Let $n$ be the smallest composite number such that it can be written as the product of two positive integers that differ by 10?

Answers

Answer 1

Answer:

The smallest composite number for [tex]n[/tex] is 24, which is the product 2 and 12.

Step-by-step explanation:

A composite number is an integer that is not a prime number, that is, a number that can be divided only by one and itself. Let be [tex]n[/tex] the smallest composite number such that there are two positive integers [tex]x[/tex], [tex]y[/tex] such that [tex]x - y = 10[/tex] and [tex]x\cdot y = n[/tex]. [tex]n[/tex] is a positive integer, since both integers are positive. Then, we can use the following formula:

[tex](y+10)\cdot y = n[/tex]

[tex]y^{2}+10\cdot y = n[/tex]

[tex]y^{2}+10\cdot y - n = 0[/tex] (1)

We obtain the roots of this second order polynomial by means of the Quadratic Formula:

[tex]y = \frac{-10\pm \sqrt{10^{2}-4\cdot (1)\cdot (-n)}}{2}[/tex]

[tex]y = -5\pm \sqrt{25+n}[/tex] (2)

Given that [tex]y > 0[/tex], we must observe the following inequation:

[tex]-5\pm \sqrt{25+n}>0[/tex] (3)

[tex]\sqrt{25+n} > 5[/tex]

[tex]25 + n > 25[/tex]

[tex]n > 0[/tex]

Let is find the values of x and y by iterative means:

x = 11, y = 1

[tex](11)\cdot (1) = 11[/tex]

11 is not a composite number, but a prime number.

x = 12, y = 2

[tex](12)\cdot (2) = 24[/tex]

24 is a composite number, which contains the following product of prime numbers:

[tex]2^{3}\cdot 3 = 24[/tex]

The smallest composite number for [tex]n[/tex] is 24, which is the product 2 and 12.


Related Questions

Which is a solution to the equation 7g-2=47

Answers

5 the answer is 5.......

Answer:

g=7

Step-by-step explanation:

7g-2=47

   +2  +2

7g=49

÷7   ÷7

g=7

(01.02 MC)Which of the following expressions shows how to rewrite 4 − 5 using the additive inverse and displays the expression correctly on a number line?
1.The expression 4 plus negative 5 is written on top. A number line from negative 10 to positive 10 is shown, with numbers labeled at intervals of 1. An arrow is shown from point 0 to 4. Another arrow points from 4 to negative 1.
2.The expression 4 plus negative 5 is written on top. A number line from negative 10 to positive 10 is shown, with numbers labeled at intervals of 1. An arrow is shown from point 0 to 4. Another arrow points from 4 to 5.
3.The expression 4 minus negative 5 is written on top. A number line from negative 10 to positive 10 is shown, with numbers labeled at intervals of 1. An arrow is shown from point 0 to 4. Another arrow points from 4 to negative 5.
4.The expression 4 minus negative 5 is written on top. A number line from negative 10 to positive 10 is shown, with numbers labeled at intervals of 1. An arrow is shown from point 0 to 4. Another arrow points from 4 to 1.

Answers

Answer:

I think the answer is 1. The expression 4 plus negative 5 is written on top. A number line from negative 10 to positive 10 is shown, with numbers labeled at intervals of 1. An arrow is shown from point 0 to 4. Another arrow points from 4 to negative. So the answer is A

hope this helps sorry if it wrong

pls let me now if right or wrong

The expression 4 plus negative 5 is written on top. A number line from negative 10 to positive 10 is shown, with numbers labeled at intervals of 1. An arrow is shown from points 0 to 4. Another arrow points from 4 to negative 1. Option A is correct.

What is a number line?

A number line is defined as the number marked on the line calibrated into an equal number of units. For example -1, 0, 1, and so on.

Here,
4  + (- 5)

The expression 4 plus negative 5 is written on top. A number line from negative 10 to positive 10 is shown, with numbers labeled at intervals of 1. An arrow is shown from points 0 to 4. Another arrow points from 4 to negative 1.

