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GalinKa [24]
3 years ago
13

Which of these numbers is a common factor of 54 and 81? 54 = 2 x 3 x 3 x 3 81 = 3 x 3 x 3 x 3 A) 2 B) 6 C) 9 D) 18

Mathematics
2 answers:
stealth61 [152]3 years ago
6 0

Answer:

C) 9

Step-by-step explanation:

54 = 2 x 3 x 3 x 3

81 = 3 x 3 x 3 x 3

common factor of 54 and 81 = 3 x 3 = 9

Answer: 9

VLD [36.1K]3 years ago
4 0

Answer:

C) 9

Step-by-step explanation:

Note that the factors are already given to you:

54 = 2 * 3 * 3 * 3

81 = 3 * 3 * 3 * 3

Note that they all have 3 3's. However, there is not a choice for 27 (as 3 * 3 * 3 = 27), therefore, choose the next option: 3 * 3 = 9

C) 9 is your answer.

~

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NNADVOKAT [17]

Answer:

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The correct answer is B.

7 0
3 years ago
Find an equation for the nth term of the arithmetic sequence.
Irina18 [472]

Answer:

The equation of the nth term is an = -621 + 42n

Step-by-step explanation:

* Lets revise the arithmetic sequence

- There is a constant difference between each two consecutive numbers

- Ex:

# 2  ,  5  ,  8  ,  11  ,  ……………………….

# 5  ,  10  ,  15  ,  20  ,  …………………………

# 12  ,  10  ,  8  ,  6  ,  ……………………………

* General term (nth term) of an Arithmetic sequence:

- U1 = a  ,  U2  = a + d  ,  U3  = a + 2d  ,  U4 = a + 3d  ,  U5 = a + 4d

- Un = a + (n – 1)d, where a is the first term , d is the difference

  between each two consecutive terms

, n is the position of the term

* Lets solve the problem

∵ an = a + (n - 1)d

∴ a14 = a + (14 - 1)d

∴ a14 = a + 13d

∵ a14 = -33

∴ a + 13d = -33 ⇒ (1)

- Similar we can find another equation from a15

∵ a15 = a + (15 - 1)d

∴ a15 = a + 14d

∵ a15 = 9

∴ a + 14d = 9 ⇒ (2)

- We will solve equations (1) and (2) to find a and d

* Lets subtract equation (2) from equation (1)

∴ (a - a) + (13 - 14)d = (-33 - 9)

∴ -d = -42 ⇒ × both sides by -1

∴ d = 42

- Substitute this value of d in equation (1) or (2)

∵ a + 13d = -33

∵ d = 42

∴ a + 13(42) = -33

∴ a + 546 = -33 ⇒ subtract 546 from both sides

∴ a = -579

* Now lets write the equation of the nth term

∵ an = a + (n - 1)d

∵ a = -579 and d = 42

∴ an = -579 + (n - 1) 42 ⇒ open the bracket

∴ an = -579 + 42n - 42

∴ an = -621 + 42n

* The equation of the nth term is an = -621 + 42n

6 0
3 years ago
Which of the following are roots of the following polynomial x^3-11x^2+33x+45
Mandarinka [93]
For x^3-11x^2+33x+45 , we can make it an equation so <span>x^3-11x^2+33x+45=0. Next, we can find out if -1 or -3 is a factor. If -1 is a factor, than (x+1) is factorable. Using synthetic division, we get 

      x^2-12x+45
       ___ ________________________
x+1 | x^3-11x^2+33x+45

      - (x^3+x^2)
       _________________________
            -12x^2+33x+45
          - (-12x^2-12x)
          ______________
            45x+45
         -(45x+45)
___________
0


Since that works, it's either B or D. We just have to figure out when
</span> x^2-12x+45 equals 0, since there are 3 roots and we already found one. Using the quadratic formula, we end up getting (12+-sqrt(144-180))/2=
(12+-sqrt (-36))/2. Since sqrt(-36) is 6i, and 6i/2=3i, it's pretty clear that B is our answer
8 0
3 years ago
A tuna can weighs eighty-five grams. What is the weight of eleven tuna cans?
Anika [276]

Answer:

85g*11=935g

Step-by-step explanation:

1 tuna can = 85g

11 tuna cans is= 1*11

so 85g*11

3 0
2 years ago
Read 2 more answers
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