Will give Brainliest and 100 points! Prove the divisibility of the following numbers: 5^5-5^4+5^3 by 7

Will Give Brainliest And 100 Points! Prove The Divisibility Of The Following Numbers: 5^5-5^4+5^3 By

Answers

Answer 1

Answer:

See Below.

Step-by-step explanation:

We have the expression:

[tex]5^5-5^4+5^3[/tex]

And we want to prove that it is divisible by 7.

To do so, we can factor out a 5³ from the expression. This yields:

[tex]=5^3(5^2-5^1+1)[/tex]

Simplify the parentheses:

[tex]=5^3(25-5+1)=5^3(21)[/tex]

We can see that the resulting expression is a value being multiplied by 21.

Since 21 is divisible by 7, our original expression must also be divisible by 7.

Hence proven.

Answer 2

Answer:

SEE BELOW

Step-by-step explanation:

to understand thisyou need to know about:PEMDASgiven:[tex] \displaystyle \sf\frac{ {5}^{5} - {5}^{4} + {5}^{3} }{7} [/tex]let's solve:[tex] \sf \: factor \: out \: {5}^{3} : \\ \displaystyle \sf\frac{ {5}^{3}( {5}^{2} - {5}^{} + 1) }{7} [/tex][tex] \sf simlify \: parentheses \{squre \} : \\ \sf \frac{ {5}^{3} (25 - 5 + 1)}{7} [/tex][tex]\sf simlify \: parentheses \{addition \} : \\ \sf \frac{ {5}^{3} (25 - 4)}{7} [/tex][tex]\sf simlify \: parentheses \{substraction \} : \\ \sf \frac{ {5}^{3} (21)}{7} [/tex][tex] \sf \: cancel \: 7 \: and \: 21 : \\ \frac{ {5}^{3} \cancel{(21) } \ ^{3} }{ \cancel{ \: 7 \: }} [/tex]we can see 21 is divided by 7 therefore our original expression must also be divisible by 7

Related Questions

A restaurant wants to study how well its salads sell. The circle
graph shows the sales of salads during the past few days. If 5 of
the salads sold were Caesar salads, how many total salads did
the restaurant sell?

Answers

Answer:

25

Step-by-step explanation:

20 : 100 = 5 : x

x = (5 x 100) / 20 = 25

Factorise the following.​

Answers

Answer:

This is your answer

Can I get some help on these two

Answers

9514 1404 393

Answer:

  cone: 138.16 in²

  pyramid: 352 m²

Step-by-step explanation:

Use the appropriate formula from your list of area and volume formulas.

Area of a Cone

  A = πr(r +h) . . . . . where r is the radius and h is the slant height

The radius is half the diameter, so is 4 inches.

  A = π(4 in)(4 in + 7 in) = 44π in² ≈ 138.16 in²

__

Lateral Area of a Square Pyramid

  A = 2sh . . . . . where s is the side length of the base and h is the slant height

  A = 2(8 m)(22 m) = 352 m²

4. Se contrata un bus para hacer una excursión, si se hubieran completado los asientos el costo del
pasaje por persona hubiera sido de $10, pero faltaron 10 personas, entonces el costo del pasaje por
persona es de $15.¿Cuántos asientos tiene el bus ?​

Answers

Answer:

???

Step-by-step explanation:

simplify fully (9(x+7))÷(3(x-1))​

Answers

Answer:

3x + 60

Step-by-step explanation:

9(x + 7) ÷ 3(x - 1) =

9x + 63 ÷ 3x - 3 =

9x ÷ 3x + 63 - 3 =

3x + 60

Note: For the third equation which is 9x ÷ 3x and etc, you have to put alphabets and numbers at one side seperately to be able to simplify easily.

Elena went to a sporting goods store that
was having a sale. She bought a tennis
racket and 3 cans of tennis balls. How much
will she pay for everything, including tax?

Answers

Are there any other numbers to this question? I will be glad to help.

Find the area of the trapezoid.

