3 to the power 2x+3 is subtracted by 9 which is equal to 2 times 9 to the power x+1 and is subtrcted by 6

Answers

Answer 1

Answer:

x = -0.5

Step-by-step explanation:

Here we have the sentence:

"3 to the power 2x+3 is subtracted by 9 which is equal to 2 times 9 to the power x+1 and is subtracted by 6"

The first part:

"3 to the power 2x+3 is subtracted by 9..."

This can be written as:

[tex]3^{2x + 3} - 9[/tex]

"... is equal to 2 times 9 to the power x+1 and is subtracted by 6"

[tex]3^{2x + 3} - 9 = 2*9^{x + 1} - 6[/tex]

Let's solve this for x.

First, we can add 9 in both sides:

[tex]3^{2x + 3} = 2*9^{x + 1} - 6 + 9 = 2*9^{x + 1} + 3[/tex]

We also know the relations:

[tex]a^n*a^b = a^{n + b}[/tex]

and

[tex](a^n)^m = a^{n*m}[/tex]

We can write the left part as:

[tex]3^{2x + 3} = 3^{2x}*3^3 = (3^2)^x*3^3 = 9^x*27[/tex]

And the right side as:

[tex]2*9^{x + 1} + 3 = 2*9^x*9 + 3 = 18*9^x + 3[/tex]

Then the equation becomes:

[tex]27*9^x = 18*9^x + 3[/tex]

Now let's move both terms with 9^x to the left side:

[tex]27*9^x - 18*9^x = 3\\[/tex]

[tex](27 - 18)*9^x = 3[/tex]

[tex]9*9^x = 3[/tex]

[tex]9^x = 3/9 = 1/3[/tex]

Now remember that:

Ln(a^b) = b*Ln(a)

Then if we apply the Ln( ) function to both sides, we get:

[tex]Ln(9^x) = Ln(1/3)[/tex]

[tex]x*Ln(9) = Ln(1/3)[/tex]

[tex]x = \frac{Ln(1/3)}{Ln(9)} = -0.5[/tex]


Related Questions

What is the degree of the following polynomial: . 3x3 + 2x - 4

Answers

Answer:

3

Step-by-step explanation:

look for the greatest exponent

Refer to the isosceles trapezoid shown. Find z

Answers

Answer:

look at the picture i sent......

A rectangle has a perimeter of 46 meters and a base of 8 meters. What is the height?​

Answers

Answer:

15 metres

Step-by-step explanation:

perimeter of rectangle = 2(base + height)

=2(8+h) = 46

= 16 + 2h = 46

= 2h = 46 - 16

= 2h = 30

= h = 15

15 metres is the height of rectangle

Find the value of x in the triangle

Answers

Answer:

55+x+74+54=180

183+x=180

x=180-183

x=-3

Step-by-step explanation:

This is the graph of f(x). What is the value of f(2)?
A. 8
O O
B. 4
C. 2
D. 16

Answers

Answer:

c.2

Step-by-step explanation:

f(x)=2 and where is x you place it with 2 and it won't change because there is no another number is the equation of f(X)

What is the domain of the function on the graph?

Answers

Domain is the numbers that the x can be so it will be all real numbers

You notice that another cupboard door is in the shape of a square that is divided into two isosceles triangles. You measure the height of the cupboard to be 16 inches. What is the area of one of the triangles shown on the face of the cupboard door? Show your work. ​

Answers

Answer:

i wrote "13 8/9 because 16 2/3 x 16 2/3= 50/3 x 50/3 = 250/9 then 250/9 ÷ 2 = 125/9 = 13 8/9"

Step-by-step explanation: if u add in some words or something so you teacher isnt sus hope you pass!!

I’m having trouble on this problem, anyone know the answer?

Answers

Answer:

the answer is 35 cm

Step-by-step explanation:

to make sure that you dont have a problem next time here is a formula

area of any polygon is the sum of all sides so 9 + 9 + 12 + 5 = 35

Answer: 66cm^2

To find the area of ABCDE, the two equations you will need are:
Rectangle = l • w
Triangle = (b • h)/2

Since rectangles are symmetrical, we can ignore the triangle for now.

