Answer:
[tex]3 + 3^2 + 3^3 ...+ 3^n = \frac{3(3^n - 1)}{2}[/tex]
Step-by-step explanation:
Given
[tex]3 + 3^2 + 3^3 ...+ 3^n[/tex]
Required
Show that the sum of the series is [tex]\frac{3(3^{n}-1)}{2}[/tex]
The above shows the sum of a geometric series and this will be calculated as shown below;
[tex]S_n = \frac{a(r^n - 1)}{r - 1}[/tex]
Where
a = First term;
[tex]a = 3[/tex]
r = common ratio
[tex]r = \frac{3^2}{3} = \frac{3^3}{3^2}[/tex]
[tex]r = 3[/tex]
Substitute 3 for r and 3 for a in the formula above;
[tex]S_n = \frac{a(r^n - 1)}{r - 1}[/tex] becomes
[tex]S_n = \frac{3(3^n - 1)}{3 - 1}[/tex]
[tex]S_n = \frac{3(3^n - 1)}{2}[/tex]
Hence;
[tex]3 + 3^2 + 3^3 ...+ 3^n = \frac{3(3^n - 1)}{2}[/tex]
I don't know where to place it I'm confused? Would someone help me with this.
Answer:
Step-by-step explanation:
PLEASE ANSWER!!!!!!
Which of the following is true? a) |−4| < 3 b) |−4| < |3| c) |−3| < −4 | d) −3| < |−4|
Answer:
The answer is D
Step-by-step explanation:
the first one is equal to the equation 4 < 3 because of absolute value, second 4 < 3, third 3 < -4, fourth -3 < 4
How many pumpkins are in Leonard's patch?
Answer:
You can do 4+5+8+6+2.
and It is 25.
so, 25 pumpkins!
Step-by-step explanation:
plz give me brainliest.
thank you and have a nice day!
Answer:
[tex]\huge\boxed{ 25\ pumpkins}[/tex]
Step-by-step explanation:
By looking at the given histogram and determining the no. of pumpkins, we get:
Number of Pumpkins = 4 + 5 + 8 + 6 + 2
=> 25 pumpkins
i need the answer plz
Answer:
Step-by-step explanation:
The second answer choice correctly shows the result of multiplying functions m and n together.
WILL GIVE BRAINLY!!!!!! NEED HELP ASAP!!!!!!!! what is the range of f(x)=3^x+9
Answer:
y > 9
Step-by-step explanation:
The range of a function is the interval of all possible y-values that make the function true.
Here, one way to figure this out is to look at a graph of the function (see attachment).
From the graph, we can see that y-values approach very closely the value 9 and then the line rises beyond 9 forever. Thus, we can conclude that the range for f(x) is y > 9.
~ an aesthetics lover
Simplify the expression 2x(4 + x - 9 + 3x)
A. 8x - 10
B. -2x²
C. -10x²
D. 8x² - 10
E. 8x² - 10x
Answer:
E. 8x² - 10x
Step-by-step explanation:
4+x-9+3x
=x+3x+4-9
=4x+4-9
=4x-5
=2x(4x-5)
=8x² - 10x
11. Find the slope of the following coordinate points: (11,4)
and (5.-3)
Answer:
7/6
Step-by-step explanation:
We can find the slope by using the slope formula
m = (y2-y1)/(x2-x1)
= ( -3 -4)/(5 -11)
-7/-6
=7/6
Answer:
7/6
Step-by-step explanation:
m = (y2 - y1)/(x2 - x1)
m = (-3 - 4)/(5 - 11)
m = -7/(-6)
m = 7/6
Which equation could you use to solve for x in the proportion StartFraction 4 over 5 EndFraction = StartFraction 9 over x EndFraction?
Answer:
x = 9x5 / 4
x = 45/4
(either one)
Step-by-step explanation:
[tex]\frac{4}{5}[/tex] = [tex]\frac{9}{x}[/tex]
Multiple known diagonals and divide by number opposite to unknown number (x).
Hope that helped!!! k
Answer:
(b) 4 x = 4 5 is the needed expression to solve for the value of x.
Step-by-step explanation:
Here, the given proportion is simplified as:
4/5=9/x
Now, to simplify any proportion of the form the simplest way is cross multiplication.