Recall : (b + b) h

Answers

Answer:

36 Sq cm

Step-by-step explanation:

Area of the trapezoid

[tex] = \frac{1}{2} \{8 + (4 + 8 + 4) \} 3\\ \\ = \frac{1}{2} \{8 + 16 \} 3\\ \\ = \frac{1}{2} \times 24 \times 3\\ \\ = 12 \times 3 \\ \\ = 36 \: {cm}^{2} [/tex]

Mai bank account is overdrawn by $125 which means her balance is negative 125 she gets $85 for her birthday and deposit into her account how much does she have in her bank

Answers

the answer is -125+85= -40 because she is adding -125 by 85 which equals-40

A city council wants to know if residents would like a dog park . They sent a survey to every household in the city . The results of those who responded are shown in the table below . What is the experimental probability that a household has 2 or more dogs ?

Answers

Answer:

probability= event / sample space

= 129/860

=3/20

=0.15(15%)

Name
Use the given information to answer Problems 7-11.
Leon and Jacey work for a florist. They each program a drone
to deliver boxes of flowers to neighbors. With Leon's program,
he must manually attach the box to the drone. With Jacey's
the drone can pick up one box at a time from a pile.
program,
ram
Please help!!

Answers

Answer:

#7:  30 seconds On The Graph The Drone Has Not Moved and The Time Is At 30 Seconds :)

#8 : 20  Seconds On The Graph All The times go Up by 20 So that is the only Possible answer

#9: Leon Drone Is Faster Look At The Graph 60 Seconds = 10 Feet  And Jacey's Graph its 80 Seconds For 10 Feet And I could Go On

#10 The Time In Seconds

#11 With slow speed you can guarantee it will not be broken or damaged

I Hope This Helps :) Please Give Brainiest If It Makes Sense To You !

Thanks :)

1. Simplify 3 + 5[5 + (7 - 3) - 32]

Answers

Answer:

48

step by step explanation:

3+5(5+(7-3)-32)

8(12-2)-32

96-16-32

80-32

48

Tony's Tires has shown growth over the last month that follows the
equation Sales = 4(Day of the month) +16. On what day of the month will
Tony's Tires double its first day sales?​

Answers

Answer:

Step-by-step explanation:

The sales will double on the 6th day of the month

The equation sales for last month = 4(day of the month) + 16

let

x = day of the month

The day of the month could be 1, 2, 3, 4, 5, 6, 7, 8...…31. The numbers represents the first, second, third ,...… thirty first day.

Sales = 4x + 16

From the equation, on the first day his sales  will be :

sales = 4(1) + 16 = 20 units

The double of 20 units is 40 units. Therefore, the day of the month which the sales will double can be calculated below

40 = 4x + 16

40 - 16 = 4x

4x = 24

x = 24 / 4

x = 6

it will double on the 6th day.

Check here for similar question : https://brainly.com/question/8763059?referrer=searchResults

If a student were going to write about their favorite food, they would want to include sensory language that focuses on. help please

Answers

Answer:

Here are the answers

Step-by-step explanation:

1. taste and smell

2. they allow the reader to feel as if he or she is in the story

3. touch

4. to make the writing more interesting and vivid, to provide greater detail to a narrative

Language Arts 6 B  Unit 7 Lesson 13

Students would want to include sensory language which describes in the solution part that focuses on writing about their favorite food.

What is sensory language?

Sensory Language is a word or words used to evoke mental imagery and help the reader visualize the tale or poetry. Imagery is a literary method that appeals to the reader's senses, whereas Sensory Language is a writing style and how writers utilize words to generate images for the readers.

When writing about their favorite food, a student might want to include sensory language that focuses on how the food looks, smells, tastes, feels, and sounds. This can help to paint a vivid picture for the reader and make the experience of reading about the food more immersive.

For example, if the student's favorite food is pizza, they might describe the golden, crispy crust; the savory, spicy tomato sauce; the gooey, melted cheese; the spicy sausage and bell peppers; and the satisfying crunch that it makes when they take a bite. They might also describe the way the warm, comforting aroma of the pizza fills the room as it cooks, or the way the different textures and flavors come together in each bite to create a satisfying and delicious meal. By using descriptive language that focuses on the senses, the student can help the reader to better understand and share in their love of the food.