Observe that the left side of the rectangle states 5 cm, and the bottom side states 12 cm. With this information we can infer that:

Area of rectangle is 12cm(5cm) = 60cm^2

Alright, now we can look at the triangle. What we’ll do is subtract 5cm from 9cm to get the height 4 cm; and we’ll subtract 9 cm from 12 cm to get the base 3 cm.

With this information, we can conclude that the area of the triangle (3cm(4cm)/2 = 6cm^2

Adding both the triangle and rectangle area together, we get 66cm^2

BRAINIEST TO WHOEVER RIGHT

Answers

1. is false
2. is true

A sequence starts 5 10 20 40 80
What is the term to term rule of the sequence?

Answers

Answer:

Finding the 6th term is really easy, we can simply double two more times to get 5, 10, 20, 40, 80, 160.

Step-by-step explanation:

A photo booth in the shape of a rectangular prism has edge lengths of 3 ft by 4 ft by 7 ft. What is the volume of the space inside the photo booth?

Answers

Answer:

V=84ft³

Step-by-step explanation:

Answer:

Heyaa!! My name is Pinky and im here to inform you that your answer is...

Step-by-step explanation:

!!! V=84ft³ !!!

My clarification or my work is:

V=w h l= 4· 7· 3 =84ft³

w= Width

L= Length

H= Height

Have an amazing dayy!!

~Pinky~

Here are two rectangular prisms: K, L. K= 6, 4, 5. L=5,5,5 1. Which figure do you think has the longer diagonal. 2. Calculate the lengths of both diagonals. Which one is actually longer?

Answers

Answer:

sorry. I need points.

Step-by-step explanation:

.......................


Steven has 17 baseball caps. He has 2 blue caps and he has 3 more green caps than blue ones. The rest of his caps are black.
How many black caps does Steven have?

Answers

Answer:

12

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Use the equation below to find c, if a = 43 and b = 49. c=180-a-) ?​

Answers

Answer:

88

Step-by-step explanation:

43 + 49= 92.

Then 180 - 92= 88

C= 88

a dog is leashed 48 feet to the corner of a house.howmuch running area does the dog have?​

Answers

Answer:

The dog has 1357.5 square feet of running space.

Step-by-step explanation:

48 feet is the diameter of the circle in which the dog can run, minus 1/4 of the total circle (assuming the dog can not run through walls).

The formula of how to find the area of a circle is...

A =  π r²

A stands for area, pi(π) is 3.14, and r means radius.

Radius is half of the diameter, so the radius would be 24 feet. Let's plug those numbers into the formula:

A = π x 24²

A = π x 576

A = 1809.56 square feet

Now, we have to subtract 1/4 of 1810 (rounded up).

1810 times 0.75 = 1357.5 feet.

I hope this helps you! :-)

3. During geometry class, Mr. Jones constructed the perpendicular bisector of segment AB as
shown below.

If AC = 4x + 12 and BC = 2x + 18, find AB.
A. 3
B. 6
C. 24
D. 48

Answers

Answer:

D

Step-by-step explanation:

Find the area of the kite below.

Answers

Answer:

160 unit^2.

Step-by-step explanation:

Area = xy/2 where x and y are the length of the diagonals, so here:

Area = (16*20)/2

= 320/2

= 160.

What is the solution to the system of linear equations graphed below?

Answers

Answer:

(1/2,4)

Step-by-step explanation:

because that is where the line crosses each other

the x is 1/2

the y is 4

pleas help due to night​​

Answers

Answer:

w = 28.4 yds

Step-by-step explanation:

P = 12.7 + 4 + 2w

73.5 = 16.7 + 2w

56.8 = 2w

w = 56.8/2

w = 28.4

Answer:

w = 28.4 yards. Sorry need the points.

