1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
erma4kov [3.2K]
3 years ago
12

Identify the 12th term of the arithmetic sequence in which a7 = 40 and a18 = 106.

Mathematics
1 answer:
Lady_Fox [76]3 years ago
3 0

we are given

airthematic sequence

we can use nth term formula

a_n=a_1+(n-1)d

n is number of terms

an is nth term

d is common difference

a1 is first term

We are given

a7=40

we can use it

a_7=a_1+(7-1)d

40=a_1+6d

a_1+6d=40

a18 = 106

a_1_8=a_1+(18-1)d

a_1+17d=106

we can subtract both equations

a_1+17d-a_1-6d=106-40

11d=66

d=6

now, we can find a1

a_1+6d=40

we can plug d=6

a_1+6*6=40

a_1=4

12th term:

a_1_2=a_1+(12-1)d

now, we can plug values

a_1_2=4+(12-1)*6

a_1_2=4+66

a_1_2=70

so, 12th term is 70...........Answer

You might be interested in
Worked 16 3/4 hours in past two days and plan to work 12 3/4 hours in the next two days
Burka [1]

16 3/4 + 12 3/4

16 +12 = 28

3/4 +3/4 = 1 1/2

28 + 1 1/2 = 29 1/2 hours total

8 0
3 years ago
What is the vertex of the quadratic function below?
zysi [14]

Answer:

Option A: (4, -15).

Step-by-step explanation:

Given the quadratic function, y = x² - 8x + 1, where a = 1, b = -8, and c = 1:

<h3><u>Solve for the x-coordinate of the vertex:</u></h3>

We can use the following equation to solve for the x-coordinate of the vertex:

\displaystyle\mathsf{x\:=\:\frac{-b}{2a}}

Substitute the given values into the formula:

\displaystyle\mathsf{x\:=\:\frac{-b}{2a}\:=\:\frac{-(-8)}{2(1)}\:=\:\frac{8}{2}\:=\:4}

Hence, the x-coordinate of the vertex is 4.

<h3><u>Solve for the y-coordinate of the vertex:</u></h3>

Next, substitute the x-coordinate of the vertex into the given quadratic function to solve for its corresponding y-coordinate:

y = x² - 8x + 1

y = (4)² - 8(4) + 1

y = 16 - 32 + 1

y = -15

Therefore, the vertex of the given quadratic function, y = x² - 8x + 1, is: x = 4, y = -15, or (4, -15).  Thus, the correct answer is Option A: (4, -15).

3 0
2 years ago
Read 2 more answers
(8b+3)(2b-9) what's the answer and how u get it
gulaghasi [49]
You would distribute so
(8b+3)(2b-9)
foil it to get
16b^2-72b+6b-36
simplify to 16b^2-66b-36
4 0
3 years ago
What is the constant of proportionality in the equation y = 7x? constant of proportionality =
stiks02 [169]
The constant of proportionality is 7.
6 0
3 years ago
Read 2 more answers
Compute the total pay.
a_sh-v [17]
The answer is the compute the total pay is $33.85
3 0
3 years ago
Other questions:
  • Factor the polynomial completely using x method x2+16x+48
    8·2 answers
  • Solve x2 - 8x - 9 = 0. Rewrite the equation so that it is of the form x2 + bx = c.
    8·2 answers
  • A line joins the point
    11·1 answer
  • HELP ASAP!!!!!! please show work too! tysm!
    10·2 answers
  • Pls help I need to find x
    15·1 answer
  • Simplify this expression. 2 square root 5 (13 + square root 2)
    9·1 answer
  • A wild 30 points appears!
    7·1 answer
  • PLEASE HELP FAST 2 EASY QUESTIONS FOR DOUBLE THE POINTS AND BRAINLIST MAKE SURE YOU READ IT CORRECTLY!
    10·1 answer
  • Order these numbers from least to greatest​
    13·1 answer
  • Consider the expression.
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!