The logarithmic expression [tex]log_{b}(\frac{1}{b^{-b}} )[/tex] where b > 0, is equal to

a) [tex]b^{-b}[/tex]

b) [tex]b^{b}[/tex]

c) [tex]-b[/tex]

d) [tex]b[/tex]

Answers

Answer 1

[tex]\log_b \left(\dfrac 1{b^{-b}}\right)\\\\=\log_b (b^{-b})^{-1}\\\\=\log_b b^b\\\\=b \log_b b\\\\=b \cdot 1\\\\=b[/tex]


Related Questions

Congruence Criteria for a Parallelogram's two triangles is:

ASA
HL
AAS
SSS

Answers

Answer:

ASA

Step-by-step explanation:

two angles are the same and one side is the same

WILL GIVE BRAINLIEST
HELP ASAP!! WILL ADD 5 STAR RATING !!!

ANY AND ALL LINKS OR WRONG ANSWERS WILL BE REPORTED !!!!

Answers

X=-3
Y=4,5
.........

What is the factored form of n3+512 (pleas help fast)

A- (n-8)(n^2+8n+64)
B- (n+4)(n^2-4n+128)
C- (n-4)(n^2+4n+128)
D- (n+8)(n^2-8n+64)

Answers

Answer:

Since both terms are perfect cubes, factor using the sum of cubes formula,

a³+b³=(a+b)(a²-ab+b²) where

a=n and b=8

(n+8)(n²-8n+64)

Answer

(n+8)(-8n+64)

hi

have a good day

thank me later

Carryonlearing

Answer:

Step-by-step explanation:

The only one that has a chance of being correct is D. That's because the first term is correct and you have to assume that the second one is as well.

cubrt(512) = 8

The first term is (n + 8)

The second term is (n^2 - 8*n + 8^2) = n^2 - 8n + 64

All the other answers have the wrong first term

A: it should be n + 8 not n - 8

B and C are both wrong because the cube root of 512 is 8 not 4.

hellllllllllllllllllllppppppppppppppppppppp

Answers

Answer:

Y-intercept: (0, -10)

X-intercepts: (5,0), (1,0)

Axis of symmetry: (3,0)

Step-by-step explanation:

You can tell what the y-intercept is by looking at the function. At the end there is a “-10”, which indicates that it’s the y-intercept.

There are many ways to find x-intercepts. You can factor the function, use the quadratic formula, or complete the square.

By factoring it, you get

-2(x-5)(x-1)=0

If one part of it equals zero, than the whole function equals zero.

So it can be split up like this

(x-5)=0

(x-1)=0

So...

x=5 and x=1 are the the zeros or (5,0) and (1,0)

Finally, you convert the function from standard form to vertex form. By doing -b/2a, you can find the x-coordinate of the vertex, which is the axis of symmetry. The answer is 3 or (3,0) because -12/2(-2)= 3.

State what information is required to know that the triangles are congruent.
-GEOMETRY

Answers

[tex]\huge \bf༆ Answer ༄[/tex]

The additional information needed to prove that the triangles are congruent is ~ A

[tex] \sf\angle M \cong \angle V \: \: or \: \: \angle N \cong\angle U[/tex]

From his eye, which stands 1.61 meters above the ground, Jacob measures the angle
of elevation to the top of a prominent skyscraper to be 25°. If he is standing at a
horizontal distance of 281 meters from the base of the skyscraper, what is the height
of the skyscraper? Round your answer to the nearest tenth of a meter if necessary.

Answers

Step-by-step explanation:

we have a right-angled triangle, that is "hovering" 1.61 m above the ground.

the Hypotenuse (the side opposite of the 90 degree angle) is the line of sight from the eye to the top of the skyscraper.

one leg is the height of the skyscraper (minus the 1.61 m).

the other leg is the ground distance from Jacob to the skyscraper (281 m).

we know already 2 angles : the 90° angle between the ground distance and the skyscraper height. and the 25° between the ground distance and the line of sight.

and as we know that the sum of all angles in a triangle is always 180°, we know that the third angle (between the line of sight and the skyscraper height) is

180 - 90 - 25 = 65°

now we can use the law of sines

a/sin(A) = b/sin(B) = c/sin(C)

