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3 years ago

What is the factored form x^3 - 1 ?

Mathematics

1 answer:

amid [387]3 years ago

7 0

Answer: x^3 - 1 = (x - 1)(x^2 + x + 1)

Explanation:

This is a type of factorizing called the sum or difference of 2 cubes:

a^3 - b^3 = (a - b)(a^2 + ab + b^2)

The sum of the cubes is factored as:

a^3 + b^3 = (a + b)(a^2 - ab + b^2)

In this case, we have: x^3 - 1 so follow the rule above.

x^3 - 1 = (x - 1)(x^2 + x + 1)

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Simplify (12xy)^2 show steps please

vivado [14]

<span>(12xy)^2

Expand:

12^2*x^2*y^2
= 144x^2*y^2</span>

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3 years ago

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What is the slope of a line perpendicular to the line whose equation is 5x - y = -7.

BARSIC [14]

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

$5x-y=-7\implies 5x-y+7=0 \\\\\\ \stackrel{\stackrel{m}{\downarrow }}{5} x+7=y\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}$

so a line perpendicular to that one above will have a slope of

$\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{5\implies \cfrac{5}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{5}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{5}}}$

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2 years ago

Can someone please help me

VARVARA [1.3K]

Answer:

You can use a hint

Step-by-step explanation:

Press the Use a hint button, the first time it won't count, only then the second one won't count.

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3 years ago

10 rugs cost $650. If the rugs all cost the same amount, how much does each rug cost?

yan [13]

65$ each devils 650$ by 10

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3 years ago

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A researcher takes a simple random sample of 83 homes in a city and finds that the mean square footage is 1628 with a standard d

Anna [14]

Answer: (1583.63, 1672.37)

Step-by-step explanation:

Given : Sample size : n= 83

Sample mean : $\overline{x}=1628$

Sample standard deviation : $\sigma=243$

The population standard deviation $(\sigma)$ is unknown .

The confidence interval for population mean :

$\overline{x}\pm t_{\alpha/2}\dfrac{s}{\sqrt{n}}$

For 90% confidence , significance level = $\alpha=1-0.90=0.10$

Using t-distribution table , Critical t-value = $t_{(\alpha/2, n-1)}=t_{0.05,82}=1.6636$

, where n-1 is the degree of freedom.

Now , 90% confidence interval for the mean square footage of all the homes in that city will be :-

$1628\pm (1.6636)\dfrac{243}{\sqrt{83}}\\\\ 1628\pm (1.6636)(26.672715)\\\\\\\\\approx1628\pm 44.37\\\\=(1628- 44.37,\ 1628+ 44.37)\\\\=(1583.63,\ 1672.37)$

Hence, the 90% confidence interval for the mean square footage of all the homes in that city = (1583.63, 1672.37)

7 0

3 years ago