What is the least positive integer which when divided by 5 gives a remainder of 4, when divided by 6 gives a remainder of 5, when divided by 7 gives a remainder of 6, when divided by 8 gives a remainder of 7, when divided by 9 gives a remainder of 8, and when divided by 10 gives a remainder of 9

Answers

Answer 1

Answer:

  2519

Step-by-step explanation:

In each case, the remainder is 1 less than the divisor. This means the number of interest will be 1 less than the least common multiple of 5, 6, 7, 8, 9, 10.

The prime factors of these numbers are ...

  5 = 5

  6 = 2·3

  7 = 7

  8 = 2³

  9 = 3²

  10 = 2·5

The unique factors are 2, 3, 5, 7. When they are used to their highest powers, the resulting product is ...

  2³·3²·5·7 = 2520

The number of interest is 1 less than this, so is 2519.

2519 is the least positive integer that will give the required remainders.


Related Questions

Find the value of c that makes the trinomial a perfect square: x^2– 40x + c

Answers

Answer:

c=400

Step-by-step explanation:

Use the perfect square formula:

ax^2+bx+c=0

x^2-40x+c=0

bring c to the other side

x^2-40x+___=-c

divide -40 by 2 then square it; 400

add 400 to each side

c=400

(x-20)(x-20)

The value of c that makes the trinomial a perfect square x²– 40x + c is 400.

What is quadratic equation?

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

We have to find the  value of c that makes the trinomial a perfect square: x²– 40x + c

Lets use the perfect square formula:

ax²+bx+c=0

The given equation is given below.

x²-40x+c=0

Take the c term to the right hand side

x²-40x=-c

x²-40x+400=-c+400

c=400

Hence, the value of c that makes the trinomial a perfect square x²– 40x + c is 400.

To learn more on Quadratic equation click:

https://brainly.com/question/17177510

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Write an EQUATION with an undefined slope:

Answers

Answer:

Example of an equation with an undefined slope: x = 2

Step-by-step explanation:

Definitions

The standard form of linear equations with an undefined slope is x = a, whose graph represents a vertical line. The value of a in the standard form is the x-intercept, (a, 0).  

The slope is the ratio of the vertical change in y-values to the horizontal change in x-values.

[tex]\displaystyle\mathsf{Slope(m) =\:\frac{\triangle y}{\triangle x}\:=\frac{y_2 - y_1}{x_2 - x_1}}[/tex]

The slope of a vertical line is undefined because if we were to solve its slope, the denominator will be zero. As we know, division by zero is an undefined operation.  

Example:

For example, suppose that we have the following points (2, 5) (2, 10).

Let (x₁, y₁) = (2, 5)

     (x₂, y₂) = (2, 10)

Substitute these values into the slope formula:

[tex]\displaystyle\mathsf{Slope(m) =\:\frac{\triangle y}{\triangle x}\:=\frac{y_2 - y_1}{x_2 - x_1}\:=\:\frac{10\:-\:5}{2\:-\:2}\:=\frac{5}{0}}[/tex]

Dividing the numerator, 5, by the denominator, 0, will have an undefined quotient.

Thus, the equation of the vertical line will be: x = 2, where a = 2.

BRAINLIEST
Do one of the above and show your work

Answers

Answer:

10,   C = circumference = 2 pi 11 = 69.11 since the radius = 6

PR = C / 2 = 34.6  since PR is 1/2 the circumference

PS = 34.6 - 16 = 18.6    since PS is 16 ft short of C/2

Answer:

Step-by-step explanation:

Need help please if anyone one can help me now I will like that

Answers

Answer:

.

Step-by-step explanation:

Step-by-step equation

Plzzzz help asap
This table shows input and output values for a linear function
f(х)
What is the positive difference of outputs for any two inputs that
are three values apart?

Enter your answer in the box.

Answers

Answer:

2

Step-by-step explanation:

From what I understand from the question,

you're looking for the difference between f(x) and f(x+4)

lets take the points f(-3) and f(1)

the difference is 0.5 - -1.5=2

PLS HELP ASAP ILL GIVE BRAINLKEST PLS THANKS

Answers

It is y=2/3x. Think rise over run. It rises 2 and goes across 3

what is 3 1/2 X 2 X 9 1/3

Answers

Answer: 21

Steps: Convert the mixed number to an improper fraction and Reduce the numbers with the greatest common factor

- 7/2 * 2 * 3

Reduce the numbers with the greatest common factor

7 * 3

Answer = 21

Someone plz help :(

Side Lengths Angle Measures

6.6 in. 45∘

9.4 in. 90∘

6.6 in. 45∘

Based on the measurements, which answer best describes the triangle?

obtuse scalene triangle

obtuse isosceles triangle

acute scalene triangle

right isosceles triangle

right scalene triangle

right equilateral triangle

acute isosceles triangle

Answers

[tex]\huge \bf༆ Answer ༄[/tex]

According to the given information, The Triangle should be ~

[tex] \sf Right \: \: Isosceles \: \: triangle [/tex]

It's because the Triangle has two equal sides 6.6 inches each. and One right angle (90°) ~

I WILL GIVE 30 POINTS TO THOSE WHO FILL IN THE BLANK CORRECTLY. Find the value of X

Answers

Answer:

x = 12.81

Step-by-step explanation:

Is this triangle a right triangle? Explain.