(the ratio between a side and its opposing angle)

to get all missing side lengths.

the 25° angle is opposite of the skyscraper height, and the 65° angle is opposite of the ground distance (the only side length we know so far).

so,

height/sin(25) = 281/sin(65)

height = 281 × sin(25)/sin(65) = 131.0324519... m

to get the full height of the skyscraper, we need to add the 1.61 m that the described triangle was "hovering" above ground.

therefore, the height of the skyscraper is

131.0324519... + 1.61 = 132.6424519... ≈ 132.6 m


I don’t understand this. Can I plz get some help

Answers

There are 3 right triangles in this picture, and they are all mutually similar.

• the smallest triangle has legs 4 and y, and hypotenuse z

• the middle one has legs y and 16, and hypotenuse x

• the largest one has legs z and x, and hypotenuse 16 + 4 = 20

Note the order in which I've listed the sides (shortest to longest). Because these triangles are similar, the corresponding sides occur in a fixed ratio. In particular, we have

4/y = y/16 = z/x … (ratios of each side of the smallest and middle triangles)

4/z = y/x = z/20 … (ratios of the sides of the smallest and largest triangles)

y/z = 16/x = x/20 … (ratios of the sides of the middle and largest triangles)

We just want to find x, which we can do easily with the last equality,

16/x = x/20

Solve for x :

20 • 16/x = 20 • x/20

320/x = x

x • 320/x = x • x

320 = x²

⇒   x = √320 = √(64 • 5) = 8√5

Mrs. Rainer would like to buy 28
composition notebooks for her math class.
If they are on sale for $0.94 each, how
much will she spend, not including tax?

Answers

Answer:

$26.32

Step-by-step explanation:

0.94x28 = 26.32

(Meeting character limit)

Evaluate the expression for x = 5 and y = -1
xy - y =

Answers

Answer:

-4

Step-by-step explanation:

xy-y = ?

(5)(-1)-(-1) = ?

-5 + 1 = -4

Hope that helps

someone please help, will give branliest

consider a sequence with the common difference of 5 and whose fiftieth term is 259. what are the first three terms of this sequence?

A- 15,20,25
B- 13,18,23
C- 9,14,19
D- 14-19,24
E- 10,15,20

Answers

The answer is C (9,14,19)

Here is a free 100 points annnnd brainliest

This question is about strategy
Skill
Precision


Alr here it is:
Problem one: Molly bought and infinite amount of bottles of dish soap. She had an infinite amount of money. When she bought the dish soap, she lost all of it.

How is this possible?

Problem one (part two): Molly then called her friend Blitzo over. Blitzo then gave Molly and infinite amount of money without losing all of his money.

How is this possible

If you have questions or want hints, ask in comments below this question

Answers

1. She bought the infinite dish soap with her money

2. you can't lose anything infinite

3. remeber our deal? brainliest pls.

−3.6−1.9t+1.2+5.1t ////////////////////////////////////////////////////////////

Answers

Answer:

3.2t -2.4

Step-by-step explanation:

Combine like terms then solve (-1.9t +5.1t)+(-3.6+1.2)

(0, 2), (1,7) create a equation that passes through each pair of points

Answers

Answer:

y = 5x + 2

Step-by-step explanation:

Given the equation 5x + 2

Plug in 0

y = 5(0) + 2

y = 2

(0,2)

Given the equation 5x + 2

Plug in 1

y = 5(1) + 2

y = 7

(1,7)

What are the coordinates of C if translated 5 units upward?

Answers

(6, 11)

hope this helps!


It costs $10 to rent a canoe and $5.50 to use the canoe for an hour. You have $21. Write an equation that represents the number h of hours you can rent the canoe.

Answers

Answer:

21 = 10 + 5.5h

Step-by-step explanation:

Total cost = initial cost + hourly cost

21 = 10 + hourly cost

hourly cost = 5.5 per hour, or 5.5 * h as we add 5.5 for each hour

21 = 10 + 5.5h

Answer:

Step-by-step explanation:

$10 + $5.50h ≤ $21

Let h stand for the hours the canoe is rented.

Fixed cost = $10, regardless of h.

$5.50h for the cost of n hours of rental.

