Prove that if a and b are integers, then for any integer k one has (a,b) = (a + kb,b). (Hint: Show that they are mutually divisible.)

Answers

Answer 1

Answer:

The operation:

(a,b) is equal to the rest of the division of a by b.

Now, if we have:

(a + kb,b) = (a,b) + (k*b,b)

But if we have that k and b are integers, then:

(k*b)/b = k

So b divides k*b into a whole number, this means that (k*b,b) = 0

then:

(a + kb,b) = (a,b) + (k*b,b) = (a,b) + 0 = (a,b)


Related Questions

List the angles in order from the largest to the smallest for ABC.
AB= 14, AC = 15, BC = 16

Answers

Answer:

B. ∠A, ∠B, ∠C

Step-by-step explanation:

1. Draw a model with AB as the shortest line and BC as the longest line.

∠A connects the two shortest lines, making it the largest angle.

∠B connects the shortest and the longest lines, making it the second largest angle.

∠C connects the two longest lines, making it the smallest angle.

Answer:

A > B > C

Step-by-step explanation:

Ypu probably wouldn't think about it unless someone pointed it out, but if you look at a triangle of any type you can see that the sizes of the sides are directly related to the sizes of the angles opposed to them.

By this I mean, the largest side will have the largest angle across from it and the smallest side will have the smallest angle.

Based off of my drawing, it looks like the order is angle A, then B, then, and then C.

Apply the square root property of equality.

x + =

Answers

Answer:

Step-by-step explanation:

Answer:

+ 1/16 = +- 2/3

What number is halfway between 250 and 300

Answers

Answer:

the number that is halfway between 250 and 300 is 275

Step-by-step explanation:

250+300= 550/2= 275

The number i,e halfway is 275.

Important information:The two numbers is 250 and 300.

calculation:

[tex]= (250 + 300) \div 2\\\\= 550 \div 2[/tex]

= 275

Find out more information about the Number here : https://brainly.com/question/17429689?referrer=searchResults

The graph represents this system of equations
y=4
y=3 - 1/2x . What is the solution to the system of equations
(-2,4)
(3,4)
(4,-2)
(4,3)

Answers

Hey there! I'm happy to help!

When graphing a system of equations, the solution is the point where the two lines meet. We see that they intersect at (-2,4).

Therefore, the solution to the system of equations is (-2,4).

Have a wonderful day! :D

Answer:

A

Step-by-step explanation:

edge 2020 Dec 9


The sum of the reciprocals of two consecutive even integers is 3/4
Find the two integers.

Answers

[tex] \Large{ \underline{ \underline{ \bf{ \orange{Solution:}}}}}[/tex]

Let one of those even numbers be x, Then other even number would be x + 2.

According to question,

⇛ Their reciprocal add upto 3/4

So, we can write it as,

⇛ 1/x + 1/x + 2 = 3/4

⇛ x + 2 + x / x(x + 2) = 3/4

⇛ 2x + 2 / x² + 2x = 3/4

Cross multiplying,

⇛ 3(x² + 2x) = 4(2x + 2)

⇛ 3x² + 6x = 8x + 8

⇛ 3x² - 2x - 8 = 0

⇛ 3x² - 6x + 4x - 8 = 0

⇛ 3x(x - 2) + 4(x - 2) = 0

⇛ (3x + 4)(x - 2) = 0

Then, x = -4/3 or 2

☃️ It can't be -4/3 because it is fraction and negative number. So, x = 2

Then, x + 2 = 4

✤ So, The even numbers are 2 and 4.

━━━━━━━━━━━━━━━━━━━━

If 6x +3= 2x+ 19, then x =

Answers

Answer:

x = 4

Step-by-step explanation:

6x + 3 = 2x + 19  ------ subtract 3 both sides

6x + 3 - 3 = 2x + 19 - 3   simplify

6x = 2x + 16         ------ subtract 2x both sides

6x - 2x = 2x + 16 - 2x      simplify

4x = 16

x = 16 / 4

x = 4

Answer: x = 4

Step-by-step explanation: If the variable appears on both sides of the equation, we put the variables together on one side of the equation and the numbers together on the other side of the equation.

