Select the correct answer.
A polygon is translated and then stretched vertically. Which statement is correct?

A.
The translation does not preserve side lengths and angles, but the vertical stretch preserves side lengths and angles of the preimage.
B.
Neither the translation nor the vertical stretch preserves side lengths and angles of the preimage.
C.
The translation preserves side lengths and angles, but the vertical stretch does not preserve side lengths and angles of the preimage.
D.
Both the translation and the vertical stretch preserve side lengths and angles of the preimage.

Answer:

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

g(f(1)) simply means we first get f(1), and that result becomes the input value for g(x). and that is then the end result.

so,

f(1) = 4

and then

g(f(1)) = g(4) = 14

Replace [tex]x\mapsto \tan^{-1}(x)[/tex] :

[tex]\displaystyle \int_0^{\frac\pi2} \sqrt[3]{\tan(x)} \ln(\tan(x)) \, dx = \int_0^\infty \frac{\sqrt[3]{x} \ln(x)}{1+x^2} \, dx[/tex]

Split the integral at x = 1, and consider the latter one over [1, ∞) in which we replace [tex]x\mapsto\frac1x[/tex] :

[tex]\displaystyle \int_1^\infty \frac{\sqrt[3]{x} \ln(x)}{1+x^2} \, dx = \int_0^1 \frac{\ln\left(\frac1x\right)}{\sqrt[3]{x} \left(1+\frac1{x^2}\right)} \frac{dx}{x^2} = - \int_0^1 \frac{\ln(x)}{\sqrt[3]{x} (1+x^2)} \, dx[/tex]

Then the original integral is equivalent to

[tex]\displaystyle \int_0^1 \frac{\ln(x)}{1+x^2} \left(\sqrt[3]{x} - \frac1{\sqrt[3]{x}}\right) \, dx[/tex]

Recall that for |x| < 1,

[tex]\displaystyle \sum_{n=0}^\infty x^n = \frac1{1-x}[/tex]

so that we can expand the integrand, then interchange the sum and integral to get

[tex]\displaystyle \sum_{n=0}^\infty (-1)^n \int_0^1 \left(x^{2n+\frac13} - x^{2n-\frac13}\right) \ln(x) \, dx[/tex]

Integrate by parts, with

[tex]u = \ln(x) \implies du = \dfrac{dx}x[/tex]

[tex]du = \left(x^{2n+\frac13} - x^{2n-\frac13}\right) \, dx \implies u = \dfrac{x^{2n+\frac43}}{2n+\frac43} - \dfrac{x^{2n+\frac23}}{2n+\frac23}[/tex]

[tex]\implies \displaystyle \sum_{n=0}^\infty (-1)^{n+1} \int_0^1 \left(\dfrac{x^{2n+\frac43}}{2n+\frac43} - \dfrac{x^{2n+\frac13}}{2n-\frac13}\right) \, dx \\\\ = \sum_{n=0}^\infty (-1)^{n+1} \left(\frac1{\left(2n+\frac43\right)^2} - \frac1{\left(2n+\frac23\right)^2}\right) \\\\ = \frac94 \sum_{n=0}^\infty (-1)^{n+1} \left(\frac1{(3n+2)^2} - \frac1{(3n+1)^2}\right)[/tex]

Recall the Fourier series we used in an earlier question [27217075]; if [tex]f(x)=\left(x-\frac12\right)^2[/tex] where 0 ≤ x ≤ 1 is a periodic function, then

[tex]\displaystyle f(x) = \frac1{12} + \frac1{\pi^2} \sum_{n=1}^\infty \frac{\cos(2\pi n x)}{n^2}[/tex]

[tex]\implies \displaystyle f(x) = \frac1{12} + \frac1{\pi^2} \left(\sum_{n=0}^\infty \frac{\cos(2\pi(3n+1)x)}{(3n+1)^2} + \sum_{n=0}^\infty \frac{\cos(2\pi(3n+2)x)}{(3n+2)^2} + \sum_{n=1}^\infty \frac{\cos(2\pi(3n)x)}{(3n)^2}\right)[/tex]

[tex]\implies \displaystyle f(x) = \frac1{12} + \frac1{\pi^2} \left(\sum_{n=0}^\infty \frac{\cos(6\pi n x + 2\pi x)}{(3n+1)^2} + \sum_{n=0}^\infty \frac{\cos(6\pi n x + 4\pi x)}{(3n+2)^2} + \sum_{n=1}^\infty \frac{\cos(6\pi n x)}{(3n)^2}\right)[/tex]

