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nexus9112 [7]
3 years ago
11

WILL GIVE BRAINLIEST!!!

Mathematics
1 answer:
Kaylis [27]3 years ago
5 0

Answer:

1: 3z+5

2: 50+20x

3: (15y+18)-4

4: 12a+8

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∆ABC has vertices A(–2, 0), B(0, 8), and C(4, 2)
Natali [406]

Answer:

Part 1) The equation of the perpendicular bisector side AB is y=-\frac{1}{4}x+\frac{15}{4}

Part 2) The equation of the perpendicular bisector side BC is y=\frac{2}{3}x+\frac{11}{3}

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

Part 4) The coordinates of the point P(0.091,3.727)

Step-by-step explanation:

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

we have

A(–2, 0), B(0, 8)

<em>step 1</em>

Find the slope AB

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

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

substitute the values

m=\frac{8-0}{0+2}

m=4

<em>step 2</em>

Find the slope of the perpendicular line to side AB

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=-\frac{1}{4}

<em>step 3</em>

Find the midpoint AB

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

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

substitute the values

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

M(-1,4)

<em>step 4</em>

Find the equation of the perpendicular bisectors of AB

the slope is m=-\frac{1}{4}

passes through the point (-1,4)

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}

so

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

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

we have

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

<em>step 1</em>

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}

m=-\frac{3}{2}

<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

The slope is equal to

m=\frac{2}{3}

<em>step 3</em>

Find the midpoint BC

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

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

substitute the values

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

M(2,5)

<em>step 4</em>

Find the equation of the perpendicular bisectors of BC

the slope is m=\frac{2}{3}

passes through the point (2,5)

The equation in slope intercept form is equal to

y=mx+b

substitute

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

solve for b

b=5-\frac{4}{3}

b=\frac{11}{3}

so

y=\frac{2}{3}x+\frac{11}{3}

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

we have

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}

m=\frac{1}{3}

<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

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

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

substitute the values

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

M(1,1)        

<em>step 4</em>

Find the equation of the perpendicular bisectors of AC

the slope is m=-3

passes through the point (1,1)

The equation in slope intercept form is equal to

y=mx+b

substitute

1=(-3)(1)+b

solve for b

b=1+3

b=4

so

y=-3x+4

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

5 0
3 years ago
10. Mr. Sanchez goes to the movies every 18 days. His brother goes to the
mestny [16]
90 days.

For this question you just need to find the least common multiple of 18 and 30. That can be found by first finding the prime factorization of each number. 18 = 2 * 3 * 3 and 30 = 2 * 3 * 5. Then you multiply the 2 * 3 * 3 * 5, you ignore the 3 from 30 because 18 has more 3s. The answer is 90.
5 0
2 years ago
The box plot shows the number of home runs hit by 43 players during a baseball season which stament best describes the data
ozzi

The number of data values between the lower quartile and the median is less than the number of data values between the upper quartile and the median.

Hope this helps!

6 0
3 years ago
Simplify the expression<br><br> x³<br> ÷ x^4×x^5
miss Akunina [59]
Answer is = X^6

Please give me the brainliest

4 0
3 years ago
Get Geordi Through the Door geometry worksheet
Murljashka [212]

Answer:

what does that even mean'

Step-by-step explanation:

3 0
3 years ago
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