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weqwewe [10]
11 months ago
6

Write the number as a product of primes. 99= ? (answer is not 33)

Mathematics
1 answer:
antoniya [11.8K]11 months ago
5 0

Answer:

Prime factorization: 99 = 3 x 3 x 11, which can also be written 99 = 3² x 11

Step-by-step explanation: HOPE THIS HELPS

99 = 3 x 3 x 11, which can also be written 99 = 3² x 11.

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Ryan has x stamps in his collection if he was 6 times as many stamps as penny, how many stamps does penny have in her collection
Free_Kalibri [48]

The number of stamps with penny in terms of x is \frac{x}{6}

<em><u>Solution:</u></em>

Given that,

Ryan has x stamps in his collection

Number of stamps of Ryan = x stamps

Let the stamps with penny be "a"

Ryan has 6 times as many stamps as penny

Therefore,

Number of stamps in Ryan = 6 times as many stamps as penny

\text{Number of stamps in Ryan } = 6 \times a\\\\x = 6a\\\\a = \frac{x}{6}

Thus number of stamps with penny in terms of x is \frac{x}{6}

7 0
3 years ago
Dont really understand how to do this
bija089 [108]

Answers:

t_{10} = -22 \ \text{ and } S_{10} = -85

========================================================

Explanation:

t_1 = \text{first term} = 5\\t_2 = \text{first term}-3 = t_1 - 3 = 5-3 = 2

Note we subtract 3 off the previous term (t1) to get the next term (t2). Each new successive term is found this way

t_3 = t_2 - 3 = 2-3 = -1\\t_4 = t_3 - 3 = -1-3 = -4

and so on. This process may take a while to reach t_{10}

There's a shortcut. The nth term of any arithmetic sequence is

t_n = t_1+d(n-1)

We plug in t_1 = 5 \text{ and } d = -3 and simplify

t_n = t_1+d(n-1)\\t_n = 5+(-3)(n-1)\\t_n = 5-3n+3\\t_n = -3n+8

Then we can plug in various positive whole numbers for n to find the corresponding t_n value. For example, plug in n = 2

t_n = -3n+8\\t_2 = -3*2+8\\t_2 = -6+8\\t_2 = 2

which matches with the second term we found earlier. And,

tn = -3n+8\\t_{10} = -3*10+8\\t_{10} = -30+8\\t_{10} = \boldsymbol{-22} \ \textbf{ is the tenth term}

---------------------

The notation S_{10} refers to the sum of the first ten terms t_1, t_2, \ldots, t_9, t_{10}

We could use either the long way or the shortcut above to find all t_1 through t_{10}. Then add those values up. Or we can take this shortcut below.

Sn = \text{sum of the first n terms of an arithmetic sequence}\\S_n = (n/2)*(t_1+t_n)\\S_{10} = (10/2)*(t_1+t_{10})\\S_{10} = (10/2)*(5-22)\\S_{10} = 5*(-17)\\\boldsymbol{S_{10} = -85}

The sum of the first ten terms is -85

-----------------------

As a check for S_{10}, here are the first ten terms:

  • t1 = 5
  • t2 = 2
  • t3 = -1
  • t4 = -4
  • t5 = -7
  • t6 = -10
  • t7 = -13
  • t8 = -16
  • t9 = -19
  • t10 = -22

Then adding said terms gets us...

5 + 2 + (-1) + (-4) + (-7) + (-10) + (-13) + (-16) + (-19) + (-22) = -85

This confirms that S_{10} = -85 is correct.

6 0
2 years ago
What is the length of the hypotenuse of the triangle when x=10​?
Schach [20]

Answer:

84 (nearest whole number)

Step-by-step explanation:

If x = 10,

Longest leg = (7 x 10) + 4 = 74

Shortest leg = 4 x 10 = 40

Using Pythagoras' Theorem a² + b² = c² (where a and b are the legs and c is the hypotenuse of a right triangle):

⇒ 74² + 40² = c²

⇒ 7076 = c²

⇒ c = √7076 = 84.11896...

⇒ hypotenuse = 84 (nearest whole number)

5 0
2 years ago
Read 2 more answers
Which equation could be used to create the function table A y=3x B y=x+3 C y=4x D y=x+2
Setler79 [48]
A y=3x because 3*1 is 3 and 3*2 is 6 and so on
4 0
3 years ago
About 0.5 of all the students in the fifth grade are girls. If the fifth grade has 80 ​students, how many of the students are gi
Nookie1986 [14]

Answer:

40 Girls.

Step-by-step explanation:

80 multipled by 0.5 = 40

7 0
3 years ago
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