Learn more about sensory language here:

https://brainly.com/question/28761616

#SPJ2

Plez the answer the subject is the double angle and half angle formula

Answers

Answer:

cos 2x = (√7) / 4

Step-by-step explanation:

sin x - cos x = 1/2

(sin x - cos x)² = (1/2)²

sin²x - 2 sin x cos x + cos² x = 1/4

1 - 2 sinx cosx = 1/4

2 sinx cosx = 3/4

sin 2x = 2 sinx cosx = 3/4

sin² 2x = 9/16

cos² 2x = 1 - sin² 2x = 1 - 9/16 = 7/16

cos 2x = (√7) / 4

A researcher is trying to show evidence for extra-sensory perception (ESP). She performs a test in which the subject is asked 10 yes or no question whose answer depends on information which the subject has not observed. Suppose that for each test, in the absence of ESP, the subject gets each question correct with 50% probability a) In the absence of ESP, what is the probability that a given test subject will answer at least 8 out of 10 questions correctly

Answers

Answer:

The answer is "0.0547".

Step-by-step explanation:

[tex]P(Correct) = 0.50\\\\n = 10\\\\x = 8[/tex]

Using the binomial distribution:

[tex]\to P(x,n) = n_{C}_x \times p^x \times (1-p)^{(n-1)}\\\\\to P(x \geq 8) = 1 - P( \leq 7)[/tex]

Calculating the excel formula:

[tex]=BINOM.DIST(7,10,0.50,TRUE)[/tex]

[tex]\to P(x \geq 8) = 1 - 0.9453\\\\ \to P(x \geq 8) = 0.0547[/tex]

1) How many ink cartridges can you buy with 77 dollars if one cartridge costs 11 dollars ?​

Answers

7 Ink Cartridges

11x7=77
7 is the answe cuz 11 22 33 44 55 66 77 count those and u get 7

You invested $101 and received $106.05 after one year.what was the interest rate?

Answers

The person below me is true

Find f'(x) for the given function.

f(x) = 5/3-x

Answers

Answer:

The derivative is:

[tex]f^{\prime}(x) = -\frac{5}{x^2-6x+9}[/tex]

Step-by-step explanation:

We are given the following function:

[tex]f(x) = \frac{5}{3-x}[/tex]

Derivative of a quotient:

Suppose we have a quotient:

[tex]f(x) = \frac{g(x)}{h(x)}[/tex]

The derivative is:

[tex]f^{\prime}(x) = \frac{g^{\prime}(x)h(x) - h^{\prime}(x)g(x)}{h(x)^2}[/tex]

In this question:

Numerator [tex]g(x) = 5, g^{\prime}(x) = 0[/tex]

Denominator [tex]h(x) = 3 - x, h^{\prime}(x) = -1[/tex]

So

[tex]f^{\prime}(x) = \frac{0(3-x) - 5}{(3 - x)^2} = -\frac{5}{x^2-6x+9}[/tex]

The derivative is:

[tex]f^{\prime}(x) = -\frac{5}{x^2-6x+9}[/tex]

If m= 3 in the equation 2m=4-n, find the value of n.​

Answers

Answer:

-2

Step-by-step explanation:

n=-2
explanation: since m=3 replace m with 3 to multiply it with 2. 2(3)=6 so the equation now is 6=4-n. Subtract 4 on both sides and get 2=-n which would be n=-2.

Suppose f is a linear function such that f(4)= 8 and f(9)= 1. Find the equation for f.

Answers

solving for f(x) linear function i need help finding the equation to get those answers

X times 3+6 when X equals four

Answers

Step-by-step explanation:

4 x 3 + 6

12 + 6

= 18

or

4 x (3+6)

4 x 9

= 36

depends whether the 3+6 is in brackets :)

Answer:

if x = 4

then,

4 (3 + 6)

12 + 24

= 36

Depends whether they are in brackets but usually i would consider it in this problem.

Without the brackets would be:

4 x 3 + 6

12 + 6 = 18

our less than the quotient of ten and a number, increased by eight; evaluate when y = 2 A 2-column table with 7 rows. Column 1 is labeled Key Words with entries four, less than, quotient, ten, a number, increased by, eight. Column 2 is labeled Replace with entries 4, minus, divided by, 10, y +, 8. Write and evaluate the expression. Then, complete the statements. First, write the expression . Second, 2 in for the variable, y. Third, by using . The answer is .

