When you look into a mirror, you see your reflection. Explain how this relates to reflections in
geometry.

Answer:

[tex]\displaystyle \int (\ln(x))^2\, dx=x(\ln(x)^2-2\ln(x)+2)+C[/tex]

Step-by-step explanation:

We want to evaluate the integral:

[tex]\displaystyle \int\left(\ln x\right)^2 \, dx[/tex]

We can use Integration by Parts. Rewriting the integral yields:

[tex]\displaystyle =\int 1\cdot (\ln(x))^2\, dx[/tex]

Recall that IBP is given by:

[tex]\displaystyle \int u\, dv = uv - \int v \, du[/tex]

Let u be (ln(x))². And let dv be (1) dx. Therefore:

[tex]\displaystyle du = 2\ln x \cdot \frac{1}{x}\, dx[/tex]

Simplify:

[tex]\displaystyle du=\frac{2\ln(x)}{x}\, dx[/tex]

And:

[tex]dv=(1)dx\Rightarrow v = x[/tex]

Therefore:

[tex]\displaystyle \int (\ln(x))^2\, dx=\underbrace{\ln(x)^2}_{u}\underbrace{x}_{v}-\int\underbrace{x}_{v}\cdot \underbrace{\frac{2\ln(x)}{x}\, dx}_{du}[/tex]

Simplify:

[tex]\displaystyle =x\ln(x)^2-2 \int\ln(x)\, dx[/tex]

We can perform IBP again. Let u = ln(x) and v = 1. Hence:

[tex]\displaystyle du = \frac{1}{x} \, dx[/tex]

And:

[tex]dv=(1)dx\Rightarrow v = x[/tex]

Thus:

[tex]\displaystyle =x\ln(x)^2-2\left(x\ln(x)-\int (x)\frac{1}{x}\, dx\right)[/tex]

Simplify:

[tex]\displaystyle =x\ln(x)^2-2\left(x\ln(x)-\int (1)\, dx\right)[/tex]

Evaluate:

[tex]=x\ln(x)^2-2(x\ln(x)-x)+C[/tex]

Simplify:

[tex]\displaystyle =x\ln(x)^2-2x\ln(x)+2x[/tex]

Factor:

[tex]=x(\ln(x)^2-2\ln(x)+2)[/tex]

Therefore:

[tex]\displaystyle \int (\ln(x))^2\, dx=x(\ln(x)^2-2\ln(x)+2)+C[/tex]

Answer:

Alternate-exterior angles theorem.

Step-by-step explanation:

Two parallel lines are cut by a transversal, and if there are a pair of congruent angles that are outside of the parallel lines, and on opposite sides of the transversal, you will have the alternate-exterior angles theorem.

Answer:

$375 is what i got on

Answer: K=23

Step-by-step explanation:

Answer:

k=9

Step-by-step explanation:

4k+44 because you distribute the 4 to the parenthesis

new equation: 4k+44-2=6

add 2 to 6 which would be 8 because you have to get k by itself

4k+44=8 subtract 44 from 8

-36=4k

divide by four

k=-9

if the equation is really 4(k+11)--2=6

do the same first steps so 4k+44

but the -2 would become positive cuz of the double negative

so:

4k+44+2=6

4k+46=6

subtract 46 from 6

4k=-40

divide -40 by 4

k=-10

Answer: negative numbers

Explanation: Notice that on the number line, 0 is in  the middle, all numbers to the left of 0 are negative, and all numbers to the right of 0 are positive.

Since the numbers highlighted only include numbers

to the left of 0, negative numbers are shown here.

Step-by-step explanation:

Hey there!!

It's so simple.

While finding the coordinates of any point if the midpoint is there it will be much easier. You must remember the midpoint formulae.

Let's simply work with it.

Here, A (2,-1) and midpoint M(3,3) are given.

Let another coordinate be B(x,y).

By midpoint formulae,

[tex]midpoint(x.y) = \frac{x1 + x2}{2} ,\frac{y1 + y2}{2} [/tex]

Putting their values,

[tex]m(3 , 3) = \frac{2 + x}{2} , \frac{ - 1 + y}{2} [/tex]

As they are equal, equating with their corresponding elements we get,

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

6= 2 + x

x = 6-2

Therefore, the value of a is 4.

Again,

[tex]3 = \frac{ - 1 + y}{2} [/tex]

6 = -1 + y

Therefore, the value of y is 7.

Therefore, the coordinates are B (4,7)

Hope it helps....

Answer:

The coordinates of B is (4, 7)

Step-by-step explanation:

To find the answer for B, you have to do the inverse of the midpoint formula, which is M equals (x1 multiplied by x2, over 2; y1 multiplied by y2, over 2).

