Billy graphed the system of linear equations to find an approximate solution. y = A system of equations. y equals negative Start
Fraction 7 over 4 EndFraction x plus StartFraction 5 over 2 EndFraction. y equals StartFraction 3 over 4 EndFraction x minus 3.x + y = x – 3 A coordinate grid with 2 lines. The first line is labeled y equals negative StartFraction 7 over 4 EndFraction x plus StartFraction 5 over 2 EndFraction and passes through the (0, 2.5) and (2.2, negative 1.4). The second line is labeled y equals StartFraction 3 over 4 EndFraction x minus 3 and passes through (0, negative 3, 0.14) and (2.2, negative 1.4) Which points are possible approximations for this system? Select two options. (1.9, 2.5) (2.2, –1.4) (2.2, –1.35) (1.9, 2,2) (1.9, 1.5)
2 answers:
Response:
Second option:
Third option:
Detailed explanation:
The missing graph has been provided.
The attached image illustrates the graphing of the following system of linear equations:
Notice the intersection of the lines.
According to the definition, if lines in a system of equations intersect, then there is only one solution. This implies that the intersection point is the solution to that system. This can be expressed as:
Represented by "x" for the x-coordinate and "y" for the y-coordinate.
Here, it's noticeable that:
- The x-coordinate of the intersection point lies between and
.
- The y-coordinate of the intersection point is situated between and
.
Therefore, you can conclude that the forthcoming points (Refer to the options given in the exercise) are potential approximations for this system:
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Question:
Which statement is accurate concerning the function’s discontinuities
A) There are gaps at x = 7 and.
B) Asymptotes exist at x = 7 and.
C) Asymptotes exist at x = –7 and.
D) Gaps are present at (–7, 0) and.
Answer:
B) Asymptotes exist at x = 7 and
Step-by-step explanation:
Given:
Goal:
Identify the correct statement
We need to factor the denominator first.
To express x in terms of (3x+4) and (x-7):
3x + 4 =
3x = -4
Divide both sides by 3:
x - 7
x = 7
Next, evaluate the limit when and at (x = 7)
lim f(x) as = ±∞
lim f(x) as (x=7) = ±∞
Since both scenarios result in the denominator approaching zero, they represent asymptotes.
Thus, asymptotes are found at and x=7
Option B is determined to be correct