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

Urgent!

18. A tennis ball is launched straight upward with an initial velocity of 24.5 m/s from the edge of a cliff that is 117.6 meters above the ground. Which quadratic equation could be used to correctly determine when the ball will hit the ground:



4.9t2 + 24.5t + 117.6 = 0

-4.9t2 - 24.5t + 117.6 = 0

-4.9t2 + 24.5t - 117.6 = 0

4.9t2 + 24.5t - 117.6 = 0

-4.9t2 + 24.5t + 117.6 = 0



19. Solve the equation you chose in question 18 to determine when the ball will hit the ground. (HINT: If you don't get one of the answers listed for this question, then maybe you chose the wrong equation in #18. Use this opportunity to double check your work!)

t = 8 seconds

t = 4 seconds

t = 3 seconds

t = -3 seconds

The ball will never reach the ground.



20. Using the same equation, determine when the ball is at a height of 49 meters.

Answers

Step-by-step explanation:

18.

the last one.

-4.9t² + 24.5t + 117.6 = 0

the ball starts at 117.6 meters height. then, during the first seconds the thrust upwards is adding height, until finally, with more and more seconds passing, gravity will win with a vengeance and pulls the ball down faster and faster than any other force in any other direction.

19.

the general solution for a quadratic equation

y = ax² + bx + c

is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = t

a = -4.9

b = 24.5

c = 117.6

t = (-24.5 ± sqrt(600.25 - -4×4.9×117.6))/-9.8 =

= (-24.5 ± sqrt(600.25 + 2304.96))/-9.8 =

= (-24.5 ± sqrt(2905.21))/-9.8 = (-24.5 ± 53.9)/-9.8

t1 = (-24.5 + 53.9)/-9.8 = -3

t2 = (-24.5 - 53.9)/-9.8 = 8

a negative time does not make any sense, so the real solution is : the ball reached the ground after 8 seconds.

20.

now the equation is

-4.9t² + 24.5t + 117.6 = 49

but this is quickly transformed again into a "= 0" equation :

-4.9t² + 24.5t + 68.6 = 0

t = (-24.5 ± sqrt(600.25 - -4×4.9×68.6))/-9.8 =

= (-24.5 ± sqrt(600.25 + 1344.56))/-9.8 =

= (-24.5 ± sqrt(1944.81))/-9.8 = (-24.5 ± 44.1)/-9.8

t1 = (-24.5 + 44.1)/-9.8 = -2

t2 = (-24.5 - 44.1)/-9.8 = 7

again, negative time does not make sense.

the ball will be at 49 m height after 7 seconds.


Which equation could define the function below?
y= (x+1)(x+ .5) (x+ 3.5)
y= (x+1) (X - .5) (x-3.5)
y = (x-1) (X-.5) (x-3.5)
y= (x+1) (X- .5) (x +3.5)

Answers

Answer:

y= (x+1)(x+ .5) (x+ 3.5)

y= (x+1) (X - .5) (x-3.5)

y = (x-1) (X-.5) (x-3.5)

y= (x+1) (X- .5) (x +3.5)

Step-by-step explanation:

The value of y varies directly with the value of x. When y= 24, x = 4.
-
What is the value of x when y = 48?
O 6
0 8
O 28
0 288

Answers

Answer:

8

Step-by-step explanation:

whatever was done to y needs to be done to  x.

in this case (y) was 2x so you need to 2x (x) making 4 into 8

pls help
Determine if each pair of ratios is equivalent or not. 6/8 21/36

Answers

Answer:

Not

Step-by-step explanation:

6/8 In Simplest Form 3/4

21/36 In Simplest Form 7/12 May Be The Answer Will Be Not Equivalent

Hope To Help!!!

Is 92.248 an integer? Yes or no

Answers

Answer:

NO no no non

Step-by-step explanation:

IHOPE THIS CORELRECT ANSWER

In the equation = + , what does b represent?

Answers

Answer:

Although the equation is incomplete (b doesn't appear), I'll venture a guess that the correct equation looks something like this:

y = 2x + b [or y = mx+b]

b is the y-intercept.

Step-by-step explanation:

In the format of y = 2x + b, b represents the y-intercept (the value of y when x = 0).  

find the sides marked with letters

Also explain how to solve it ​

Answers

Answer:

m = 10

Step-by-step explanation:

The triangles are similar. The scale factor is 15/9.