So, cross multiplying a/b=c/d -> ad=bc
Similarly cross multiplying 4/5=9/x, we get:
4 (x) = (9) (5)
Solve for x show work plz
Answer:
20
Step-by-step explanation:
We know that ΔBAC and ΔBED are similar becuase of the AA Postulate (they both have a right angle and they both share ∠B). Since AC is 15/3 = 5 times longer than ED, the scale factor is 5 which means AB is 5 times longer than EB. This makes EB = 25 / 5 = 5. Since AB = AE + EB and we know that AB = 25, AE = x and EB = 5, 25 = x + 5 which means x = 20.
Can someone help me out with this one? + add an explanation on how you got the answer? Thanks!
Answer:
Hello,
Answer B: 7
Step-by-step explanation:
In order to find f2), we don't need to know f^(-1) !!!
f(x)=3x+1
f(2)=3*2+1=6+1=7
Answer:
B
Step-by-step explanation:
To evaluate f(-2) plug 2 into f(x) so f(x)=3(2)+1 or 7.
Kara has twenty-four thousand, five hundred sixty stickers in her album.
Raul has 20,000 + 4,000 + 500 + 60 stickers in his collection.
Answer:
they are both the same thing the first one with kara is in numbers and with raul it is in words
Step-by-step explanation:
hope i helped and have a great day :)
A building 50ft tall is on top of a hill A surveyor is at a point on the hill and observes that the angle of elevation to the top of the
building measures 48° and to the bottom of the building is 20°. How far is the surveyor from the bottom of the building?
Answer:
48-20
Step-by-step explanation:
The distance of the surveyor from the bottom of the building is 125.1 feet.
What is the angle of elevation?You look straight parallel to the ground. But when you have to watch something high, then you take your sight up by moving your head up. The angle from horizontal to the point where you stopped your head is called the angle of elevation.
Assume the distance of the surveyor from the bottom of the building is represented by x.
First, we have to know that the Tan of 48° is equal to 1.11.
The equation to get the distance will then be;
tan(48) = 50/h
h = 45.05 feet
Now, tan(20) = 45.05 /x
x = 45.05 / 0.36
x = 125.1 feet
The distance of the surveyor from the bottom of the building is 125.1 feet.
Learn more about trigonometric;
brainly.com/question/21286835
#SPJ5
Identify the function:
1 5
2 20
3 80
4 320
Quadratic function
Can't determine
Linear function
Exponential function
Answer:
Linear function
Step-by-step explanation:
5 x 4 = 20
20 x 4 = 80
80 x 4 = 320
Phillip deposited $5,670 into a savings account 19 years ago. The account has an interest rate of 4.1% and the balance is currently $12,356.04. How often does the
interest compound?
Answer:
$12165.97
Step-by-step explanation:
100 + 4.1 = 104.1%
104.1% = 1.041
$5670 x 1.041^19 = $12165.97
Answer:
daily
Step-by-step explanation:
To answer this try plugging in each type of compund: daily, monthly, quarterly, and annually.
5670(1+0.041/365)^(365*19)
= 12356.04
365= daily
so your answer would be that the interest compounds daily.
A. Only sequence A
B. Only sequence B
C. Both
D. Neither
40 POINTS OMG
Answer:
B. ONLY Sequence B
Step-by-step explanation:
I hope this helped!
help me plz i want help
Answer:
200in²
Step-by-step explanation:
I separated the shaded face into two squares. Both squares would be 10 by 10.
Area of a square: [tex]a=s^2[/tex]
For each square, they have a side of 10 in.
[tex]a=10^2\\\\a=100[/tex]
The area for one square is 100in². This means that for the whole face, which is made out of 2 squares, the area would be 200in².
The second option should be the correct answer.
the first one is supposed to be 1 over 2
1/2(4a+10=2a+
Step-by-step explanation:
1/2(4a+10)=2a
expand
2a+5=2a
-2a -2a
=5
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the
correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag
the item to the trashcan. Click the trashcan to clear all your answers.
