (-16, 12)}

Option B is the correct answer.

We have,

The function h(x) is given as:

h(x) = {(3, -5), (5, -7), (6, -9), (10, -12), (12, -16)}

To find h¹(x) (the inverse of h(x)), we need to swap the x and y values in each ordered pair.

The inverse function will have the y-values of h(x) as the x-values, and the x-values of h(x) as the y-values.

So,

h¹(x) would be:

h¹(x) = {(-5, 3), (-7, 5), (-9, 6), (-12, 10), (-16, 12)}

Thus,

The inverse of the function h(x) is

B. h'(x) = ((-5, 3), (-7, 5), (-9, 6), (-12, 10), (-16, 12)}

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Answer:

84.82 cm

Step-by-step explanation:

Volume of a cone: [tex]\frac{1}{3} \pi r^2h[/tex]

[tex]\frac{1}{3} \pi r^2h\\\\\\\\= \frac{1}{3}\pi (3)^2(9)\\\\= \frac{1}{3}\pi(9)(9)\\\\\\\= \frac{1}{3} \pi (81)\\\\= 27\pi \\[/tex]

≈ 84.82 cm

The width of the rectangular backyard is 9 yards.

The width of the yard is three less than four times the length.

Therefore,

w = 4l - 3

Perimeter of a rectangle = 2l + 2w

where

l = length

w = width

Hence,

24 = 2l + 2(4l - 3)

24 = 2l + 8l - 6

24 = 10l - 6

24 + 6 = 10l

30 = 10l

l = 30 / 10

l = 3 yards

Hence,

w = 4(3) - 3

w = 12 - 3

w = 9 yards

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The expression that best represents the air pressure at an altitude of 3,000 meters above the surface of the Earth is 3,000ρg.

The air pressure at an altitude of 3,000 meters above the surface of the Earth is calculated as follows;

Po = ρgh

where;

Substitute the value of altitude into the equation;

Po = 3,000ρg

Thus, the expression that best represents the air pressure at an altitude of 3,000 meters above the surface of the Earth is 3,000ρg.

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Using the z-distribution, the 99% confidence interval for the true population mean textbook weight is (72.37, 81.63).

The confidence interval is:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

In this problem, we have a 99% confidence level, hence[tex]\alpha = 0.99[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.

The other parameters are given as follows:

[tex]\overline{x} = 77, \sigma = 12.2, n = 46[/tex]

Hence the lower and upper bound of the interval are given, respectively, by:

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Answer: -9/4.

The slope formula of the line passing through the points

Answer:

3.528

Step-by-step explanation:

the scale factor from the large triangle to the smaller triangle is 1/2.  All of the side lengths of the small triangle is 1/2 the side lengths of the large triangle.

A = 1/2 (bh)  The area of a triangle.  I need to know the base and the height of the little triangle to figure out the area.  If I use AC as the base, the length is given to me.  It is 4.2.  I do not have the height of the base, but I know that it is half of the height of the large triangle and that number is given to me.  It is 3.36, if I divide that by 2, I get 1.68.  Now I know all that I need to find the area.

A = 1/2(4.2)(1.68)

3.528Units^2

The first graph represents sin(2x), the second graph represents sin(-x) and the third graph represents sin(x/2) .

There are some rules for transformation of graph of various functions which are as follows :-

 By keeping in mind these rules it is easily observable that the first graph is sinx squashed horizontally by a factor of 2 while second graph is reflection of sinx about the y-axis and the third graph is sinx horizontally stretched by a factor of 2.

Thus the first graph represents sin(2x), the second graph represents

sin(-x) and the third graph represents sin(x/2)

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The coordinates of QRTW after dilation by factor 10 are (-20,30),(-30,10),(20,-10),(-20,40).

Given that coordinates of QRTW before dilation are (-2,3),(-3,1),(2,-1),(-2,4) and figure QRTW is dilated by factor 10.

We know that if a figure is dilated its area, increases. The new coordinates can be calculated as x*factor from which it is dilated.

Coordinates are the points on the graph surface.

In our figure Q(-2,3), R(-3,1), S(2,-1), T (-2,4).

We have to just multiply each value with 10 to get the new coordinates of QRTW after dilation.

Q after dilation=(-2*10,3*10)=(-20,30)

R after dilation=(-3*10,1*10)=(-30,10)

S after dilation=(2*10,-1*10)=(20,-10)

T after dilation=(-2*10,4*10)=(-20,40)

Hence the vertices of the image QRTW after dilation are (-20,30),(-30,10),(20,-10),(-20,40).

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Answer:

172.03 m²

Step-by-step explanation:

Hello!

Area of a circle: [tex]A = \pi r^2[/tex]

Plug in the radius into the formula to find the area.

The area is approximately 172.03 m².

To calculate the radius of this circle, we must take into account that:

Data:

To calculate the area of the circle, we apply the following formula:

a = area

π = pi

r = radius

Substituting the values of the equation:

Taking the square root

Multiplying

Answer: The approximate area of the circle is 171.95 m².