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1 year ago

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

Mathematics

1 answer:

antoniya [11.8K]1 year 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