How many sides has a regular polygon whose interior angles are 120°each
4
5
6
3
Correct answer is C
Each exterior angle = 180 − 120=60
Exterior angle =360/n
60 = 360/n
n =360/6
= 6
Solve the equation
5(x−2)=(1÷125)(x+3)
3/2
− 7/4
4/7
7/4
Correct answer is B
5(x−2)=(125−1)(x+3)5(x−2)=(5−3)x+35(x−2)=5−3x−9x+3x=−9+24x=−7x=−74
The sum of two numbers is 5; their product is -14. Find the numbers.
x = 5 or 1
x = 7 or 1
x = 7 or 0
x = 7 or − 2
Correct answer is D
Let x represent the first number;
Then, the other is (5 − x) , since their sum is 5 and their product is 14
x(5 − x) = 14
5x − x2 = 14
x2 − 5x − 14 = 0
(x2 − 7x) + (2x − 14) = 0
x(x − 7) + 2(x − 7) = 0
(x − 7)(x + 2) = 0
Either (x − 7) = 0 or (x + 2) = 0
x = 7 or x = − 2
The two numbers are 7 and − 2
If √ (2x + 2) − √x =1 ,find x.
x = 1 twice
x = 0 or 1
x = 3 or 1
x = 2 twice
Correct answer is A
√(2x + 2 ) − √x = 1
√(2x + 2) = 1 + √x
Square both sides
√(2x + 2)2 = (1 + √x)2
((2x + 2)2)½ = 1 + √x + √x+ x
2x + 2 = 1 + 2√x +x
Collect the like term together
2x − x + 2 − 1 = 2 √x
x + 1 = 2√x
Square both sides
(x + 1)2 = (2√x)2
x2 + 2x + 1 = 4x
x2 + 2x − 4x + 1 = 0
(x2− x)(x + 1)= 0
x(x − 1) −1(x − 1)
(x − 1)(x −1)
Either (x − 1) = 0 or (x − 1) = 0
x = 1 or 1
x = 1 twice