what is the value of a when we rewrite 8^x as a^-x/9​

Answers

Answer 1

Answer:

[tex]a = \frac{1}{134217728}[/tex]

Step-by-step explanation:

Given

[tex]8^x = a^{-x/9}[/tex]

Required

Find a

Take log of both sides

[tex]log(8^x) = log(a^{-x/9})[/tex]

Apply law of logarithm

[tex]x\ log(8) = (-x/9) log(a)[/tex]

Divide both sides by a

[tex]log(8) = -\frac{1}{9} log(a)[/tex]

Multiply both sides by -9

[tex]-9\ log(8) = log(a)[/tex]

Apply law of logarithm

[tex]log(8^{-9}) = log(a)[/tex]

Cancel out log

[tex]8^{-9} = a[/tex]

Rewrite as:

[tex]a = 8^{-9}[/tex]

Apply law of indices

[tex]a = \frac{1}{8^9}[/tex]

[tex]a = \frac{1}{134217728}[/tex]


Related Questions

The area of the state of Nevada can be estimated using a trapezoid. Estimate the area of the state of Nevada.
A. 31,672 mi2
B. 78,980 mi2
C. 110,622 mi2
D. 131,327 mi2

Answers

Answer: 31,672 mi2

Step-by-step explanation:

The area of the state of Nevada can be estimated using a trapezoid

Determine the values of the following quantities. (Round your answers to three decimal places.) A button hyperlink to the SALT program that reads: Use SALT. (a) t0.10, 18 1.735 Incorrect: Your answer is incorrect. (b) t0.05, 18 2.101 Incorrect: Your answer is incorrect. (c) t0.05, 23 1.714 Correct: Your answer is correct. (d) t0.05, 60 1.671 Correct: Your answer is correct. (e) t0.005, 60 2.915 Incorrect: Your answer is incorrect.

Answers

Answer:

1.330391 ; 1.734064 ; 1.713872 ; 1.670649 ;

Step-by-step explanation:

a) t0.10, 18

α = 0.10 ; df = 18

From table, critical value = 1.330

(b) t0.05, 18

α = 0.05 ; df = 18

From table, critical value = 1.734

(c) t0.05, 23

α = 0.05 ; df = 23

From table, critical value = 1.714

(d) t0.05, 60

α = 0.05 ; df = 60

From table, critical value = 1.671

(e) t0.005, 60

α = 0.05 ; df = 60

From table, critical value = 2.660

The dot plots show the number of hours a lightbulb lasts from two different brands. Brand A. Number of hours per lightbulb 1000 4200 1400 1500 1800 2000 Brand B Number of hours per lightbulb .. 1200 1400 1600 1800 2000 Which of the following statements is correct? A. There were more lightbulbs in the dot plot for brand B than in the dot plot for brand A. B. The mean for brand A is the same as the mean for brand B. C. The mean for brand A is higher than the mean for brand B. D. The mean for brand B is higher than the mean for brand A.​

Answers

Answer:

Step-by-step explanation:

The mean for brand A is higher than the mean for brand B

The mean for brand A is higher than the mean for brand B because the mean for A is 1983.33 and the mean for B is 1600 statement (C) is correct.

What is mean?

It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.

We have:

For brand A:

The number of hours per lightbulb:

1000, 4200, 1400, 1500, 1800, 2000

Mean for brand A:

[tex]\rm Mean(A) = \frac{Sum \ of \ all \ data \ values}{Number \ of \ data \ in \ the\ set}[/tex]

[tex]\rm Mean(A)= \frac{1000+4200+1400+1500+1800+ 2000}{6}[/tex]

[tex]\rm Mean(A)= \frac{11900}{6}\\\\\rm Mean(A) = 1983.33[/tex]

For Brand B:

The number of hours per lightbulb:

1200, 1400, 1600, 1800, 2000

Mean for brand B:

[tex]\rm Mean(B) = \frac{Sum \ of \ all \ data \ values}{Number \ of \ data \ in \ the\ set}[/tex]

[tex]\rm Mean(B)= \frac{1200 +1400 +1600 +1800 +2000}{6}[/tex]

[tex]\rm Mean(B)= \frac{8000}{5}\\\\\rm Mean(B) = 1600[/tex]

We can see that:

Mean(A) > Mean(B)

Thus, the mean for brand A is higher than the mean for brand B because the mean for A is 1983.33 and the mean for B is 1600 statement (C) is correct.