Answers

Answer:

✔ 10/y – 4 + 8

.

Second,

✔ substitute

2 in for the variable, y.

Third,

✔ simplify

by using

✔ order of operations

.

The answer is

✔ 9

Step-by-step explanation:

i hope this helps-

what ia a right triangle?

Answers

a 90° angle i think???

(-1) + 1 = 0 is which inverse​

Answers

Answer:

Heya mate....

Step-by-step explanation:

This is ur answer....

--> ADDITIVE INVERSE!

Additive inverse simply means changing the sign of the number and adding it to the original number to get an answer equal to 0. The properties of additive inverse are given below, based on negation of the original number. For example, x is the original number, then its additive inverse is -x.

Hope it helps you,

mark me brainliest pls.....

Follow me! :)

Solve for x

I don’t have much time pls help. Round to the nearest hundredth

Answers

tan37=x:31
x=31*tan37
x=23.36

Melissa's mother bought . pounds of strawberries to make strawberry
smoothies. She estimates that she will need of a pound of strawberries for
each smoothie. How many smoothies can she make with the strawberries she
bought?

Answers

Answer:

depends on the ammount

Step-by-step explanation:

Mark has, in his kitchen, the ingredients needed to prepare 78 different recipes with two ingredients

each. Of those 78 different recipes, there are no two recipes that share the exact same two ingredients.

How many ingredients does he have?

Answers

Answer:

13 ingredients

Step-by-step explanation:

The number of different recipes that can be made from 2 ingredients = 78

Since there are no two recipes that share the exact same two ingredients ;

The number of recipes in Mark's kitchen is:

nCk = 78

k = Number of ingredients per recipe = 2

n = total number of ingredients in kitchen

Total recipes made = 78

n! / (n-r)!r! = 78

n! / (n - 2)!2! = 78

n(n-1)(n-2)! / (n-2)! * 2 * 1 = 78

n(n - 1) / 2 = 78

n(n-1) = 156

n² - n = 156

n² - n - 156 = 0

Factorize :

n² - 13n + 12n - 156 = 0

n(n - 13) +12(n-13) = 0

(n-13) = 0 ; (n+12) = 0

n = 13 or n = - 12

n cannot be negative

Hence, n = 13

Number of ingredients is 13

find each measurement indicated. Round your answers to the nearest tenth. Please SHOW WORK!!​

Answers

9514 1404 393

Answer:

  9) 39.7°

  10) insufficient information

  11) 20.0 in

  12) 19.0 m

Step-by-step explanation:

These Law of Sines problems are all worked the same way. For sides a, b, and opposite angles A, B, the relevant relationship is ...

  a/sin(A) = b/sin(B)

This gives rise to formulas for angle and side:

  A = arcsin(a/b·sin(B))

  a = b·sin(A)/sin(B)

If the longest given side is not opposite the largest given angle, there may be two solutions.

_____

9) B = arcsin(8/12.5·sin(87°)) = 39.7°

10) missing a side or angle; insufficient information

11) f = (5 in)·sin(70.4°)/sin(13.6°) = 20.0 in

12) p = (22 m)·sin(59°)/sin(180°-59°-24°) = 19.0 m

Pls help, i will give brainliest:
Consider the graphs which summarize the data on the number of hours per week of television viewing by two groups: 12-17 year-old Girls and 12-17 year-old Boys. Choose all that are correct.
The median for the girls is 16.
The median for the boys is 22.
The interquartile range for the girls is 28
The interquartile range for the boys is 16
The difference between the medians as a multiple of the IQR is 1/4

Answers

Answer:

a,b,e

Step-by-step explanation:

Answer:

B, D, E

OR

The median for the boys is 22

The interquartile range for the boys is 16

The difference between the medians as a multiple of the IQR is 1/4

Step-by-step explanation:

I just did it and got it right

Which is proportional

Answers

Answer:

B

Step-by-step explanation:

It goes up the same amount ($0.75) for every bar you get.

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