If you substitute in A's coordinates for x1 and y1, you come up with (3, 3) = (2+x, over 2; and -1+y, over 2)

If the x coordinate answer for AB was 3, you can create an equation like this to solve for B's x coordinate: 2+x over 2 equals 3.

          you multiply 2 by 3 to get 6---> 2+x=6-----> x=4

If the y coordinate for AB was also three, you can create another equation to solve for B's y coordinate: -1+y over 2 equals 3.

         you multiply 2 by 3 to get 6 again---->so -1+y=6---->y=7

so the answer for B's coordinates is (4, 7).

Answer:

Hey there!

30/40 are cheddar flavored, so 10/40 are cream cheese flavored.

10/40=25, so 25% of the chips are cream cheese flavored (assuming that the rest of the chips are all cream cheese flavored)

Let me know if this helps :)

Answer:

54

Step-by-step explanation:

38-11= 27

27×2= 54 so he started with 54 comic books

Correct question is;

If f(x) = x³, evaluate the difference quotient: [f(6 + h) − f(6)]/h

Answer:

h² + 108h + 18

Step-by-step explanation:

We are given f(x) = x³

Thus;

f(6 + h) = (6 + h)³ = (36 + 12h + h²)(6 + h) = 216 + 72h + 6h² + 36h + 12h² + h³ = 216 + 108h + 18h² + h³

Then, f(6) = 6³ = 216

Thus;

[f(6 + h) − f(6)]/h = [216 + 108h + 18h² + h³ - 216]/h = (h³ + 108h + 18h²)/h

This gives;

h² + 108h + 18

Answer:

fewaf

Step-by-step explanation:

fsdfadfsadfasfas

Bring all the equation from the right side to the left.

2x² - 2 = - 5x - 1

2x² + 5x - 2 + 1 = 0 (take note that as you bring the number over you also have to flip the sign)

Therefore,

2x² + 5x + 1 = 0 (shown)

( this ans is similar to the form of ax² + bx + c = 0 )

The equation below written in the form ax² + bx +c= 0 is 2x² + 5x + 1 = 0

In algebra, a quadratic equation is any equation that can be rearranged in standard form as where x represents an unknown, and a, b, and c represent known numbers, where a ≠ 0. If a = 0, then the equation is linear, not quadratic, as there is no ax² term.

Examples of quadratic equations are: 6x² + 11x – 35 = 0, 2x² – 4x – 2 = 0, 2x² – 64 = 0, x² – 16 = 0, x² – 7x = 0, 2x² + 8x = 0 etc.

given:

2x² - 2 = - 5x - 1

2x² + 5x + 1 = 0.

Here, the above equation is in standard form as ax² + bx +c= 0.

Learn more about quadratic equation here:

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Answer:

x=1

Step-by-step explanation:

(x+1)(x+2)(x+3)(x+4)=120

Split 120 in it's factors: 2x3x4x5

=>(x+1)(x+2)(x+3)(x+4)=2x3x4x5

=>x+1=2 (Take any one in order)

=>x=1

Answer:

x=1

Step-by-step explanation:

120=2^3*3*5=2*3*4*5=(x+1)(x+2)(x+3)(x+4)

so x+1=2

    -1      -1

    x=1

Answer:

Step-by-step explanation:

Let the two numbers be x and y. If the sum of the numbers is 65, then;

x+y = 65........ 1

Given twice the smaller number is 10 more than the larger number, this can be written as 2x = 10+y (taking x as the smallest and y as the largest)

Therefore 2x = 10+y

x = 10+y/2 ....... 2

Substitute equation 2 into 1 to have;

10+y/2 +y = 65

Find the LCM

(10+y+2y)/2 = 65

10+3y/2 = 65

cross multiply

10+3y = 130

3y = 130 -10

3y = 120

y = 120/3

y = 40

Since 2x =10+y

2x = 10+40

2x = 50

x = 50/2

x = 25

Therefore the two numbers are 40 and 25

Answer:

40 and 25

Step-by-step explanation:

Answer:

( x + 2) ( x - 2 )

Step-by-step explanation:

f(x) = x^2 -4x

-4 = x^2 - 4x

0 =  x^2 - 4x + 4

0 = ( x + 2) ( x - 2 )

( x + 2) ( x - 2 )

Answer: h = 70ft

Step-by-step explanation: To find the height the ball reached after 2 seconds, substitute variable t for 2 and calculate height:

[tex]h=4+65t-16t^{2}[/tex]

[tex]h=4+65.2-16.2^{2}[/tex]

[tex]h=4+65.2-16.4[/tex]

[tex]h=4+130-64[/tex]

h = 70

After 2s, the football reached a height of 70 feet.

Answer:

if its for 3 seconds the answer is 55

Step-by-step explanation:

Answer:

Step-by-step explanation:

4x - 3y = 6

7x + 3y = 27

11x = 33

x = 3

7(3) + 3y = 27

21 + 3y = 27

3y = 6

y = 2

(3,2)

Answer:

x=3 and y=2

Step-by-step explanation:

Let's solve your system by substitution.

