(Area of 1) + (Area of 2) = (Area of 3) this statement about the squares must be true.
What is Right angle traingle?
A right-angled triangle is a particular kind of triangle in which one of the angles is 90 degrees. The combined angles of the other two are 90 degrees. The triangle's base and perpendicular sides both include the right angle. The longest of the three sides, known as the hypotenuse, is the third side.
we know that;
By applying the Pythagorean Theorem;
.............................(1)
Area of the square says A1;
A1 = a^2 unit^2 ...............................(2)
Area of the square says A2;
A2 = b^2 unit^2 .................................(3)
Area of the square says A1;
A3 = c^2 unit^2 ..................................(4)
Replace the A1, A2, and A3 values in the equation 1 ;
A3 = A1 + A2
therefore;
(Area of 1) + (Area of 2) = (Area of 3).
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Start at 4 on the y axis
move 2 units up and 3 units right
Might have to experiment a bit to choose the right answer.
In A, the first term is 456 and the common difference is 10. Each time we have a new term, the next one is the same except that 10 is added.
Suppose n were 1000. Then we'd have 456 + (1000)(10) = 10456
In B, the first term is 5 and the common ratio is 3. From 5 we get 15 by mult. 5 by 3. Similarly, from 135 we get 405 by mult. 135 by 3. This is a geom. series with first term 5 and common ratio 3. a_n = a_0*(3)^(n-1).
So if n were to reach 1000, the 1000th term would be 5*3^999, which is a very large number, certainly more than the 10456 you'd reach in A, above.
Can you now examine C and D in the same manner, and then choose the greatest final value? Safe to continue using n = 1000.
Answer:
Distance travelled by Monarch butterfly = 2000 miles
Distance travelled by desert locust = 2800
Distance travelled by pink-spotted hawk moth= 7800 miles
Step-by-step explanation:
Let the distance travelled by Monarch butterfly be "X" miles
Distance travelled by desert locust is equal to X + 800 miles
Distance travelled by pink-spotted hawk moth is equal to 4X -200 miles
The total distance travelled by the three is equal to 12600 miles

Distance travelled by Monarch butterfly = 2000 miles
Distance travelled by desert locust = 2000 + 800 = 2800
Distance travelled by pink-spotted hawk moth = 4 * 2000 -200 = 7800 miles