This is the concept of algebra: The answers to the questions will be as follows: 1. What is AD/AM in the simplest form: AD/AB is the ratio of AD to AB. This will calculated as follows: AD=9 units AB=3 units thus: 9/3=3 Hence, we conclude that the answer is D. 3
2] What is slope of BE/ slope of AE in simplest form: slope=(Δy-axis)/(Δx-axis) slope of AE =(5-0)/(4-0) =5/4 slope BE slope=(5-0)/(4-3)=5/1=5 therefore the ratio of the two slope will be: BE/AE =5/(5/4) =4 The answer is A.4
3. What is the value of x in the proportion (x-1)/5=(4x+2)/35? To get the value of x we solve the above proportion: (x-1)/5=(4x+2)/35 35(x-1)=5(4x+2) 35x-35=20x+10 putting like terms together we get: 35x-20x=10+35 15x=45 dividing both sides by 15 x=45/15 x=3 Hence the answer is B.3
4. What is the value of x in the proportion: (x+1)/(x+3)=15/21 to get the value of x we solve the above: first we begin by cross multiplying the proportion, this will give us: 21(x+1)=15(x+3) 21x+21=15x+45 putting like terms together we get: 21x-15x=45-21 6x=24 dividing both sides by 6 we get x=4 ∴ x=4
5. The lengths of the sides of a triangle are in extended ratio 3:10:12. The perimeter is 400 cm. What is the length of the longest side in cm. solution: Here we introduce the variable x such that the perimeter is: 3x+10x+12x=400 25x=400 x=400/25 x=16 The longest side will be: 12×16=192 cm
