(01.07 MC) Lines BC and ED are parallel. They are intersected by transversal AE, in which point B lies between points and E. The
y are also intersected by transversal EC. Angle ABC measures 70 degrees. Angle CED measures 30 degrees. Given: line BC is parallel to line ED m∠ABC = 70° m∠CED = 30° Prove: m∠BEC = 40° Statement Justification line BC is parallel to line ED Given m∠ABC = 70° Given m∠CED = 30° Given m∠BEC + m∠CED = m∠BED Angle Addition Postulate m∠BEC + 30° = 70° Substitution Property of Equality m∠BEC = 40° Subtraction Property of Equality Which of the following accurately completes the missing statement and justification of the two-column proof? m∠ABC = m∠CED; Corresponding Angles Theorem m∠ABC = m∠CED; Alternate Interior Angles Theorem m∠ABC = m∠BED; Corresponding Angles Theorem m∠ABC = m∠BED; Alternate Interior Angles Theorem
2 answers:
Answer:
m∠ABC = m∠BED; Corresponding Angles Theorem
Step-by-step explanation:
<u>Given:</u> line BC is parallel to line ED m∠ABC = 70° m∠CED = 30°
<u>Prove:</u> m∠BEC = 40°
Statement Justification
1. line BC is parallel to line ED - Given
2. m∠ABC = 70° - Given
3. m∠CED = 30° - Given
4. m∠BEC + m∠CED = m∠BED - Angle Addition Postulate
5. m∠ABC = m∠BED - Corresponding Angles Theorem
6. m∠BEC + 30° = 70° - Substitution Property of Equality
7. m∠BEC = 40° Subtraction Property of Equality
You might be interested in
Answer:
5 feet
Step-by-step explanation:
The path traveled by a bottlenose dolphin as it jumps out of water is modeled by the equation,
where y is the height above water and x is the horizontal distance in feet.
If a beam of light is shone upward at an angle modeled by the equation
A beam of light hit the dolphin.
So, line must be intersect path of dolphin.
Using substation method,
Substitute y=10-x into dolphin equation.
Hence, The beam hit dolphin at 5 feet.
six pipes are laid end to end to form a row. Each pipe is 9 1/3 inches long. how long is the row of pipes, in feet?
Answer:
4.67 feet or 4 feet 8 inches or feet
Step-by-step explanation:
Let x be the length of the row pipes.
Given:
Number of pipes = 6
Each pipe has length inches. and six pipes are laid end to end to form a row.
The total length of the row is equal to length of the 6 pipes.
So, total length of row = Number of pipes Length of the pipe
inches
convert inch into feet.
Therefore, The length of the row is 4.67 feet or 4 feet 8 inches or feet .
Answer:
- The total amount accrued, principal plus interest, from compound interest on an original principal of $ 300.00 at a rate of 6% per year compounded 2 times per year over 0.5 years is $ 309.00.
- The total amount accrued, principal plus interest, from compound interest on an original principal of $ 300.00 at a rate of 6% per year compounded 2 times per year over 1 year is $ 318.27.
Step-by-step explanation:
a) How much will you have at the middle of the first year?
Using the formula
where
- Principle = P
- Annual rate = r
- Compound = n
- Time = (t in years)
- A = Total amount
Given:
Principle P = $300
Annual rate r = 6% = 0.06 per year
Compound n = Semi-Annually = 2
Time (t in years) = 0.5 years
To determine:
Total amount = A = ?
Using the formula
substituting the values
$
Therefore, the total amount accrued, principal plus interest, from compound interest on an original principal of $ 300.00 at a rate of 6% per year compounded 2 times per year over 0.5 years is $ 309.00.
Part b) How much at the end of one year?
Using the formula
where
- Principle = P
- Annual rate = r
- Compound = n
- Time = (t in years)
- A = Total amount
Given:
Principle P = $300
Annual rate r = 6% = 0.06 per year
Compound n = Semi-Annually = 2
Time (t in years) = 1 years
To determine:
Total amount = A = ?
so using the formula
so substituting the values
$
Therefore, the total amount accrued, principal plus interest, from compound interest on an original principal of $ 300.00 at a rate of 6% per year compounded 2 times per year over 1 year is $ 318.27.