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3 years ago

Find the smallest 3-digit number which gives the remainder 1 when divided by 3 and by 4.

1 answer:

4 0

Multiples of 3 plus 1 remainder are:

3n+1

Multiples of 4 plus 1 remainder are:

4n+1

Since these multiples must be the same number must be a multiple of 12 plus a remainder of one, which is:

12n+1

And the smallest such three digit number is:

12n+1>99 subtract 1 from both sides

12n>98 divide both sides by 12

n>8.17

Since n must be an integer, n=9

So then number is 12n+1

12(9)+1=109

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What are the solutions to the equation <br><img src="https://tex.z-dn.net/?f=2%20%7Cx%20-%202%7C%20%20-%208%20%3D%2020" id="TexF

leva [86]

The solutions of the equation are -12 and 16

Step-by-step explanation:

Absolute value describes the distance of a number on the number line from 0 without considering which direction from zero the number lies. The absolute value of a number is never negative, if IxI = a, where a > 0, then

x = a
x = -a

∵ 2Ix - 2I - 8 = 20

- At first add 8 to both sides

∴ 2Ix - 2I = 28

- Then divide both sides by 2

∴ Ix - 2I = 14

Now By using the notes above equate x - 2 by 14 and -14

∵ x - 2 = 14

- Add 2 to both sides

∴ x = 16

∵ x - 2 = -14

- Add 2 to both sides

∴ x = -12

The solutions of the equation are -12 and 16

Learn more:

You can learn more about solving equations in brainly.com/question/2386054

#LearnwithBrainly

4 0

3 years ago

Which descriptions from the list below accurately describe the relationship between triangle QRS and triangle TUV check all that

abruzzese [7]

Answer:

Step-by-step explanation:

From the given figure, from ΔQRS and ΔTUV, we have

∠Q=∠T(56°(given))

∠R=∠U(83°(given))

∠S=∠V(41°(given))

Thus, by AAA similarity of triangles, ΔQRS is similar to ΔTUV.

Also, All the three angles made by both triangles are equal, and also they are similar thus they have same shape.

Thus, option C and D are correct.

6 0

3 years ago

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Which polynomial expression represents a sum of cubes? (6 – s)(s2 + 6s + 36) (6 + s)(s2 – 6s – 36) (6 + s)(s2 – 6s + 36) (6 + s)

Nadusha1986 [10]

Answer:

Option 3 is correct that is $(6+s)(s^2-6s+36)$

Step-by-step explanation:

We have general formula for sum of cube which is

$a^3+b^3=(a+b)(a^2+b^2-ab)$

Here, we have a=s and b=6

on substituting the values in the formula we will get

$6^3+s^3=(6+s)(s^2+6^2-6s)$

After simplification we will get

$6^3+s^3=(6+s)(s^2+36-6s)$

After rearranging the terms we will get

$6^3+s^3=(6+s)(s^2-6s+36)$ which exactly matches option 3 in the given options.

Therefore, option 3 is correct that is $(6+s)(s^2-6s+36)$

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3 years ago

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Please help with the this give tiny explanation

Mila [183]

Answer:

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3 years ago

So, last year the chess club had 20 members. This year the club has 15 members. Find the percent of change, and state whether th

Basile [38]

So it is a decreace because 20 is more than 15

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3 years ago

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