The statement as given is not true. For n = 1, the left side is just the first term, 1, while the right side would be 3(1) - 1 = 2, and 1 ≠ 2.
I think what you meant to write was the equation
1 + 4 + 7 + ... + (3n - 2) = 1/2 n (3n - 1)
which can be easily proved by induction.
For n = 1, we have
1 = 1/2 (1) (3(1) - 1) → 1 = 1
which is of course true.
Now for the inductive step. Assume the equation holds for n = k, so that
1 + 4 + 7 + ... + (3k - 2) = 1/2 k (3k - 1)
and use this to show it holds for n = k + 1.
We would have
1 + 4 + 7 + ... + (3k - 2) + (3(k + 1) - 2)
which reduces to
1/2 k (3k - 1) + (3k + 1)
3/2 k² + 5/2 k + 1
1/2 (3k² + 5k + 2)
1/2 (k + 1) (3k + 2)
which is precisely what the formula gives on the right side for n = k + 1. QED
Convert 245 yards to inches.
Answer:
8820
Step-by-step explanation:
Answer:
245 yards = 8820 inches
Step-by-step explanation:
multiply the length value by 36
In the diagram, ABCD is a parallelogram. The
diagonals of the parallelogram intersect at point T.
HELP
Answer:
A. 100 degrees
Step-by-step explanation:
Given:
[tex] m\angle ABC = 3y + 5 [/tex]
[tex] m\angle ADC = 5y - 45 [/tex]
Required:
[tex] m\angle BCD [/tex]
SOLUTION:
✍️First, create an equation that you will use to find the value of y.
[tex] m\angle ABC = m\angle ADC [/tex] (opposite angles of a parallelogram are congruent to each other)
[tex] 3y + 5 = 5y - 45 [/tex] (substitution)
Collect like terms
[tex] 3y - 5y = -5 - 45 [/tex]
[tex] -2y = -50 [/tex]
Divide both sides by -2
[tex] y = 25 [/tex]
✍️Next, find [tex] m\angle ABC [/tex] and [tex] m\angle ADC [/tex].
[tex] m\angle ABC = 3y + 5 [/tex]
Plug in the value of y
[tex] m\angle ABC = 3(25) + 5 = 75 + 5 = 80 [/tex]
[tex] m\angle ADC = 5y - 45 [/tex]
Plug in the value of y
[tex] m\angle ADC = 5(25) - 45 = 125 - 45 = 80 [/tex]
✍️Next, find [tex] m\angle BCD [/tex].
[tex] m\angle BCD + m\angle ADC = 180 [/tex] (consecutive angles in a parallelogram are supplementary)
[tex] m\angle BCD + 80 = 180 [/tex] (substitution)
Subtract 80 from each side
[tex] m\angle BCD = 180 - 80 [/tex]
✅[tex] m\angle BCD = 100 [/tex]
EXPRESAR CADA UNO DE LOS VALORES NUTRICIONALES DE LA NARANJA COMO FRACCIÓN. cuál es el valor nutricional total de la naranja
Answer:
This question is incomplete. You need to specify each of the nutritional values of the orange which are the following:
Fat: 0.2 Carbohydrates: 21.6 Sugars: 17.2 Proteins: 1.7 Water: 159.6 Dietary Fiber: 4.4Step-by-step explanation:
With this information we know that the total traditional value of an orange is 204.7 grams.
To transform each of these values into a fraction, we must place the same figure without decimals in the numerator and divide by a multiple of 10, with as many zeros as decimals the figure had and then we take the figure to its minimum expression
Fat 0.2 = 2/10 = 1/5 Carbohydrates = 21.6 = 216/10 = 108/5 Sugars = 17.5 = 175/10 = 35/2 Proteins = 1.7 = 17/10 Water = 159.6 = 1596/10 = 798/5 Dietary fiber = 4.4 = 44/10 = 22/5
This brings us to the following total nutritional value of the orange:
Total Nutritional Value = 204.7 = 2047/10
A classroom has 4 bookcases that weigh 174 pounds altogether. If they all weigh the same amount, how much does each bookcase weigh?