Thus, option A is correct.

Learn more about number line here:

brainly.com/question/17683084

#SPJ2

Solve the following equation: -3 = 1 3/5 + m.

-2 3/5
-4 3/5
-4 2/5
-1 2/5

Answers

Answer:

-4 3/5

Step-by-step explanation:

I subtracted 1 3/5 from -3 and got -4 3/5. I also added 1 3/5 + -4 3/5 to check my work and it is correct.

Solve.

−35x=18

−30

−1045

1045

30

Answers

Answer:

if you're trying to solve  -35x= 18   .. then do the following

Step-by-step explanation:

x = -18 / 35

x= -0.5142857143

I'm guessing that b/c the answer is not an easy number that you probably are trying to do something else. .. ask again  :)

Answer:

−30

Step-by-step explanation:

HELP ASAP FOR BRAINLIEST

Answers

Answer: i am pretty sure its the first one

Step-by-step explanation:

i don't know for sure

1st one: find the y-coordinate when the x-coordinate is at 0

Logically if you think about it, when x is at zero the y-value is also at 0. The number 0 will not find you the amount of wood gathered per hour.

As long as you can connect the hours (x-value) with the amount of wood (y-value) that meets on the line, then you should be able to determine the amount.

I hope that’s not too confusing. If so, send a comment and i can explain it to you further (:

Which of the following best describes an Extraneous Solution?

Answers

Answer:

An extraneous solution is a solution obtained through algebraic manipulations that is not a solution to the original equation.

Step-by-step explanation:

An extraneous solution is a solution obtained through algebraic manipulations that is not a solution to the original equation.

A boy wants to purchase 1,400 green marbles. If there are 70 green marbles in each bag, how many bags of marbles should the boy buy?

Answers

Answer:

20 bags

Step-by-step explanation:

1400/70

Answer:

20 bags

Step-by-step explanation:

1400 ÷ 70 = 20

HELP I WILL GIVE MANY THX AND BRAINLIST (it says high school but im in middle)
what is 5⁴ in expanded form

Answers

Answer:

5 * 5 * 5 * 5

Step-by-step explanation:

=625

(ii) Use the quadratic formula to solve 4x2 +11x-300 = 0.
Show all your working and give your answers correct to 2 decimal
places.
... or x =
[4]
mm​

Answers

x=-b+-sqrt (b^2-4ac)/2a
x=-11+-sqrt (11^2-4(8)(-300)/16
x=-11+-sqrt (121+9600)/16
x=-11+-sqrt (9721)/16
x=-11+-98.6/16
x=5.48 or x=-6.85

What is the approximate area of the circle shown below?
A. 94 cm2
B. 11,310 cm2
C. 2827 cm2
D. 188 cm2

Please help

Answers

Answer:

Step-by-step explanation:

we have the diameter =60 cm, the radius is 60/2=30 cm

A circle is 3.14*r^2=2827 cm^2

Answer: C. 2827 cm2

Step-by-step explanation:

The area of a circle is calculated by pir^2; r = the radius

In the diagram, the diameter is provided. The radius is half of the diameter. 60/2 = 30, so the radius is 30 cm.

Plug these values into the formula

A = 3.14*30^2

A = 2827.43, which would round to 2827 cm2


What is the probability that Mark and Bobby will both choose mushrooms?

Answers

what is the rest of the question

Answer: choose mushrooms out of what?

Will give crown help

Answers

Answer:

There are 5 spaces between point J and I

Point J is at (-7,-2)

Point I is at (-2,-2)

They have the same y value, but a difference of 5 in the x value. So, they are 5 units apart.

amanda had to pay sales tax on a new iphone case she purchased last week. The iphone case was 35.00 and she pid 2.45 in taxes, what percent of the original price did she pay in taxes?

HELP

Answers

Answer:

7%

Step-by-step explanation:

[tex]\frac{2.45}{35} = \frac{x}{100}[/tex]

[tex]2.45*100[/tex] and [tex]35x[/tex]

[tex]\frac{245}{35} = \frac{35x}{35}[/tex]

[tex]245/35=7[/tex]

It is 49,280 yards from Topeka to Tonko. How many miles
is this?