We multiply 6 by the scale factor and get m:

m = 6 * 15/9 = 10

Then we see that m (10) is also the lenght of a side in the smaller triangle, so we multiply 10 by 15/9 and find a.

a = 16,6 (circa)

find 3 arithmetic means between -4 and 16​

Answers

Therefore, the arithmetic means are 1, 6, 11

Step-by-step explanation:
-4,_,_,_,16
Solution:
16= -4+(5-1)d
16= -4+4d
16+4= 4d
20=4d
4 4
d=5
-4 1 6 11
+5 +5 +5 +5
1 6 11 16
-4 ,1 ,6 ,11 ,16

Can someone please take the time out of their day and help me with this question

Answers

Answer:

76, 76 104

Step-by-step explanation:

Angle 3 is vertical so it is congruent to Angle 2.

Angle 6 is corresponding, so it is congruent to Angle 2.

Angle 8 is linear to Angle 6, so they add to 180

Answer:

see explanation

Step-by-step explanation:

(a)

∠ 2 and ∠ 3 are vertically opposite angles and are congruent , then

∠ 3 = 76°

(b)

∠ 3 and ∠ 6 are corresponding angles and are congruent , then

∠ 6 = 76°

(c)

∠ 2 and ∠ 8 are same- side exterior angles and sum to 180° , that is

∠ 8 + 76° = 180° ( subtract 76° from both sides )

∠ 8 = 104°

thank you in advance to whoever answers this question !!!!

Answers

It seems to be the answer B.

√16 + 9 equals √16 + √9
true or
False

Answers

Answer:

True

Step-by-step explanation:

Please help! What does the clock, rope, and shoe equal?

Answers

Answer:

shoe = 5, clock = 3, rope = 13

Step-by-step explanation:

hope this helped :) i just used guess and check knowing that the shoe is clock+2 hahah

How would I solve this?

Answers

Answer:

2a+3b=4a-3b

a+3=4b

b=3

a=9

Step-by-step explanation:

2a+3b=4a-3b

-2a=-6b

a=3b

a+3=4b

3b+3=4b

3=b

a=9

What is the measure of angle PNL?

43°
47°
86°
94°

Answers

Answer:

43°

Step-by-step explanation:

Answer:

A-   43

Step-by-step explanation:

ed2022

Help PLEASE!!! I really need it I really do please anyone

Answers

Answer:

5. alternate interior angles

7. angle addition postulate

Ankita height is 135 cm and Nita height is 150 express Ankita height as a percentage of Nita height​

Answers

Answer: 90%

135/150 * 100

45*2

90

Choose the best selection for the
quadrilateral with vertices at the
following points:
(0,0), (3,2), (6,0), (3,-2)
Hint: Start by graphing the points.
Distance Formula: d= V(x2-x1)2 + (y2 - y1)2
A. Rectangle
B. Square
C. Rhombus
D. Trapezoid

Answers

The quadrilateral with vertices at the  points: (0,0), (3,2), (6,0), (3,-2) is a square

The vertices (or coordinates) of the quadrilateral is given as:

[tex](x,y) = (0,0), (3,2), (6,0), (3,-2)[/tex]

Calculate the distance between subsequent points, using the following distance formula

[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}[/tex]

So, we have:

[tex]AB = \sqrt{(0 -3)^2 + (0 -2)^2}[/tex]

[tex]AB = \sqrt{13}[/tex]

[tex]BC = \sqrt{(3 -6)^2 + (2 -0)^2}[/tex]

[tex]BC = \sqrt{13}[/tex]

[tex]CD = \sqrt{(6 -3)^2 + (0 --2)^2}[/tex]

[tex]CD = \sqrt{13}[/tex]

[tex]DA = \sqrt{(3 -0)^2 + (-2 -0)^2}[/tex]

[tex]DA = \sqrt{13}[/tex]

Notice that the sides of the quadrilateral are congruent.

Hence, the quadrilateral is a square

Read more about quadrilaterals at:

https://brainly.com/question/1543115

Answer:

it's not a

Step-by-step explanation:

what is the slope of the line?

Answers

Answer:

-8/3

Step-by-step explanation:

rise/run

rise: -8

run: 3

-8/3

Marla earns an 8% commission on a house that she sells for $450,000. How 1 point
much does she earn in commission for this sale?”