Type the expressions as radicals
y3/5
Answer:
[tex]\sqrt[5]{y^3}[/tex]
Step-by-step explanation:
[tex]y^{3/5}[/tex] is simply [tex]\sqrt[5]{y^3}[/tex]
i’ll mark you brainliest, please show work!! i’ll also give more points
Answer:
414
Step-by-step explanation
80+10hrs=230
23bacteria:1hr
414bacteria:18hrs
NEED HELP PLEASE
A football is kicked at 40 yards away from a goal post that is 10 feet high. Its path is modeled by y = -0.03x 2 + 1.6x, where x is the horizontal distance in yards traveled by the football and y is the corresponding height above the ground in feet.
Does the football go over the goal post? How far above or below the goal post is the football? Use two or more complete sentences to explain your answers. (Hint: The unit conversion is built into the given function.)
Answer:
It goes over the goal post by 6 feet
Step-by-step explanation:
The football will be at the same x position as the goal when x = 40. When x = 40, y = -0.03 * 40² + 1.6 * 40 = 16. The height of the goal post can be represented by the equation y = 10. Since 16 > 10, the football goes over the goal post by 16 - 10 = 6 feet.
May someone help me with this question?(Extra points maybe brainliest for the person who I think helped the most best way.
Answer:
15
Step-by-step explanation:
The distance from (-2,1) to (6,1) is 8 units
The distance from (6,1) to (6,-3) is 4 units
The distance from (6,-3) to (9,-3) is 3 units
Now add 'em up: 8 + 4 + 3 = 15
The length of the biking trail is 15 units long!
Hope that helps <3
Let X, Y, and Z be points such that [tex]\frac{XZ}{XY} = \frac{ZY}{XY} = \frac{1}{2}.[/tex] If Y = (1, 7), Z = (-1, -7), then what is the sum of the coordinates of $X$?
Answer:
1
Step-by-step explanation:
1
Find the measure of c.
Answer:
140°
Step-by-step explanation:
The circle has a central angle of 80. This means that the arc it intercepts is also 80°. Therefore, the rest of the circle not intercepted by the arc is 360-80=280°
Remember that inscribed angles have one-half of the arc-length it intercepts. We can see that Angle C intercepts the entire circle except for the arc intercepted by Angle O. Therefore, the arc intercepted by Angle C is 280°. This means that Angle C is the half of 280, or 140°.
Please help As soon as possible!
Answer:
10
Step-by-step explanation:
To find the area of a parallelogram you need to use the expression A = bh
When you plug that in it will be 120 = 12b
After this, you need to solve (10)
What is the distance between points A and B on the grid? (the grid is shown in the image). A. 3 units B. 4.5 units C. 5 units D. 5.5 units
=================================================
Explanation:
Since the x coordinates are the same, we can subtract the y coordinates to get
1.5 - (-3.5) = 1.5 + 3.5 = 5
Note how subtracting a negative is the same as adding.
-------
We can subtract in the other order
-3.5 - 1.5 = -5
but we need to make this result positive. A negative distance is not allowed. Absolute value is applied to make the result positive
|-5| = 5
Can you find x for me?
Answer:
x = 120 degrees
Step-by-step explanation:
Since the angle given is 30 and the four lengths given are equal corresponding the angles opposite to their given sides for the top left triangle and bottom right triangle, the corresponding angles are equal and also 30 degrees. Since x is where the top left triangle is, we need an equation to relate x. The sum of all the angles in the top left triangle is 180. So, x + 30 + 30 = 180.
Therefore,
x = 180-30-30 = 120
Answer:
Step-by-step explanation:
There are two equal Angels in the triangle so!
X=180°- (30+30)°
=180-60
=120°
Need Help ASAP!!!!!!!!!!!!!!!!
