Answer:
10x − 1.44y
Step-by-step explanation:
(6.15x + 0.24y) ÷ 1.5 + 5.9x − 1.6y =
= 4.1x + 0.16y + 5.9x − 1.6y
= 10x − 1.44y
They are simple linear equations with one unknown, lets tackle them, one step at the time solving for the unknown:
4x - 2(x - 5) = x + 13
4x - 2x + 10 = x + 13
2x + 10 = x + 13
2x - x = 13 - 10
x = 3
that is the solution.
3(6 - x) - 4 = 5x + 2(7x + 3)
18 - 3x - 4 = 5x + 14x + 6
14 - 3x = 19x + 6
14 - 6 = 19x + 3x
8 = 22x
x = 8/22 = 4/11
The quadratic function given by:
is in vertex form. The graph of
is a parabola whose axis is the vertical line
and whose vertex is the point
. So:
To translate the graph of a function to the right, left, upward or downward we have:

By knowing this things, we can solve our problem as follows:
FIRST.
- Translating <em>11 units to the left:</em>

- Then translating<em> 5 units down:</em>

Since the new function is fatter, the factor we need to multiply the term
<em>must be</em> less than 1, to make the graph fatter. So, according to our options, there are two factors 1/2 and 2.
<em>Therefore, the right answer is </em><em>b. f(x) = 1/2(x + 11)^2 - 5</em>
SECOND.
- Translating <em>8 units to the right:</em>

- Then translating<em> 1 unit down:</em>

As explained in the previous case, there are two factors 1/3 and 3, so we choose the first one.
<em>Therefore, the right answer is </em><em>a. g(x) = 1/3(x - 8)^2 - 1</em>