prove that 5^(2n - 1) is divisible by 8​

Answers

Answer 1

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.


Related Questions

What are the combining like terms plz

Answers

Answer:

-7q and 9q, 2 and 6

Step-by-step explanation:

they are like each other

Answer: Terms that have identical variable parts (same variable(s) and same exponent(s)). So in this case the like terms are -7q and 9q AND 2 and 6 are like terms *REMEMBER: constant (which are numbers with NO variables can also be like terms)

but to solve this:

first group the like terms so:

(-7q+9q) that gives us 2q

(2+6) that gives us 8

*In your FINAL answer ALWAYS put the number(s) with variables first so the final answer is 2q+8

how many gallons are equivalent to 20 points

Answers

Answer:

2.31964e-7

Step-by-step explanation:

Answer:

3 gallons

Step-by-step explanation:

help me please
………………….

Answers

Answer:

here is your answer

so the lengjt value of. n = 60

What is the constant of proportionality for the graph?

Answers

Answer:

k = 5

Step-by-step explanation:

y = kx

10 = 2k

k = 5

Which list shows the values of the changes in order, from least to greatest?Stock A, Stock B, Stock C, Stock DStock B, Stock D, Stock A, Stock CStock C, Stock A, Stock D, Stock BStock D, Stock C, Stock B, Stock A

Answers

Answer:

c

Step-by-step explanation:

edge 2022

Help

Dealing with corresponding write reasons as well pls

Answers

Answer:

X=60°

Step-by-step explanation:

A1=100° vertically opposite angles

100°=2x-20°

120°=2x

X=60°

Rylee finds a recipe for a bubble solution that uses 1 cup water, 1/4 dish soap, and 1 tablespoon corn syrup. She is 2 cups of dish soap. How much water should she use? Show your work.

Answers

Answer:

65

Step-by-step explanation:

I need help please lol

Answers

Answer:

Tina ate 1/4 cornbread of the whole pan.

Step-by-step explanation:

If she has 1/2 of a pan, and ate 1/2 of that, it's 1/2*1/2, which equals 1/4! Try to imagine a pan of cornbread in your head ahaha

The equation should be: 1/2*1/2=1/4

Hopes this helps!

y=-2/3x + 7 what is the slope?

Answers

Answer:

Lucky for you i'm good at algebra:)

Step-by-step explanation:

Slope:  -2/3

Y-intercepts: (0,7)

Answer:

 Slope = -1.333/2.000 = -0.667

 x-intercept = 21/2 = 10.50000

 y-intercept = 21/3 = 7

Step-by-step explanation:

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    y-(-2/3*x+7)=0

Step 1:

Simplify    2/3

Equation at the end of step 1:

y -  ((0 -(2/3• x)) +  7)  = 0

Step 2: Rewriting the whole as an Equivalent Fraction

Rewrite the whole as a fraction using  3  as the denominator :

7 = 7/1  =  7 · 3 /3

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

-2x+7·3/3 = 21-2x/3

Equation at the end of step 2:

y-(21-2x)/3=0

Step 3:

Rewriting the whole as an Equivalent Fraction :

Subtracting a fraction from a whole

Rewrite the whole as a fraction using  3  as the denominator :

y=y/1=y·3/3

Adding fractions that have a common denominator :

 Adding up the two equivalent fractions

y • 3 - ((21-2x))     3y + 2x - 21

—————————————————  =  ————————————

        3                  3      

Equation at the end of step

3

:

 3y + 2x - 21

 ————————————  = 0  

      3      

STEP

4

:

When a fraction equals zero :

4.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

 3y+2x-21

 ———————— • 3 = 0 • 3

    3    

Now, on the left hand side, the  3  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  3y+2x-21  = 0

Equation of a Straight Line

4.2     Solve   3y+2x-21  = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  3y+2x-21  = 0 and calculate its properties

Graph of a Straight Line :

 

 

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 7/1 so this line "cuts" the y axis at y= 7.00000

 y-intercept = 21/3  =  7  

Calculate the X-Intercept :

When y = 0 the value of x is 21/2 Our line therefore "cuts" the x axis at x=10.50000

 x-intercept = 21/2  = 10.50000  

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 7.000 and for x=2.000, the value of y is 5.667. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 5.667 - 7.000 = -1.333 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

   Slope     = -1.333/2.000 = -0.667  

Geometric figure: Straight Line

 Slope = -1.333/2.000 = -0.667

 x-intercept = 21/2 = 10.50000

 y-intercept = 21/3 = 7

what is 4 times 4 divded by 8

Answers

Answer:

2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

4 groups of 4, or 4x4=16.