4x−3y=6;7x+3y=27

Step: Solve4x−3y=6for x:

4x−3y=6

4x−3y+3y=6+3y(Add 3y to both sides)

4x=3y+6

4x /4 = 3y+6 /4  (Divide both sides by 4)

x= 3 /4 y+ 3 /2

Step: Substitute

3 /4 y+ 3 /2  for x in7x+3y=27:

7x+3y=27

7( 3 /4 y+ 3 /2 )+3y=27

33 /4 y+ 21 /2

=27 (Simplify both sides of the equation)

33 /4 y+ 21 /2 + (−21 /2 )

=27+ (−21 /2) (Add (-21)/2 to both sides)

33 /4 y= 33 2

33/4y=33/2

33 /4  =33/4 (Divide both sides by 33/4)

y=2

Step: Substitute 2 for y in x= 3 /4 y+ 3 /2

x= 3 /4 y+ 3 /2

x= 3 /4  (2)+ 3 /2

x=3 (Simplify both sides of the equation)

Answer:

x=3 and y=2

HOPE THIS HELPS!!!! :)

<333333333333333

Answer:

Term in months. Number of months for this loan. Loan amount. Total amount of your loan. Interest rate. Annual ...

Step-by-step explanation:

The statement that a clock that is set fifteen minutes fast is less precise than an identical clock that keeps correct time is false

When a time is set away from the correct time, the time on the clock would be incorrect.

However, this has nothing to do with the precision of the clock.

This is so because precision deals with closeness of the time measurement to the original time

Since the time is ten minutes fast, it would not be less precise

Hence, the statement is false

Read more about precision at:

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Answer:

Step-by-step explanation:

f(x) = 4x² - 6

To find f(3) substitute the value of x that's 3 into f (x) that is for every x in f (x) replace it with 3

We have

f(3) = 4(3)² - 6

= 4(9) - 6

= 36 - 6

We have the final answer as

Hope this helps you

Answer: f(3) = 30

Step-by-step explanation:

what grade math is this????????????????????

Answer:

The answer to this question is 23

Step-by-step explanation:

The reason is because....

23x3= 69

69-9=60

60+ (x+7)

23+7=30

30+60=90

The angle shown is a 90 degree angle therefore this is your answer.

Answer:

34,466

Step-by-step explanation:

Given:

Number of males born in 2000 = 2,086,814

Percentage of males bearing Jacob of all males born in 2000 = 1.6516%

Required:

Number of Jacobs born in 2000

Solution:

Number of Jacobs born in 2000 = 1.6516% of number of males born in 2000.

[tex] = \frac{1.6516}{100}*2,086,814 [/tex]

[tex] = 0.016516*2,086,814 = 34,465.82 [/tex]

Number of Jacobs born in 2000 is approximately 34,466.

Answer:

five minus y

Step-by-step explanation:

Answer:

y less than five

Step-by-step explanation:

thats your answer, please trust me

Answer:

-2/7

Step-by-step explanation:

Going from (7,-1) to ( 21,-5) we see x (the 'run') increasing by 14 and y (the 'rise') decreasing by 4.  Thus, the slope of the line connecting these two points is m = rise/run = -4/14, or -2/7.

1 = 62° ( Vertically Opposite Angles )

10 = 62° ( Corresponding Angles )

9 = 10 = 62° ( Vertically Opposite Angles )

6 = 95° ( Vertically Opposite Angles )

7 = 180° - 95° = 85° ( Linear Pair )

8 = 7 = 85° ( Vertically Opposite Angles )

5 = 8 = 85° ( Corresponding Angles )

3 = 5 = 85° ( Vertically Opposite Angles )

4 = 180° - ( 9 + 7 )

4 = 180° - ( 62° + 85° )

4 = 180° - 147°

4 = 33° ( Angle Sum Property )

2 = 4 = 33° ( Vertically Opposite Angles )

Step-by-step explanation:

Answer:

x = plus or minus 8

Step-by-step explanation:

x² - 64 = 0

x² = 64

x = [tex]\sqrt{64}[/tex]

x = ± 8

Answer: Solve  :    x2+64 = 0  

Subtract  64  from both sides of the equation :  

                     x2 = -64

When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:  

                     x  =  ± √ -64  

In Math,  i  is called the imaginary unit. It satisfies   i2  =-1. Both   i   and   -i   are the square roots of   -1  

Accordingly,  √ -64  =

                   √ -1• 64   =

                   √ -1 •√  64   =

                   i •  √ 64

Can  √ 64 be simplified ?

Yes!   The prime factorization of  64   is

  2•2•2•2•2•2  

To be able to remove something from under the radical, there have to be  2  instances of it (because we are taking a square i.e. second root).

√ 64   =  √ 2•2•2•2•2•2   =2•2•2•√ 1   =

               ±  8 • √ 1   =

               ±  8