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avanturin [10]
3 years ago
15

Given the system of inequalities:

Mathematics
2 answers:
Margaret [11]3 years ago
8 0
Answer:
First inequality: y > \frac{4}{5} x - \frac{1}{5}
Second inequality: y < 3 + x

Explanation:
The inequality in slope-intercept form has the following general formula:
y < mx + c or y > mx + c (according to the given sign)
where m is the slope and c is the y-intercept

This means that to get any inequality in slope-intercept form, we will have to isolate the y on one side of the inequality.

First given inequality:
4x - 5y < 1
4x - 5y + 5y < 1 + 5y
1 + 5y > 4x
1 + 5y - 1 > 4x - 1
5y > 4x - 1
y > \frac{4}{5} x -  \frac{1}{5}
comparing this to the general form, we would find that:
slope (m) = 4/5
y-intercept (c) = 1/5

Second given inequality:
y - x < 3
y - x + x < 3 + x
y < 3 + x
comparing this to the general form, we would find that:
slope (m) = 1
y-intercept (c) = 3

Hope this helps :)
ss7ja [257]3 years ago
5 0

Answer:

B

Step-by-step explanation:

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Alicia took a friend for a birthday dinner. The total bill for dinner was $40.86 (including tax and a tip). If Alicia paid a 20.
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3 years ago
State the domain and range of both the function and the inverse function. f(x) = 8 x + 8 f -1(x) = Domain of f(x): Range of f(x)
Katena32 [7]

Answer:

f^{-1}(x) = \frac{x+8}{8}

Domain of f(x): All real values.

Range of f(x): All real values.

Domain of f -1(x): All real values.

Range of f -1(x): All real values

Step-by-step explanation:

We are given the following function:

f(x) = 8x + 8

Since it is a line, we have that both the domain is the range is the real set.

Inverse function:

The domain of the inverse function is the range of the original function, and the range of the inverse function is the domain of the original function.

Finding the inverse function:

Exchange x and y in the original function, and isolate y. So

Original

y = 8x + 8

Exchanging:

x = 8y - 8

Isolating y:

8y = x + 8

y = \frac{x+8}{8}

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