1.Consider the system of equations. x-5y=2
1 answer:
1.Consider the system of equations. x-5y=2
3x-10y=11
(a) Jamar rewrote the first equation as –2x + 10y = –4. What justification did he have for doing this?
(b)Jamar combined the equation in Part (a) with the second equation in the system to get x = 7. Explain Jamar’s reasoning.
(c) What is the solution of the system? (d) How do you know, without graphing, that the graph of 4x – 15y = 13 passes through the point whose coordinates are the solution of the system?
3x-10y=11
(a) Jamar rewrote the first equation as –2x + 10y = –4. What justification did he have for doing this?
(b)Jamar combined the equation in Part (a) with the second equation in the system to get x = 7. Explain Jamar’s reasoning.
(c) What is the solution of the system? (d) How do you know, without graphing, that the graph of 4x – 15y = 13 passes through the point whose coordinates are the solution of the system?
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Answer:
- inverse is not a function
- unless the domain is restricted to |x| ≥ 1.2 (approximately)
Step-by-step explanation:
The test to see if the inverse function is also a function is called the "horizontal line test." The test passes if any horizontal line intersects the graph in only one place.
Here, a horizontal line can intersect the graph in 1, 2, or 3 places, so the test fails. The function does not have an inverse that is a function.
__
If the domain of the inverse relation is restricted to |x| > 1.2, then that inverse will map any x to only a single value of y. Then it will be a function.
_____
The graph shows the original function (dashed red line) and the inverse relation (blue). The green shading marks values of x for which there is a single value of y, so the inverse relation is a function in those regions.
(We could be more specific as to the limits on the domain of f^-1(x), but the given graph seems to have an unknown vertical scale factor.)
We could write such a number as
so we're done.
D.
The formula to find the circumference of a circle is:
Where "C" is circumference and "d" is diameter.
Substituting your values in, we have:
Which, when rounded, is 37.7.
The formula to find the circumference of a circle is:
Where "C" is circumference and "d" is diameter.
Substituting your values in, we have:
Which, when rounded, is 37.7.