Learn more about the mean here:

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Ben in n years old chloe is twice as old as Ben Dan is 5 years younger than Ben
The total of bens age, chloes age, and Dan’s age is T years
Find a formula for T in terms of n

Answers

Answer:

T = 4n - 5

Step-by-step explanation:

Ben = n

Chloe = 2n

Dan = n - 5

n + 2n + (n - 5) = T years

3n + n - 5 = T years

4n - 5 = T years

The selling price of 3 cucumbers is $2.00
complete the table to show the relationship between the number of cucumbers and the selling price, Inter a number in each box
Number of Cucumbers
Selling Price
$2.00
$6.00
12
PLEASE HELP FAST ILL GIVE POINTS AND BRAINIEST

Answers

Answer:

The first blank is 9  for 9 cucumbers

The second blank is 8 dollars

Step-by-step explanation:

We can use ratios to solve

3 cucumbers           x cucumbers

--------------------- = ----------------------

2 dollars                   6 dollars

Using cross products

3*6 = 2x

18 = 2x

Divide by 2

18/2 = 2x/2

9 =x

We need 9 cucumbers

For the third row

3 cucumbers           12 cucumbers

--------------------- = ----------------------

2 dollars                   y dollars

Using cross products

3*y = 2*12

3y = 24

Divide by 3

3y/3 = 24/3

y = 8

We need 8 dollars

i will give lots of points for these 4 answers

Answers

Answer:

1&3 are wrong 4 and 2 are right

Step-by-step explanation:

may i be marked brainliest

What is the distance between (-4, 8) and (12, 8) on the coordinate plane? A 16 units B 8 units C 0 units D 4 units

Answers

Answer:

16 units

Step-by-step explanation:

We need to find the distance between (-4, 8) and (12, 8) on the coordinate plane.

We know that the distance between two points on the coordinate plane is given by :

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

Put x₁ = -4, x₂ = 12, y₁ = 8 and y₂ = 8

So,

[tex]D=\sqrt{(12-(-4))^2+(8-8)^2}\\\\=16\ units[/tex]

So, the distance between the two points is equal to 16 units.

Can someone please help me with this ?

Answers

i believe the area is 704

the area of the square is 484
the area of the triangle is 220
484+220=704

The coordinates of the vertices of the triangle shown are A(2, 13), B(10, 5) and C(12, 14). What is the length of segment AB in units?

Answers

9514 1404 393

Answer:

  8√2 units

Step-by-step explanation:

The distance formula is useful.

  d = √((x2 -x1)² +(y2 -y1)²)

  d = √((10 -2)² +(5 -13)²) = √(64 +64)

  d = 8√2

The length of AB is 8√2 units.

please please i neeed help

Answers

Answer:

i have made it in above picture

hope it helps

A man is three times as old as his daughter. If the difference in their ages is 36 years, find the ages of the father and daughter.

Answers

Answer:

man's age = 54

daughter's age = 18

Step-by-step explanation:

x = man's age

y = daughters age

x = 3y

x - y = 36

substitute for x:

3y -y = 36

2y = 36

y = 18

x = 54

If a man has a daughter who is three times his age. The father and daughter will be 54 and 18, respectively, assuming their ages are 36 years distant.

What is an equation?

Equations are statements that affirm the equivalence of two expressions that are joined by the equals symbol "=". An equal sign ("=") links two expressions together to form an equation. The two expressions on each side of the equals sign are referred to as the "left-hand side" and "right-hand side" of the equation.

It is given that, A man is three times as old as his daughter. If the difference in their ages is 36 years,

We have to find the ages of the father and daughter.

Suppose the age of the father and daughter will be x and y respectively.

If the man is three times as old as his daughter,

x = 3y

If the difference in their ages is 36 years

x - y = 36

Put the value of x as,

3y -y = 36

2y = 36

y = 18

x = 54

Thus, if a man has a daughter who is three times his age. The father and daughter will be 54 and 18, respectively, assuming their ages are 36 years distant.

.Learn more about the equation here,

https://brainly.com/question/10413253

#SPJ2

A baby's weight rose from 19 1/2 pounds to 19 7/8pounds. What was the change in the baby's weight in pounds?

Answers

Answer:

it rose three eighths of a pound

Alternate exterior angles are congruent which angle forms a pair of alternate exterior angles with angle 2?

Answers

Angle 7 is the alternate exterior angle

$1,200 Is Invested in two different accounts paying 6% and 8% Interest. If a total of $81 Interest is earned after one year,
then how much money was Invested at 8%?
$1,200
$750
$450
$800

Answers

Answer:

It would be A

Step-by-step explanation:

please help and explain how you got the answer:)

Answers

using cos to get x

cos -1 of 13/20

= 49.45

then y = 40.54° using sin y= opp /hyp =13\15

then the sin-1 of 13/20 =40.54 •

Can somebody help me?

Answers

Answer:I cannot see photo

The awnser is A Im pretty sure your welcome!!!!

Find the surface area of the cone.Use 3.14 for pi and round your answer to the nearest hundredth

Answers

Answer:

145.0 cm^2

Step-by-step explanation:

Given data

r= 4cm

l= 5cm

h=??

Apply Pythagoras theorem to find h we have

h^2= 4^2+5^2

h^2= 16+25

h^2= 41

h=√41

h= 6.4cm

Substitute into the formula for the surface area of cone

A=πr(r+√h^2+r^2)

A=3.14*4(4+√6.4^2+4^2)

A=12.56(4+√40.96+16)

A=12.56(4+√56.96)

A=12.56(4+7.547)

A=12.56*11.547

A=145.0 cm^2

ab" that goes through points (0,9)
Write an exponential function in the form y
and (5,2187)

Answers

9514 1404 393

Answer:

  y = 9(3^x)

Step-by-step explanation:

We assume you want a function in the form ...

  y = a(b^x)

that passes through points (0, 9) and (5, 2187).