Answers

Answer:

Step-by-step explanation:

1 yard = 0.000568 miles

49280 yards = 28 miles

1 mile = 1,760 yards

Divide total feet by 1760

49,280 / 1760 = 28 miles.


Yyhhjfffghjjgdrttyhhhftthvfrtgvfffgf

Answers

Answer: So the star equals 4 and the triangle equals 1

Step-by-step explanation:

Answer:
(4,1)

Explanation:
Stars = 4
Triangles =1

I don’t know how to do this

Answers

Answer:

the following points: (6,-1),(2,-4), and (-2,3)

Step-by-step explanation:

imagine that the y axis is a mirror. Everything that happens is reflected. So (1,2) becomes (-1,2) so your three points are (-6, -1),(-2,-4), and (2,3) when you reflect them, you get the following points: (6,-1),(2,-4), and (-2,3)

the order of the surd 6 √2187 after simplification is​

Answers

Answer:

[tex]n = 162[/tex]

Step-by-step explanation:

Given

[tex]6\sqrt{2187[/tex]

Required

Determine the order of the surd

If a surd is represented as [tex]n\sqrt{r[/tex], then the order of the surd is [tex]n[/tex]

[tex]6\sqrt{2187[/tex]

Express 2187 as [tex]3^6 * 3[/tex]

[tex]6\sqrt{2187} = 6\sqrt{3^6 * 3}[/tex]

Split the surd

[tex]6\sqrt{2187} = 6\sqrt{3^6} * \sqrt{3}[/tex]

Apply the following law of indices:

[tex]\sqrt{a} = a^{\frac{1}{2}}[/tex]

The expression becomes:

[tex]6\sqrt{2187} = 6 * 3^{\frac{6}{2}} * \sqrt{3}[/tex]

[tex]6\sqrt{2187} = 6 * 3^{3} * \sqrt{3}[/tex]

[tex]6\sqrt{2187} = 6 * 27 * \sqrt{3}[/tex]

[tex]6\sqrt{2187} = 162 * \sqrt{3}[/tex]

[tex]6\sqrt{2187} = 162 \sqrt{3}[/tex]

By comparing [tex]162 \sqrt{3}[/tex] to [tex]n\sqrt{r[/tex], we can say that:

[tex]n = 162[/tex]

[tex]r = 3[/tex]

Conclusively, the order of the surd is 162

The image point of A after a translation right 4 units and down 4 units is the point B(12, – 7). Determine the coordinates of the pre-image point A.

Answers

Answer:

            (8, –3)

Step-by-step explanation:

Translation right or left means change of the x-coordinate.  

Translation up or down means change of the y-coordinate.

Translation right or up means adding.

Translation left or down means  subtracting.

[tex]A=(x_A, y_A)\quad\rightarrow\quad B=(x_A+4,\,y_A-4)\\\\x_A+4=12\qquad\qquad y_A-4=-7\\\\x_A=12-4\qquad\qquad y_A=-7+4\\\\x_A=8\qquad\qquad\qquad y_A=-3\\\\A=(8,-3)[/tex]

Evaluate x+y when x= −4/5 and y= 1/3. Write your answer as a fraction or mixed number in simplest form.

Answers

Answer:

-7/15

Step-by-step explanation:

=-4/5 + 1/3

=(-12+5)/15

=-7/15

Answer:

-7/15

Explanation:

x + y

-4/5 + 1/3

-12/15 + 5/15

= -7/15

At a computer store, the package of the DVDs sell for $15 each. One customer buys $120 worth of the DVDs.
Write an equation to model the number of the packages of the DVDs the customer bought, and then solve the equation. Plus, I need help with question number 9. A and B of Solve Simple Equation Word Problem will be marked as brainliest if your answer fully completed with complete step-by-step explanation! :)

Answers

Answer:

The customer bought 8 DVDs for $120.00

Step-by-step explanation:

120*15=8 DVDS or as a ratio 8:1

Which boat was farther from the dock at the beginning and which traveled more quickly

Answers

Answer:

Nvm

Step-by-step explanation:

Johns boat was 30 miles away. It traveled 20 miles in 5 hours (50-30 = 20)

20/5 = 4

It traveled at 4 miles per hour.

