A. 67 B. 135 C. 75 D. 150

When asked to write the prime factorization of the number 27 a student wrote 9 . 3. Explain the error and write the correct answ

kondor19780726 [428]

The correct prime factorization of 27 is 3 x 3 x 3

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

Given that,

When asked to write the prime factorization of the number 27 a student wrote 9 . 3

So the student has written,

prime factorization of 27 = 9 . 3

This is wrong

Let us first understand about prime factorization

Prime factorization of a number is any of the prime numbers that can be multiplied to give the original number

A prime number is a whole number greater than 1 whose only factors are 1 and itself.

The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29

Clearly from above list we can see that 9 is not a prime number

So the correct prime factorization of 27 is:

prime factorization of 27 = 3 x 3 x 3

Here "3" is a prime number

3 0

3 years ago

What expression is equivalent to ^3 square root of 2y^3 times 7 square root of 18y

Mumz [18]

Answer:

$\sqrt[3]{2y^3} * 7\sqrt{18y} = 21(y^{\frac{3}{2}})(2^{\frac{5}{6}})$

Step-by-step explanation:

The question is poorly formatted.

Given

$\sqrt[3]{2y^3} * 7\sqrt{18y}$

Required

Derive an equivalent expression

$\sqrt[3]{2y^3} * 7\sqrt{18y}$

Express 18 as 9 * 2

$\sqrt[3]{2y^3} * 7\sqrt{9 * 2y}$

Split the expression as follows:

$\sqrt[3]{2y^3} * 7\sqrt{9} * \sqrt{2y}$

Take positive square root of 9

$\sqrt[3]{2y^3} * 7*3 * \sqrt{2y}$

$\sqrt[3]{2y^3} * 21 * \sqrt{2y}$

$21*\sqrt[3]{2y^3} * \sqrt{2y}$

The cube root can be rewritten to give:

$21*\sqrt[3]{2}*\sqrt[3]{y^3} * \sqrt{2y}$

$\sqrt[3]{y^3} = y^{3*\frac{1}{3}} = y$

So, we have:

$21*\sqrt[3]{2} * y * \sqrt{2y}$

Rewrite as:

$21y *\sqrt[3]{2} * \sqrt{2y}$

Split $\sqrt{2y$

$21y *\sqrt[3]{2} * \sqrt{2} * \sqrt{y}$

Collect Like Terms

$21y*\sqrt{y} *\sqrt[3]{2} * \sqrt{2}$

Represent in index form

$21y*y^{\frac{1}{2}} *2^\frac{1}{3} *2^\frac{1}{2}$

Apply law of indices

$21*y^{1+\frac{1}{2}} *2^{\frac{1}{3} +\frac{1}{2} }$

$21*y^{\frac{2+1}{2}} *2^{\frac{2+3}{6}}$

$21*y^{\frac{3}{2}} *2^{\frac{5}{6}}$

$21(y^{\frac{3}{2}})(2^{\frac{5}{6}})$

Hence:

$\sqrt[3]{2y^3} * 7\sqrt{18y} = 21(y^{\frac{3}{2}})(2^{\frac{5}{6}})$

6 0

3 years ago

Please Help!

NNADVOKAT [17]

If you would like to know how much is the stock worth now, you can calculate this using the following steps:

1 year: 6 1/2 % of $875 = 6.5% * $875 = 6.5/100 * 875 = $56.875
$875 + $56.875 = $931.875
2 year: 6 1/2 % of $931.875 = 6.5% * $931.875 = 6.5/100 * 931.875 = $60.572
$931.875 + $60.572 = $992.447
3 year: 6 1/2 % of $992.447 = 6.5% * $992.447 = 6.5/100 * 992.447 = $64.509
$992.447 + $64.509 = $1056.956 = $1056.96 = $1057

The correct result would be: The stock is worth $1057 now.

3 0

4 years ago

Just need the answer please

Kisachek [45]

Answer:

19.34cm

Step-by-step explanation:

Rigth Angled triangle

use SOHCAHTOA

Cos°=adj/hyp

Cos 71=6.3/BC

BC=6.3/COS 71

COS 71°= 0.3256

BC=6.3/0.3256

BC= 19.34cm

3 0

3 years ago

enter the expression −2c⃗ 6d⃗ in the answer box using the notation just described. express your answer in terms of c⃗ and d⃗ . u

liraira [26]

The expression $-2\vec C+6\vec D$ in the ordered pair notation is (16,-16).

The vector components of a vector are represented as the ordered pair of its x and y components.

For example, if a vector has x - component 'a' and y- component 'b' , then the ordered pair notation for the vector is (a, b), where the vector is $a \vec i+b \vec j$ .

Now the vector C has its x- component = -2

y- component of C = -1

Therefore, ordered pair notation of C = (-2, -1)

x- component of D = 2

y-component of D = -3

Therefore, ordered pair notation of D = (2,-3)

So the expression $-2\vec C+6\vec D$ = -2 (-2,-1) +6 (2,-3) = (4,2) + (12, -18)

= (16, -16) in the ordered pair notation.

That is, the vector $\bold {-2\vec C+6\vec D}$ is a vector with x-component 16 and y-component -16.

Learn more about vectors at brainly.com/question/3184914

#SPJ4

4 0

2 years ago