We can find a formula for nth term of the given sequence as follows:
1, 5, 12, 22, 35
The 1st differences between terms:
4, 7, 10, 13
The 2nd differences :
3, 3, 3
Since it takes two rounds of differences to arrive at a constant difference between terms, the nth term will be a 2nd degree polynomial of the form: [tex]a n^2 + b n + c[/tex], where c is a constant. The coefficients a, b, and the constant c can be found.
We can form the following 3 equations with 3 unknowns a, b, c:
[tex]1 = a\cdot1^2 + b\cdot1 + c\\5 = \cdot2^2 + b\cdot2 + c\\12 = a\cdot3^2 + b\cdot3 + c[/tex]
Solving for a, b, c, we get:
a = 3/2, b = -1/2, c = 0
Therefore, the nth term of the given sequence is:
[tex]\boxed{ a_n = \dfrac{3}{2}n^2- \dfrac{1}{2} n}[/tex]
please help me I'm going to fail if you don't help me
Answer:
B
Step-by-step explanation:
Shigaraki told me
Select the correct answer from each drop-down menu. The table represents function f, and the graph represents function g.
The line of symmetry for function F is _____
A.Y=9
B.X=-2
C.X=2
D.Y=9
and the line os symmetry for function G is____
A.x=1
B.y=7
C.x=-1
D.y=-7
The y-intercept of function F is____
A.less than
B.equal to
C.greater than
The y-intercept of function G.
Over the interval [2,4] the average rate of change of function F is _____
A.greater than
B.equal to
C.less than.
the average rate of change of function G.
Thank you and I'm sorry for take your time.
I appreciate you
Answer:
1) -9 (this is where the y values stop and 'go the other way')
2) 1 (this is where the y values also stop and 'go the other way')
3) greater than (the y intercept on a table is found by looking where x = 0 and seeing what y equals. on a graph its just where the line crosses the y axis)
4) less than (idrk know how to explain this one sorry)
Step-by-step explanation:
hope this helps <3
Answer:
The line of symmetry for function f is
x = 2 and the line of symmetry for function g is x = 1
.
The y-intercept of function f is greater than
the y-intercept of function g.
Over the interval [2, 4], the average rate of change of function f is
less than the average rate of change of function g.
Step-by-step explanation:
please help with this
Answer:
[tex]S_{n}[/tex] = n² + 4n ; n = 11
Step-by-step explanation:
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [2 [tex]a_{1}[/tex] + (n - 1)d]
~~~~~~~~~
[tex]a_{1}[/tex] = 5
d = 7 - 5 = 2
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2(5) + 2(n - 1)] = [tex]\frac{n}{2}[/tex] ( 8 + 2n ) = 4n + n²
[tex]S_{n}[/tex] = n² + 4n
n² + 4n = 165
n² + 4n - 165 = 0
(n + 15)(n - 11) = 0 ( n ≥ 0 ) ⇒ n = 11
Which system of equations has no solution?
A.
y = 7x +5
y = 7x + 5
B.
3x - 5y = 10
-3x + 5y = -10
C.
y = 3x - 2
y = 3x + 5
D.
3x - 5y = 10
-3x - 2y = 20
Answer:
A
Step-by-step explanation:
Evaluate. 4³ +8² = ?
Answer: 128
Work: I just did 4 to the power of 3 which is 64, and I did 8 to the power of 2 which is also 64. 64 + 64 = 128, which is the answer. I hope this helps, and stay safe. :)
The sum of two consecutive integers is 199. Find the integers
The two consecutive integers will be 99 and 100.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
The sum of two consecutive integers is 199.
Let the first number be x and the next consecutive number will be (x + 1). Then the equation will be
x + x + 1 = 199
2x = 199 - 1
2x = 198
x = 198 / 2
x = 99
Then the two consecutive integers will be 99 and 100.
More about the Algebra link is given below.
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Simplify the expression and choose the appropriate result.