16 in eight groups, or 16/8 is 2.

If a salesclerk earns $5.75 per hour,
how many hours per week does she
work to earn her weekly salary of
$207?
F 30 hours
G 32 hours
H 36 hours
J 4 hours

Answers

Therefore statement: The salesclerk needs to work 36 hours per week to earn her weekly salary.

5.75 x 36 = 207

All you need to do is take the amount of money made per hour and multiply that by any number of hours in the options below. Basically trial and error

The measures of the angles of a triangle are shown in the figure below. Solve for x.
39°

Answers

Answer:

look at the photo..............

Answer:

x = 51°

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Subtract the sum of the 2 given angles from 180° for x

x = 180° - (90 + 39)° = 180° - 129° = 59°

Ozzie is 6 years older than McKenzie. Theo is Ozzie's dad and is 3 times older than McKenzie. Ozzie is 8 years old. How old is Theo?​

Answers

Answer:

If Ozzie is 8 and 6 years older than McKenzie, then McKenzie is 2 years old. So if Theo is 3 times older than McKenzie, then Theo is 6 years old.

In 2010, Utah had a population of about 2.8 x 106. The same year, Wyoming had a population of about 5.6 x 105
Which statement correctly compares the populations of these states?


A. The population of Utah is about 0.5 times the population of Wyoming


B. The population of Wyoming is about 2 times the population of Utah


C. The population of Wyoming is about 20 times the population of Utah


D. The population of Utah is about 5 times the population of Wyoming

Answers

Answer:

thank you so much

Step-by-step explanation:

Lines k and n intersect on the y-axis
a. What is the equation of line k?
(-2,6) 6-
(4,5)
b. What is the equation of line j?
710
m
(5.2)
2-
109
(-3,-1)
a. The equation of line k in slope-intercept form is
(Use integers or fractions for any numbers in the equation. Simplify your answer.)

Answers

a) The equation of line k is:

[tex]y = -\frac{202}{167}x + \frac{598}{167}[/tex]

b) The equation of line j is:

[tex]y = \frac{167}{202}x + \frac{1546}{202}[/tex]

The equation of a line, in slope-intercept formula, is given by:

[tex]y = mx + b[/tex]

In which:

m is the slope, which is the rate of change.b is the y-intercept, which is the value of y when x = 0.

Item a:

Line k intersects line m with an angle of 109º, thus:

[tex]\tan{109^{\circ}} = \frac{m_2 - m_1}{1 + m_1m_2}[/tex]

In which [tex]m_1[/tex] and [tex]m_2[/tex] are the slopes of k and m.

Line k goes through points (-3,-1) and (5,2), thus, it's slope is:

[tex]m_1 = \frac{2 - (-1)}{5 - (-3)} = \frac{3}{8}[/tex]

The tangent of 109 degrees is [tex]\tan{109^{\circ}} = -\frac{29}{10}[/tex]Thus, the slope of line m is found solving the following equation:

[tex]\tan{109^{\circ}} = \frac{m_2 - m_1}{1 + m_1m_2}[/tex]

[tex]-\frac{29}{10} = \frac{m_2 - \frac{3}{8}}{1 + \frac{3}{8}m_2}[/tex]

[tex]m_2 - \frac{3}{8} = -\frac{29}{10} - \frac{87}{80}m_2[/tex]

[tex]m_2 + \frac{87}{80}m_2 = -\frac{29}{10} + \frac{3}{8}[/tex]

[tex]\frac{167m_2}{80} = \frac{-202}{80}[/tex]

[tex]m_2 = -\frac{202}{167}[/tex]

Thus:

[tex]y = -\frac{202}{167}x + b[/tex]

It goes through point (-2,6), that is, when [tex]x = -2, y = 6[/tex], and this is used to find b.