The equation for Roberta’s boat multiplied 5 by x( number of hours) so this means her boat is traveling at 5 miles per hour.

Then 25 gets added at the end, this means her boat was 25 miles away at the beginning.

Johns boat was further away at the beginning and Robertas boat is traveling faster.

EXPERTS OR ACES PLEASE ANSWER THIS FAST DUE IN 2 MIN 50 POINTS

Answers

Answer:

24 blocks

Step-by-step explanation:

b = 2(9) + 6b = 18 + 6b = 24

sarah has a rope that is 36 feet long she is cutting it into 6 foot pieces to make jump ropes how many jump ropes can sarah make ?

Answers

Answer:

she can make 6 jump ropes

I WILL MARK BRAINLIEST!
A cylindrical well is 20 meters deep and has a diameter of 1.5 meters. Approximately how many cubic meters of soil were dug out to make the well? (Use π = 3.14.) (5 points)

11.78 cubic meters
35.33 cubic meters
121.20 cubic meters
141.30 cubic meters

Answers

Answer:

35.33

the drill use the volume formula for a cylinder then plug in the numbers

Select the correct answer from each drop-down menu.
April and Jasmine found the volume of the rectangular prism below.

5x8x6

April packed the rectangular prism with centimeter cubes to find the volume. She packed 4 layers of centimeter cubes. Each layer had 8 rows with 6 cubes in each row.

Jasmine multiplied the side lengths to find the volume.



One of the students made a mistake, and her work will result in an incorrect volume.

The student who made the mistake was
.April or Jasmine

Her mistake was
she did not multiply the correct numbers
she did not pack enough layers of centimeter cubes
she should have added the length sides
She packed too many centimeter cubes in each layer

The correct volume of the rectangular prism is cubic centimeters. 240 or 200 or 270

Answers

Answer:

AprilShe did not pack enough layers of centimeter cubes240 cubic centimeters

Step-by-step explanation:

Dimensions of the prism is 5x8x6

April made a mistake, she packed 4 layers of unit cubes instead of 5 layers

Correct  volume of the prism is:

5*8*6 = 240 cm³

Correct answer choices:

AprilShe did not pack enough layers of centimeter cubes240 cubic centimeters

This is the one that will decide my note, help once more please

Answers

Answer: x = 17

Step-by-step explanation:

180 - 94 = 86

So all the inside angles of a triangle = 180

180 - 86 - 60 = 34

34/2 = 17

Answer:

it's answer is 17

Step-by-step explanation:

we know exterior angle of a triangle is equal to the sum of two opposite interior angles. So,

2x + 60° = 94°

2x = 94° - 60°

2x = 34°

x = 34° /2

x = 17°

Write the equation of the line that is parallel to y = -6x + 10 and crosses the y-axis at -4.

Answers

Answer:

y= -6x-4

Step-by-step explanation:

As two lines are parallel, their slope is same which is -6

Now, use:y-y1=m(x-x1)

y-(-4)= -6(x-0) (y1=-4,x1=0, cause the equation of y axis is x=0)

So,y= -6x-4

Please help! Divide. Write the quotient in lowest terms.

Answers

The correct answer for this would be 32/5

A type of opinion based on observation and evidence.

Answers

Answer:

hypothesis

Step-by-step explanation:

Answer:

It is a hypothesis

Step-by-step explanation:

u gather evidence and based on the info u have, u make an opinion (hypothesis)

whats 9 + 10? if you get it right brainliest

Answers

Since brainily make me write more than 20 character this is the answer 9+10=12

Answer:

19.  

Step-by-step explanation:

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