3(2 + 3g)
Solve forX
9(x + 1) = 25 + x
Ox=2
Ox=3
Ox=4
Ox=5
Answer:
x=2
Step-by-step explanation:
9x+9=25+x
subtract 9 on both sides
9x=16+x
subtract x on both sides
x=2
The solution of equation 9(x + 1) = 25 + x is x =2, which is option A.
What is an equation?An equation is a pair of algebraic equations with the equal sign (=) in the middle and the same value.
Given information:
The equation is 9(x + 1) = 25 + x.
To solve for x, we need to isolate x on one side of the equation.
9(x + 1) = 25 + x
First, we can distribute the 9:
9x + 9 = 25 + x
Next, we can simplify by subtracting x and 9 from both sides:
8x = 16
Finally, we can solve for x by dividing both sides by 8:
x = 2
Therefore, the solution is x = 2.
To learn more about the equation;
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0.4,0.7,1.0,1.3 what is the sequence rule
Answer:
3 plus 3, that is the sequence
A jar contains 24 blue marbles 16 red marbles and 14 white marbles find the simplified ratio of total marbles to red marbles
Answer:
27:2
Step-by-step explanation:
can someone help please
dijkstra's algorithm
Step-by-step explanation:
Answer my question....Bdjsdjrrnnrnnddddsnjjejjeje
What is the solution to the equation 9(x + 2) = 27? (1 point) Group of answer choices x = 2.5 x = 0.5 x = −0.5 x = −3.5
Answer:
Well i got 1
Step-by-step explanation:
because you need to take 9*x and 9*2
9x + 18= 27
-18 -18
9x =9 divide by 9 on each side and get one
True or False?
The sample space is a collection of outcomes from an event?
the force of gravity depends on the distance between objects? true or false
Answer:
True
Step-by-step explanation:
It depends on two factors :mass of the objects and distance between the objects
hope this will help u
solve the following equation for y
x+y=3
9514 1404 393
Answer:
y = 3 -x
Step-by-step explanation:
Subtract x from both sides of the equation.
x -x +y = 3 -x
y = 3 - x
Answer:
y=3-x
explanation
its that
111.2 please help 20 points!!!!
Answer:
111.2
Step-by-step explanation:
It would just remain 111.2
The square root and the squared cancel out on eachother
For, square roots of number will be what times what gives you that number while squared numbers will give you a number multiplied by utsekf,
Part C
Question
Determine the missing values in the table.
Recall that x represents the number of tickets sold and y represents the amount of money earned from ticket sales.
Type the correct answer in each box. Use numerals instead of words.
X
$20
3
6
20
$400
Answer:
40$,160$ & 60
Step-by-step explanation:
First,find the equation using y-y1/ y1-y2=x-x1=x1-x2
y-0/0-20=x-0/0-3
y=20x/3
Now put the values of x& y in the equation, for the 1st one,
y=20×6/3
=40
2nd one.y=20×24/3
=160
3rd one,
400=20x/3
X=400×3/20
=60
The values at different number of tickets and the tickets that can be bought at $400 has been determined.
What is Direct Variation?When a variable varies directly with the other variable, i.e. on increasing one variable the other variable also increases, this relation is called Direct Variation.
Let x represent the number of tickets sold
Let y represent the amount of money earned from ticket sales.
y ∝ x
y = kx
k is the proportionality constant.
The value in the table will be used to determine the value of k,
For 3 tickets, the ticket amount is $20
20 = k * 3
k = 20/3
The relation is given by
y = (20/3) x
For 6 tickets, the value will be,
y = (20/3 ) *6 = $40
For 24 tickets the value will be,
y = (20/3) * 24 = $160
For $400, how many tickets can be bought,
400 = (20/3) * x
400*3 /20 = x
60 tickets can be bought for $400
To know more about Direct Variation
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Based on a survey, assume that 31% of consumers are comfortable having drones deliver their purchases. Suppose that we want to find the probability that when consumers are randomly selected, exactly of them are comfortable with delivery by drones. Identify the values of n, x, p, and q.
