Which pair shows equivalent expressions?
A.2(2/5x + 2)=2 2/5x + 1
B.2(2/5x + 2)=4/5x + 4
C.2(2/5x + 4)=4/5x + 2
D.2(2/5x + 4)=2 2/5x + 8
Solution:
Let us distribute 2 inside the parenthesis.
That is, we use distributive property:
a(b+c)=ab+ac
So, 
Answer:Option (b)
Applying distributive property, a(b+c)=ab+ac
So, Option (B) is correct.
Option C is correct because it is a trinomial with a leading coefficient of 3 and a constant term of -5
Step-by-step explanation:
We need to pick the expression that matches this description:
A trinomial with a leading coefficient of 3 and a constant term of -5
First lets explain the terms:
Trinomial: a polynomial having 3 terms
Leading coefficient: The constant value of variable having highest power
Constant term: Having no variable and value cannot be changed.
Now using these definitions, we can choose the correct option
Option A is incorrect because the expression has 2 terms
Option B is incorrect because it is a trinomial but the leading coefficient is -5 and not 3 constant term is 3 and not -5.
Option C is correct because it is a trinomial with a leading coefficient of 3 and a constant term of -5
Option D is incorrect because it is a trinomial but the leading coefficient is 3 but constant term is 1 and not -5.
So, Option C is correct.
Keywords: Algebra
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The y-value changes from 10 to 70 as the x-value changes from 0 to 10. That makes the slope (70 -10)/(10 -0) = 6, and the y-intercept = 10.
Selection A is the appropriate equation.
Answer:
A. 0
Step-by-step explanation:
The circles are concentric. I.e there is no point where the circumferences of both circles ever touch each other. Hence there can be no tangent line possible that can be common to both circles at the same time.
A. 16 is divisible by 2 but not divisible by 3
B. 23 is not divisible neither by 2 nor 3
C. 27 is not divisible by 2, however it's divisible by 3
D. 36 is divisible both by 2 and 3
So the only number we can focus on is 36:
36 ÷ 2 = 18
36 ÷ 3 = 12
36 ÷ 6 = 6
Answer: D, 36 supports the given conjecture.
