Answer:
Step-by-step explanation:
Prove that 52n − 1 is divisible by 8 for all n ∈ N.
Solution
To prove by induction, we must
1. Show it is true for n = 1
2. Assume true for n and prove it is true for n + 1.
Let P(n) be the statement 52n − 1 is divisible by 8.
When n = 1, 52 − 1 = 24, which is divisible by 8.
This proves P(1).
Suppose that P(n) is true, i.e., 52n − 1 is divisible by 8.
Then 52(n+1) − 1 = 52
· 5
2n − 1 = 52
(52n − 1) + (52 − 1).
Note that 52n −1 is divisible by 8 using P(n) and also 52 −1 = 24 is divisible
by 8. Thus we have proved that P(n + 1) is true.
We conclude that P(n) is true for all n ∈ N.
*
Gas Station and Park
Alternate Exterior Angles
Corresponding Angles
Same-Side
rior Angles
Alternate Interior Angles
Vertical Angles
Answer:
Alternate Interior Angles
Step-by-step explanation:
rg
True or False: A biconditional statement is a statement in which a conclusion is true if the conditions of a particular hypothesis are true.
Answer:
thats false
Step-by-step explanation:
y-6= -3(x-1) use integers A B C
y=-3x+9 this should be the answer you are looking for
Please help asap, correct answer will get brainliest
Answer:
im not sure if my answer is correct
( BRAINLIEST QUEATION)
A bank offers 2% simple interest per year. A woman opens an account with deposit of 900 pounds. She closes the account 2 years later. How much will she withdraw.
simple interest formulae = PRT/100
where
p stands for percentage (2%)
r stands for rate ( 900)
t stands for time (2 years )
2×900×2/100
=3600/100
=36
Deposit interest
Level : SHS Keyword : deposit interest, simple interestDeposit Interest in 2 years
= D × i × T/365 days
= 900 pounds × 2% × (365 × 2 years)/365 days
= 900 pounds × 0.02 × 730 days/465 days
= 900 pounds × 0.02 × 2
= 36 pounds
Her Deposit in 2 years
= 900 pounds + 36 pounds
= 936 pounds
So, her deposit if she will withdraw is 936 pounds
#LearnWithEXO
Solve for p.
-5(-9p + 7) = 6 - 3 + 7p
Answer:
p = 1Step-by-step explanation:
[tex] - 5( - 9p + 7) = 6 - 3 + 7p \\ 45p - 35 = 3 + 7p \\ 45p - 7p = 35 + 3 \\ 38p = 38 \\ p = \frac{38}{38} \\ p = 1 \\ [/tex]
The polynomial function P(X) = 30x - 97,000 models the Relationship between the number of computer briefcases x that a company sells and the Profit the company makes , P(x). find p(4000) computer Briefcases
Answer:
A Is the mega super duper pooper hooper flooper booper answer
Step-by-step explanation:
Brainlyyyyyyyy
The area of a square is 676 square feet. what is the perimeter of the square?
Given : The area of a square is 676 square feet. what is the perimeter of the square?
Solution :
Area of Square = 676 ft²
Let's assume the constant multiple be α (alpha)
Length × Breadth = 676α × α = 676α² = 676α = √676α = 26So, now getting perimeter
As we know that, Perimeter = 4(Side)
Perimeter = 4(26) Perimeter = 104Henceforth, the perimeter of square is 104 ft
Please help with this math problem ASAP! I will give brainliest!
Step-by-step explanation:
x = 112°
y = z = 180° - 112° = 68°
Plz help
input the correct Anwser as OS For One Solution, NS for no solution and INF for infinite
Answer:o
Step-by-step explanation:o
Answer:
1) INF
2) NS
Because:
1 is INF because both sides of the equation are the same
x can be replaced with any number therefor, there are infinite solutions.
2 is NS because you are left with 12=2 so there would not be a solution.
Please, help me in this!
solve the inequality. 1/3b + 1 < -6
Answer:
b<-21
Step-by-step explanation:
1/3b+1<-6
1/3b<-7
*3 *3
b<-21
Answer:
b < - 21
Step-by-step explanation:
[tex]\frac{1}{3}[/tex] b + 1 < - 6 ( subtract 1 from both sides )
[tex]\frac{1}{3}[/tex] b < - 7 ( multiply both sides by 3 to clear the fraction )
b < - 21
Order the number \pi ,3, and \sqrt(11 )from least to greatest
Firstly, let's write these out to help us see:
[tex]\pi[/tex] = 3.1415
3
[tex]\sqrt{11}[/tex] = 3.3166
We can see that [tex]\sqrt{11}[/tex] is 0.3166 greater than 3, and 0.1751 greater than pi. Therefore, it's the biggest number.
Pi is second biggest because it is less than [tex]\sqrt{11}[/tex] but greater than 3.
Therefore, your order would be:
3, [tex]\pi[/tex], [tex]\sqrt{11}[/tex]
Hope this helps! :)
how many digits do you need to write all of the 2-digit numbers?
Answer:
I think it's 180 digits
Answer:
2
Step-by-step explanation:
any 2 digits using 0 through 9
if you are told to distribute Rs 1,200 among 15 children what mathamatical operation will be used? if you answer this i will put you a brainalist
Answer:
dividing
Step-by-step explanation:
because dividing is the one and the only method to give 15 children equal money
9. If a train travels 270 mi. in 9 hr., what is its average speed?
20 mph
O
30 mph
d
40 mph
50 mph
Answer:
30 miles per hour
Step-by-step explanation:
You divide the distance by time to receive the average speed.