Median of 93 87, 81, 80, 78, 95, 83, 81, 76, 74, 88, 86, 85, 76, 60,

Answers

Answer:

The answer is median :81

Step-by-step explanation:

5. In the regular decagon shown, what is the measure of angle 1? *


1 point


One Exterior Angle of a REGULAR Polygon


OneEx 4 = 360


(


18 degrees


O


36 degrees


72 degrees


0


180 degrees

Answers

The image of the hexagon is missing, so i have attached it.

Answer:

∠1 = 36°

Step-by-step explanation:

From the image attached, we can see that the polygon is regular and has 10 sides.

Formula for an interior angle of a regular polygon is;

θ = 180(n - 2)/n

Where n is the number of sides of the polygon.

Thus;

θ = 180(10 - 2)/10

θ = 144°

Now, ∠1 forms a straight line with one of the interior angles of the polygon.

Thus, θ + ∠1 will be equal to 180° because sum of angle on a straight line is 180°

Thus;

144° + ∠1 = 180°

∠1 = 180° - 144°

∠1 = 36°

24% written as a fraction in simplest form

Answers

The answer is 6/25 or 6 over 25

Answer:

6/25

Step-by-step explanation:

According to Math.way 24% converted to the simplest fraction form you would get 6/25.

Hope this helps :)

Find the volume of the prism below.
3 ft
8 ft
6 ft

Answers

Answer:

3: 27

8; 512

6; 216

Step-by-step explanation:

PLEASE HELP! WILL MARK BRAINLIEST!


The path of a seat on a new Ferris wheel is modeled by x = –25sin(StartFraction pi Over 30 EndFraction t) and y = –25cos(StartFraction pi Over 30 EndFraction t) + 30, where distances are measured in feet. What is the maximum height a rider will experience?


50 feet

55 feet

60 feet

80 feet

Answers

Answer:

The maximum height a rider will experience is 55 feet.

Step-by-step explanation:

Let's start writing the function that defines the path of a seat on the new Ferris wheel. This function will depend of the variable ''t'' which is time.

[tex]X(t)=(x,y)[/tex]

In which [tex]X(t)[/tex] are the coordinates of the seat (the x - coordinate and the y - coordinate) that depend from time.

[tex]''x''[/tex] and [tex]''y''[/tex] are functions that depend from the variable ''t''.

For this exercise :

[tex]X(t)=[-25sin(\frac{\pi}{30}t);-25cos(\frac{\pi}{30}t)+30][/tex]

In order to find the maximum height a rider will experience we will study the behaviour of the y - component from the function [tex]X(t)[/tex].

The function to study is [tex]y(t)=-25cos(\frac{\pi}{30}t)+30[/tex]

To find its maximum, we will derivate this function and equalize it to 0. Doing this, we will find the ''critical points'' from the function.

⇒ [tex]y(t)=-25cos(\frac{\pi}{30}t)+30[/tex]  ⇒

[tex]y'(t)=\frac{5}{6}\pi sin(\frac{\pi}{30}t)[/tex]

Now we equalize [tex]y'(t)[/tex] to 0 ⇒

[tex]y'(t)=0[/tex] ⇒ [tex]\frac{5}{6}\pi sin(\frac{\pi}{30}t)=0[/tex]

In this case it is easier to look for the values of ''t'' that verify :

[tex]sin(\frac{\pi}{30}t)=0[/tex]

Now we need to find the values of ''t''. We know that :

[tex]sin(0)=0\\\\sin(\pi)=0\\sin(-\pi)=0[/tex]

Therefore we can write the following equivalent equations :

[tex]\frac{\pi}{30}t=0[/tex] (I)

[tex]\frac{\pi}{30}t=\pi[/tex] (II)

[tex]\frac{\pi}{30}t=-\pi[/tex] (III)

From (I) we obtain [tex]t_{1}=0[/tex]

From (II) we obtain [tex]t_{2}=30[/tex]

And finally from (III) we obtain [tex]t_{3}=-30[/tex]

We found the three critical points of [tex]y(t)[/tex]. To see if they are either maximum or minimum we will use the second derivative test. Let's calculate the second derivate of [tex]y(t)[/tex] :

