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3 years ago

2 points

Mathematics

1 answer:

miskamm [114]3 years ago

5 0

The x - intercept of 5x - 3y = 15 is (3, 0)

The y -intercept of 5x - 3y = 15 is (0, -5)

<h3>Solution:</h3>

Given equation is 5x - 3y = 15

To find: x - intercept and y -intercept

The x intercept is the point where the line crosses the x axis. At this point y = 0

The y intercept is the point where the line crosses the y axis. At this point x = 0.

Finding x - intercept:

To find the x intercept using the equation of the line, plug in 0 for the y variable and solve for x

So put y = 0 in given equation

5x - 3(0) = 15

5x = 15

x = 3

So the x - intercept is (3, 0)

Finding y - intercept:

To find the y intercept using the equation of the line, plug in 0 for the x variable and solve for y

So put x = 0 in given equation

5(0) - 3y = 15

-3y = 15

y = -5

So the y - intercept is (0, -5)

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Answer:

The inverse of a non-function mapping is not necessarily a function.

For example, the inverse of the non-function mapping $\lbrace (0,\, 0),\, (0,\, 1),\, (1,\, 0),\, (1,\, 1) \rbrace\!$ is the same as itself (and thus isn't a function, either.)

Step-by-step explanation:

A mapping is a set of pairs of the form $(a,\, b)$ . The first entry of each pair is the value of the input. The second entry of the pair would be the value of the output.

A mapping is a function if and only if for each possible input value $x$ , at most one of the distinct pairs includes $x\!$ as the value of first entry.

For example, the mapping $\lbrace (0,\, 0),\, (1,\, 0) \rbrace$ is a function. However, the mapping $\lbrace (0,\, 0),\, (1,\, 0),\, (1,\, 1) \rbrace$ isn't a function since more than one of the distinct pairs in this mapping include $1$ as the value of the first entry.

The inverse of a mapping is obtained by interchanging the two entries of each of the pairs. For example, the inverse of the mapping $\lbrace (a_{1},\, b_{1}),\, (a_{2},\, b_{2})\rbrace$ is the mapping $\lbrace (b_{1},\, a_{1}),\, (b_{2},\, a_{2})\rbrace$ .

Consider mapping $\lbrace (0,\, 0),\, (0,\, 1),\, (1,\, 0),\, (1,\, 1) \rbrace\!$ . This mapping isn't a function since the input value $0$ is the first entry of more than one of the pairs.

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Answer:

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Step-by-step explanation:

Solve for x:

3125 = 3 x + 1/9765625

Put each term in 3 x + 1/9765625 over the common denominator 9765625: 3 x + 1/9765625 = (29296875 x)/9765625 + 1/9765625:

3125 = (29296875 x)/9765625 + 1/9765625

(29296875 x)/9765625 + 1/9765625 = (29296875 x + 1)/9765625:

3125 = (29296875 x + 1)/9765625

3125 = (29296875 x + 1)/9765625 is equivalent to (29296875 x + 1)/9765625 = 3125:

(29296875 x + 1)/9765625 = 3125

Multiply both sides of (29296875 x + 1)/9765625 = 3125 by 9765625:

(9765625 (29296875 x + 1))/9765625 = 9765625×3125

(9765625 (29296875 x + 1))/9765625 = 9765625/9765625×(29296875 x + 1) = 29296875 x + 1:

29296875 x + 1 = 9765625×3125

9765625×3125 = 30517578125:

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Subtract 1 from both sides:

29296875 x + (1 - 1) = 30517578125 - 1

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29296875 x = 30517578125 - 1

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