Filling in the given point values, we have ...

  9 = a(b^0) = a

  2187 = a(b^5) = 9(b^5) . . . . using the above value of 'a'

Dividing the second equation by 9 and taking the 5th root, we find b.

  (2187/9) = b^5

  243^(1/5) = b = 3

The exponential function is ...

  y = 9(3^x)

How do you solve for 4-9i/-6i

Answers

Answer:

6i

Step-by-step explanation:

THIS IS 7TH GRADE MATH SO ITS EASY

Answers

Answer:

b

Step-by-step explanation:

i believe it is the second one sorry if im wrong :/

Find the 9th term of the geometric sequence 5, -25, 125, ...

Answers

9514 1404 393

Answer:

  1,953,125

Step-by-step explanation:

The first term is a1 = 5; the common ratio is r = -25/5 = -5. The generic term is ...

  an = a1×r^(n-1)

  an = 5×(-5)^(n-1)

So, the 9th term is ...

  a9 = 5×(-5)^(9-1) = 1,953,125

find the value for x y and z

Answers

Answer:

All triangles add up to 180 degrees so...

180 - 43 - 59 = 78 degrees.

So x - 78 degrees.

x and y are supplementary angles so...

180 - 78 = 102.

So y = 102.

180 - 102 - 49 = 29 degrees

So z = 29 degrees

Hope this helps!

A pair of flip flops is $30. How much will they cost after a 20% discount and 6.5% tax?

Answers

Answer:

$6.39

Step-by-step explanation  

well, 20% of $30 is $6, so then you just have to add on the tax, which is 39 cents, coming to $6.39

Answer:

25.56

Step-by-step explanation:

30 divided by 4 is 6 so 30- 6=24

6.5% of 24=1.56 sooooo           24+1.56=25.56

Mis abuelos ______ profesores de matemáticas. *
son
están
Yo _____ enfermo hoy. *
soy
estoy
Tú ______ en la clase de historia. *
eres
estás
Tomás ______ de Argentina. *
es
está
Ustedes ________ argentinos también. *
son
están
Nosotros ________ muy cansadas. *
somos
estamos
Los libros ________ muy interesantes. *
son
están
Los libros _______ en la biblioteca. *
son
están

Answers

Answer: son, estoy, estas, es, son, estamos, son, estan

Step-by-step explanation:

If it is talking about someone else then try to use, son. Like the first one. For words for yo use words like estoy. I don´t really know how to explain them but they make sense.

What is the value of log, 81?
2
3
4
5

Answers

Answer:

log 81 = 1.90849

Step-by-step explanation:

log 81 = log 9^2 = 2 log 9 = 2(0.95424) = 1.90849

If f(x) = 3x + 5, find f(2).

f(2) = ?

Answers

Answer:

[tex]3 \times 2 + 5 = 6 + 5 = 11[/tex]

will give brainliest <3! please help! no fake answers please

Answers

Answer:

input 1 output 1 ×7 =7

input 2 output 2 ×7 =14

input 3 output 3 ×7=21

input 4 output 4×7=28

Answers are 7, 14, 21 and 28

With individual lines at its various windows, a post office finds that the standard deviation for normally distributed waiting times for customers on Friday afternoon is 7.2 minutes. To test this claim, the post office experiments with a single, main waiting line and finds that for a random sample of 25 customers, the waiting times for customers have a standard deviation of 3.5 minutes. a) With a significance level of 5 percent, conduct an appropriate test on the claim. (State your null hypothesis, test statistic, critical value, decision rule, conclusion) (15 points) b) What is the 95% confidence interval for the population variance

Answers

Answer:

H0 : σ²= 7.2²

H1 : σ² < 7.2

We can conclude that the mean waiting time of customers vary less, Than 7.2 minutes.

Step-by-step explanation:

H0 : σ²= 7.2²

H1 : σ² < 7.2²

The test statistic :

X² = [(n - 1)*s² ÷ σ²]

s² = 3.5

n = sample size = 25. ; s²

X² = [(25 -1)*3.5² ÷ 7.2²

X² = (24 * 3.5^2) / 7.2^2

X² = 5.67

Pvalue from Chisquare statistic :

P(X² < 5.67) = 0.000042

Pvalue < α ; we reject the Null.

Hence, we can conclude that the mean waiting time of customers vary less, Than 7.2 minutes.

What are the center and radius of a circle whose equation is:

(x−A)2+(y−B)2=C
Question options:

a)

Center: (−A,−B), radius = C

b)

Center: (−A,−B), radius =C −−√

c)

Center: (A, B), radius = C

d)

Center: (A, B), radius =C −−√

Answers

Answer:

d)

Step-by-step explanation:

Equation of circle with center at point (h, k) and radius, r.

[tex] (x - h)^2 + (y - k)^2 = r^2 [/tex]

This problem:

(x − A)^2 + (y − B)^2 = C

The center is (A, B).

The radius is sqrt(C).

Answer: d)

Pls help ASAP I’ll pay u 30$ cash. App

Answers

Answer:

how about no

Step-by-step explanation:

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