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]
What is the degree of the following polynomial: . 3x3 + 2x - 4
Answer:
3
Step-by-step explanation:
look for the greatest exponent
Refer to the isosceles trapezoid shown. Find z
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?
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
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
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?
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.
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?
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
BRAINIEST TO WHOEVER RIGHT
A sequence starts 5 10 20 40 80
What is the term to term rule of the sequence?
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?
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?
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?
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-) ?
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?
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
Answer:
D
Step-by-step explanation:
Find the area of the kite below.
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?
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
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,
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
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
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
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
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?
Help please with this math ;-; I beg of you
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
Answer:mode
Step-by-step explanation:5+4+9+9+3+75+1=mode
hey i’ll give brainliest please help
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
Answer:
.....Your answer is D
...
.
What’s this answer ?
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