[tex]y = -\frac{202}{167}x + b[/tex]

[tex]6 = -\frac{202}{167}(-2) + b[/tex]

[tex]b = 6 - \frac{404}{167}[/tex]

[tex]b = \frac{6(167)-404}{167}[/tex]

[tex]b = \frac{598}{167}[/tex]

Thus. the equation of line k, in slope-intercept formula, is:

[tex]y = -\frac{202}{167}x + \frac{598}{167}[/tex]

Item b:

Lines j and k intersect at an angle of 90º, thus they are perpendicular, which means that the multiplication of their slopes is -1.

Thus, the slope of line j is:

[tex]-\frac{202}{167}m = -1[/tex]

[tex]m = \frac{167}{202}[/tex]

Then

[tex]y = \frac{167}{202}x + b[/tex]

Also goes through point (-2,6), thus:

[tex]6 = \frac{167}{202}(-2) + b[/tex]

[tex]b = \frac{(2)167 + 202(6)}{202}[/tex]

[tex]b = \frac{1546}{202}[/tex]

The equation of line j is:

[tex]y = \frac{167}{202}x + \frac{1546}{202}[/tex]

A similar problem is given at https://brainly.com/question/16302622

Distribute: -6(3x – 4) a-18x + 10 b-18x + 24 c-18x - 4 c-18x - 24​

Answers

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\text{The DISTRIBUTIVE PROPERTY formula is}\downarrow\\\large\textsf{a(b + c)}\\\large\textsf{= a(b) + a(c)}\\\large\textsf{= ab + ac}[/tex]

[tex]\large\text{Now that we have the formula, we can solve for your question/answer.}[/tex]

[tex]\large\text{YOUR EQUATION: \underline{\underline{\textsf{-6(3x - 4)}}}}}\\\\\large\textsf{= -6(3x) - 6(-4)}\\\large\textsf{= -6(3x) + 6(4)}\\\large\textsf{= -18x + 24}\\\huge\boxed{\rm{Therefore, your\ answer\ is: \mathsf{-18x + 24}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

If y=104x, what is the unit rate (without units)

Answers

In a unit rate, the denominator is always 1. So, to find unit rate, divide the denominator with the numerator in a way that the denominator becomes 1. For example, if 50km is covered in 5.5 hours, the unit rate will be 50km/5.5 hours = 9.09 km/hour.

You are selling flowers for a fundraiser . You pay $ 1.50 for each flower plus a flot rate delivery fee of $ 15 . You are selling the flowers for $ 3 . At least how many flowers do you need to sell to make a profit ?​

Answers

Answer:

15÷1 .50=10

Because you are already paying a flat rate of $15. You make 1.50 off of each flower. So you have to sell over 10 flowers to make a profit.

At least 11 flowers should be sold to make a profit.

What is the equation?

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that is equal.

Given:

Total cost for the buying flower = 1.5 * number flowers  + 15

For n=10                                       = 1.5 * 10 + 15

                                                     = 30

By selling 10 flowers                    =10 * 3

                                                     = $30

For n =11                                        = 1.5 * 11 + 15

                                                      = 31.5

By selling 11 flowers                    = 11 * 3

                                                     = 33

Therefore, At least 11 flowers should be sold to make a profit.

Learn more about equation here:

brainly.com/question/10413253

#SPJ5

PLEASE HELP!!! WORTH 20 POINTS!
For each pair of points, find the slope of the line that passes through both points. If you get stuck, try plotting the points on graph paper and drawing the line through them with a ruler. Use fractions, not decimals, and make sure to simplify all fractions.

Answers

Answer:

a. 1 1/2 (or 3/2)

b. 2/3

c. 1

d. 1

Step-by-step explanation:

Part A: (1,1) (7,5)

To determine the slope, you will use the equation m=(y2-y1)/(x2-x1). Keep in mind that it doesn't matter what point you use for (x1, y1) or (x2, y2).

Let's plug in the numbers for part a:

m=(7-1)/(5-1)

Let's then solve the problems inside the parentheses:

m=6/4

And finally, we simplify:

m=3/2 (or 1 1/2 depending on what your teacher wants for an answer)

For these others, I will just go through the steps and not explain them, if you need help or don't understand something I'm doing, either look back at what I did for part a or comment on this answer.

