Answer:
The value of
is 17-18x and
is -7-18x.
Step-by-step explanation:
It is given in the question functions f(x) as 3x+2 and g(x)=5-6x.
It is required to find
and
.
To find
, substitute g(x) for x in f(x) and simplify the expression.
To find
, substitute f(x) for x in g(x) and simplify the expression.
Step 1 of 2
Substitute g(x) for x in f(x) and simplify the expression.

Step 2 of 2
Substitute f(x) for x in g(x) and simplify the expression.

Answer:
(A) 4.03 x 10^14
Step-by-step explanation:
403,000,000,000,000
Scientific notation is of the form
a * 10 ^b
where a is a number from 1 to a number less than 10
Put the decimal in the number
403,000,000,000,000.
We need to move the decimal 14 places to the left to get the number to be between 1 and 10
4.03000000000000 so the b is 14
Since we moved it to the left b is positive
We can drop the extra zeros at the end (after the last nonzero digit)
4.03 *10^14
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:
x = 17.5 and y = 35
Step-by-step explanation:
2x + 10 = y + 10 ( alternate angles )
subtract 10 from both sides
2x = y ⇒ 6x = 3y → (1)
the sum of the 3 angles in the triangle = 180°
6x + y + 10 + 30 = 180 ( replace 6x by 3y )
3y + y + 40 = 180
4y + 40 = 180 ( subtract 40 from both sides )
4y = 140 ( divide both sides by 4 )
y = 35
substitute y = 35 into (1)
2x = 35 ( divide both sides by 2 )
x = 17.5