270 / 9 = 30
Answer:
The train travels 30 miles in 1 hour
Step-by-step explanation:
First, you take the miles and divided it by the hours. That will give you the average speed/MPH (miles per hour)
12+17-3x2 rewrite this in perenthesis
Answer:
(12+17)-(3x2)
Step-by-step explanation:
Answer:
12+17-(3x2)
Step-by-step explanation:
You do multiblecation before addition so you put it in parenthesis
PLZZZ HELPPPP ILL MARK BRAINLIEST TO FIRST AND CORRECT ANSWER THAT HAS WORK AND A THX TO SECOND AND CORRECT ANSWER.
Answer:
b
Step-by-step explanation:
I know that it is b becuase everthing esle has a higher number and when it's higher more chance of getting a full number
Twenty decreased by 2 times a
number is the same as 10 less
than 3 times the number.
Answer:
6
Step-by-step explanation:
Alan's parents are both in their forties. The sum of their ages is eighty-four. The product of their ages is 1,763. How old is Alan's oldest parent?
A. 41
B. 43
C. 45
D. 47
PLEASE ANSWER
4(6 – x) = 8
Solve for x
Answer:
4
Step-by-step explanation:
24 - 4x = 8
-4x = 8 - 24
-4x = -16
x = 4
Find and correct the error!
Answer:
Step-by-step explanation:
Jen 's drawing shows that the lines are parallel in fact they are not parallel ! Since their slopes are not equal !
[tex]\displaystyle \left \{ {{y=2x+3} \atop {-y=2x+1}\ \ |\cdot (-1) } \right. => \left \{ {{y=\boldsymbol {2}x+3} \atop {y=\boldsymbol {-2}x-1}} \right. => -2\neq 2[/tex]
They will intersect at point A with coordinates :
[tex]2x+3=-2x-1 \\\\ 4x=4 \\\\ x=-1 \ ; \ y=1 => A(-1 \ ; \ 1)[/tex]
What is the value of the 3 in this number?
is the value of this number.
Answer:
3?
Step-by-step explanation:
What are the coordinates of the point on the directed line segment from (−8,5) to (4,−3) that partitions the segment into a ratio of 5 to 3?
Answer:
(-0.5, 0)Step-by-step explanation:
Directed line segment from (−8,5) to (4,−3).
Ratio is 5/3.
The required coordinates are:
x = -8 + 5/8*(4 - (-8)) = -8 + 5/8(12) = -8 + 7.5 = -0.5y = 5 + 5/8*(-3 - 5) = 5 + 5/8(-8) = 5 - 5 = 0Gavin and Jim win some money and share it in the ratio 1:3. Gavin gets £15. How much did Jim get?
Answer:
£7
Step-by-step explanation:
15×203_3[2
w820362
45
Rhombus ABCD has vertices A(1,1), B(5,3), C(7.7), and D(3,5). After a translation, the image A'
is located at (-2,8). What are the coordinates of C'?
Answer:
C'(4, 14)
Step-by-step explanation:
Which side is the hypotenuse of XYZ
What is the equation of the line through the longs (1,1) (5,4) (9,7) and (13,10)
Answer:
y= [tex]\frac{3x}{4}[/tex] + [tex]\frac{1}{4}[/tex]
you first find the gradient of the line by picking out any two coordinates then u fill the values in the equation of a line
Three consecutive integers add up to 120. What is the smallest integer?
(A) 38
(B) 39
(C) 40
(D) 41
(E) 42
Answer:
39
Step-by-step explanation:
havent used this website in a minute lol
100 points show ALL steps
[tex]\\ \sf\longmapsto \sqrt{108x^2y^3}-\sqrt{12x^2y^3}+x\sqrt{75y^3}[/tex]
[tex]\\ \sf\longmapsto \sqrt{2\times 2\times 3\times 3\times 3\times x\times x\times y\times y\times y}-\sqrt{2\times 2\times 3\times x\times x\times y\times y\times y}+\sqrt{5\times 5\times 3\times y\times y\times y}[/tex]
[tex]\\ \sf\longmapsto 6\sqrt{3}xy\sqrt{y}-2\sqrt{3}xy\sqrt{y}+5\sqrt{3}xy\sqrt{y}[/tex]
[tex]\\ \sf\longmapsto \sqrt{3}xy\sqrt{y}(6-2+5)[/tex]
[tex]\\ \sf\longmapsto 9\sqrt{3}xy\sqrt{y}[/tex]
Answer:
[tex]9xy\sqrt{3y}[/tex]Step-by-step explanation:
See the steps below:
[tex]\sqrt{108x^2y^3} -\sqrt{12x^2y^3} +x\sqrt{75y^3} =[/tex][tex]\sqrt{36*3x^2y^2y} -\sqrt{4*3x^2y^2y} +x\sqrt{25*y^2y} =[/tex][tex]6xy\sqrt{3y} -2xy\sqrt{3y} +5xy\sqrt{3y} =[/tex][tex](6 - 2+ 5)xy\sqrt{3y} =[/tex][tex]9xy\sqrt{3y}[/tex]