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3 years ago

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Volunteers for a political campaign gave out 21/38 of their fliers. They gave out the remaining 612 fliers in another neighborho

od. What is the total number of fliers they gave out

1 answer:

dmitriy555 [2]3 years ago

4 0

The volunteers gave 1368 fliers in total.

Step-by-step explanation:

Given,

Fliers given by volunteers in first neighborhood = $\frac{21}{38}$

Remaining fliers = 612

Fraction of remaining fliers = $1-\frac{21}{38}=\frac{38-21}{38}$

Fraction of remaining fliers = $\frac{17}{38}$

Let,

x be the total fliers given by volunteers.

$\frac{17}{38}\ of\ x=612$

$\frac{17}{38}x=612$

Multiplying both sides by $\frac{38}{17}$

$\frac{38}{17}*\frac{17}{38}x=612*\frac{38}{17}\\\\x=\frac{23256}{17}\\\\x=1368$

The volunteers gave 1368 fliers in total.

Keywords: fraction, division

Learn more about fractions at:

#LearnwithBrainly

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4. The equation of the perpendicular bisector is y = $\frac{3}{4}$ x - $\frac{1}{8}$

5. The equation of the perpendicular bisector is y = - 2x + 16

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Step-by-step explanation:

Lets revise some important rules

The product of the slopes of the perpendicular lines is -1, that means if the slope of one of them is m, then the slope of the other is $-\frac{1}{m}$ (reciprocal m and change its sign)
The perpendicular bisector of a line means another line perpendicular to it and intersect it in its mid-point
The formula of the slope of a line is $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$
The mid point of a segment whose end points are $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is $(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$
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4.

∵ The line passes through (7 , 2) and (4 , 6)

- Use the formula of the slope to find its slope

∵ $x_{1}$ = 7 and $x_{2}$ = 4

∵ $y_{1}$ = 2 and $y_{2}$ = 6

∴ $m=\frac{6-2}{4-7}=\frac{4}{-3}$

- Reciprocal it and change its sign to find the slope of the ⊥ line

∴ The slope of the perpendicular line = $\frac{3}{4}$

- Use the rule of the mid-point to find the mid-point of the line

∴ The mid-point = $(\frac{7+4}{2},\frac{2+6}{2})$

∴ The mid-point = $(\frac{11}{2},\frac{8}{2})=(\frac{11}{2},4)$

- Substitute the value of the slope in the form of the equation

∵ y = $\frac{3}{4}$ x + b

- To find b substitute x and y in the equation by the coordinates

of the mid-point

∵ 4 = $\frac{3}{4}$ × $\frac{11}{2}$ + b

∴ 4 = $\frac{33}{8}$ + b

- Subtract $\frac{33}{8}$ from both sides

∴ $-\frac{1}{8}$ = b

∴ y = $\frac{3}{4}$ x - $\frac{1}{8}$

∴ The equation of the perpendicular bisector is y = $\frac{3}{4}$ x - $\frac{1}{8}$

5.

∵ The line passes through (8 , 5) and (4 , 3)

- Use the formula of the slope to find its slope

∵ $x_{1}$ = 8 and $x_{2}$ = 4

∵ $y_{1}$ = 5 and $y_{2}$ = 3

∴ $m=\frac{3-5}{4-8}=\frac{-2}{-4}=\frac{1}{2}$

- Reciprocal it and change its sign to find the slope of the ⊥ line

∴ The slope of the perpendicular line = -2

- Use the rule of the mid-point to find the mid-point of the line

∴ The mid-point = $(\frac{8+4}{2},\frac{5+3}{2})$

∴ The mid-point = $(\frac{12}{2},\frac{8}{2})$

∴ The mid-point = (6 , 4)

- Substitute the value of the slope in the form of the equation

∵ y = - 2x + b

- To find b substitute x and y in the equation by the coordinates

of the mid-point

∵ 4 = -2 × 6 + b

∴ 4 = -12 + b

- Add 12 to both sides

∴ 16 = b

∴ y = - 2x + 16

∴ The equation of the perpendicular bisector is y = - 2x + 16

6.

∵ The line passes through (6 , 1) and (0 , -3)

- Use the formula of the slope to find its slope

∵ $x_{1}$ = 6 and $x_{2}$ = 0

∵ $y_{1}$ = 1 and $y_{2}$ = -3

∴ $m=\frac{-3-1}{0-6}=\frac{-4}{-6}=\frac{2}{3}$

- Reciprocal it and change its sign to find the slope of the ⊥ line

∴ The slope of the perpendicular line = $-\frac{3}{2}$

- Use the rule of the mid-point to find the mid-point of the line

∴ The mid-point = $(\frac{6+0}{2},\frac{1+-3}{2})$

∴ The mid-point = $(\frac{6}{2},\frac{-2}{2})$

∴ The mid-point = (3 , -1)

- Substitute the value of the slope in the form of the equation

∵ y = $-\frac{3}{2}$ x + b

- To find b substitute x and y in the equation by the coordinates

of the mid-point

∵ -1 = $-\frac{3}{2}$ × 3 + b

∴ -1 = $-\frac{9}{2}$ + b

- Add $\frac{9}{2}$ to both sides

∴ $\frac{7}{2}$ = b

∴ y = $-\frac{3}{2}$ x + $\frac{7}{2}$

∴ The equation of the perpendicular bisector is y = $-\frac{3}{2}$ x + $\frac{7}{2}$

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3 years ago