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2 years ago

3 (x+2)+9<6(x-3) solve the inequality and write the solution using interval notation

Mathematics

1 answer:

Darya [45]2 years ago

6 0

Answer:

(11, ∞).

Step-by-step explanation:

3 (x+2)+9<6(x-3)

3x + 6 + 9 < 6x - 18

-3x < -18 - 6 - 9

-3x < -33

x > 11 (Note the inequality flips as we are dividing by a negative value).

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What is the Circumference of a circle if its radius in 15 inches? Please help always a procrastinator in math! Thanks!

Tems11 [23]

Circumference Formula:
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3 years ago

Find S5 for a geometric series for which a1=81 and r=1/9.

Minchanka [31]

ANSWER

$S_5=91\frac{10}{81}$

EXPLANATION

The sum of the first $n$ terms of a geometric sequence is given by;

$S_n=\frac{a_1(1-r^n)}{1-r} ,-1$

Where $n$ , is the number of terms and $a_1$ is the first term.

When $n=5$ , we have $a_1=81$ , we get;

$S_5=\frac{81(1-(\frac{1}{9})^5)}{1-\frac{1}{9}}$

$S_5=\frac{81(1-\frac{1}{59049})}{1-\frac{1}{9}}$

$S_5=\frac{81(\frac{59048}{59049})}{\frac{8}{9}}$

$S_5=\frac{7381}{81}$

$S_5=91\frac{10}{81}$

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3 years ago

Hilary's Horse Hideaway is buying dirt to fill their circular training area. The training circle is 28 feet across. What is the

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Answer:

A = 615.75

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615.75/5.75 = 107.08

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2 years ago

A regular polygon has an odd number of sides. Which statement is true about the lines of reflection for the polygon that will ma

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3 years ago

Find the equation of a line that is perpendicular to y = 3x – 5 and passes through the point (1, -3).

Svetradugi [14.3K]

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

$\begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\qquad \qquad y = \stackrel{\stackrel{m}{\downarrow }}{3}x-5$

well then therefore

$\stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{3\implies \cfrac{3}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{3}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{3}}}$

so we're really looking for the equation of a line with slope of -1/3 and that passes through (1, -3 )

$(\stackrel{x_1}{1}~,~\stackrel{y_1}{-3})\qquad \qquad \stackrel{slope}{m}\implies -\cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{-\cfrac{1}{3}}(x-\stackrel{x_1}{1})\implies y+3=-\cfrac{1}{3}x+\cfrac{1}{3} \\\\\\ y=-\cfrac{1}{3}x+\cfrac{1}{3}-3\implies y=-\cfrac{1}{3}x-\cfrac{8}{3}$

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2 years ago

3 (x+2)+9<6(x-3) solve the inequality and write the solution using interval notation​

3 (x+2)+9<6(x-3) solve the inequality and write the solution using interval notation