So let's put our variables on the left side by first subtracting

2x from both sides of the equation to get 4x + 3 = 19.

Next, we subtract 3 from both sides to get 4x = 16.

Finally, we divide both sides by 4 to get x = 4.

If the area of the square is A(s) = s², find the formula for the area as a function of time, and then determine A(s(3)).

Answers

A(t) = 100t^2 + 500t + 625

3,025 square pixels

Answer:

A(t) equals 100t²+ 500t + 625.

The area of the square image after 3 seconds is 3,025 square pixels.

what is area of this tile? ​

Answers

the area is 24 inch^2

At a local high school, the student population is growing at 12% a year. If the original population was 242 students, how long will it take the population to reach 300 students? Round to the nearest tenth of a year.

Answers

Answer: 2 years

Step-by-step explanation:

The exponential growth function is given by :-

[tex]y=A(1+r)^x[/tex] (i)

, where A = initial value , r = rate of growth and  x= time period.

As per given ,

A= 242

r= 12% = 0.12

To find : t when y= 300.

Put all the values in (i)

[tex]300=242(1+0.12)^x\\\\\Rightarrow\ \dfrac{300}{242}=(1.12)^x\\\\\Rightarrow\ 1.23967=(1.12)^x[/tex]

Taking log on both sides , we get

[tex]\log (1.2396) = t \log (1.12)\\\\\Rightarrow\ 0.09328=t(0.049218)\\\\\Rightarrow t=\dfrac{0.09328}{0.049218}=\approx2[/tex]

hence, it will take 2 years.


Fill in the missing values to make the equations true .

Answers

Answer:

a) 15

b) 9

c) 2

Step-by-step explanation:

im try it by using trial and error by calculator

Find the value of x.

Answers

Answer:

x=3

Step-by-step explanation:

I guessed and checked which x value would make ABC proportional to DBE. If x=3, than DB=8 which is double BE. If x=3, than AB=14 which is double BC. Since it is proportional, It should be correct. I don't remember the actual way you solve this with a formula but this makes sense to me.

Answer:

x=3

Step-by-step explanation:

We can use ratios to solve since the triangles are similar

x+5                   4

------------ = ---------------

x+5 +2x          4+3

Simplifying

x+5                   4

------------ = ---------------

3x+5             7

Using cross products

7(x+5) = 4(3x+5)

Distribute

7x+35 = 12x+20

Subtract 7x from each side

35 = 5x+20

Subtract 20 from each side

15 = 5x

Divide by 5

3 =x

When a dummy variable is included in a multiple regression model, the interpretation of the estimated slope coefficient does not make any sense anymore.

a. True
b. False

Answers

Answer: b. False

Step-by-step explanation:

A dummy variable is a numerical variable used in regression analysis to represent values for categorical data by using value 0 (shows absence of particular category) or 1  (shows presence of particular category) .We cannot use categorical data to evaluate the slope coefficient (numerical value) until we convert them into dummies.

Hence, the given statement is absolutely false.

A sample of 255 observations is selected from a normal population with a population standard deviation of 27. The sample mean is 20. Determine the standard error of the mean.

Answers

Answer:

1.691

Step-by-step explanation:

Standard error of the mean is expressed as SEM = S/√n

S is the population standard deviation

n is the sample size (number of observation)

Given S = 27 and n = 255

SEM = 27/√255

SEM = 27/15.97

SEM = 1.691

Hence the standard error of the mean is 1.691

If the function Q(t)=4e-0.00938t models the quantity (in kg) of an element in a storage unit after t years, how long will it be before the quantity is less than 1.5kg? Round to the nearest year.

