$r = \frac{18}{6} \\ 
r = 3 \\ 
 \\ 
 a_{n} = a_{1} * r^{n-1} \\ 
 a_{8} = 6 * 3^{8 - 1} \\ 
a_{8} = 6 * 3^{7} \\
a_{8} = 6 * 2187 \\
a_{8} = 13122 

$

7 0

3 years ago

The line y =3x-5 meet x-axis at the point M.

dusya [7]

y = 3x - 5 meets the x-axis at the x-intercept, and that happens when y = 0

$\bf \stackrel{y}{0}=3x-5\implies 5=3x\implies \cfrac{5}{3}=x~\hspace{5em}\stackrel{M}{\left( \frac{5}{3},0 \right)}$

3y + 2x = 2, meets the y-axis when x = 0, and that'd be the y-intercept

$\bf 3y+2(\stackrel{x}{0})=2\implies 3y=2\implies y=\cfrac{2}{3}~\hspace{5em}\stackrel{N}{\left( 0,\frac{2}{3} \right)}$

so let's find the equation of the line with points M and N in standard form, bearing in mind that

standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

$\bf M(\stackrel{x_1}{\frac{5}{3}}~,~\stackrel{y_1}{0})\qquad N(\stackrel{x_2}{0}~,~\stackrel{y_2}{\frac{2}{3}}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{~~\frac{2}{3}-0~~}{0-\frac{5}{3}}\implies \cfrac{2}{3}\cdot -\cfrac{3}{5}\implies -\cfrac{2}{5}$

$\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-0=-\cfrac{2}{5}\left( x-\cfrac{5}{3} \right)\implies y=-\cfrac{2}{5}x+\cfrac{2}{3} \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{15}}{15y=-6x+10}\implies \stackrel{\textit{standard form}}{6x+15y=10}\implies 6x+15y-10=0$

3 0

3 years ago

Name the object that exhibits rotational symmetry.

salantis [7]

Answer:

circular plate

Step-by-step explanation:

Rotational symmetry is attained on a figure if it is possible to achieve the same image of the figure after rotating it. For example , rotating a circular plate marked with numbers 1 to 6 through a 360° rotation, the number marked 1 with attain a position similar like that before rotation.

8 0

3 years ago

The lines shown below are perpendicular. If the green line has a slop of 2/5, what is the slope of the red line?

aivan3 [116]

The slope of the red line that is perpendicular to the green line is: -5/2.

<h3>What are the Slope Values of Perpendicular Lines?</h3>

When one line lies perpendicular to another line, the slope of one must be the negative reciprocal of the other line.

<h3>What is the Negative Reciprocal of a Number?</h3>

If given a number, i.e. a/b, the negative reciprocal of a/b would the opposite value of the reciprocal of a/b.

Reciprocal of a/b is b/a. Negative reciprocal of a/b would therefore be: -b/a.

Given that the slope of the green line is: 2/5. And it is perpendicular to the red line. The slope of the red line would be the negative reciprocal of 2/5.

Negative reciprocal of 2/5 is -5/2.

Therefore, the slope of the red line is: -5/2.

Learn more about slope of perpendicular lines on:

brainly.com/question/1362601

#SPJ1

5 0

1 year ago