Answer
By using the exterior angle property
The measure of exterior angle is equal to the sum of two opposite interior angles.
In ∠QSR is exterior angle.
∠SPQ and ∠SQP are the opposite interior angle of the exterior angle ∠QSR .
Thus
∠QSR = ∠SPQ + ∠SQP
As given in the diagram
∠QSR = 2x , ∠SQP = x
Put in the above
2x = x + ∠SQP
∠SQP = 2x - x
∠SQP = x
Thus
∠SPQ = ∠SQP = x
By using the property
if two angles are equal in a triangle than their opposite sides are also equal .
Thus
PS = SQ
Two sides of triangle are equal .
therefore Δ PQS is a isosceles triangle .
Answer:
45 minutes
Step-by-step explanation:
At 30 mph for 1/4 hour, Peter has a 7.5 mile head start. After he leaves, Mitchell closes that gap at the rate of 40-30 = 10 miles per hour. It will take him ...
t = d/s
t = (7.5 mi)/(10 mi/h) = 0.75 h
to catch Peter.
Mitchell will catch Peter in 45 minutes.
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<em>Alternate Solution</em>
Another way to look at it is that Mitchell's 10 mph advantage is 1/3 of Peter's speed, so it will take 1/(1/3) = 3 times the period of Peter's head start:
3 × 15 minutes = 45 minutes . . . for Mitchell to catch Peter
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You can write equations involving time and distance and see where the distances traveled become the same. You need to be careful choosing the time reference, since you're concerned with Mitchell's travel time. I personally prefer to work "head start" problems by considering the differences in time and speed, as above. This is where you end up using the equations approach, anyway.
Answer:
x = 1 and y = 5
Step-by-step explanation:
Use substitution because you know that x = y - 4, and plug this into the first equation to get -10(y - 4) + 3y = 5, or -10y + 40 + 3y = 5. This is -7y = -35 so y = 5. Plug this into the 2nd equation to get that x = 1 and y = 5.
You know that 6x+3 equals 45 because the two sides are equal. So you first put the equation 6x+3=45. Then you use the subtraction property of equality and subtract 3 from both sides. This gives you 6x=42. Then you divide 6 from both sides to get you final answer, x=7
