What can 7/8 be rewritten as?

5x-15=5+4x

    +15 +5

   5x=20+4x

  -4x       -4x

     x= 20

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

I think the question is whether: "a plumber has a 20-foot piece of PVC pipe. how many 7/5 foot pieces can be cut from the 20-foot piece?"

The fractional part vanishes when the argument is an integer; in this case, for

[tex]\left\{\dfrac1{1-xy}\right\} = 0 \iff \dfrac1{1-xy} = n \iff xy = \dfrac{n-1}n[/tex]

which are hyperbolas in the [tex](x,y)[/tex]-plane.

Observe that between neighboring hyperbolas, we have

[tex]\dfrac{n-1}n < xy < \dfrac n{n+1} \\\\ ~~~~ \implies \dfrac1{n+1} < 1-xy < \dfrac1n \\\\ ~~~~ \implies n < \dfrac1{1-xy} < n+1 \\\\ ~~~~ \implies \left\{\dfrac1{1-xy}\right\} = \dfrac1{1-xy} - \left\lfloor\dfrac1{1-xy}\right\rfloor = \dfrac1{1-xy} - n[/tex]

Split up the integral over [tex][0,1)^2[/tex] along the curves [tex]xy=\frac{n-1}n[/tex]. The subregions somewhat resemble the layers or scales of an onion (see attached plot with the first 5 "scales").

Let [tex]S_n[/tex] denote the [tex]n[/tex]-th ([tex]n\in\Bbb N[/tex]) "scale", starting from the blue region closest to the origin and counting diagonally upward in the direction of (1, 1).

In Cartesian coordinates, the integral over [tex]n[/tex]-th "scale" is

[tex]\displaystyle \iint_{S_n} x \left(\frac1{1-xy} - n\right) \, dy \, dx \\\\\\ ~~~~~~~~= \int_{(n-1)/n}^{n/(n+1)} \int_{(n-1)/(nx)}^1 x \left(\frac1{1-xy} - n\right) \, dy dx \\\\\\ ~~~~~~~~~~~~~ + \int_{n/(n+1)}^1 \int_{(n-1)/(nx)}^{n/((n+1)x)} x \left(\frac1{1-xy} - n\right) \, dx[/tex]

(see attached plot of the 2nd "scale" for reference)

The integral is trivial, so I'll leave it to you to confirm that it drastically reduces to

[tex]\displaystyle \iint_{S_n} x \left(\frac1{1-xy} - n\right) \, dy \, dx = \frac1{2n (n+1)^2} = \frac12 \left(\frac1n - \frac1{n+1} - \frac1{(n+1)^2}\right)[/tex]

Now we recover the original integral by summing over [tex]\Bbb N[/tex].

[tex]\displaystyle \int_0^1 \int_0^1 x \left\{\frac1{1-xy}\right\} \, dy \, dx = \frac12 \sum_{n=1}^\infty \left(\frac1n - \frac1{n+1} - \frac1{(n+1)^2}\right) \\\\ ~~~~~~~~ = \frac12 \left(\left(1-\frac12\right)+\left(\frac12-\frac13\right)+\left(\frac13-\frac14\right)+\cdots\right) - \frac12 \sum_{n=2}^\infty \frac1{n^2} \\\\ ~~~~~~~~ = \frac12 - \frac12 \left(\sum_{n=1}^\infty \frac1{n^2} - 1\right) \\\\ ~~~~~~~~ = \frac12 - \frac12 \left(\frac{\pi^2}6 - 1\right) = \boxed{1 - \frac{\pi^2}{12}}[/tex]

Answer:

2[tex] {}^{5} [/tex]

Step-by-step explanation:

2×2×2×2×2 = 2[tex] {}^{5} [/tex]

The vertex of the quadratic function f(x) = (x + 3)² - 4 is (-3,-4)

Given a quadratic function, the equation of the quadratic function in vertex form is given by f(x) = a(x - h)² + k where

Now, given the quadratic function f(x) = (x + 3)² - 4, we require the vertex of the quadratic function.

Comparing the function f(x) = (x + 3)² - 4 with f(x) a(x - h)² + k, we see that

Since the vertex of the quadratic function is (h, k), we see that the vertex of the quadratic function f(x) is (-3,-4)

So, the vertex of the quadratic function is (-3,-4)

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The Domain is   [-4, -2] U  [-1, 1)  and range is [4, 0)

The domain of a function is the set of values that we are allowed to plug into our function.

The range of a function is the set of values that the function assumes.

Given:

The left piece has its other endpoint at x = -2.

So, the interval for the domain is [-4, -2] and the other part is [-1, 1)

So, the domain is [-4, -2] U  [-1, 1)

and the range is the vertical range of the right part.

So, range is [4, 0)

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Answer:(7/9)^12

Step-by-step explanation:

Answer:

C. (7/9)^12

Step-by-step explanation:

(49/81)^6 = (7^2/9^2)^6 = (7/9)^(2x6) = (7/9)^12

Answer:

diameter is 24 inches

Step-by-step explanation:

diameter is basically two times the radius

Answer:

$32.07

Step-by-step explanation:

Just add them together.

Answer:

256, 8192

{This is an educated guess}

Step-by-step explanation:

The problem seems to be a variation of the Fibonacci sequence: 1, 1, 2, 3, 5, 8...

1 ⇒ 2: 1*2

2 ⇒ 2: 2*1

2 ⇒ 4: 2*2

4⇒8:4*2

8⇒32:8*4

32⇒256: 32*8

256*32 = 8192

Answer:

No

Step-by-step explanation:

B/c trinomial has exactly 3 terms and binomial only have 2

The system of nonlinear equations have two solutions: (x, y) = (0.114, 0.354), (x, y) = (1.432, 1.103).

In this problem we find a system of two nonlinear equations involving radical expressions. We proceed to resolve the system of nonlinear equations by algebra properties:

(2 · x - 1)² + 8√(2 · x · y) = 4

8√(2 · x · y) = 4 - (2 · x - 1)²

8√(2 · x · y) = 4 - 4 · x² + 4 · x - 1

8√(2 · x · y) = 4 · x - 4 · x² + 3

64 · (2 · x · y) = [(4 · x + 3) - 4 · x²]²

128 · x · y = (4 · x + 3)² - 8 · (4 · x + 3) · x² + 64 · x⁴

128 · x · y = 16 · x² + 24 · x + 9 - 32 · x³ - 24 · x² + 64 · x⁴            (1)

4 · y - √(8 · x · y - 1) = 1

4 · y - 1 = √(8 · x · y - 1)

(4 · y - 1)² = 8 · x · y - 1

16 · y² - 8 · y + 2 = 8 · x · y                                                             (2)

Now we plot two equations on a graphing tool and find that the system has the following two solutions: (x, y) = (0.114, 0.354), (x, y) = (1.432, 1.103).

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Answer: 66.2=54.5+3gg

gg=3.9 gigabytes

Step-by-step explanation:

66.2=54.5+3gg

3gg=66.2-54.5

3gg=11.7

gg=3.9 gigabytes

3.9 number of gigabytes of data William can use while staying within his budget.

Two or more expressions with an Equal sign is called as Equation.

Given,

William pays a flat cost of $54.50 per month and $3 per gigabyte.

He wants to keep his bill at $66.20 per month.

We need to solve this and to find number of gigabytes of data William can use while staying within his budget.

This can be written as equation

66.2=54.5+3gg

Subtract 54.5 from both sides

66.2=54.5+3gg

3gg=66.2-54.5

3gg=11.7

Divide both sides by 3

gg=3.9 gigabytes

Hence, 3.9 number of gigabytes of data William can use while staying within his budget.

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Answer:

-7 i + 16

Step-by-step explanation:

Simplify the following:

(-2 i + 1) (5 i + 6)

(1 - 2 i) (6 + 5 i) = (1) (6) + (1) (5 i) + (-2 i) (6) + (-2 i) (5 i):

6 + 5 i - 2 i×6 - 2 i×5 i

-2×6 = -12:

6 + 5 i + -12 i - 2 i×5 i

-2 i×5 i = -2 i^2 5:

6 + 5 i - 12 i + -2 i^2×5

i^2 = -1:

6 + 5 i - 12 i - 2-1×5

-2 (-5) = 10:

6 + 5 i - 12 i + 10

6 + 5 i - 12 i + 10 = (6 + 10) + (5 i - 12 i) = 16 - 7 i:

Answer:  -7 i + 16

Answer: your answer to this question would be 16-7i

Step-by-step explanation:

Answer: the answer is MO=5

Step-by-step explanation:

Answer:

5,11 , 17, 23, 29, 35

Step-by-step explanation:

Answer:

5, 11, 17, 23, 29, 36

Step-by-step explanation:

To get from 5 to 11, we add 6. Similarly, to get from 11 to _, we add 6, and get 17. This also works with 29 to _. We get 36.

Answer:

2556285=68358556

Step-by-step explanation:

+58385-5838688(68589)8999=9858288

The output values of ​g(​-6), ​g(1​), and ​g(8​) in the given piecewise function are -1, 6 and -6 respectively.

Given the piecewise function in the question;

                   x + 5, for x ≤ 1

                   2 - x, for x > 1

Determine the output value of g(-6), -6 falls in the domain of x ≤ 1,

Hence;

g(x) = x + 5

g(-6) = -6 + 5

g(-6) = -1

Determine the output value of g(1), 1 falls in the domain of x ≤ 1,

Hence;

g(x) = x + 5

g(1) = 1 + 5

g(1) = 6

Determine the output value of g(8), 8 falls in the domain of x > 1,

Hence;

g(x) = 2 - x

g(8) = 2 - 8

g(8) = -6

Therefore the output values of ​g(​-6), ​g(1​), and ​g(8​) in the given piecewise function are -1, 6 and -6 respectively.

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Let the another side be x m.

Therefore, the longer side = (4 + 4x) m.

Now,

[tex]{\sf{→x \times (4 + 4x) = 224 \\ →4x + 4x {}^{2} - 224 = 0 \\→ x {}^{2} + x - 56 = 0 \\ →x {}^{2} + 8x - 7x - 56 = 0 \\ →x(x + 8) - 7(x + 8) = 0 \\ →(x - 7)(x +8 ) = 0 \\ →x = 7 \: or \: x = - 8 \\ \\ length \: cannot \: be \: negative \\ possible \: solution \: (x) = 7}}[/tex]

Length of shorter side = x = 7 metres.

[tex]{\sf{answer\: \\ss}}[/tex]

Answer:

x+4+2x-7=180

3x-3=180

3x=183

x=61

Answer:

(b-5)(b-3)

Step-by-step explanation:

To factor this equation we have to find 2 numbers that combine to equal -8 and multiply together to equal 15

these numbers would be -3 and -5

after that you just put them in an equation like so:

(b-5)(b-3)

you can check your work by just multiplying those back together

If you want future explanation on how to do this just ask

hope this helps :D

Answer:

[tex]\sqrt{4}[/tex], [tex]\sqrt{9}[/tex], [tex]\sqrt{16}[/tex]

Step-by-step explanation:

I think that you are asking for 3 examples of square roots that are rational.  All perfect squares are rational.  If the square root is not a perfect square then the number is irrational.

[tex]\sqrt{4[/tex] = 2 and -2.  The number multiplied by itself is an integer.  Integers are the whole numbers and their opposites: ...-3, -2, -1,  0, 1, 2, 3...  

1/2 is not an integers.  0.75 is not an integer.

[tex]\sqrt{9}[/tex]  is 3 and -3

[tex]\sqrt{16}[/tex] is 4 and -4

Numbers like:

[tex]\sqrt{3}[/tex] is irrational because this number in a decimal form never terminates or repeats.  

Answer:

3.75

Step-by-step explanation:

15/4=3.75

Answer:

12 1/3

Step-by-step explanation:

because when you find the total cost plus divide it gives u the answer

Answer:

3rd option

Step-by-step explanation:

One of our exponent rules tells us that [tex](\frac{x}{y} )^{z}[/tex] =  [tex]\frac{x^{z} }{y^{z} }[/tex]. So, knowing that exponent rule, we know that it has to be the third option. But what if we didn't know that rule? Then how could we solve this?

We know that 3/2 = 1.5. Do some math and you can figure out that 1.5^3 is 3.375. If we were to evaluate expression number 3, we would get 27/8, which, if you were to further evaluate it, you would also get 3.375.

Let me know if you have any questions!

Answer:

(1, 1,-3)

Step-by-step explanation:

The composition of the functions, f(g(-1)) = 2.

To find the composition of the functions, f(g(-1)), first, find the function, g(-1) by tracing the value of y that will give an x-value of -1 on the function graph.

The next step is to use the value you get in the first step to trace which value of y will give an x-value equivalent to what you got in the first step on the second function graph.

Thus, from the graph of g(x), g(-1) = 0. Using the graph of f(x), the value of y when x = 0 is 2.

Therefore, the composition of the functions, f(g(-1)) = 2.

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88 kilometers per hour in miles per hour is 54.68 mi/hr

Note that:

1 km = 0.6214 miles

The measurement to convert is 88 kilometers per hour

Multiply 88 kilometers per hour by 0.6214 to convert to miles per hour

88 kilometers per hour = 88 x 0.6214 miles per hour

88 kilometers per hour = 54.6832 miles per hour

88 kilometers per hour =  54.68 mi/hr

Therefore, 88 kilometers per hour in miles per hour is 54.68 mi/hr

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