Total cost = $10 + $5.50h

The total cannot exceed $21, legally.  

So we should write:

$10 + $5.50h ≤ $21  

If $10 + $5.50h ≥ $21  then ║║║║║║║

Equations that represent a line parallel to y=8x+4

Answers

y=8x+b, b being any number, is parallel to y=8x+4.

For example:

y=8x+2

y=8x+(1/2)

y=8x+937382

y=8x-4

after the outbreak of a mysterious disease, the average wait time at a hospital by 70%. Before the outbreak, the average wait time at a hospital is m minutes

Answers

Answer:

1.7m

Step-by-step explanation:

Given that 'm' was the waiting time before the outbreak

After the outbreak, waiting time increased by 70%.

This implies that :

70% of m increase

m + 70% of m

m + 70/100 of m

m + ( 70÷100 ) × m

m + 0.7m

= 1.7m

Step-by-step explanation:

radius=12 round up to the nearest tenth

Answers

Answer:

12.0

Step-by-step explanation:

Answer:

452.4

Step-by-step explanation:

Ayudaaaaaa es para hoy

Answers

Answer:

Step-by-step explanation:

a  (2³)² = 2³ˣ² = 2⁶

b (7⁰)¹ = 7⁰ˣ¹ = 7⁰ = 1

c (5⁶)³ = 5⁶ˣ³ = 5¹⁸

d (6²)⁴ = 6²ˣ⁴ = 6⁸

e (8³)⁴ = 8³ˣ⁴ = 8¹²

f (4³)² = 4³ˣ² = 4⁶

g (9¹)² = 9¹ˣ² = 9² = 81

h (3⁷)² = 3⁷ˣ² = 3¹⁴

i (10²)³ = 10²ˣ³ = 10⁶

j (11²)⁴ = 11²ˣ⁴ = 11⁸

Jill takes 2 hours to paint a room, Jim takes 3 hours to paint a room. How long (in minutes) will it take both of them to paint a room

Answers

Jill will take 120 minutes to paint a room

Jim will take 180 minutes to paint a room

All together Jim and Jill will take 200 minutes to paint a room

Answer:

  72 minutes

Step-by-step explanation:

The sum of the rates of work in rooms per hour is ...

  Jill's rate + Jim's rate

  = (1/2 room/hour) +(1/3 room/hour) = (3/6 +2/6 room/hour) = 5/6 room/hour

__

Then the combined rate in hours per room is ...

  1/(5/6 room/hour) = 6/5 hours/room = (6/5 hours/room)(60 minutes/hour)

  = 72 minutes per room

Jill and Jim can paint the room in 72 minutes when they work together.

Which of these actions would decrease heat transfer between two objects?

increasing the temperature of the warmer object
increasing the area of their contact
reducing the thermal energy of the cooler object
reducing the time of their contact
(Fr ran out of free answers)

Answers

Answer:

increasing the area of their contact

Please find the range of these numbers

Answers

Answer:7

Step-by-step explanation:range is highest number subtracted by lowest

Answer:

17

Step-by-step explanation:

The formula for range is max-min.

The max is 91 and the min is 74

91-74=17

what is 69+69-69+1-1+0

Answers

The answer is 69 , because it just cancels out the numbers

Answer:

207

Step-by-step explanation:

explain why the area of the large rectangle is 2a + 3a + 4a

Answers

Answer:

The area of the large rectangle = the sum of the areas of the three smaller rectangles

areas of the smaller rectangles are : 2a, 3a, and 4a respectively

Therefore the area of the lage rectangle = 2a + 3a + 4a

The sum of the area of all the rectangles will be 2a + 3a + 4a.

What is the area of the rectangle?

Let W be the rectangle's width and L its length.

The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be

Area of the rectangle = L×W square units

The dimensions of the rectangle are 2 by a, 3 by a, and 4 by a.

The area first rectangle is given as,

⇒ 2 × a

⇒ 2a

The area second rectangle is given as,

⇒ 3 × a

⇒ 3a

The area third rectangle is given as,

⇒ 4 × a

⇒ 4a

The total area of the rectangle will be given as,

A = 2a + 3a + 4a

More about the area of the rectangle link is given below.

https://brainly.com/question/20693059

#SPJ2

Calculate the average speed of an airplane, in miles per hour, if it travels 1,000 miles in 2

2 1 2

hours.

