Which matrix represents the system of equations shown below
2 answers:
Answer:
C) option is correct.
Step-by-step explanation:
Given : 4x + 2y - 4 and 12x -y - 26.
To find : Which matrix represents the system of equations shown below.
Solution : We have given
4x + 2y - 4 = 0
12x -y - 26 = 0
Expressing Systems of Equations as Matrices:
ax +by = α
cx +dy = β
Can be represent in matrices as .
Then,
On comparison matrix would be
.
Therefore, C) option is correct.
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Answer:
Step-by-sep explanation:
To create an equation that represents the shortest oath of the swimmer that is perpendicular to the shoreline, we need to find the slope, m, and the y-intercept, b.
The slope of the path would be the negative reciprocal of the slope of the shoreline, since they are perpendicular.
Let's find the slope of the shoreline.
Using two points on the shoreline, (0, 1) and (4, 4),
Slope (m) =
Therefore the slope, m, of the swimmer's path that is perpendicular to the shoreline would be -⁴/3.
Use the point of the swimmer and the slope of the path to find b.
Substitute m = -⁴/3, (x, y) = (6, 1) in
Add 8 to both sides
Now that we know the slope, m = -⁴/3, and the y-intercept, b = 9, plug in their values into .
The equation of the path would be:
True statements:
The domain of h(x) is the set of all real numbers.
The range of h(x) is the set of all real numbers
Step-by-step explanation:
The function given in this problem is
Now let's analyze the statements given:
- The domain of h(x) is the set of all real numbers. --> TRUE. The domain of a function is the set of values allowed for x. Here there is no restriction for the value of x, since the argument of an odd root can have any value (either positive or negative), so the domain of h(x) is the set of all real numbers.
- The range of h(x) is the set of all real numbers. --> TRUE. The range of a function is the set of values that the y can take. In this case, y can take any value: in fact, as , then
, and as
, then
, and since there are no points of discontinuity in the function, this means that it can take any value of y.
For all points (x, h(x)), h(x) exists if and only if x – 4 > 0 --> FALSE. As we stated in part 1), the argument of a cubic root can be either positive or negative, so the function is defined also for x - 4 < 0.
The graph of h(x) is a translation of f(x) down 4 units. --> FALSE. The form of f(x) is not given so we can't evaluate this statement.
The graph of h(x) intercepts the x-axis at (4, 0). --> FALSE. In fact, when , the value of the function is
which is different from 4.
Learn more about domain and range:
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