Part B: (1,1) (5,7)

m=(5-1)/(7-1)

m=(4/6)

m=2/3

Part C: (2,5) (-1,2)

m=(-1-2)/(2-5)

m=(-3/-3)

m=1

Part D: (2,5) (-7,-4)

m=(-7-2)/(-4-5)

m=(-9/-9)

m=1

The difference between two positive numbers , 12/(x + 1) and 12/x , 1. () Form an equation in x and show that it reduces to x ^ 2 + x - 12 = 0 . (ii) Solve the equation x ^ 2 + x - 12 = 0 . () Hence , find the two numbers .

Answers

Answer:

Step-by-step explanation:

12

Answer this question please

Answers

Answer:

1/8362

Step-by-step explanation:

Student picked at random/Number of students

A line is drawn so that it passes through the points (-6,0) and (10,2). What is the slope of the line?

Answers

Answer:

hope you like my answer its -4

PLEASE HELP ME!!! BOTH PICTURES ARE RELATED!

Answers

Answer:

the answer is 22 percent which is science

Answer:

100 marks have been obtained in the hindi subject.

Step-by-step explanation:

First you have to find how many marks are obtained by one degree. So you have:

450marks/360°=1.25marks/degree

Then you have to find how many marks are obtained for each subject.

1.25marks/degree×80°= 100 marks

1.25×72= 90 marks

1.25×70= 87.5 marks

1.25×90= 112.5 marks

1.25×48= 60 marks

100+90+87.5+112.5+60=450 marks

What is the y-intercept of a line that has a slope of 3 and passes through point (-1, -7)?
O-10
O4
O 3
O 7

Answers

It must be -4, but the second choice is a positive 4, I am not sure if you typed the choices wrongly..

2 of 4
A, B & C lie on a straight line.
BD = CD.
Z BDC = 30° and Z ADB = 25°.
Work out X, explaining each stage of your working in the comment box.

Answers

so I don't know the answer but need to answer a question

Plz hurry

18. A shipwreck is 300 meters away from a diving station. An undersea
explorer travels away from the station at a speed of 2 meters per second.
The explorer is x meters away from the station and will reach the
shipwreck in 100 seconds. What is the value of x?

Answers

Answer:

me too jaja

Step-by-step explanation:

The value of x is 100 meters if the shipwreck is 300 meters away from a diving station. An undersea explorer travels away from the station at a speed of 2 meters per second.

What is the distance?

Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.

It is given that:

A shipwreck is 300 meters away from a diving station.

An undersea explorer travels away from the station at a speed of 2 meters per second.

The explorer is x meters away from the station and will reach the

shipwreck in 100 seconds.

As we know,

Distance = time×speed

Distance = 100×2

Distance = 200 meterse

x = 300 - 200

x = 100 meters

Thus, the value of x is 100 meters if the shipwreck is 300 meters away from a diving station. An undersea explorer travels away from the station at a speed of 2 meters per second.

Learn more about the distance here:

brainly.com/question/26711747

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Cortney had 5 pieces of candy Cortney ate 1 piece how many pieces does Cortney have left?

Answers

4. 5-1=4. Hope this helps :)

The area of a square is 676 square root. what is the perimeter of the square?

Answers

Answer:

the perimeter of the square is 104

Step-by-step explanation:

to find the perimeter of a square we need to use the formula P = 4a

P is perimeter and a is the side of the square

if a is the side and the formula of Area is A = a^2

that means the side of the square is a = 26 because 26 * 26 = 676

now we take 26 and place it in the a spot of the perimeter formula

P = 4 * 26   (P = 104)

can i get brain if this helps and is correct plz and thxs <(^w^)>

Answer:

It's 104

Step-by-step explanation:

[tex] \sqrt{676 = 26} [/tex]Square perimeter formula : P=4×aP=4×aP=4×26P=104

Taylor multiplied 8.25 * 10^4 and 0.4 * 10^4 and got 8.65 * 10^4. Explain Taylor's mistake. SOME ONE PLEASE HELP ME GET THIS ANSWER!

Answers

Answer: I believe the answer is 3.3 x 10^8

A tree is 28.05 feet tall. What is its height in meters? Use the following conversion: 1 meter is 3.3 feet.

Answers

Answer:

It is 8.5 meters tall

Step-by-step explanation:

28.05 / 3.3 = 8.5

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