Answers
9514 1404 393
Answer:
next term: 15an = n(n+1)/2Step-by-step explanation:
Each term is the previous term with the current term number added. The 5th term will be 5 + (4th term) = 5 + 10 = 15.
The next term is 15.
_____
The sequence of triangular numbers is given by the explicit formula ...
an = n(n+1)/2
__
Finding the Formula
The sequence of first differences is ...
3 -1 = 2
6 -3 = 3
10 -6 = 4
And the sequence of second differences is ...
3 -2 = 1
4 -3 = 1
These are constant, indicating the sequence is described by a polynomial function of 2nd degree.
There are several ways to find the coefficients of the quadratic function. One is to solve for them using a system of equations.
n = 1
a1 = 1 = a(1)^2 +b(1) + c
n = 2
a2 = 3 = a(2)^2 + b(2) +c
n = 3
a3 = 6 = a(3)^2 +b(3) +c
To solve, we can subtract each equation from the next:
a2 -a1 = (3) -(1) = a(4 -1) +b(2 -1) +c(1 -1)
2 = 3a +b
and
a3 -a2 = (6) -(3) = a(9 -4) +b(3 -2) +c(1 -1)
3 = 5a +b
Now we can subtract the first of these equation from the second:
(3) -(2) = a(5 -3) +b(1 -1) ⇒ 1 = 2a ⇒ a = 1/2
Then ...
2 = 3(1/2) +b
1/2 = b
1 = a + b + c ⇒ 1 = 1/2 + 1/2 + c ⇒ c = 0
So, the quadratic function describing the sequence of triangular numbers is ...
an = (1/2)(n^2 +n)
an = n(n+1)/2
Related Questions
What is 0.68 multiplied by 675?!!!?
Answers
Answer:
459
Step-by-step explanation:
Hope this helped!
Friction is not related to the efficiency of a machine.
True or False
Answers
Answer: False, Step-by-step explanation: Genuine mechanical benefit and ideal mechanical benefit are not equivalent. Valid. Work yield can never be more prominent than work input.
2. Any number that can result from
multiplying our given number by any other
number is a
B. multiple
D. product
A. factor
C. LCM
Answers
Complete the Square
x2 + 10x +
Answers
Answer:
( + 10)
Hope this helps you out
Which expression is equal to
сол
(A
5x8
8 x 5
C8= 5
5=8
Answers
And have a nice day
sebuah pesawat penyelam terbang dengan kecepatan 55.0 m/s dengan ketinggian konatan h 400m dengann gaya gravitasi 9.8 m/s kuadrat.tentukan sudut elevasi !!
help
Answers
Answer:
Step-by-step explanation:
Hand d hands. I Nnendjejw ndndnenend nsdnd nsrjer
5.
Write the slope-intercept form of the equation for the line.
A. y = – 2x – 1
B. y= (1)/(2)x + 1
C. y= (1)/(2)x - 1
D. y = 2x – 1
Answers
The slope is 2, the y-intercept is -1.
$750 at 6% for 3 years
Answers
Answer:
This is your answer ☺️☺️
If mAPW = 20°, then the measure of WPZ is
Answers
Answer:
The answer to the question is 20
because angle ZPA is 90°.
So,
It's 90-20 = 70°.
the mod
784 sq. in
28 in
Approximately how much cardboard did he use in all to make the model?
828 square inches
1,092 square inches
О
1,400 square inches
o
2,016 square inches
о
Answers
Answer:
Step-by-step explanation:
base = 784 sq in² 28 in tall pyramid
each side of the square base = √784 also equals 28
using the Pythagorean theorem the length of each side of the pyramid from the base to the point is
(side/2)² + height² =( length of the pyramid face)²
(28/2)² + 28² = 196 + 784 = 980 = (face length)²
face length = √980 = 31.3
area of the pyramid = 4 sides × area of each face + the area of the base
= 4×[(1/2)(base)(face length)] + side²
= 4(1/2)(28)(31.3) + 784
= 2537 sq in² Not in the solution set
help me plsssssssssssss
Answers
9514 1404 393
Answer:
(a) $2.857 million
(b) vertical compression by 1/3; shift left by 6; shift up by 2
Step-by-step explanation:
(a) Find the year difference (2021-2010=11) and put that value where x is. Then do the arithmetic.
g(11) = (∛(11+6))/3 +2 = (∛17)/3 +2 ≈ 2.57128/3 +2 ≈ 0.857 +2
g(11) ≈ 2.857 . . . 2021 revenue in millions of dollars
__
(b) For parent function f(x), the transformation ...
g(x) = a·f(x -h) +k
represents a vertical scaling by a factor of 'a', right shift by h units, and up shift by k units.
Comparing this form to the given g(x), we see ...
a = 1/3 . . . vertical compression by a factor of 1/3
h = -6 . . . .right shift 6 units
k = 2 . . . . up shift 2 units
_____
Additional comment
The vertical scaling is called "compression" when the scale factor is less than 1, and "stretch" when the scale factor is greater than 1. Here, the scale factor of 1/3 means the graph is vertically compressed.
A penguin walks 10 feet in 6 seconds. At this speed how far does the penguin walk in 45 seconds?
Answers
Answer:
The penguin will walk 75.15 feet in 45 seconds. It will take the penguin 26.95 seconds to walk 45 feet
Step-by-step explanation:
hope it helps !
Answer: 75 feet
Step-by-step explanation:
Question #4. A $25 baseball hat is on sale for 25% off. What is the sale
price?
Answers
the sale price is $18.75
simplify to the lowest terms
Answers
Answer:
1/2
Step-by-step explanation:
divide the numerator & denominator by 4
"Please help!" Find the range of the data in the box plot below.
