The van is traveling about 55.9 miles per hour.
Answer:
Step-by-step explanation:
Remember that
Area of Circle = 
They told us that for this circle, the area is 
If you put it back into the formula for area of a circle we get:
Area of Circle =
Divide both sides by 
.
144 = 
Now we want to solve for r (r = radius).
You need to square root each side
So now we know the radius, 
metres
Also remember that
Diameter = 
So,
Diameter = 2 times 12 = 24 metres
Fiona and Pip win some money and share it in the ratio 6:1. Fiona gets £35 more than Pip. How much did they get altogether?
Let Pip get be x and fiona get be x+35
Ratio = 6:1
Since segment AC bisects (aka cuts in half) angle A, this means the two angles CAB and CAD are the same measure. I'll refer to this later as "fact 1".
Triangles ABC and ADC have the shared segment AC between them. By the reflexive property AC = AC. Any segment is equal in length to itself. I'll call this "fact 2" later on.
Similar to fact 1, we have angle ACB = angle ACD. This is because AC bisects angle BCD into two smaller equal halves. I'll call this fact 3
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To summarize so far, we have these three facts
- angle CAB = angle CAD
- AC = AC
- angle ACB = angle ACD
in this exact order, we can use the ASA (angle side angle) congruence property to prove the two triangles are congruent. Facts 1 and 3 refer to the "A" parts of "ASA", while fact 2 refers to the "S" of "ASA". The order matters. Notice how the side is between the angles in question.
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Once we prove the triangles are congruent, we use CPCTC (corresponding parts of congruent triangles are congruent) to conclude that AB = AD and BC = BD. These pair of sides correspond, so they must be congruent in order for the entire triangles to be congruent overall.
It's like saying you had 2 identical houses, so the front doors must be the same. The houses are the triangles (the larger structure) and the door is an analogy to the sides (which are pieces of the larger structure).
Answer:
x=100
Step-by-step explanation:
2x + 100 = 300
-100 -100
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2x = 200
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2 2
x=100