Evaluate f and its Fourier expansion at x = 1/2 :

[tex]\displaystyle 0 = \frac1{12} + \frac1{\pi^2} \left(\sum_{n=0}^\infty \frac{(-1)^{n+1}}{(3n+1)^2} + \sum_{n=0}^\infty \frac{(-1)^n}{(3n+2)^2} + \sum_{n=1}^\infty \frac{(-1)^n}{(3n)^2}\right)[/tex]

[tex]\implies \displaystyle -\frac{\pi^2}{12} - \frac19 \underbrace{\sum_{n=1}^\infty \frac{(-1)^n}{n^2}}_{-\frac{\pi^2}{12}} = - \sum_{n=0}^\infty (-1)^{n+1} \left(\frac1{(3n+2)^2} - \frac1{(3n+1)^2}\right)[/tex]

[tex]\implies \displaystyle \sum_{n=0}^\infty (-1)^{n+1} \left(\frac1{(3n+2)^2} - \frac1{(3n+1)^2}\right) = \frac{2\pi^2}{27}[/tex]

So, we conclude that

[tex]\displaystyle \int_0^{\frac\pi2} \sqrt[3]{\tan(x)} \ln(\tan(x)) \, dx = \frac94 \times \frac{2\pi^2}{27} = \boxed{\frac{\pi^2}6}[/tex]

Answer:

It's a fraction

Step-by-step explanation:

You have to figure out the meaning of the letters and find what goes on top

Answer:

B. 20πb³ + 12πb²

Step-by-step explanation:

The equation for the volume is incorrect, the volume of a cylinder with radius (r), and height (h), is πr²h.

The volume of the cylinder in terms of[tex]20\pi b^3 + 12\pi b^2[/tex]. Option B is correct.

A cylinder is a three-dimensional figure with two bases that are joined with a curved surface.

The total space occupied by the three-dimensional figure is called volume.

Given that:

The Volume is V = [tex]\pi r^2 h[/tex]

Radius r =  2b

Height,h = 5b +3

Substitute the values into the formula for the volume of a cylinder

V = πr²h

V =[tex]\pi \times (2b)^2 \times (5b + 3)[/tex]

Simplify the expression:

V = [tex]4\pi b^2 \times (5b + 3)[/tex]

Use the distributive property to get the values.

V = [tex]20\pi b^3+ 12\pi b^3[/tex]

So, the volume of the cylinder in terms of[tex]20\pi b^3 + 12\pi b^2[/tex]. Option B is correct.

Learn more about cylinder here:

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Answer:

x=1 y=2

Step-by-step explanation:

Isolate x for 4x -y =2: x=2+y/4

Substitute x= 2+y/4

(2+13y/4) +3y=7

simplify 2+13y/4) =7

Isolate y for 2+13y/4) =7: y=2

Forx= 2+y/4

Substitute y =2

x=2+2/4

x=1

Answer:

see explanation

Step-by-step explanation:

under a reflection in the x- axis

a point (x, y ) → (x, - y ) , then

(3, 4 ) → (3, - 4 )

(3, 1 ) → (3, - 1 )

(5, 1 ) → (5, - 1 )

Answer:

Points would be (3,-1) (5,-1) (3,-4)

Step-by-step explanation:

So its asking for a reflection on the x-axis, which means you simply take the shape and move the points to the same spot on the other side of the boldest horrizontal line, or in other words, you can just add a negative to the y variable in the points, because the rule is (x,-y).

[tex]y=-x+5~~~~~.....(i)\\\\x-y=1~~~~~~.....(ii)\\\\\\(i)-(ii):\\\\~~~~~y-x+y=-x+5-1\\\\\implies 2y=4\\\\\implies y= \dfrac 42\\\\\implies y=2\\\\\text{Substitute y=2 in eq (ii):}\\ \\~~~~ x-2 = 1\\\\\implies x= 1+2\\\\\implies x = 3\\\\\\\text{Hence,}~~ (x,y) = (3,2)[/tex]

Answer:

1.33 hours(If it doesn't let you type that in, just do 1 hour for rounding purposes)

Step-by-step explanation:

First, we take the 350 gal variable and divide that by 4.39, we now get 79.73

Now, we convert that into hours(60mins per hour), so 79.73 divided by 60.

We get 1.33, which is your answer!