Answers

Answer:

105 years

Step-by-step explanation:

Given the function :

Q(t) = 4e^(-0.00938t)

Q = Quantity in kilogram of an element in a storage unit after t years

how long will it be before the quantity is less than 1.5kg

Inputting Q = 1.5kg into the equation:

1.5 = 4e^(-0.00938t)

Divide both sides by 4

(1.5 / 4) = (4e^(-0.00938t) / 4)

0.375 = e^(-0.00938t)

Take the ln of both sides

In(0.375) = In(e^(-0.00938t))

−0.980829 = -0.00938t

Divide both sides by 0.00938

0.00938t / 0.00938 = 0.980829 /0.00938

t = 104.56599

When t = 104.56599 years , the quantity in kilogram of the element in storage will be exactly 1.5kg

Therefore, when t = 105 years, the quantity of element in storage will be less than 1.5kg

In order to study the mean blood pressure of people in his town, Richard samples the population by dividing the residents by age and randomly selecting a proportionate number of residents from each age group. Which type of sampling is used?
a. Convenience sampling
b. Cluster sampling
c. Stratified sampling
d. Systematic sampling

Answers

Answer:

C Stratified sampling

Step-by-step explanation:

Stratified sampling : Stratified sampling is a type of sampling technique in which the total population is divided into smaller groups or strata to complete the sampling process. The strata is formed based on some common characteristics in the data of the population.

One of the advantage of stratified random sampling is that it covers important population characteristics in the sample.

can someone show me how to do this please​

Answers

Answer:

[tex]volume = 0.32 m^3[/tex]

Step-by-step explanation:

The object shown above consists of 5 cubes having side lengths of ⅖m each.

Volume of a cube = [tex] a^3 [/tex]

Where, a = side length = ⅖ m

Volume of the object = [tex]5* (\frac{2}{5})^3[/tex]

[tex]volume = 5*\frac{8}{125} = 5*0.064 = 0.32 m^3[/tex]

Find the Vertical asymptotes of the graph of f
[tex]f(x) = \frac{x + 2}{ {x}^{2} - 4}[/tex]

Answers

Answer:

x = 2 and x = -2

Step-by-step explanation:

To find the vertical asymptotes, set the denominator equal to zero and solve for x:

vertical asymptotes are x = 2 and x = -2

What’s the next number is this series 31,29,24,22,17,

Answers

Answer:

15

Step-by-step explanation:

Just find out the pattern.  It is decreasing, so let's find out how much it is decreasing by.

31-29= -2

29-24= -5

24-22= -2

22-17= -5

The pattern is -2, -5, -2, -5... So the next one should be -2 again!  17-2=15.

Remember, a pattern doesn't always have to be subtracting, adding, dividing, or multiplying at a constant number!  It can switch between two, like this problem!

A pharmacy has purchased 550 products over a period of 3 months. If their average inventory was 235 products in a 3 month period what was their inventory turnover rate for this period

Answers

Answer:

2.34

Step-by-step explanation:

A pharmacy purchased 550 products over a period of 3 months

The average inventory was 235 products during the period of 3 months

Therefore, the inventory turnover rate for this period can be calculated as follows

= 550/235

= 2.34

Hence the inventory turnover rate for this period is 2.34

Plz answer quick will give good rate and thanksss
h(x) = (x - 3)^2 determine which x-value whether it is in the domain of h or not

In domain not in domain
0
3
4

Answers

Answer:

Hey there!

All of the values: 0, 3, and 4 are in the domain.

This is because h(x) = (x - 3)^2 is a parabola, or a quadratic. By definition, the domain, or the possible x values of a parabola are infinite.

