Two triangle ABE and MNP are similar by AA criterion
Step-by-step explanation:
Given that ABE is an isosceles Δ with ABE= 100°
this means that some of the other two angles must be =180°-100°=80°
Since the triangle is an isosceles Δ meaning two sides measure must be equal, it means the other two sides measure 40° each.
∠BAC=∠ACB=40°
In MNP one of the base angles is 40° and the triangle is isosceles. For an isosceles triangle base angles are always equal hence other base angle is also 40° meaning
the angle measures come out to be 40°,40° and 100°
Since all the angle measures are same the two triangles are similar in aspect by AA criterion where AA refers to "angle-angle"
Answer: The boats are 44.82 miles from each other.
Step-by-step explanation:
The direction of movement of Marcus and Sandra forms a right angle triangle.
The distance sailed by Marcus due North would represent the opposite side of the right angle triangle.
The distance sailed by Sandra due east would represent the adjacent side of the right angle triangle.
The distance, h between the both of them after 2 hours represents the hypotenuse of the right angle triangle.
To determine h, we would apply Pythagoras theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
h² = 35² + 28² = 1225 + 784
h² = 2009
h = √2009
h = 44.82 miles
$36 because 20% of 45 is 9 and 45 - 9 is 36!
Answer:
Cost: $13,680.82
Number of pairs of skates: 1057.25 / 1057-1058
Step-by-step explanation:
To find the cost of the wheels, we need to multiply the cost of a set, $6.47, by the number of wheels needed, 8458, for a quotient of 54723.26. We then divide this quotient by 4, the number of wheels in each set, to get the cost of $13,680.82.
Next, to find the number of pairs that Adam can put wheels on, we divide 8458, the number of wheels Adam has, by 8, the number of wheels Adam puts on each pair of skates. This leaves us with a quotient of 1057.25 pairs. The two whole numbers this number is between are 1057 and 1058.
