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zmey [24]
3 years ago
13

Rewrite as a simplified fraction 1.6 <-- repeating=?

Mathematics
1 answer:
Norma-Jean [14]3 years ago
6 0
1.6666...=1.\overline{6}=1.(6)\\\\x=1.6666...\ \ \ |multiply\ both\ sides\ by\ 10\\10x=16.6666...\\\\10x-x=16.6666...-1.6666...\\9x=15\ \ \ \ |divide\ both\ sides\ by\ 9\\\\x=\frac{15}{9}\\\\\boxed{x=1\frac{6}{9}}\\\\simplify\\\\x=1\frac{6:3}{9:3}=\boxed{1\frac{2}{3}}
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Which of the following shows the prime factorization of 200 using exponential notation?
Vilka [71]

Answer:

The prime factorization of 200 using exponential notation is 2^{3}\times 5^{2}.

Step-by-step explanation:

First, we decompose the number given on statement by applying prime numbers in ascending order. We see that 200 is an even number, therefore, we infer that smallest prime number within is 2.

1) \frac{200}{2} = 100 (Even number)

2) \frac{100}{2} = 50 (Even number)

3) \frac{50}{2} = 25 (Even number)

4) \frac{25}{5} = 5 (Odd number, not a multiple of 3, but a multiple of 5 since last digit is 5)

5) \frac{5}{5} = 1 (Odd number, not a multiple of 3, but a multiple of 5 since last digit is 5)

Now, we construct the prime factorization using exponential notation:

200 = 2^{3}\times 5^{2}

The prime factorization of 200 using exponential notation is 2^{3}\times 5^{2}.

8 0
3 years ago
E
Allushta [10]

Answer:

Step-by-step explanation:

We can use Hypotenuse Theorem for this:

For triangle ABC,

AC²=CB²+BA²

9²=CB²+3²

Switch the sides

-CB²=3² -9²

-CB²= 9-81

-CB²= -72

the signs cut each other

CB²=72

the square changes sides

CB=√72

CB= 8.49 cm

Now triangle CBD

We have the length of CB but not the other two whereas we have the angle

It will be sin

As we know sin= O/H

Here O is CB whereas H is CD

Put the values

sin 50= 8.49/H

H= 8.49 ÷sin 50

Calculate

H=11.1 cm

As we know H is CD so CD is 11.1 cm

Hope it helps

8 0
3 years ago
Find the distance between points P(6, 5) and Q(2, 4) to the nearest tenth.
trasher [3.6K]

Answer:

√10

Step-by-step explanation:

√(x2-x1)^2+(y2-y1)^2=√10

3 0
3 years ago
What is 72/5 in decimal form
horsena [70]

Answer:

14.4

Step-by-step explanation:

72/5 in decimal form equals 14.4

8 0
3 years ago
Read 2 more answers
Please simplify 6-(2-4x)
umka2103 [35]

I'm pretty sure the answer would be 4+4x

6 0
3 years ago
Read 2 more answers
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