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3 years ago

Question 7 please????

Mathematics

2 answers:

Ahat [919]3 years ago

7 0

Answer:

I think it would be 17 because if you subtract 47 by 13 it will give you 34 and if you divide it by 2 it will give you 17.

Make me brainliest

Andreyy893 years ago

7 0

Answer:

The length of longer piece is 30 inches.

Step-by-step explanation:

Firstly, you have to make an expression in terms of x where x represents the length of the shorter piece . Given that the total length is 47 inches and the longer piece is 13 inches longer that the shorter one. Using this information, you can form an expression :

Shorter piece =>

x inches

Longer piece =>

(13 + x) inches

Total length =>

x + 13 + x = 47

2x + 13 = 47

now, you can solve to find the value of x by substracting 13 to both sides then divide it by 2:

2x + 13 - 13 = 47 - 13

2x = 34

2x ÷ 2 = 34 ÷ 2

x = 17 inches

We have found the shorter piece. The question wants to find the longer piece so you have to substitute the value of x into the expression of longer piece :

Let x be 17 inches,

13 + x = 13 + 17

= 30 inches

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Step-by-step explanation:

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

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step 1

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

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substitute the values

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step 2

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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

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step 3

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

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substitute the values

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step 4

Find the equation of the perpendicular bisectors of AB

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The equation in slope intercept form is equal to

$y=mx+b$

substitute

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

solve for b

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

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

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Part 2) Find the equation of the perpendicular bisector side BC

we have

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

step 1

Find the slope BC

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

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

substitute the values

$m=\frac{2-8}{4-0}$

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step 2

Find the slope of the perpendicular line to side BC

Remember that

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therefore

The slope is equal to

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step 3

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

substitute the values

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Find the equation of the perpendicular bisectors of BC

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Part 3) Find the equation of the perpendicular bisector side AC

we have

A(–2, 0) and C(4, 2)

step 1

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

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

$m=\frac{1}{3}$

step 2

Find the slope of the perpendicular line to side AC

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

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Part 4) Find the coordinates of the point of concurrency of the perpendicular bisectors (P)

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

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