Hope this helps :)

The area of the triangle is 5.88 square centimeters.what is the length of the base.the heights is 2.1

Answers

Answer:

base = 5.6 cm

Step-by-step explanation:

area of a triangle = 1/2 * base * height

area = 5.88 cm²

height = 2.1 cm

5.88 = 1/2 * base * 2.1

5.88 = 1.05 base

5.88 / 1.05 = base

base = 5.6 cm

the area of triangle is 5.25 sq cm what is length of base

i will give brainliest and 5 stars if you help ASAP​

Answers

Answer:

£39.20

Step-by-step explanation:

→ Identify which ratio goes to each person

2 : 1 : 5

2 = Paul

1 = Colin

5 = Brian

→ Divide the total tip by the total sum of the ratio's

£78.40 ÷ ( 2 + 1 + 5 ) ⇔ £78.40 ÷ 8 = £9.80

→ Now we know one part is equal to £9.80 we multiply this number by each of the associated ratio's

Paul = £9.80 × 2 ⇔ £19.60

Colin = £9.80 × 1 ⇔ £9.80

Brian = £9.80 × 5 ⇔ £49

→ Minus Brian's tip against Colin's tip

£49 - £9.80 = £39.20

Jayden, who burns 345 calories in 45 min
while hiking is preparing for a 6 hour hike.
He uses a special supplement beverage
pack that provides water, needed
electrolytes, and 310 calories. The goal is to
replace roughly 1/3 of the calories burned
while carrying as light a load as possible.
How many packs should he take?

Answers

I think that she should bring three packs. 6 hours=360 minutes. 360/45=8. 345x8=2760. 2760/3=920 and 310x3=930. :)

This question is solved using proportions.

First, we find how many calories he will burn in the hike.Then, we find how many calories he will need to replace, and the number of packs needed.

Doing this, we get that he should take 3 packs.

How many calories he burns in the hike?

In 45 minutes, he burns 345 calories. How many calories in 6*60 = 360 minutes?

45 minutes - 345 calories

360 minutes - x calories

Applying cross multiplication:

[tex]45x = 345*360[/tex]

[tex]x = \frac{345*360}{45}[/tex]

[tex]x = 2760[/tex]

He burns 2760 calories in the hike.

How many calories he wants to replace?

Roughly 1/3, so he have to find one third of 2760, that is:

[tex]\frac{2760}{3} = 920[/tex]

How many packs?

One pack recovers 310 calories, how many packs for 920 calories?

1 pack - 310 calories

x packs - 920 calories

Applying cross multiplication:

[tex]310x = 920[/tex]

[tex]x = \frac{920}{310}[/tex]

[tex]x = 2.97[/tex]

Rounding up, he should take 3 packs.

A similar question is found at https://brainly.com/question/14426926

Alex wants to sew a pillow in the shape below. How many square yards of fabric are needed to sew the pillow? Fabric is only sold in increments of ¼ yard.

Answers

The shape is missing, so i have attached it.

Answer:

2.6

Step-by-step explanation:

From the image attached, the diameter of the inner semi - circle is 0.5 yards while the length of each side of the pillow is 0.2 yards.

Thus, for us to find the length of the seam which is along the edges of the pillow, we will calculate the perimeter of the outer semicircle, then add the perimeter of the inner semicircle and also add the sides too.

Now, due to the fact that the length of the sides of the pillow are 0.2 yards each, the diameter of the outer circle would be;

0.5 + 0.2 + 0.2 = 0.9 yards. So, the perimeter of the outer semicircle is,

P0 = πd/2 = π × 0.9/2 =0.45π yds

The perimeter of the inner semicircle would be given as;

PI = πd/2 = π × 0.5/2 =0.25π yds.

Thus, we can calculate the total perimeter of the pillow as;

PT = P0 + PI + 0.2 + 0.2

PT = 0.45π + 0.25π + 0.2 + 0.2

PT ≈ 2.6 yards

Alex will need 2.6 yds

Answer:

0.5

Step-by-step explanation:

F
13
5
H
12
G
se
Find mZH to the nearest degree.
67
O 18
O 45
O 23

Answers

Answer:

∠ H ≈ 23°

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan H = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{FG}{HG}[/tex] = [tex]\frac{5}{12}[/tex] , thus

∠ H = [tex]tan^{-1}[/tex] ( [tex]\frac{5}{12}[/tex] ) ≈ 23° ( to the nearest degree )

Solve 2(x - 1) + 3 = x - 3(x + 1) (make sure to type the number only)

Answers

Answer:

x = -1

Step-by-step explanation:

2(x - 1) + 3 = x - 3(x + 1)

Distribute

2x -2+3 = x -3x-3

Combine like terms

2x +1 = -2x-3

Add 2x to each side

2x+1 +2x = -2x-3+2x

4x+1 = -3

Subtract 1 from each side

4x+1-1 = -3-1

4x= -4

Divide by 4

4x/4 = -4/4

x = -1

please help me in these question ????

