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3 years ago

For all positive integers x ,what is the greatest common factor of the numbers 256x and 144x

1 answer:

4 0

First, let's factor both of these numbers.

256x:

$2^{8} * x$

144x:

$3^{2} * 2^{4} * x$

Both of these numbers contain $2^{4} * x$ , so that would be the greatest common factor. This could also be written as 16x.

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Which function is equivalent to the inverse of y=sec(x)

kipiarov [429]

From the identity:

$sec(x)= \frac{1}{cos(x)}$

$f(x)=sec(x)= \frac{1}{cos(x)}$

the inverse of f is g such that f(g(x))=x,

we must find g(x), such that $\frac{1}{cos[g(x)]}=x$

thus, $cos[g(x)]= \frac{1}{x}$

$g(x)=cos^{-1} (\frac{1}{x})$

Answer: b. g(x)=cos^-1(1/x)

6 0

4 years ago

The volume of the rectangular solid below is 1,440 cubic inches. What could be the length and width of this rectangular solid?

Rudik [331]

C. 8 inches by 20 inches

5 0

3 years ago

"If triangle vuw is equiangular, find k and t

balu736 [363]

The answer is b. k=64 t=52.

5 0

4 years ago

Which equations have a unit rate of change of 4.5 ? select 2 answers

Maurinko [17]

Answer:

Options A and C

Step-by-step explanation:

<u>To have a unit rate of change of 4.5 means to have the slope at 4.5</u>

A. y = 62 + 4.5x GOOD

B. c = 4.5 + 3h - 1 WRONG

C. c = 12 + 4.5h - 4.5 GOOD

D. y = 3.5x + 1 WRONG

E. y = 4.5 + 20x WRONG

Answer: Options A and C

3 0

3 years ago

This is Matrix for pre calc

gavmur [86]

The given system of equations in augmented matrix form is

$\left[\begin{array}{cccc|c}3&2&-4&2&-23\\-6&1&2&4&-12\\1&-3&-3&5&-20\\-2&5&6&0&12\end{array}\right]$

If you need to solve this, first get the matrix in RREF:

Add 2(row 1) to row 2, row 1 to -3(row 3), and 2(row 1) to 3(row 4):

$\left[\begin{array}{cccc|c}3&2&-4&2&-23\\0&5&-6&8&-58\\0&11&5&-13&37\\0&19&10&4&-10\end{array}\right]$

Add 11(row 2) to -5(row 3), and 19(row 1) to -5(row 4):

$\left[\begin{array}{cccc|c}3&2&-4&2&-23\\0&5&-6&8&-58\\0&0&-91&153&-823\\0&0&-164&132&-1052\end{array}\right]$

Add 164(row 3) to -91(row 4):

$\left[\begin{array}{cccc|c}3&2&-4&2&-23\\0&5&-6&8&-58\\0&0&-91&153&-823\\0&0&0&13080&-39240\end{array}\right]$

Multiply row 4 by 1/13080:

$\left[\begin{array}{cccc|c}3&2&-4&2&-23\\0&5&-6&8&-58\\0&0&-91&153&-823\\0&0&0&1&-3\end{array}\right]$

Add -153(row 4) to row 3:

$\left[\begin{array}{cccc|c}3&2&-4&2&-23\\0&5&-6&8&-58\\0&0&-91&0&-364\\0&0&0&1&-3\end{array}\right]$

Multiply row 3 by -1/91:

$\left[\begin{array}{cccc|c}3&2&-4&2&-23\\0&5&-6&8&-58\\0&0&1&0&4\\0&0&0&1&-3\end{array}\right]$

Add 6(row 3) and -8(row 4) to row 2:

$\left[\begin{array}{cccc|c}3&2&-4&2&-23\\0&5&0&0&-10\\0&0&1&0&4\\0&0&0&1&-3\end{array}\right]$

Multiply row 2 by 1/5:

$\left[\begin{array}{cccc|c}3&2&-4&2&-23\\0&1&0&0&-2\\0&0&1&0&4\\0&0&0&1&-3\end{array}\right]$

Add -2(row 2), 4(row 3), and -2(row 4) to row 1:

$\left[\begin{array}{cccc|c}3&0&0&0&3\\0&1&0&0&-2\\0&0&1&0&4\\0&0&0&1&-3\end{array}\right]$

Multiply row 1 by 1/3:

$\left[\begin{array}{cccc|c}1&0&0&0&1\\0&1&0&0&-2\\0&0&1&0&4\\0&0&0&1&-3\end{array}\right]$

So the solution to this system is $(w,x,y,z)=(1,-2,4,-3)$ .

6 0

4 years ago