Triangle ABC is an isosceles triangle.
Solution:
Given data:
∠ABC = 70° and ∠ACD = 55°
<em>If two parallel lines are cut by a transversal, then alternate interior angles are congruent.</em>
m∠BAC = m∠ACD
m∠BAC = 55°
<em>Sum of the angles in a straight line add up to 180°.</em>
m∠ACD + m∠ACB + m∠ABC = 180°
55° + m∠ACB + 70° = 180°
m∠ACB + 125° = 180°
Subtract 125° from both sides, we get
m∠ACB = 55°
In triangle ABC,
∠BAC = 55° and ∠ACB = 55°
∠BAC = ∠ACB
Two angles in the triangle are equal.
Therefor triangle ABC is an isosceles triangle.
Answer:
A system of two linear equations can have one solution, an infinite number of solutions, or no solution. Systems of equations can be classified by the number of solutions. If a system has at least one solution, it is said to be consistent . If a consistent system has exactly one solution, it is independent .
Step-by-step explanation:
Mrs. Walters gets 14.4 miles per gallon.
Mr. Walters gets 15 miles per gallon.
So Mr. Walters car is better because he gets more miles out of one gallon of gas.
360/25=14.4 480/32=15
Stephen can read 90 pages in 6 days witch means he reads 15 pages per day. Which means it will take him 20 days to read a 300 page book.
90/6=15 300/15=20
Answer:
Step-by-step explanation:
Hi there!
<u>What we need to know:</u>
- Linear equations are typically organized in slope-intercept form: where m is the slope and b is the y-intercept (the value of y when x is 0)
- Parallel lines always have the same slope
<u>1) Determine the slope of line S using line R (m)</u>
We can identify clearly that the slope of the line is , as it is in the place of m. Because parallel lines always have the same slope, the slope of line S would also be . Plug this into :
<u>2) Determine the y-intercept of line S (b)</u>
Plug in the given point (-4,3) and solve for b
Subtract 1 from both sides to isolate b
Therefore, the y-intercept is 2. Plug this back into :
I hope this helps!