A school bag contains 12 pens of which 5 are red and the other are black. 4 pens are selected from the bag.
(a) How many different samples of size 4 pens are possible?
(b) How many samples have 3 red pens and 1 black pen?
(c) How many samples of size 4 contain at least two red pens?
(d) How many samples of size 4 contain


If the average yield of cucumber acre is 800 kg, with a variance 1600 kg, and that the amount of the cucumber follows the normal distribution.
1- What percentage of a cucumber give the crop amount between and 834 kg?
2- What the probability of cucumber give the crop exceed 900 kg ?

Answers

Answer:

Step-by-step explanation:

A school bag contains 12 pens of which 5 are red and the other are black. 4 pens are selected from the bag.

(a) How many different samples of size 4 pens are possible?

12C4=12!/(4!*8!)=495

(b) How many samples have 3 red pens and 1 black pen?

5C3*7C1

5C3=5!/(3!*2!)=10

7C1=7!/(1!*6!)=7

=>5C3*7C1=10*7=70

(c) How many samples of size 4 contain at least two red pens?

(5C2*7C2)+(5C3*7C1)+(5C4*7C0)

5C2=5!/(2!*3!)=10

7C2=7!/(2!*5!)=21

5C3=5!/(3!*2!)=10

7C1=7!/(1!*6!)=7

5C4=5!/(4!*1!)=5

7C0=7!/(0!*7!)=1

=>(5C2*7C2)+(5C3*7C1)+(5C4*7C0)=285

(d) How many samples of size 4 contain at most one black pen?

(7C1*5C3)+(7C0*5C4)

7C1=7!/(1!*6!)=7

7C0=7!/(0!*7!)=1

5C3=5!/(3!*2!)=10

5C4=5!/(4!*1!)=5

=>(7C1*5C3)+(7C0*5C4)=(7*10)+(1*5)=75

PLEASE HELP MEEEEEEEEEEEEEEE

Answers

Answer:

x=16.1

Step-by-step explanation:

open the brackets

-4.5= -0.5x-3.55

Take 3.55 to the other side.

-4.5-3.55 = -8.05

5/10x= -805/100

0.5x= - 8.05 = 16.1

According to​ psychologists, IQs are normally​ distributed, with a mean of 100 and a standard deviation of 15 . a. What percentage of the population has IQs between 85 and 100 ​?

Answers

Answer: 34%.

By definition of normal distribution, ≈68% of the data is within 1 standard deviation of the mean. Therefore 68% of IQs are between 85 and 115, and half of that is on the lower end, 85 to 100.

This year Alex’s age is 1/6 of his dads. Four years later, Alex’s age is 1/4 of his dads. How old is Alex and his dad this year?

Answers

Answer:

This year:

dads: 36 years

Alex: 6 years

Step-by-step explanation:

a = d/6

a+4 = (d+4)/4

a = Alex´s actual age  

d = actual age of the dad

d/6 + 4 = (d+4)/4

4{(d/6) + 4} = d+4

4*d/6 + 4*4 = d+4

4d/6 + 16 = d + 4

4d/6 = d + 4 - 16

4d = (d-12)*6

4d  = 6*d +6*-12

4d = 6d - 72

4d - 6d = -72

-2d = -72

d = -72/-2

d = 36

a = d/6

a = 36/6

a = 6

probe:

a+4 = (d+4)/4

6 + 4 = (36+4)/4

10 = 40/4

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