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]
Find the slope of this graph
What is the value of f(1)?
Answer:
A function normally tells you what y is if you know what x is.
Please help me with this question. I need to submit today. Question number 4. Lhakpa is a name of the person.
Answer:
Known:
width: 1/3
length: 3/5
Ask:
the area of floor?
Solution:
We need to multiply the width and length first!
width × length
= 1/3 × 3/5
= 3/15
= 1/5
Next subtract the number of floor witch has full fraction 1/1, so
= 1/1 - 1/5
= 5/5 - 1/5
= 4/5
So, the area of the floor is 4/5
hope it helps ^°^
What is the value of (-3 + 3) + (-2 + 3)?
0-5 - 61
D-5 + Bi
5 + 61
5-61
Answer:
1
Step-by-step explanation:
(-3 + 3) + (-2 + 3) =
= 0 + 1
= 1
Pls answer I need help please give me an answer and a explanation
Answer:y=4x
Step-by-step explanation:
Answer:
4x = y
Step-by-step explanation:
Since we see that "X" multiplied by 4 is "Y" in every pattern,
we get the equation that 4 times of x (4x) is equal to the corresponding y.
and Thus we have the final answer of 4x = y.
Hope this helps!
this is just a personal question if i have 47 assignments to do and i have to finish by the 20th of august how many do i need to do a day
Answer:
Hey there!
Today is August 7th, 2020.
Thus, August 20th is in 13 days.
If you have 47 assignments, you would have to do 3-4 a day to finish on time.
Hope this helps :) And good luck with your assignments.
Answer:
You have to do about 3 and a half assements a day.
Step-by-step explanation:
Just do 47 divides by 20 but since it is the 7th do 47 divides by 13
Have a nice day!
What is -8.64 -0.024?
360
- 36
-360
36
Answer:
(-8.64) / (-0.024) = 360
Step-by-step explanation:
You have to type like this in your question;
(-8.64) / (-0.024)
or [tex]\frac{-0.024}{-8.64}[/tex].
Bye!
f(x)2x/x+3,x≠-3 can somebody please explain.
Answer:
x cannot equal -3 because if -3 is plugged in for x, there will be a zero in the denominator and you cannot divide by 0
Sala earns 12 dollars each hour working part-time at a bookstore. She earns one additional dollar for each book that she sells. Let A be the amount (in dollars) that Salma earns in an hour if she sells B books. Write an equation relating A to B. Then graph your equation using the axes below.
Answer:
y=12a+b
Step-by-step explanation:
Someone pls help . Thank you sm ! i forgot how to do this lol .
Answer:
x = - 20, h = 34
Step-by-step explanation:
i can't tell ypou what the class period is, but for -x = 20, multiply each side by -1, then you get x = -20
-32 = 2-h
+32 . +32
0=34-h
+h . +h
34=h
flip
h=34
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;
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If you're good at bearings please help meeeeee with full working out tyyyyyy
Jill paid $36 for calendars marked down $5 apiece from the original price, she could have gotten 5 fewer calendars. How many cards did she buy
Answer:
she bought 7 cards
Step-by-step explanation
7x5=35 and im sure there is tax
Sasha deposited $1,400 in an account that pays 1.5% simple interest. She created a graph of her
account balance equation (A = Prt + P) with a slope of 21.
true or false?
Answer:
The answer is False.
To make a large poster of the bill of rights to hang on the classroom wall, a poster that is 22 inches by 46 inches is copied. In the classroom version is to be 3 1/2 times scale, what are the dimensions of the new document? PLEASE ANSWER QUICKLY WILL GIVE BRAINLIEST WHOEVER ANSWERS FIRST!! MUST BE CORRECT!!!!
Answer:
77 inches by 161 inches
Step-by-step explanation:
This is because you need to multiply 22 by 3.5(3 1/2) and the answer you get is 77 then you multiply 46 by 3 1/2 and the answer you get is 161.
So the dimensions of the new document is 77 inches by 161 inches.
5. Given that x=-2 is a zero of P(x)=2x3 + x² - 1 1x –10, factor
P(x) as a product of its linear factors. Then find the other zeros.
Step-by-step explanation:
x = -2 is a zero, so x + 2 is a factor of P(x).
Use grouping to factor.
