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otez555 [7]
2 years ago
10

Find the area of the triangle. Height = 4 ft Base = 12 1/2 ft Area = ? square feet

Mathematics
1 answer:
Nikolay [14]2 years ago
5 0
Answer:
25 square feet

Explanation:
Area of triangle= 1/2 * height * base
1/2 * 4ft * 12 1/2 ft
2ft * 12 1/2 ft
25 square feet

Hope this helps you :)
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4d = -16 <br><br> what’s the value of d
prohojiy [21]

4d =  - 16 \\  \\ d = \cancel  \frac{ - 16}{4}  \\  \\ d =  - 4

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9 + 15m<br><br><br><br>factorisation of algebraic expression that contain common factor​
Svet_ta [14]
The common factor would be 3 because 3 is the highest multiple of 15 and 9
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3 years ago
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A triangle is formed from the points L(-3, 6), N(3, 2) and P(1, -8). Find the equation of the following lines:
Dima020 [189]

Answer:

Part A) y=\frac{3}{4}x-\frac{1}{4}  

Part B)  y=\frac{2}{7}x-\frac{5}{7}

Part C) y=\frac{2}{7}x+\frac{8}{7}

see the attached figure to better understand the problem

Step-by-step explanation:

we have

points L(-3, 6), N(3, 2) and P(1, -8)

Part A) Find the equation of the  median from N

we Know that

The median passes through point N to midpoint segment LP

step 1

Find the midpoint segment LP

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

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

we have

L(-3, 6) and P(1, -8)

substitute the values

M(\frac{-3+1}{2},\frac{6-8}{2})

M(-1,-1)

step 2

Find the slope of the segment NM

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

m=\frac{y2-y1}{x2-x1}  

we have

N(3, 2) and M(-1,-1)

substitute the values

m=\frac{-1-2}{-1-3}

m=\frac{-3}{-4}

m=\frac{3}{4}

step 3

Find the equation of the line in point slope form

y-y1=m(x-x1)

we have

m=\frac{3}{4}

point\ N(3, 2)

substitute

y-2=\frac{3}{4}(x-3)

step 4

Convert to slope intercept form

Isolate the variable y

y-2=\frac{3}{4}x-\frac{9}{4}

y=\frac{3}{4}x-\frac{9}{4}+2

y=\frac{3}{4}x-\frac{1}{4}  

Part B) Find the equation of the  right bisector of LP

we Know that

The right bisector is perpendicular to LP and passes through midpoint segment LP

step 1

Find the midpoint segment LP

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

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

we have

L(-3, 6) and P(1, -8)

substitute the values

M(\frac{-3+1}{2},\frac{6-8}{2})

M(-1,-1)

step 2

Find the slope of the segment LP

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

m=\frac{y2-y1}{x2-x1}  

we have

L(-3, 6) and P(1, -8)

substitute the values

m=\frac{-8-6}{1+3}

m=\frac{-14}{4}

m=-\frac{14}{4}

m=-\frac{7}{2}

step 3

Find the slope of the perpendicular line to segment LP

Remember that

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

m_1*m_2=-1

we have

m_1=-\frac{7}{2}

so

m_2=\frac{2}{7}

step 4

Find the equation of the line in point slope form

y-y1=m(x-x1)

we have

m=\frac{2}{7}

point\ M(-1,-1) ----> midpoint LP

substitute

y+1=\frac{2}{7}(x+1)

step 5

Convert to slope intercept form

Isolate the variable y

y+1=\frac{2}{7}x+\frac{2}{7}

y=\frac{2}{7}x+\frac{2}{7}-1

y=\frac{2}{7}x-\frac{5}{7}

Part C) Find the equation of the altitude from N

we Know that

The altitude is perpendicular to LP and passes through point N

step 1

Find the slope of the segment LP

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

m=\frac{y2-y1}{x2-x1}  

we have

L(-3, 6) and P(1, -8)

substitute the values

m=\frac{-8-6}{1+3}

m=\frac{-14}{4}

m=-\frac{14}{4}

m=-\frac{7}{2}

step 2

Find the slope of the perpendicular line to segment LP

Remember that

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

m_1*m_2=-1

we have

m_1=-\frac{7}{2}

so

m_2=\frac{2}{7}

step 3

Find the equation of the line in point slope form

y-y1=m(x-x1)

we have

m=\frac{2}{7}

point\ N(3,2)

substitute

y-2=\frac{2}{7}(x-3)

step 4

Convert to slope intercept form

Isolate the variable y

y-2=\frac{2}{7}x-\frac{6}{7}

y=\frac{2}{7}x-\frac{6}{7}+2

y=\frac{2}{7}x+\frac{8}{7}

7 0
3 years ago
The perimeter of equilateral triangle ABC is 81/3 centimeters, find the length of the radius and apothem.
MAXImum [283]

There is a typo error, the perimeter of equilateral triangle ABC is 81/√3 centimeters.

Answer:

Radius = OB= 27 cm

Apothem = 13.5 cm

A diagram is attached for reference.

Step-by-step explanation:

Given,

The perimeter of equilateral triangle ABC is 81/√3 centimeters.

Substituting this in the formula of perimeter of equilateral triangle =3\times\ side

3\times\ side =[tex]81\sqrt{3}

Side = \frac{81\sqrt{3} }{3} =27\sqrt{3} \ cm

Thus from the diagram , Side AB=BC=AC= 27\sqrt{3} \ cm

We know each angle of an equilateral triangle is 60°.

From the diagram, OB is an angle bisector.

Thus \angle OBC = 30°

Apothem is the line segment from the mid point of any side to the center the equilateral triangle.

Therefore considering ΔOBE, and applying tan function.

tan\theta =\frac{perpendicular}{base} \\tan\theta=\frac{OE}{BE} \\tan\theta=\frac{OE}{\frac{27\sqrt{3}}{2}  } \\tan30\times {\frac{27\sqrt{3} }{2} }= OE\\\frac{1}{\sqrt{3} } \times\frac{27\sqrt{3} }{2} =OE\\

Thus ,apothem  OE= 13.5 cm

Now for radius,

We consider ΔOBE

cos\theta=\frac{base}{hypotenuse} \\cos30= \frac{BE}{OB} \\Cos30 = \frac{\frac{27\sqrt{3} }{2}}{OB}  \\OB= \frac{\frac{27\sqrt{3} }{2}}{cos30} \\OB= \frac{\frac{27\sqrt{3} }{2}}{\frac{\sqrt{3} }{2} } \\OB =27 \ cm

Thus for

Perimeter of equilateral triangle ABC is 81/√3 centimeters,

The radius of equilateral triangle ABC is 27 cm

The apothem of equilateral triangle ABC is 13.5 cm

4 0
3 years ago
11.4÷35.7 answer estimated<br>(15 points)(brainliest included)<br>(incorrect answer=report)​
Gre4nikov [31]

Answer:

0.31932773109

Step-by-step explanation:

  • Set it up
  • Move the decimal point one place to the right for both of them
  • Then, do the long division
  • Keep adding zeros at the end until you have your answer
  • You can round it to 0.32 if you want
8 0
3 years ago
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