Factor completely. 21a^2 - 57a + 30

Mathematics

2 answers:

Kryger [21]3 years ago

8 0

The answer is 3(a-2)(7a-5)

hoa [83]3 years ago

5 0

21a2-57a+30 Final result : 3 • (a - 2) • (7a - 5) 
hope i helped

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The mean height for American adult men is 5 feet 10 inches (5’10"). The standard deviation is roughly 3 inches. Is a 5’7" man co

Helen [10]

Solution :

Given :

The mean height of an American adult = 5 feet 10 inches

Therefore converting feet into inches,

We know, 1 feet = 12 inches

So, 5 feet = 5 x 12 = 60 inches

The mean height in inches = 60+10

= 70 inches

The standard deviation = 3 inches

x = 5 feet 7 inches

= 5 x 12 + 7

= 67 inches

∴ z score = $\frac{x-mean}{sd}$

$=\frac{67-70}{3}$

$=\frac{-3}{3}$

$=-1$

Therefore, the man's height is 1 standard deviation below mean

Any score above greater than 3 or less than -3 is considered to be an outliner.

Here its only -1 and it is less than -3.

Therefore, the height of the man 5'7'' is not considered abnormally short.

6 0

3 years ago

Dose anybody know how to solve this problem

exis [7]

check the transformation template below, hmmm so to get the graph of "y" move to the right by 1 unit, we can simply make C = -1.

$y=\stackrel{A}{1}\log_2(\stackrel{B}{1}x+\stackrel{C}{0})+\stackrel{D}{0}\qquad \qquad y=\stackrel{A}{1}\log_2(\stackrel{B}{1}x+\stackrel{C}{1})+\stackrel{D}{0} \implies y=\log_2(x-1)$

now, the x-intercept is simply where the graph touches the x-axis, and when that happens y = 0, so

$\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad a^{log_a x}=x\leftarrow \textit{let's use this rule} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{y}{0}~~ = ~~\log_2(x-1)\implies 2^0=2^{\log_2(x-1)}\implies 2^0=x-1 \\\\\\ 1=x-1\implies 2=x~\hspace{10em}\stackrel{x-intercept}{(2~~,~~0)}$