[tex]y'(t)=\frac{5}{6}\pi sin(\frac{\pi}{30}t)[/tex] ⇒

[tex]y''(t)=\frac{\pi ^{2}}{36}cos(\frac{\pi }{30}t)[/tex]

Now given that we have an arbitrary critical point ''[tex]t_{n}[/tex]'' ⇒

If [tex]y''(t_{n})>0[/tex]  then we will have a minimun at [tex]t_{n}[/tex]

If [tex]y''(t_{n})<0[/tex] then we will have a maximum at [tex]t_{n}[/tex]

Using the second derivative test with [tex]t_{1},t_{2}[/tex] and [tex]t_{3}[/tex] ⇒

[tex]y''(t_{1})=y''(0)=\frac{\pi ^{2}}{36} >0[/tex] ⇒ We have a minimum for [tex]t_{1}=0[/tex]

[tex]y''(t_{2})=y''(30)=\frac{-\pi^{2}}{36}<0[/tex] ⇒ We have a maximum for [tex]t_{2}=30[/tex]

[tex]y''(t_{3})=y''(-30)=\frac{-\pi^{2}}{36}<0[/tex] ⇒ We have a maximum for [tex]t_{3}=-30[/tex]

The last step for this exercise will be to find the values of the maximums.

We can do this by replacing in the equation of [tex]y(t)[/tex] the critical points [tex]t_{2}[/tex] and [tex]t_{3}[/tex] ⇒

[tex]y(t_{2})=y(30)=55[/tex]

[tex]y(t_{3})=y(-30)=55[/tex]

We found out that the maximum height a rider will experience is 55 feet.

Answer:

B

Step-by-step explanation:

3 − –403,593 positive or negative?

Answers

If it’s 3-(-403593), then is should be positive, but if it’s 3+(-403593) then it would be negative

Help please with this math ;-; I beg of you

Answers

Answer:

49 - 9π

Step-by-step explanation:

Area of white portion = area of triangle - area of circle

To find the area of the triangle:

The area of a triangle can be calculated using this formula

[tex]A=\frac{bh}{2}[/tex] where b = base length and h = height

The height given is 7m and the base length given is 14m

That being said we plug in the given values into the formula

[tex]\frac{14*7}{2} \\14*7=98\\\frac{98}{2} =49[/tex]

Hence, the area of the triangle is 49 sq meters.

To find the area of circle

( note that the area is in terms of pi; shown by the answer choices. )

Formula for area of a circle = [tex]A=\pi r^2[/tex]

We are given the diameter  ( 6m )

However, we need the radius

To convert diameter to radius we divide by 2

6/2 = 3 so the radius = 3m

Now we plug in 3 into the formula

[tex]A=\pi 3^2\\3^2=9\\A=9\pi[/tex]

Remember we do not apply pi because the answer should be in terms of pi.

Now we subtract the two

Area of white portion = 49 - 9π

Hence, the answer is A

Answer:

49 - 9π

Step-by-step explanation:

Hope this helps

10 Students were surveyed.
How many hours do you study a week?
8 2 2 6 14 10 3 5 4
Determine the following:
A) Mean
B) Mode
C) Median
Show work please
Will mark brainlisted

Answers

Answer:mode

Step-by-step explanation:5+4+9+9+3+75+1=mode

hey i’ll give brainliest please help

Answers

i believe the answer is the fourth option.

Amy said 4/9 of her teammates got hits during a recent softball game. Which decimal represents this same amount?
A 0.49
B. O 0.444
c. O 0.49
D. 0.444

Answers

Answer:

.....Your answer is D

...

.

What’s this answer ?

Answers

Answer:

12

Step-by-step explanation:

The average rate of change for f(x) in the closed interval [ a, b ] is

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

Here [ a, b ] = [ 1, 3 ] , then

f(b) = f(3) = 27 ← value of y from table for x = 3

f(a) = f(1) = 3 ← value of y from table for x = 1

average rate of change = [tex]\frac{27-3}{3-1}[/tex] = [tex]\frac{24}{2}[/tex] = 12

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