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DanielleElmas [232]

3 years ago

8

A total of 348 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student t

ickets sold was two times the number of adult tickets sold . How many adult tickets were sold?

2 answers:

seropon [69]3 years ago

7 0

Let Student tickets be S,Let Adult tickets be A.S = 2A

total S+A = 348

(2A) +A =348

3A = 348

devide both sides by 3

A = 116

now S = 2 * 116

S = 232

maw [93]3 years ago

3 0

Lets say y is number of adult tickets and x is number of student tickets x+y=348 2x+y=348 (2x since I know that the student tickets are twice as much as adult tickets) I now know that that student tickets make up 2/3 of the total number of tickets and 1/3 make up the number of adults tickets. So... 1/3 x 348= 116 adult tickets 2/3 x 348=232 student tickets

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Part 3) The equation of the perpendicular bisector side AC is $y=-3x+4$

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Step-by-step explanation:

Part 1) Find the equation of the perpendicular bisector side AB

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<em>step 2</em>

Find the slope of the perpendicular line to side AB

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<em>step 3</em>

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<em>step 4</em>

Find the equation of the perpendicular bisectors of AB

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passes through the point $(-1,4)$

The equation in slope intercept form is equal to

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substitute

$4=(-\frac{1}{4})(-1)+b$

solve for b

$b=4-\frac{1}{4}$

$b=\frac{15}{4}$

so

$y=-\frac{1}{4}x+\frac{15}{4}$

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we have

B(0, 8) and C(4, 2)

<em>step 1</em>

Find the slope BC

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substitute the values

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<em>step 2</em>

Find the slope of the perpendicular line to side BC

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

therefore

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$m=\frac{2}{3}$

<em>step 3</em>

Find the midpoint BC

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$M(\frac{x1+x2}{2},\frac{y1+y2}{2})$

substitute the values

$M(\frac{0+4}{2},\frac{8+2}{2})$

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<em>step 4</em>

Find the equation of the perpendicular bisectors of BC

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substitute

$5=(\frac{2}{3})(2)+b$

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A(–2, 0) and C(4, 2)

<em>step 1</em>

Find the slope AC

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{2-0}{4+2}$

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<em>step 2</em>

Find the slope of the perpendicular line to side AC

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

therefore

The slope is equal to

$m=-3$

<em>step 3</em>

Find the midpoint AC

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$M(\frac{x1+x2}{2},\frac{y1+y2}{2})$

substitute the values

$M(\frac{-2+4}{2},\frac{0+2}{2})$

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<em>step 4</em>

Find the equation of the perpendicular bisectors of AC

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substitute

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so

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we know that

The point of concurrency of the perpendicular bisectors is called the circumcenter.

Solve by graphing

using a graphing tool

the point of concurrency of the perpendicular bisectors is P(0.091,3.727)

see the attached figure

5 0

3 years ago