Answers
Answer:
12
Step-by-step explanation:
the range is the difference between the highest and lowest data value
the lowest data value is zero and the highest is twelve
Factor completely 64x2
Answers
Step-by-step explanation:
not factorable....rational numbers
PLS HELP, WILL REWARD BRAINLIEST ASAP :)
Answers
A circle has a radius of 50 cm. Which of these is closest to its area?
Answers
Answer:
Approximately 7853.98
Step-by-step explanation:
The formula to finding the area of a circle based on radius is [tex]\pi r^2\\[/tex], where r is radius. Hope this helped :D
I purchased a new book that was on sale for 40% off. I saved $24.00 because of the sale. What was the original price? (6 points)
Pls Answer I need it for my test thats due Monday
Answers
Answer:
60
Step-by-step explanation:
24 dividend by 4 equals 6.
this means 10% of the original price is 6.
6 times 10 equals 60
hope this helps!!!
A turtle and a snail are 300 feet apart when they start moving towards each other. The
turtle is moving at a speed of 5 feet per minute, and the snail is moving at a speed of 1
foot per minute.
How fast are they approaching each other?
Answers
Answer:
6 feet per minute
Step-by-step explanation:
Answer:
6 feet per minute.
Step-by-step explanation:
5ft + 1ft = 6ft per minute.
can someone help me with these problems I don't get it very well
Answers
this is my answer but you need to check with your teacher
Answer:
25 & 26Complementary angles sum to 90°Angle:
90° - 47° = 43°Find x
2x -3 = 432x = 46x = 2327 & 28Vertical angles are congruentAngle
82°Find y
5y + 12 = 825y = 70y = 1429 & 30Adjacent angles forming a straight line are supplementary and sum to 180°Angle:
180° - 115° = 65°Find n:
4n - 5 = 654n = 70n = 17.531 & 32Angle addition postulate
∠XYZ = ∠XYW + ∠WYZAngle
m∠XYW = 110° - 72° = 38°Find x:
3x + 2 = 383x = 36x = 1233 & 34Complementary and vertical angles (mentioned above)Angle
90° - 35° = 55°Find n:
5n = 55n = 11c) Work out
√6 x √6 x √6
Answers
Answer:
√6 × √6 × √6 = 6√6
Step-by-step explanation:
[tex] \rm \sqrt{6} \times \sqrt{6} \times \sqrt{6} [/tex]
[tex] \rm = \sqrt{36} \times \sqrt{6} [/tex]
[tex] \blue{\boxed{\rm = 6 \sqrt{6} }}[/tex]
2(x+11)=3x=42simplify
Answers
Answer:
2x+22=42
Step-by-step explanation:
2x+22-22=42-22. which is 2x=20 divide both sides with 2,therefore the answer is 10
Un contenedor de 120 lt de capacidad contiene 90 lt de un líquido ¿que porcebtaje de la capacidad del tanque está desocupado
Answers
Answer:
25%
Step-by-step explanation:
Paso 1
Calcula la cantidad del contenedor que no estaba ocupado.
Esto se calcula como
Tamaño del recipiente: cantidad de líquido en el recipiente
= 120 lt - 90lt
= 30 litros
Paso 2
El porcentaje de la capacidad del tanque que está desocupado se calcula como:
= Capacidad del tanque que estaba desocupado / Capacidad del tanque × 100
= 30lt / 120lt × 100
= 25%
i just need the equation!
Answers
Answer:
let the no. of students in art class be x
then
9+4x=101
now u can solve it! u will get x = 23
Let's say that a cell phone provider offers a new phone for $600 with a
$70 monthly plan. Find the equation that represents the average cost of
the phone, C(x), to use for x amount of months.
Can someone please answer this?
Answers
Answer:
Total=600+70(x)
The average cost of the phone is C(x) = (600 + 70x)/x.
How to calculate the average?In order to calculate average, divide the total sum of the data to the total number of data. An average is a standard number for a given data whose value can both be more or less than it.
Given that,
The fixed price of the cellphone is $600.
And, the monthly plan is $70.
Now, the cost of the phone increases with the number of months and the average cost is the total cost divided by the number of months.
As per the question the average cost can be written as,
C(x) = (600 + 70x)/x
Where x is the number of months.
Hence, the average cost of the given phone can be written in terms of the function of month as C(x) = (600 + 70x)/x.
To know more about average click on,
https://brainly.com/question/12322912
#SPJ2
A numerical expression is evaluated as shown.
32 ÷ {57 – 49} × 4 + 27
Step 1: 32 ÷ 8 × 4 + 27
Step 2: 32 ÷ 32 + 27
Step 3: 1 + 27
Step 4: 28
In which step does a mistake first appear?
Answers
Answer:
step 2
Step-by-step explanation:
BODMAS they multiplied first instead of dividing
Six more than the quotient of a number be in 30 is greater than three
Answers
Answer: 14
Step-by-step explanation: To get this answer you would first of all 6 more means we're adding.
Quotient means division. What we're dividing is an unknown quantity -- x -- and 3.
The final total says 14. That gives us the following:
6 + x/3 = 14
Mr. Choe solved the inequality and his work is shown below. 3x+5≤−1 −5 −5 3x≤−6 ÷3 ÷3 x≥−2 Identify and explain Mr. Choe's error.
Answers
Answer:
x ≤ - 2
Step-by-step explanation:
Given the inequality :
3x+5≤−1
Subtract 5 from both sides
3x + 5 - 5 ≤ - 1 - 5
3x ≤ - 6
Divide both sides by 3
3x/3 ≤ - 6/3
x ≤ - 2
Mr.Choe's error was that he changed the inequality sign. The inequality sign in this case does not need to be changed.
please help me with these questions!!!!!!
Answers
Step-by-step explanation:
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