P(x) = 2x³ + x² − 11x − 10
P(x) = 2x³ + 4x² − 3x² − 11x − 10
P(x) = 2x² (x + 2) − (3x² + 11x + 10)
P(x) = 2x² (x + 2) − (x + 2) (3x + 5)
P(x) = (x + 2) (2x² − (3x + 5))
P(x) = (x + 2) (2x² − 3x − 5)
P(x) = (x + 2) (x + 1) (2x − 5)
The other zeros are x = -1 and x = 5/2.
hey im sry if im asking to many questions i really want help
Answer:
V= 6,000 cm^3
Step-by-step explanation:
(15*20*10) + (10*20*15)
3000 + 3000
6000 cm^3
Answer:
6000 cm³
Step-by-step explanation:
20 * 10 * 15 + (20 * 10 * 15) = 6000 cm³
Whats 7 over 10m plus 9 plus 3 over 1 I need help
Answer:
12.7
Step-by-step explanation:
(7/10)+((9+3)/1)
(0.7)+(12)
12.7
Amir drove from Jerusalem down to the lowest place on Earth, the Dead Sea, descending at a rate of 12 meters per minute. He was at sea level after 30 minutes of driving. Graph the relationship between Amir's altitude relative to sea level (in meters) and time (in minutes).
Answer:
Graph these two points: (0, 360), (30, 0)
Step-by-step explanation:
Since Amir drove for 30 minutes at a rate of 12 meters, that means that he started at an elevation of 360 feet. The easiest way to graph this, is to place one dot at (0, 360), and at (30, 0).
The straight line joining the points (0, 360) and (30, 0) will be the graph.
What is the equation of a straight line? What do you mean by domain and range of a linear function?The general equation of a straight line is -
y = mx + c
where -
[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.
Other possible equations of lines are -
(y - y₁) = m(x - x₁) {Point - slope form}
(y - y₁) = (y₂ - y₁) × (x - x₁)/(x₂ - x₁) {Two point - slope form}
x/a + y/b = 1 {intercept form}
x cos(β) + y sin(β) = L {Normal form}
For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.
We have Amir who drove from Jerusalem down to the lowest place on Earth, the Dead Sea, descending at a rate of 12 meters per minute. He was at sea level after 30 minutes of driving.
We can write the equation of graph as -
y = - 12t + 360
At t = 0 -
y = 0 + 360
y = 360
and
at t = 30 minutes -
y = - 12 x 30 + 360
y = - 360 + 360
y = 0
The straight line joining the points (0, 360) and (30, 0) will be the graph.
Therefore, the straight line joining the points (0, 360) and (30, 0) will be the graph.
To solve more questions on straight lines, visit the link below-
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Which linear inequality is represented by the graph?
y
Answer:
the third one
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
wat is (12+6-5*3)*(2*2+1-7+2)=
Answer:
[tex]\huge\boxed{0}[/tex]
Step-by-step explanation:
First we have to do the operation of multiplication
=> (12+6-15)*(4+1-7+2)
Now, Solving the terms inside the brackets
=> (18-15)*(5-7+2)
=> (3)*(-2+2)
=> (3)*(0)
=> 0
Answer:
[tex]\Huge \boxed{{0}}[/tex]
Step-by-step explanation:
[tex](12+6-5*3)*(2*2+1-7+2)[/tex]
Solve brackets.
[tex](12+6-15)*(4+1-7+2)[/tex]
[tex](3)*(0)[/tex]
Multiply both numbers.
[tex]3 \times 0 = 0[/tex]
The steepness or grade of a road is expressed as a percent. if a road rises 6feet for every 24 horizontal feet. What is the slope of the road? what percent grade is this ?
Answer:
25%
Step-by-step explanation:
The ratio of rise to run is ...
rise/run = 6 ft/24 ft = 1/4
Expressed as a percentage, this is ...
1/4 × 100% = 25%
_____
Comment on this grade
Interstate highways are limited to a 7% grade. Most local jurisdictions limit the grade of a road to somewhere between 12% and 15%.
A state highway department uses a salt storage enclosure that is in the shape of a cone, as shown above. If the volume of the storage enclosure is 48π m3, then what is the diameter of the base of the cone, in meters?
Answer:
Diameter of the base of the cone = 8 meters
Step-by-step explanation:
State highway department uses a salt storage enclosure which is in the shape of a cone.
Height of the storage in conical shape = 9 meters
Volume of the storage = 48π m³
Let the radius of this conical storage = r meters
Formula to get the volume of a cone = [tex]\frac{1}{3}\pi r^{2}h[/tex]
Here 'r' is the radius of the base of the cone and 'h' is the height of the cone.