Answer:
43.5
Step-by-step explanation:
174/4= 43.5
Hi guys, do you know where i can get multi choice maths questions for year 9 ?? thanks guys
Please look at the picture;;
I thought it was Y=7x-48 and I’m not sure what to do
9514 1404 393
Answer:
y = 7x -48
Step-by-step explanation:
Your answer is correct. You just need to write it in the box without the "y =".
__
The 2-point form of the equation for a line is ...
y = (y2 -y1)/(x2 -1x)(x -x1) +y1
y = (8 -(-6))/(8 -6)(x -6) +(-6)
y = 14/2(x -6) -6
y = 7x -42 -6
y = 7x -48
You probably want your answer to look like ...
[tex]y=\boxed{7x-48}[/tex]
David drove 172 miles in 4 hours. If he drove at a constant rate, how far did
he travel in one hour?
What is the height of a right triangle?
Answer:
b×h/2 b=base h-height so h=2 * area /b.
How much sales tax will be charged at Store B?
Answer:
7 % $94.50(SALES TAX) Question only asks for the SALES TAX THOUGH
Step-by-step explanation:
$1350.00 x .07 =$94.50
$94.50 is your sales tax on B
$1444.50 (total) x 15% gratuity is $1444.50 x .15 = $216.68
$1444.50 + $216.68 =$1661.18
$1661.18 x .02 =$33.22
$1661.18 + $33.22 = $1694.40 Total cost of your computer repair
George and five of his friends are taking a trip to new York they decide to split the cost of the tolls equally if the total cost of the tolls is 21 how much would it be
What is the value of x in the equation 2(8%+4)-6+ 2%= 3(4%+3)+1
O 1
O 3
04.
O 6
Answer:
20 feet
Step-by-step explanation:
The speed of horse A is
The speed of horse B is
We define the speed as distance divided by time.
Given that the horses started the race at the same time (and assuming in the same position) we can write :
After 5 seconds for Horse A :
After 5 seconds, Horse A will have traveled 160 feet
After 5 seconds for Horse B :
After 5 seconds, Horse B will have traveled 140 feet
The difference between the distances :
is how much farther Horse A will have traveled.
After 5 seconds, The Horse A will have traveled 20 feet farther than the Horse B.
douwdek0 and 17 more users found this answer helpful
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Hi!!!! HOW IS EVERY ONE TODAY?????
HELP ME PLEASE IM DUMB
Help me please, plato math test
Write a polynomial function that has the zeros -3, 1, -1 and has a leading coefficient of 1.
Write an equation in slope-intercept form (y = mx + b) for the line that has a y-intercept of (0, -5) and a slope of 2/3
what is the value of p?
You mix 2 pints of blue paint for every 5 pints of red paint to make purple paint. You use 18 pints of red paint. How much purple paint do you make?
FREE POINTS& just spam me with fried requests XDDDD
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Step-by-step explanation:
I need to know if this is correct
i thinks its correct.
1. Classify the quotient of -35+ -5 as
positive or negative.
Answer:
-40
Step-by-step explanation:
-35+-5
-35-5
=-40
P.S. You said quotient, a quotient is the answer to a division problem.
Hope this helped! :)
It took Scott an hour more than twice as long as Kim to complete his homework. Which expression shows the time it took for Scott to complete his homework in comparison to Kim
Answer:
2x + 1 = y
Step-by-step explanation:
x = Kim
y = Scott's time.
If F(x) =
2x-3/5
which of the following is the inverse of F(x)?
let the f(x) be x
2x-3/5=y
or,2x-3= 5y
or, x= 2y-3/5
inter changing the relation of x and y
x= 2y-3/5
:. f(x)= 2x-3/5
Step-by-step explanation:
2y-3/5 is the inverse of f(x)
What are the zeros of this function?
MAFS.912.G-C0.3.10
If TW = VW = 23, TU = y + 24 and UV = 9y, what is the value of y?
w
(please answer and give me the work) i have until 8 AM
Answer:
y = 3
Step-by-step explanation:
Given that,
TW = VW = 23,
TU = y + 24,
UV = 9y
∆TWU and ∆VWU are congruent by SAS Congruence Theorem.