Answer:
P(X = 2) = 0.3157
Step-by-step explanation:
Let assume that the question wants us to determine the probability that, let say when 5 customers are randomly selected, exactly 2 of the customers are comfortable.
Then;
p = 0.31
n = 5; x = 2
q = 1 - p
= 1 - 0.31
= 0.69
∴
The probability mass function is:
[tex]P(X =x) = ^n C_r * p^x *q^{n-x}[/tex]
[tex]P(X =x) = ^5 C_2 * (0.31)^2 *0.69^{5-2}[/tex]
[tex]P(X =2) = \dfrac{5!}{2!(5-2)!} * (0.31)^2 *0.69^{3}[/tex]
[tex]P(X =2) = \dfrac{5!}{2!(3)!} * (0.31)^2 *0.69^{3}[/tex]
[tex]P(X =2) = \dfrac{5*4*3!}{2!(3)!} * (0.31)^2 *0.69^{3}[/tex]
[tex]P(X =2) = \dfrac{5*4}{2!} * (0.31)^2 *0.69^{3}[/tex]
[tex]P(X =2) =10* (0.31)^2 *0.69^{3}[/tex]
P(X = 2) = 0.3157
Can someone help me I appreciate it
It says that I need to find x for the missing angle in the equation.
Answer:
Could you possible elaborate on the question more?
HELPPPPPP I DONT GET THIS AT ALL
Answer:
1x1 and 20x32
Step-by-step explanation:
Your payment is $375 per month for 36 months and you made a $2,500
Answer:
375 times 36
Step-by-step explanation:
6/8 and 24/40 are they proportional
Answer:
no they are not
Step-by-step explanation:
The Precision Writing Instruments Company makes two pen designs - the Cordova design and the Savannah design. These data apply, regardless of which of two pen designs is being implemented. Materials cost per pen is $6. Labor cost per pen is $5. Production overhead is
$1,000,000. Advertising and promotion is $1,000,000. Marketing research has estimated the following demand functions for the next year of sales for the two pen designs where Q represents demand in thousands and P represents price. For the Cordova design, Q = 150 - 2.5P. For the Savannah design, Q = 175 - 2.1P. A penetration strategy is proposed for the Savannah design and a price of $25 is selected. What will be the profit or loss for the first year?
9514 1404 393
Answer:
loss of $285,000
Step-by-step explanation:
The demand for the Savannah design is estimated to be ...
Q = 175 -2.1P = 175 -2.1(25) = 122.5 . . . . thousand pens
Then the contribution margin from sales will be ...
122,500($25 -$6 -$5) = $1,715,000
Against a total of $2,000,000 in production and advertising costs, the net will be a loss of ...
$2,000,000 -1,715,000 = $285,000
The first-year loss will be $285,000.
Two fair dice, one yellow and one blue, are rolled. The value of the blue die is subtracted from the value of the yellow die. Which of the following best describes the theoretical probability distribution?
Answer:
symmetric
Step-by-step explanation:
its correct.
Answer:
B symmetric
Step-by-step explanation:
The students at Southern Junior high School are divided into four home rooms. Benjamin just moved into the school district and will be randomly assigned to one home room
Answer:
A 4 side dice.
Step-by-step explanation:
Benjamin has 4 possible homerooms with the same probability. This means that every homeroom has a 1/4 = 0.25 (or 25%) probability of getting chosen.
You could emulate this situation with a 4 sided dice (are like little pyramids) where each side of the dice would represent the selection of one of the homerooms.
Logs5(3x-2) = 1 + Logs5 (x-4)
Answer:
57
Step-by-step explanation:
Please help me with this problem
If ∧ ASC ≅ ∧ KSC then ∠8 is congruent to which angle?
Answer:
B. angle 5
Step-by-step explanation: