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3 years ago

Verify this closure property of subtraction x= -4/5 , y= 1/-10

Mathematics

1 answer:

Rom4ik [11]3 years ago

4 0

Answer:

x - y is also a rational number. Hence satisfies the closure property.

Step-by-step explanation:

$x =\frac{-4}{5} , y = \frac{1}{-10} = \frac{-1}{10}\\$

Closure property of subtraction states that for any two integers a and b, (a - b) must also be an integer.

Here x and y are rational numbers. so x - y must also be rational to satisfy the closure property.

$x - y = -\frac{4}{5}- ( - \frac{1}{10}) = -\frac{4}{5} + \frac{1}{10} = \frac{-8 +1 }{10} = \frac{-7}{10}$

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Find the formula for an exponential function that passes through the two points give.

Ksenya-84 [330]

Answer:

$y=3(2)^{x}$

Step-by-step explanation:

Given.

Two points are given.

$(x, y)=(-1,\frac{3}{2})$ and $(x, y)=(3,24)$

An exponential function is in the general form.

$y=a(b)^{x}$ -------(1)

We know the points $(-1,\frac{3}{2})$ and $(3,24)$

put the first point value in equation 1

$\frac{3}{2}=a(b)^{-1}$

$\frac{3}{2}=\frac{a}{b}$

$a=\frac{3}{2}\times b$ --------(2)

put the second point value in equation 1

$24=a(b)^{3}$ ----------(3)

Put the a value from equation 2 to equation 3

$24=\frac{3}{2}\times b(b)^{3}$

$b^{3+1}=\frac{24\times 2}{3}$

$b^{4} = 16\\b=\sqrt[4]{16} \\b=2$

Put the b value in equation 2

$a=\frac{3}{2}\times 2$

$a=3$

Put the a and b value in equation 1

$y=3(2)^{x}$

So, the exponential function that passes through the points $(-1,\frac{3}{2})$ and $(3,24))$ are $y=3(2)^{x}$ .

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3 years ago

Complete the table of values for y = 2x^2 + x

tigry1 [53]

Answer: -2, 0 and 0, 2 and 2, 4

Step-by-step explanation:

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3 years ago

Say a hacker has a list of n distinct password candidates, only one of which will successfully log her into a secure system. a.

alexdok [17]

Answer:

The probability is $\frac{1}{n}$

Step-by-step explanation:

If she has n distinct password candidates and only one of which will successfully log her into a secure system, the probability that her first first successful login will be on her k-th try is:

If k=1

$P = \frac{1}{n}$

Because, in her first try she has n possibles options and just one give her a successful login.

If k=2

$P=\frac{n-1}{n} *\frac{1}{n-1} =\frac{1}{n}$

Because, in her first try she has n possibles options and n-1 that are not correct, then, she has n-1 possibles options and 1 of that give her a successful login.

If k=3

$P=\frac{n-1}{n} *\frac{n-2}{n-1} *\frac{1}{n-2} = \frac{1}{n}$

Because, in her first try she has n possibles options and n-1 that are not correct, then, she has n-1 possibles options and n-2 that are not correct and after that, she has n-2 possibles options and 1 give her a successful login.

Finally, no matter what is the value of k, the probability that her first successful login will be (exactly) on her k-th try is 1/n

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3 years ago

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svet-max [94.6K]

Answer:

C (The third one)

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3 years ago

Determine the x- and y-intercepts of the graph ofx−4y=8Then plot the intercepts to graph the equation.

Over [174]

The x-intercept is the point where the graph cuts the x-axis, and the y-intercept is the point where the graph cuts the y-axis.

The x-axis is the line y = 0 and the y-axis is the line x = 0. To find the intercept between each axis and our graph, we just need to evaluate our function at x = 0 and y = 0.

Calculating the x-intercept, we have

$\begin{gathered} x-4\cdot0=8 \\ x=8 \end{gathered}$

The x-intercept is (8, 0).

Calculating the y-intercept, we have

$\begin{gathered} 0-4y=8 \\ y=-\frac{8}{4} \\ y=-2 \end{gathered}$

The y-intercept is (0, -2).

8 0

1 year ago

Verify this closure property of subtraction x= -4/5 , y= 1/-10​

Verify this closure property of subtraction x= -4/5 , y= 1/-10