Answers

Answer:

$36,000

Step-by-step explanation:

8% of $450,000 = $36,000

what is the area of the rhombus with one side as 32cm and one diagonal as 18 meters​

Answers

the area of the rhombus=32cm; one diagonal (q)=18meters

p=(2×area)/q

p=(2×32)/18=18

therefore the length of the unknown diagonal is 18.

the unknown diagonal can be calculated using the perimeter of the rhombus which is given as 32cm; one diagonal (p)=18 half of this diagonal

=18÷2=9units

If you can help, I’ll give brainliest

Answers

Answer:

sum of interior angles =180×3= 540°

m<F= 540-105-113-107-87

=128°

m<F= 128°

Evaluate.

[2−∣∣−14−2(−35)∣∣]÷(−6)

What is the value of the expression?

Enter your answer as a simplified fraction in the box.

Answers

-7/40

/////

I honestly didn't know how to do this one. But thats the correct answer.

The solution of the mathematical expressions will be 0.175.

What is Number system?

A system of writing to express the number is called number system.

Given that;

The mathematical expressions are,

⇒ [ 2 - | - 1/4 - 2 (-3/5) | ] ÷ -6

Now,

Solve the mathematical expression as;

⇒  [ 2 - | - 1/4 - 2 (-3/5) | ] ÷ -6

Using the BODMAS rule to solve the expressions as;

⇒ [ 2 - | - 1/4 - 2 (-3/5) | ] ÷ -6

⇒ [ 2 - | - 1/4 + 6/5 | ÷ -6

⇒ [ 2 - 19/20 ] ÷ -6

⇒  [ 21/20] ÷ -6

⇒ 21/20 x 1/-6

⇒ - 7 / 40

Therefore,

The solution of the mathematical expressions will be 0.175.

Learn more about the mathematical expression visit:

brainly.com/question/2164351

#SPJ5

A recursive rule for an arithmetic sequence is a1 = −4; an = an−1 + 11

a. What is a1?

b. What is d?

c. What is the iterative rule for the arithmetic sequence above? You do NOT need to simplify.

d. Find a10

Answers

It’s a for sure I really think it’s A i don’t know

The perimeter of the figure below is 41.6 in.
Find the length of the missing side.

Answers

Answer:

the answer is 5.9 since both sides are the same and on the other side its 5.9

Hope This Helps!!!

The answer is 5.7 because when you add sides up you get a sum of 35.9 then you subtract that from 41.6

pls help me answer this​

Answers

Step-by-step explanation:

hope it would help you...

Danielle wants to buy a magazine for $11. The sales tax is 5%. How much would the total cost of the magazine be with tax included?

Answers

Answer:

$11.55

Step-by-step explanation:

If we convert the percentage to 1.05 and multiply it by 11, it's 11.55.

Is -9 a real or imaginary number?

Answers

A real number is a number that can represent any continuous quantity.It includes both rational and irrational numbers.Since, -9 is a rational number, then it is a real number.

Answer:

-9 is a real number.

Hope you could get an idea from here.

Doubt clarification - use comment section.

Find the slope of the line passing through the points (-8, -3) and (-3,4).

Answers

Answer:

7/5

Step-by-step explanation:

4 + 3 = 7

-3 + 8 = 5

7/5

Alisha has a five–year car loan of $15,000 with an interest rate of 6 percent. If the interest is compounded annually, how much will she pay in total for her car?

Answers

Answer:

$20,073.38

Step-by-step explanation: Step 1: Find the percentage. The formula for annual compound interest is A = P(1 + r)^t, where A = amount (total amount), P = principal (initial amount), r = rate (percentage), and t = time (in years). Our rate is 6%, which is 0.06 in decimal form. Add it to 1. 1 + 0.06 is 1.06.

Step 2: Raise 1.06 to the 5th power. Because we are finding the amount in 5 years, we do that step. 1.06^5 is 1.3382255776.

Step 3: Do not delete the decimal from the calculator. Multiply it by 15,000 to find the total amount. When you do, you get 20,073.383664 or 20,073.38 when rounded to the nearest hundredth.

Which of the following is a square root of -18 ?

Answers

Answer:

It should be [tex]3\sqrt{2} i[/tex]

Step-by-step explanation:

Answer:

4.242.....

Step-by-step explanation:

Hope this helped!

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