1. ∠1 ≅ ∠3 1. given
∠1 and ∠6 are supplementary angles
∠3, ∠4, and ∠5 are supplementary angles
2. m∠1 = m∠3 2. definition of congruency
3. m∠1 + m∠6 = 180° 3. definition of supplementary angles
m∠3 + m∠4 + m∠5 = 180°
4. m∠3 + m∠4 + m∠5 = m∠1 + m∠6 4. transitive property
5. m∠3 + m∠4 + m∠5 = m∠3 + m∠6 5. substitution property
6. m∠4 + m∠5 = m∠6 6. subtraction property of equality
Answer:
22 units
Step-by-step explanation:
The perimeter of a polygon is said to be the sum of the length of it's sides.
From the question, we have 5 vertices. This means the polygon is a pentagon. It's given vertices are
A = (−1, 3)
B = (−1, 6)
C = (2, 10)
D = (5, 6)
E = (5, 3)
To find the distance between two points, we use the formula
d = √[(y2 - y1)² + (x2 - x1)²]
Between A and B, we have
d(ab) = √[(6 - 3)² + (-1 --1)²]
d(ab) = √(3²) + 0
d(ab) = √9 = 3
Between B and C, we have
d(bc) = √[(10 - 6)² + (2 --1)²]
d(bc) = √[4² + 3²]
d(bc) = √(16 + 9) = √25 = 5
Between C and D, we have
d(cd) = √[(6 - 10)² + (5 - 2)²]
d(cd) = √[(-4)² + 3²]
d(cd) = √(16 + 9) = √25 = 5
Between D and E, we have
d(de) = √[(3 - 6)² + (5 - 5)²]
d(de) = √(-3)² + 0
d(de) = √9 = 3
Between E and A, we have
d(ea) = √[(3 - 3)² + (5 --1)²]
d(ea) = √[0 + (6)²]
d(ea) = √36 = 6
The perimeter is given as
d(ab) + d(bc) + d(cd) + d(de) + d(ea) =
3 + 5 + 5 + 3 + 6 = 22 units
Answer:
answer: 189
Step-by-step explanation:
Formula to find triangles area is base x height ÷ 2 So... 7 x 10 = 70 70 ÷ 2 = 35 Now sense we have 4 identicle triangles we will just do 35 × 4 amd 35 × 4 = 140 now for the square its simply just base x height so 7 × 7 = 49 now we will add these up...140 + 49 = 189 so 189 is the area. Hope this helps!
Answer:
<u>Cost = 25 + 50h</u>
cost for 8 hours of work = $425
cost for 10 hours of work = $525
Step-by-step explanation:
The question is as following:
A plumber charges $25 for a service call plus $50 per hour of service write an equation to represent the cost of hiring this plumber.
what will be the cost for 8 hours of work? 10 hours of work?
=======================================================
A plumber charges $25 for a service call plus $50 per hour
<u>Cost = 25 + 50h</u>
Where h is the number of hours of service
8 hours of work: h = 8
Substitute with h = 8 at the equation of cost
<u>Cost = 25 + 50* 8 = $425</u>
10 hours of work: h = 10
Substitute with h = 10 at the equation of cost
<u>Cost = 25 + 50 * 10 = $525</u>
Answer:
49, 49 , 98
Step-by-step explanation:
AC = AB + BC = 2AB
- 3x - 31 = 2(x+6)
- 3x - 31 = 2x + 12
- 3x - 2x = 12 +31
- x = 43
AB= BC = x + 6 = 43 + 6 = 49
AC = 2AB = 2* 49 = 98