Answer:

it is 57

Step-by-step explanation:

Answer:

A. √57

Step-by-step explanation:

√47 would be off the number line because it's below the number 7

√65 would be past 8 but the red dot comes before the number 8

√72 would be past 8 as well and it would be past √65 but the dot is before number 8

This leaves our answer as √57 beause the square root of 57 is 7.549 (etc.) which is between the numbers 7 and 8, while also being slightly higher than 7.5 :)

Have a good day!

[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{"f" varies inversely with "L"}}{f=\cfrac{k}{L}}\qquad \textit{we also know that} \begin{cases} f=\stackrel{lbs}{20}\\ L=\stackrel{ft}{1.5} \end{cases} \\\\\\ 20=\cfrac{k}{1.5}\implies 30=k~\hfill \boxed{f=\cfrac{30}{L}} \\\\\\ \textit{when L = 6, what is "f"?}\qquad f=\cfrac{30}{6}\implies f=5[/tex]

Answer:

3

Step-by-step explanation:

((7x-4)^2) - (7x-4)(7x-4) + 3

(7x-4)(7x-4) is 7x-4^2

So its (7x-4)^2 - (7x-4)^2 + 3

(7x-4)^2 cancel out.

Answer is 3

Answer:

[tex]derivative n thof \: sin2x [/tex]

Answer:

trigonometric function whose value for the complement of an angle is equal to the value of a given trigonometric function of the angle itself the sine is the cofunction of the cosine.

Answer:

-56

Step-by-step explanation:

First lets solve the bottom of the fraction :

1/7 * -1/8 is equal to -1/56 because to multiply two fractions we multiply there numerators and denominators

Now we have to divide 1 by -1/56 which is equal to :

1 *-56= -56 becasue when dividing by a fraction you want to switch its numerator and denominator

At the end you get -56

WHEN GRAPHING

Step 1. Convert to y = mx + b

Step 2. Graph like normal

Step 3. Shade as indicated by the inequality symbol

Step 4. If  ≤ or ≥ ONLY, then also shade the line

FOR THIS PROBLEM

1. Graph each equation

2. Shade ABOVE line for each

3. Shade line first equation as well

Hope this helps and God bless!

Answer:

13

Step-by-step explanation:

The coefficient is the number placed before the given variable.

In this case:

Coefficient: 13

Variable: y

Power: 3

The coefficient is a number in front of the variable( x or y)

The coefficient would be 13

Answer:

See below

Step-by-step explanation:

sf = s0 + v0 t  + 1/2 at^2

        1  + (-3)t + 1/2 (.2t) t^2           ( weird acceleration value)

s =  1 -3t + .1 t^3           You will need a 't' value to determine the position

Answer:

[tex]\large\lim_{x\rightarrow 1} f\left( x\right)=8[/tex]

Step-by-step explanation:

[tex]\lim_{x\rightarrow 1} \frac{f\left( x\right) -8}{x-1} =10[/tex]

[tex]\lim_{x\rightarrow 1} f\left( x\right) -8=10\times \lim_{x\rightarrow 1}\left( x-1\right)[/tex]

[tex]\lim_{x\rightarrow 1} f\left( x\right) -8=10\times\left( (1)-1\right)[/tex]

[tex]\lim_{x\rightarrow 1} f\left( x\right) -8=10\times\left( 0\right)=0[/tex]

[tex]\lim_{x\rightarrow 1} f\left( x\right) -8=0[/tex]

[tex]\lim_{x\rightarrow 1} f\left( x\right) =8[/tex]

Answer:

Step-by-step explanation: yes, we belive that they start young with pyromania.  They may see as something powerful

Answer: If I did it correctly it should be 150.8

Step-by-step explanation:

The formula for the volume of a cylinder is height x π x (diameter / 2)2, where (diameter / 2) is the radius of the base (d = 2 x r), so another way to write it is height x π x radius2.

Hope this helps!

Answer:

The function is C(d) = 0.69d+25.95. The equation will be 0.69(57)+2595.

for the last question 0.69d+25.95 = 57, so 0.69d = 31.05, so d is 45

The max distance you can drive with 120 dollars is 45 miles.

Answer:

  32 pounds

Step-by-step explanation:

Pounds of potatoes can be found by multiplying pounds of onions by 5 1/3:

  (5 1/3)(6 pounds) = 32 pounds

The restaurant bought 32 pounds of potatoes.