Therefore:
TU = UV
y + 24 = 9y (substitution)
Subtract y from each side
24 = 9y - y
24 = 8y
Divide both sides by 8
24/8 = 8y/8
3 = y
y = 3
what fraction breaks 48 into 8 equal pieces
Answer:
48/6 = 8
Step-by-step explanation:
Find the gcf for 18 36 81
Answer:
9
Step-by-step explanation:
Factors of 18 : 1,2,3,6,9,18
Factors of 36: 1,2,3,4,6,9...
Factors of 81: 1,3,9...
One year after you buy a tree, it is 12 feet tall. Each year after you buy the tree, it grows 4 feet. Write a function that represents the arithmetic sequence. How long does it take for the tree to reach its maximum height of 28 feet?
Answer:
5 years
Step-by-step explanation:
Since the tree grows 4 feet every single year and the second year it was 12 feet tall then that means that when you bought the tree it was 8 feet tall (12-4 = 8). Therefore, using these values we can write an equation to calculate the number of years it will take for the height of the tree to be 28 feet. We do this by multiplying 4ft by the variable of a number of years (x) and then adding that product to 8ft which is the initial height. All of which should add up to 28 ft.
28 ft. = 8 ft. + 4x ... subtract both sides by 8
20 ft. = 4x ... divide both sides by 4
5 years = x
Therefore, it will take 5 years from the initial purchase for the tree to be 28ft tall.
What value does point P represent on the number line given?
–3.9
–3.1
–2.9
–0.3
Number line ranging from negative five to five, with the point P labeled between negative two and three
The scale for a map to actual distance is 2 cm to 100 miles. The driving distance on the map between Los Angeles and Las Vegas is 4.5 cm. What is the actual distance in miles between Los Angeles and Las Vegas?
Answer:
225 miles
Step-by-step explanation:
We start by converting it into a fraction, then multiply by the quantity
[tex]\frac{100 miles}{2 cm} *4.5 cm =225 miles[/tex]
13y-2x=3
slope intercept
Answer:
World shown below!
Step-by-step explanation:
Slope-intercept form: y = mx + b
13y - 2x = 3
Add 2x to both sides;
13y = 2x + 3
Divide both sides by 13;
[tex]y = \frac{2}{13}x+\frac{3}{13}[/tex]
Please help I am struggling.
Answer:
16in
Step-by-step explanation:
Answer:
15
Step-by-step explanation:
if you add one you get 15, and
Answer this one please and get free thanks if ur correct!
Answer: Option f i believe
Step-by-step explanation:
♡ The Question ♡
- Which of the following expressions represents the prime factorization of 196?
*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*
☆ The Answer ☆
- F. 2^2 x 7^2
*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*
♡ The Explanation/Step-By-Step ♡
Your positive integer in this is 196, the prime factorization is 2 x 2 x 7 x 7 which in Exponential form is 2^2 x 7^2. Prime[1] = 2, Prime[4] = 7!
This leads to your answer being the first choice, F! Hope this helped!
*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*
☆ Tips ☆
- No tips provided!
What is the slope of the line that runs through points (-16, -9) and (7, 14)?
Answer:
m = 1
Step-by-step explanation:
rise over run
(y2-y1) / (x2- x1)
(14+9)/(7+16)
23/23 = 1
Solve
2x = -16
a.-8
b.8
c.1/8
d.-1/8
Answer:
A
Step-by-step explanation:
The correct answer will be A
Have a great day
PLS hurry You are playing a video game. For each diamond you collect, you earn 125 points. You also earn 200 bonus points by completing the level in less than 2 minutes. You need to earn more than 2700 points to continue on to the next level. Write and solve an inequality that represents the numbers d of diamonds you must collect in less than 2 minutes to advance to the next level.
Answer:
20 diamonds
step-by-step explanation:
2700-200=2500 divided by 125=20
so 20 diamonds
There is triangle ABC triangle XYZ is similar to ABC scale factor 1/4
Answer:
The side that is labeled as 7 is 28 the side that is labeled as 5 shoud be 20 the side that is labeled as 4 should be 16
Step-by-step explanation:
Sorry I cant take a screen shot with my computer but here is the explanation it says that the scale factor is 1/4 so I just did 1/4 ÷ 7,5,and 4
PLEASE HELP ME 10 pts lol
Answer:
-2 83/100 :))))))))))))))