Answers

speed=distance ÷time1000m÷212 hours 4.71698m i hope this helps

The average speed of the airplane which travels the given distance and time is 400mph.

Speed

Speed is simply defined as distance traveled per unit of time. It is the change of position of a moving object per unit of time.

It is expressed as;

s = distance / time = d / t

Given the data in the question;

Distance travelled d = 1000miTime taken t = 2 and 1/2 hrs = 2.5hrsAverage speed; s = ?

To determine the average speed of the airplane, we substitute our given values into the expression above.

s = d / t

s = 1000mi / 2.5hrs

s = 400mph

Therefore, the average speed of the airplane which travels the given distance and time is 400mph.

Learn more about Speed and Velocity here: https://brainly.com/question/10566304

100 points!! ASAP do all problems with steps to your answer

Answers

Answer:

11. 10

12. -9v + 7

13. 1-10b

14. 5n+10

15. 12v

16. 0

17. 0

18. -4n+10

19. 9b - 9

20. 5v-8

Hope it help.

Answer: 13: 1-10b

14: 5n +10

15: 12v

16: nothing

17 0

18: 10 -4n

19: 11 + 5b

20: 5x + -8

Step-by-step explanation:

13: 6b + 4b = 10b

1-0=1

1-10b

14: n+4n = 5n

5n+10

15: 10v + 2v = 12v

16: 6v - 6v = 0

17: -2 +2 =0

18: 9 + 1 = 10

5n + n = 4n

10 - 4n

19: 10 + 1 = 11

7b-2b = 5b

11 + 5b

20: 1 -9 = -8

5x + -8

In a set of bivariate data, an additional point is added near the regression line but far away from the rest of the data. this
will the slope of the regression line and the correlation coefficient.
A slightly change, strengthen
B greatly change, weaken
C slightly change, weaken
D greatly change, strengthen
E not change, not change

Answers

Answer:

C. is the answer

Step-by-step explanation:

CARRY ON LEARNING

AND REMEMBER DO ALWAYS READ AND WRITE

patrick said that the product of any number and 4 is always double the product of that number and 2. Is patrick correct. explain

Answers

Patrick is correct, since the two parts of the statement are equal.

From the question,

Patrick said that the product of any number and 4 is always double the product of that number and 2. We are to investigate if Patrick is correct.

First, let the number be x,

From the first part of the statement

The product of any number and 4

That is,

4 × x = 4x

And

The second part of the statement,

double the product of that number and 2

That is,

2(x × 2) = 2(2x)

Now, we will investigate if

4x = 2(2x)

Expand the right hand side of the equation

That is,

4x = 2 × 2x  

Then, we get

4x = 4x

Since the two parts of the statement are equal, then Patrick is correct.

Hence, Patrick is correct, since the two parts of the statement are equal.

Learn more here: https://brainly.com/question/14176303

Hi Guys,
I am Revising for Exams.
I don't get the Topic:
PERCENTAGES OF AN AMOUNT.
Please help me to find out the Answer/Equation etc
Thank You All.

Answers

GOOD LUCK IN THE TEST!!!!!!!

point:(-5,1); slope: -
4
write in point-slope form:

Answers

Answer:

y-1=-4(x+5)

Step-by-step explanation:

y-y1=m(x-x1)

y-1=-4(x-(-5))

y-1=-4(x+5)

Answer: y - 1 = -4(x + 5)

Step-by-step explanation:

      The point-slope formula is y - [tex]y_1[/tex] = m(x - [tex]x_1[/tex]) where m is the slope and ( [tex]x_1[/tex], [tex]y_1[/tex]) is a point on the graph.

      Using the formula, we will plug in our known values to write our equation.

y - [tex]y_1[/tex] = m(x - [tex]x_1[/tex])

y - (1) = (-4)(x - (-5))

y - 1 = -4(x + 5)

        However, in the picture the slope is [tex]\frac{1}{4}[/tex], so we would write it as;

                      y - 1 = [tex]\frac{1}{4}[/tex](x + 5)

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