The given equation represents a hyperbola. Its main features are:

A hyperbola can be defined by its center, vertices,  foci and asymptotes. And it is represented algebraically  by the standard equation:  [tex]\frac{\left(y-k\right)^2}{a^2}-\frac{\left(x-h\right)^2}{b^2}=1[/tex], where:

h= x-coordinate of center

k= y-coordinate of center

a and b= semi-axis

First, you need to rewrite the given equation 9y²-x²+2x+54y+62=0 in the standard equation hyperbola:

[tex](-x^2+2x+?)+9(y^2+6y+?)=-62\\(-x^2+2x+?)+9(y^2+6y+9)=-62\\(-x^2+2x-1)+9(y^2+6y+9)=-62\\(-x^2+2x-1)+9(y^2+6y+9)=-62-1+81\\((-x^2+2x-1)+9(y^2+6y+9)=18 ) \div 18\\ \frac{(-x^2+2x-1)}{18} +\frac{9(y^2+6y+9}{18}= \frac{18}{18} \\\frac{-(x-1)^2}{18} +\frac{(y+3^2)}{2}=1\\\frac{-(x-1)^2}{(3\sqrt{2})^2} +\frac{(y+3^2)}{(\sqrt{2})^2 }=1\\\frac{\left(y+3)^2}{\left(\sqrt{2}\right)^2}-\frac{\left(x-1\right)^2}{\left(3\sqrt{2}\right)^2}=1[/tex]

Comparing the previous equation with the standard form ([tex]\frac{\left(y-k\right)^2}{a^2}-\frac{\left(x-h\right)^2}{b^2}=1[/tex]), you have:

h=1,  k=-3,  a=[tex]\sqrt{2}[/tex] and b=[tex]3\sqrt{2}[/tex] . From now, it is possible to find that the question asks:

The coordinates for center is (h,k). Thus, the center is (1,-3).

The vertices (V1 and V2) of hyperbola can be found from the coordinates of center (h,k) and the semi-axis (a).

V1= (h,k+a)= (1,-3+[tex]\sqrt{2}[/tex])

V2= (h,k-a)= (1,-3-[tex]\sqrt{2}[/tex])

The foci or the focus points can be found from the coordinates of center (h,k) and the c ([tex]\sqrt{a^2+b^2}[/tex]) which represents the distance from the center to the focus.

[tex]c=\sqrt{a^2+b^2}\\ c=\sqrt{(3\sqrt{2} )^2+(\sqrt{2} )^2}\\c=\sqrt{18+2} \\c=\sqrt{20}=2\sqrt{5}[/tex]

Thus,

F1= (h,k+c)= (1 , -3+ [tex]2\sqrt{5}[/tex] )

F2= (h,k-c)= (1 , -3 - [tex]2\sqrt{5}[/tex] )

The asymptotes are the lines the hyperbola tends to at ±∞. For hyperbola, the asymptotes are defined as: [tex]y=\pm \frac{a}{b}\left(x-h\right)+k[/tex]. Then, for this question:

[tex]y=\pm \frac{\sqrt{2}}{3\sqrt{2}}\left(x-1\right)-3\\y=\pm \frac{1}{3}\left(x-1\right)-3[/tex]

Read more about hyperbola here:

https://brainly.com/question/3351710

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Answer:

yes

Step-by-step explanation:

yes

each input (x) has exactly one output (y)

in other words

it passes the vertical line test

Answer:

[tex]x = 52[/tex]

Step-by-step explanation:

Step 1:  Create an expression

[tex]2x + 76 = 180[/tex]

Step 2:  Subtract 76 from both sides

[tex]2x + 76 - 76 = 180 - 76[/tex]

[tex]2x = 104[/tex]

Step 3:  Divide both sides by 2

[tex]\frac{2x}{2} = \frac{104}{2}[/tex]

[tex]x = 52[/tex]

Answer: [tex]x = 52[/tex]

Answer:

x = 52

Step-by-step explanation:

the 2 inside angles add up to 180 degress since they lie on the same side on the transversal line. so we set the eqaution up:

2x+76=180

2x=104

x=54

Step-by-step explanation:

the length and the width of a rectangle create a right-angled triangle, with the diagonal being the Hypotenuse of that triangle (the baseline, opposite of the 90° angle).

so, we can use Pythagoras

c² = a² + b²

with c being the Hypotenuse.

so, we have here

diagonal² = 40² + 9² = 1600 + 81 = 1681

diagonal = sqrt(1681) = 41 in