Answers

Answer:

hmm

Step-by-step explanation:

I can't see any triangle there..a right angled triangle is meant to look like this

answer in standard form PLEASE.

Answers


0.9 x 10^4

Let’s break this down into steps.

So to start off with, you need to do 4.5/5 which = 0.9.

Now we can deal with the indices. 10^-3 / 10^-7 means we have to subtract them. Therefore, -3 - -7 = 4. Altogether, we have 0.9 x 10^4

The question states we should leave our answer in standard form.

So our answer is 0.9 x 10^4.

which ratio is equivalent to 4:10? Choose ALL the equivalent ratios from i-ready

Answers

Answer:

2:5 is the simplified form.

Step-by-step explanation:

4:10 => 4/10 => 2/5=> 2:5

Conclusion:

Therefore, the simplified form of 4:10 is 2:5.

Hoped this helped.

[tex]BrainiacUser1357[/tex]

Answer:

2:5 and 12:30

I hope this helps!

From: Aug1e

write the equation of the line given the two points. (1,-2) and (1,5)

Answers

Answer:

x=1

Step-by-step explanation:

y=mx+b

5--2/1-1

7/0

Match the sentences below to the correct vocabulary word.
rational number
1. A decimal that ends in zero is a —
2. 0.7 is a __
terminating decimal
3. Ifx is not a rational number, it must be a(n) —
repeating decimal
irrational number
4. x is a terminating decimal, so it must also be a

Answers

Answer:

1) terminating decimal

2) 0.7 is a terminating decimal

3) a non-terminating, non-repeating decimal

4) a rational number

Step-by-step explanation:

How many times does 13 go in to 33

Answers

2 times at the most……..

Write a system of equations to describe the situation below, solve using elimination, and fill in
the blanks.
The manager at a community pool is looking over receipts. On a certain Monday, the pool had
16 children and 42 adults, which brought in $142. That same week on Tuesday, 24 children
and 26 adults came to the pool, which brought in $102. What are the admission prices for
children and adults?

Answers

Answer:  Child is $1 and Adult is $3, per person.

Step-by-step explanation:

We have two unknowns, so we need at least two equations.  Let C and A stand for the price of a ticket for a child and an adult, respectively.

The income for Monday and Tuesday can be calculated:

Monday:   16C + 42A = $142

Tuesday:  24C + 26A = $102

Rearrange the second equation to isolate one of the variables.  I'll pick C:

24C + 26A = $102

C  = ($102 - 26A)/24

Now use this expression for C in the first equation

16C + 42A = $142

16(($102 - 26A)/24) + 42A = $142

16(($102 - 26A)/24) + 42A = $142

(1632 - 416A)/24 + 42A = $142

(68 - 17.3333A + 42A = $142

24.6667A = 74

A = 3  [The price of an adult pool admission is $3]

Use this value in either equation to find the price of a child's admission:

24C + 26A = $102

24C + 26*($3) = $102

24C = 102 - 78

C = $1   [The price of a child's admission to the pool is $1]

Check to see if these prices satisfy both equations:

Monday:   16C + 42A = $142

Tuesday:  24C + 26A = $102

---

Monday:   16*(1) + 42*(3)  = $142   ?   YES

Tuesday:  24*(1) + 26*(3) = $102   ?    YES

Child is $1 and Adult is $3, per person.

PLEASE HELP QUESTION IN PICTURE

Answers

I think it’s B 132 because it’s an obtuse angle and those measure more than 90 degrees
It’s definitely B because ABC is a obtuse angle and B is the number above 90

What is the distance between (7, 1) and (-4, -5)?

Answers

Answer:

The distance between [tex](7,1)[/tex] and [tex](-4,-5)[/tex] is [tex]\sqrt{157}[/tex] units

Step-by-step explanation:

Use the distance formula [tex]d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex] where [tex]d[/tex] is the positive distance between [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]:

[tex]d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]

[tex]d=\sqrt{(-5-1)^2+(-4-7)^2}[/tex]

[tex]d=\sqrt{(-6)^2+(-11)^2}[/tex]

[tex]d=\sqrt{36+121}[/tex]

[tex]d=\sqrt{157}[/tex]

Therefore, the distance between [tex](7,1)[/tex] and [tex](-4,-5)[/tex] is [tex]\sqrt{157}[/tex] units

Answer: The distance between (7,1), and (-4, -5) is 12.53.

