Answer: Option C
Step-by-step explanation:
Whenever we have a main function f(x) and we want to transform the graph of f(x) by moving it vertically then we apply the transformation:
If 
then the graph of k(x) will be the graph of f(x) displaced vertically b units down.
If then the graph of k(x) will be the graph of f(x) displaced vertically b units upwards.
In this case we have
We know that this function has its vertex in point (0,0).
Then, to move its vertex 7 units down we apply the transformation:
.
Then the function k(x) that will have its vertex 7 units below f(x) is
Answer:
See explanation, and ask for more details if unclear!
Step-by-step explanation:
The perfect square of this equation is 
, since the square would be 
. 1/4=4/16, meaning that you can set up the equation in the following way:
Take the square root of both sides:
Add 1/2 to both sides:
. Hope this helps!
Answer:
(i) A truth table shows how the truth or falsity of a compound statement depends on the truth or falsity of the simple statements from which it's constructed.
Since A ∧ B (the symbol ∧ means A and B) is true only when both A and B are true, its negation A NAND B is true as long as one of A or B is false.
Since A ∨ B (the symbol ∨ means A or B) is true when one of A or B is true, its negation A NOR B is only true when both A and B are false.
Below are the truth tables for NAND and NOR connectives.
(ii) To show that (A NAND B)∨(A NOR B) is equivalent to (A NAND B) we build the truth table.
Since the last column (A NAND B)∨(A NOR B) is equal to (A NAND B) it follows that the statements are equivalent.
(iii) To show that (A NAND B)∧(A NOR B) is equivalent to (A NOR B) we build the truth table.
Since the last column (A NAND B)∧(A NOR B) is equal to (A NOR B) it follows that the statements are equivalent.
X should be 300
15/x= 0.05
x= 15/0.05= 300
x=300
Answer:
Total amount of fencing needed as an algebraic expression in terms of x is: <em>10x</em><em> </em><em>+</em><em> </em><em>3</em> .
Step-by-step explanation:
As it is given that each rectangle has the same dimensions, the dimensions of each rectangle must be: x units by 2x + 1 units.
Based on this, we can calculate the total amount of fencing needed.
Let width of each rectangle = x
Let length of each rectangle = 2x + 1
There are 4 widths and 3 lengths in total of fencing.
Therefore:
= 4 ( x ) + 3 ( 2x + 1 )
Expand:
= 4x + 6x + 3
Group like-terms:
= 10x + 3