Which relation is a function? {(–4, –6), (–3, –2), (1, –2), (1, 0)} {(–2, –12), (–2, 0), (–2, 4), (–2, 11)} {(0,1), (0, 2), (1, 2), (1, 3)} {(8, 1), (4, 1), (0,1), (–15, 1)}
Answer:
[tex]\{(8, 1), (4, 1), (0,1), (-15, 1)\}[/tex]
Step-by-step explanation:
Given
[tex]\{(-4, -6), (-3, -2), (1, -2), (1, 0)\}[/tex]
[tex]\{(-2, -12), (-2, 0), (-2, 4), (-2, 11)\}[/tex]
[tex]\{(0,1), (0, 2), (1, 2), (1, 3)\}[/tex]
[tex]\{(8, 1), (4, 1), (0,1), (-15, 1)\}[/tex]
Required
Determine which is a function
A relation is divided into 2; (x,y)
Where x represents the range and y stands for the domain
For a relation to be a function, the x column must be unique; in other words, there must be only one occurrence of x
Testing each of the given options
A. [tex]\{(-4, -6), (-3, -2), (1, -2), (1, 0)\}[/tex]
Start by splitting the relation into x and y columns
[tex](x,y)[/tex]
[tex](-4, -6)[/tex]
[tex](-3, -2)[/tex]
[tex](1, -2)[/tex]
[tex](1, 0)[/tex]
Notice that the third and fourth relation has the same x value of 1;
Hence, this is not a function
B. [tex]\{(-2, -12), (-2, 0), (-2, 4), (-2, 11)\}[/tex]
Start by splitting the relation into x and y columns
[tex](x,y)[/tex]
[tex](-2, -12)[/tex]
[tex](-2, 0)[/tex]
[tex](-2, 4)[/tex]
[tex](-2, 11)[/tex]
Notice that all relations has the same x value of -2;
Hence, this is also not a function
C. [tex]\{(0,1), (0, 2), (1, 2), (1, 3)\}[/tex]
Start by splitting the relation into x and y columns
[tex](x,y)[/tex]
[tex](0, 1)[/tex]
[tex](0, 2)[/tex]
[tex](1, 2)[/tex]
[tex](1, 3)[/tex]
Notice that the first and second relation has the same x value of 0 and the third and fourth relation has the same x value of 1;
Hence, this is also not a function
D. [tex]\{(8, 1), (4, 1), (0,1), (-15, 1)\}[/tex]
Start by splitting the relation into x and y columns
[tex](x,y)[/tex]
[tex](8, 1)[/tex]
[tex](4, 1)[/tex]
[tex](0, 1)[/tex]
[tex](-15, 1)[/tex]
Notice that relation has the unique x values of 8, 4, 0 and -15
Hence, this relation is a function
John and Maria want to repaint one of their living room walls, which is 20 feet long by 15 feet
wide. Each quart of paint covers 100 square feet. How many quarts do you suggest they purchase?
(Section 10.7) (1 point)
Answer:
3 quarts.
Step-by-step explanation:
The wall is 20 feet by 15 feet. That means the area of the wall is 20 * 15 = 300 feet squared. Since one quart of paint covers 100 square feet, they will need to purchase 300 / 100 = 3 quarts of paint.
Hope this helps!
PLEASE NEED HELP ASAP!!!!!!! WILL GIVE BRAINLY!!!!!! what are the domain, range, and asymptote of h(x)=(0.5)^x-9
Answer:
[tex]\mathrm{Domain\:of\:}\:0.5^x-9\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<x<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}\\\\\mathrm{Range\:of\:}0.5^x-9:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)>-9\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-9,\:\infty \:\right)\end{bmatrix}\\\\\mathrm{Asymptotes\:of}\:0.5^x-9:\quad \mathrm{Horizontal}:\:y=-9[/tex]
Step-by-step explanation:
Domain:
The function has no undefined points nor domain constraints. Therefore, the domain is
[tex]...-\infty \:<x<\infty \:[/tex]
Definition: The domain of a function is the set of input or argument values for which the function is real and defined.
_________________________________________________
Range:
[tex]\mathrm{The\:range\:of\:an\:exponential\:function\:of\:the\:form}\:c\cdot \:n^{ax+b}+k\:\mathrm{is}\:\:f\left(x\right)>k\\k=-9[/tex]
[tex]f\left(x\right)>-9[/tex]
Definition: The set of values of the dependent variable for which a function is defined.
_________________________________________________
Asymptotes:
[tex]\mathrm{Vertical\:asymptotes\:of\:}0.5^x-9:\quad \mathrm{None}\\\mathrm{Horizontal\:Asymptotes\:of\:}0.5^x-9:\quad y=-9\\\mathrm{Horizontal}:\:y=-9x^{2}[/tex]