Giving brainliestttyttttt

Answers

Answer:

C

Step-by-step explanation:

Because its right

yeah I didn't pay attention today ​

Answers

Answer: 314.3

Explanation: multiply 449 by .30 and then subtract your solution of that to 449 and you will have your new sum

IMPORTANT QUESTION: If i have 464 assignments to do, and want to get it done in 130 days how many assignments should I do a day?

Answers

Answer:

4 assignments per day.

Step-by-step explanation:

Since you have 464 assignments, and 130 days, then you can divide.464/130 = 3  37/65Since you have a fraction, you can round it to 4 assignments.

Answer:

3 .

Step-by-step explanation:

464 / 130

it’s not exactly like this,

if Im wrong!

Which sequence shows the numbers in order from least to
greatest?
1
2
-3
4
3
-3
OA) 2 3
} }
OB) Ź. *.
oc) * * Ź
OD) * *
4

Answers

Answer:

-3 1 2 3 4

Step-by-step explanation:

Answer:

-3 1 2 3 4

Step-by-step explanation:

Sarah rolls 2 fair dice and adds the results from each.
Work out the probability of getting a total of 2.

Answers

Answer:

1/36.

Step-by-step explanation:

She gets 1 on the first dice and 1 on the second.

This is the only way Sarah can get a sum of 2.

The total  possible outcomes is 6*6 = 36.

So the required probability is 1/36.

solve -7(4-x) + 4 is greater than or equal to -18 + 7x

Answers

Answer:

-7(4-x)≥-18+7x

-28+7x≥-18+7x

7x-7x≥-18+28

x≥10

Step-by-step explanation:

Please I need Help!!! Solve this equation by factoring by grouping x^2-4x=12. All work must be shown and no other method will be accepted.

Answers

x² - 4x = 12

x² - 4x - 12 = 0

x² + (2x - 6x) - 12 = 0

x² + 2x - 6x - 12 = 0

x (x + 2) - 6 (x + 2) = 0

(x - 6) (x + 2) = 0

Then the solutions are x = 6 or x = -2.

Please help I’ll mark brainliest!!!

Answers

Answer:

B

Step-by-step explanation:

As x gets bigger or smaller, y approaches negative infinity

Can someone please help me with these 2 problems I’ve been stuck on them for awhile :’) tysm!

Answers

Answer:

48. 95,400 mL

50a. 331 yds.

50b. 11,916 in.

Step-by-step explanation:

Some helpful conversions can solve this for you :)

1 liter = 1000 mL

1 yard = 3 feet

1 feet = 12 inches

Now we get started!

48. We have 95.4 Liters, multiply by 1000 because 1000 mL per Liter. Therefore it's 95,400.

50

a. 3 feet per yard, so 993 feet divided by 3 is 331 yards.

b. 12 inches per foot, so 993 feet multiplied by  12 is 11,916

A girl plays the same computer game lots of times.
The computer scores each game using 1 for the win, 0 for lose.
After each game, the computer calculates her overall mean score.
The graph shows the results for the first 20 games.

What percentage of the 20 games did the girl win?

Answers

Answer: 45%

From my common sense

If the graph line goes up, she wins.

If the graph line goes down, she loses.

1. Count the amounts of times which the graph line goes up.

(btw the first game she won because the graph line started at 1)

= 9

2. Calculate the winrate of her 20 games

= 9/20 * 100

= 45%

Use the information given to answer the question. An office supply store has 1,508cases of paper and
736
boxes of pens. Each case of paper contains
24
packs of paper, and each box of pens contains
50 pens.

Part A

How many packs of paper does the office supply store have?
36,192 packs of paper

36 , 192 packs of paper

36,432 packs of paper

36 , 432 packs of paper

37,700 packs of paper

37 , 700 packs of paper

37,750 packs of paper

Answers

36,192 packs of paper. It’s multiplication if you have 1,508 packs of paper and each case contains 24 packs you would multiply to see how many packs of paper you have.

PLEASE I NEED HELP, ILL MARK AS BRAINLIEST!!

Raul  is filling a 55 gallon fish tank with water. There are 18.5 gallons of water in the take 2.5 gallons of water flows from the hose each minute how many gallons of water are in the fish tank after 12 minutes

Answers

Answer:

All you do is multiply 2.5 x 12

Step-by-step explanation:

multiplying both numbers gets you a toltal of 24.60 or 24.6

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