Therefore, Volume = [tex]\frac{1}{3}(\pi ) r^{2}(9)[/tex]
[tex]48\pi=3\pi r^{2}[/tex]
r² = [tex]\frac{48\pi }{3\pi }[/tex]
r = [tex]\sqrt{16}[/tex]
r = 4 meters
Since, diameter = 2r
= 2(4)
= 8 meters
Therefore, diameter of the base of the cone = 8 metres
Sam can paint the house in 7 days by himself, while Betty can paint the same house in 42 days. How long would it take Sam and Betty to paint the same house together?
Answer:
It would take 6 days for Sam and Betty to paint the same house together.
Step-by-step explanation:
Let x represent the time it takes ( in days ) to complete painting the house working together. Our approach here is to add the rates of the two people, equal to the total rate, or 1 / 7.
Sam's rate = 1 / 7 ( 7 days to paint 1 house ),
Betty's rate = 1 / 42 ( 42 days to paint 1 house )
1 / 7 + 1 / 42 = 1 / x - now let us solve for x, our solution
1 / 7 + 1 / 42 = 1 / x ( multiply either side by 42x )
7x = 42,
x = 42 / 7 = 6 days
If you transform x2 + y2 = 25 into 4x2 + 4y2 = 25, which option below describes the effect of this transformation on the radius? A. It multiplies the radius by 2. B.It multiplies the radius by 4. C.It divides the radius by 4. D.It divides the radius by 2.
Answer:
C. It divides the radius by 4.
Step-by-step explanation:
We have x2 + y2 = 25.
If all terms were multiplied by 4, we would have 4x2 + 4y2 = 100. But, the radius is 25 units. 100 / 25 = 4. So, the radius was divided by 4.
Hope this helps!
Graph the line with the slope 1/3 that contains the point (-4, -3)
Answer:
So, 1 point is on (-4, -3)
Other point is on (-4, -7)
Step-by-step explanation:
Slope = y/x - y1/x1
=> -3 / -4 - ? = 1/3
=> -3 / -4 - 1/3 = ?
=> -3 -1 / -4 - 3
=> -4 / -7
So, -3 / -4 - (-4 / -7)
=> -3 +4 / -4 + 7
=> 1/3
So 1 point is on (-4 , -3)
Other point is on (-4, -7)
Answer:no
Step-by-step explanation:
No
The two points on the coordinate plane represent Jane's house and her friend's house. Find the distance between the houses. Question 3 options: A) units B) units C) units D) units
Answer:
8.3
Step-by-step explanation:
To do this use the distance formula
[tex]d = \sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]
First find the coordinates Jane (-5, -2) Friend (3, -4)
Now solve for d (8.246)
Answer:
10 units or approx. 8.25 units
Step-by-step explanation:
Jane's house is at coordinate (-5,-2) and her friend's house is at coordinate (3,-4).
You can find the answer in 2 ways.
1) Hypotenuse (the diagonal side or side across from the right angle) - approx. 8.25 units
2) Down and Side (go down 2 units and go side 8 units) - 10 units
Hope that helps and maybe earns a brainliest!
Have great day ahead! :)
Calculate the surface area of a cube when the length of a side a = 15cm.
Surface area = 6a^2
Answer:
[tex]\boxed{ \sf 1350 \ cm^2}[/tex]
Step-by-step explanation:
Surface area of a cube = 6a²
a = side length
The side length is given 15 cm.
[tex]6(15)^2[/tex]
[tex]6(225)[/tex]
[tex]1350[/tex]
The surface area of the cube is 1350 cm².
Please help me with this geometry question:((
Answer:
x = 13
RQ = 160°
Step-by-step explanation:
Inscribed angles are half the intercepted arc angle.
5x + 15 = ½ (RQ)
RQ = 10x + 30
Arc angles add up to 360°.
10x + 30 + 9x + 17 + 6x − 12 = 360
25x + 35 = 360
25x = 325
x = 13
Therefore, RQ = 160°.
Write the equation for the following table:
X. Y.
0 3
1 7
2 11
3 15
Answer:
[tex] y = 4x + 3 [/tex]
Step-by-step explanation:
The equation of the table of values given can be written as [tex] y = 4x + 3 [/tex] .
When x = 0,
[tex] y = 4(0) + 3 [/tex]
[tex] y = 0 + 3 = 3[/tex] this corresponds with what we have in the table above.
Let's try another.
When x = 2,
[tex] y = 4(2) + 3 [/tex]
[tex] y = 8 + 3 [/tex]
[tex] y = 11 [/tex]
This also corresponds with what we have in the table.
Therefore, the equation of the table given is [tex] y = 4x + 3 [/tex] .
