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
Sever21 [200]
3 years ago
14

Use the binomial theorem to show that 7^n + 2 is divisible by 3, where n is a positive integer.

Mathematics
1 answer:
masha68 [24]3 years ago
7 0

By the binomial theorem,

7^n=(6+1)^n=6^n+n6^{n-1}+\dbinom n26^{n-2}+\cdots+\dbinom n{n-2}6^2+n6^1+1

Each term containing a factor 6 is divisible by 3, since 3 divides 6. The remaining 1 and 2 sum to 3, which is also divisible by 3.

You might be interested in
Which of the following has a product of -4?
trapecia [35]

Hey! Your answer would be A. (1/5)(-20)

8 0
3 years ago
Read 2 more answers
What is the answer to 3x + 2 = 4x
Sedbober [7]
X=2
because if you subtract 3x on both sides you end up with x=2 <span />
5 0
3 years ago
Write the equation of the line that passes through the points (−7,5) and (-7,-8).
Viefleur [7K]

Answer:

x = -7

Step-by-step explanation:

First we find the slope using

m = ( y2-y1)/(x2-x1)

   = ( -8 - 5)/( -7 - -7)

   = (-8-5)/(-7+7)

   = -13/0

This means the slope is undefined and the line is vertical

Vertical lines are in the form

x= constant and the constant is the x value of the points

x = -7

3 0
3 years ago
Will mark brainliest <br> Thank u!
Tems11 [23]

Answer:

D

Step-by-step explanation:

Any set of three angles that add up to 180 degrees can form a triangle.

4 0
3 years ago
Read 2 more answers
determine the value of , if possible. If the triangles are congruent, state which triangle congruence condition you used. If the
PilotLPTM [1.2K]

Answer:

"Can't be determined"

Step-by-step explanation:

From the triangles given in the picture,

Given:

m∠A = m∠C

m∠B = m∠D

But for the congruence of these triangles third condition is not given.

Therefore, congruence of these triangles can not be determined.

So the answer is "Can't be determined"

4 0
2 years ago
Other questions:
  • If 2x = 5, 3y = 4, and 4z = 3, what is the value of 24xyz ?
    8·1 answer
  • How many roots does -2x^2-8=0 have​
    5·1 answer
  • 1. Explain the difference between rate and unit rate using their definitions.
    14·2 answers
  • Write as an ordered pair. 4x+2y=16 and -4y+x=4
    13·2 answers
  • What is the product written in scientific notation? (5.91×10−3)⋅(8.7×1010)
    12·2 answers
  • Please help find the percent of increase?!
    14·1 answer
  • PLEASE HELP!!! Write the expression as a single logarithm.<br> 3 log(4) + log(7)
    6·2 answers
  • 7+7x=-70 what is the answer?
    8·1 answer
  • Calculate the value of P and of Q that satisfy the following simultaneous linear equations.
    7·1 answer
  • I just need help filling in the rest of this table. I've done some, but I've been stuck for a while now. Huge thanks to anyone w
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!