Simplify the complex fraction below.

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:

6 7/8

Step-by-step explanation:

First we would need to turn the 5 1/2 into a improper fraction. Then, do the same for the 1 1/4 as well. To do this, multiply the denominator by the whole number and then add the numerator. Once you get those values, you simply multiply across, meaning the numerators get multiplied together and the denominators get multiplied together. The value you get is the improper fraction form of the simplest form. Then you can convert it back to a mixed fraction if that is the form you need. To do this divide the numerator by the denominator. Now we have a value of 11/2 x 5/4 = 55/8. So divide 55 by 8 and leave the remainder in fraction form. Therefore the answer should be 6 7/8, after it is reduced.

I hope this helps, have a blessed day! :)

Answer:

w = 3, x = -35/2, y = 8, z = -1

Step-by-step explanation:

Solve the following system:

{-3 w - 2 x - 4 y - z = -5

{2 w + y + 6 z = 8

{4 z + 4 w = 8

{-4 w = -12

In the fourth equation, look to solve for w:

{-3 w - 2 x - 4 y - z = -5

{2 w + y + 6 z = 8

{4 z + 4 w = 8

{-4 w = -12

Divide both sides by -4:

{-3 w - 2 x - 4 y - z = -5

{2 w + y + 6 z = 8

{4 z + 4 w = 8

{w = 3

Substitute w = 3 into the first, second, and third equations:

{-9 - 2 x - 4 y - z = -5

{6 z + y + 6 = 8

{4 z + 12 = 8

{w = 3

In the third equation, look to solve for z:

{-9 - 2 x - 4 y - z = -5

{6 z + y + 6 = 8

{4 z + 12 = 8

{w = 3

Subtract 12 from both sides:

{-9 - 2 x - 4 y - z = -5

{6 z + y + 6 = 8

{4 z = -4

{w = 3

Divide both sides by 4:

{-9 - 2 x - 4 y - z = -5

{6 z + y + 6 = 8

{z = -1

{w = 3

Substitute z = -1 into the first and second equations:

{-4 y - 2 x - 8 = -5

{y = 8

{z = -1

{w = 3

Substitute y = 8 into the first equation:

{-2 x - 40 = -5

{y = 8

{z = -1

{w = 3

In the first equation, look to solve for x:

{-2 x - 40 = -5

{y = 8

{z = -1

{w = 3

Add 40 to both sides:

{-2 x = 35

{y = 8

{z = -1

{w = 3

Divide both sides by -2:

{x = -35/2

{y = 8

{z = -1

{w = 3

Collect results in alphabetical order:

Answer: {w = 3, x = -35/2, y = 8, z = -1

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]

The cost of buying lemons to make two 9-inch lemon pies is $5.20.

The first step is to convert cup to tablespoons

1 cup = 16 tablespoons

one 9-inch lemon pie would require 8 tablespoons (16 /2)

two  9-inch lemon pie would require 16 tablespoons (8 x 2)

The second step is to determine how much lemons would be needed.

Lemons needed = table spoons needed / table spoon one lemon would yield

16 / 2 = 8 lemons

The total cost of lemons needs to make the pies = cost of one lemon x number of lemons needed

8 x 0.65 = $5.20

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Answer:

$32.07

Step-by-step explanation:

Just add them together.

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:

2556285=68358556

Step-by-step explanation:

+58385-5838688(68589)8999=9858288

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:

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:(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:

57, 59 and 61

Step-by-step explanation:

Let the first odd number be n The next consecutive odd number is n + 2 and the next one after that is n + 4
(consecutive odd numbers have difference of 2 between them. For example if 7 is the first odd number next one is 9(7+2) and the next one is 11(7+4)

We are given that the sum of the numbers is 177. So we have the following equation:

n + (n + 2) + (n +4) = 177

Simplifying gives

n + n + 2 + n + 4  = 177

Collect like terms:

n + n + n + 2 + 4 = 177
3n + 6 = 177

Subtract 6 from both sides
==> 3n = 177 - 6
==> 3n = 171

Divide by 3 both sides
3n/3 = 171/3

n = 57 and this is the first of the odd numbers

The next odd number is 57+ 2 = 59

and the next one after that is 59 + 2 = 61 (same as 57 + 4)

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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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 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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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:

x+4+2x-7=180

3x-3=180

3x=183

x=61

Answer:

(1, 1,-3)

Step-by-step explanation:

The linear system of equation has one solution as x = 16 and y = -12.

What is Algebraic expression ?

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

The given system of equation are :

y=-x+4..........(1)

x + 2y = -8......(2)

Now, solving the above using substitution of y in equation (2) :

x + 2y = -8

x+2(-x+4) = -8

x-2x+8 = -8

-x = -16

x = 16

Now, substituting back x value in equation (1) we get :

y = -x+4

y = -16 +4

y = -12

Therefore, The linear system of equation has one solution as x = 16 and y = -12.

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Answer: the answer is MO=5

Step-by-step explanation:

Answer:

16 meters is the answer of this question

Answer:

diameter is 24 inches

Step-by-step explanation:

diameter is basically two times the radius

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:

The room is 5 inches in the drawing.

Step-by-step explanation:

If the room is 20 feet and each inch in his drawing measures 4 feet what you need to do is see how many times 4 goes into 20.

4 times 5 = 20

So the answer would be 5

Hope it helps! =D

Using the concepts of asymptotes and inverse function, we have that:

a) For f, the vertical asymptote is x = -2/3 and the horizontal asymptote is y = 1/6.

b) The inverse function is: [tex]y = f^{-1}(x) = \frac{4x - 10}{1 - 6x}[/tex]

c) For the inverse function, the vertical asymptote is x = 1/6 and the horizontal asymptote is y = -2/3.

For this problem, the function is given by:

[tex]f(x) = \frac{x + 10}{6x + 4}[/tex]

The zero of the denominator is:

6x + 4 = 0

6x = -4

x = -4/6 = -2/3.

Hence the vertical asymptote is x = -2/3.

The horizontal asymptote is given as follows:

[tex]y = \lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} \frac{x + 10}{6x + 4} = \lim_{x \rightarrow \infty} \frac{x}{6x} = \lim_{x \rightarrow \infty} \frac{1}{6} = \frac{1}{6}[/tex]

To find the inverse function of a function y = f(x), we exchange x and y then isolate y.

Exchanging x and y, we have that:

[tex]x = \frac{y + 10}{6y + 4}[/tex]

Applying cross multiplication:

x(6y + 4) = y + 10

6xy - y = 10 - 4x

y - 6xy = 4x - 10

y(1 - 6x) = 4x - 10

[tex]y = f^{-1}(x) = \frac{4x - 10}{1 - 6x}[/tex]

Applying the same procedure, for the inverse function, the vertical asymptote is x = 1/6 and the horizontal asymptote is y = -2/3.

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Answer:

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

Step-by-step explanation:

2×2×2×2×2 = 2[tex] {}^{5} [/tex]

Considering the expression of a line, the line is y= 1/3x -2/3 and the graph of this line is shown in the attached image.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing the value of slope m, substituting this value and the value of the point in the expression of a linear equation, y = mx + b, the value of the ordinate to the origin b can be obtained.

In this case, you know:

Substituting the value of the slope m:

y= 1/3x +b

Substituting the point to calculate the value of b:

-1= 1/3×(-1) + b

-1= -1/3 + b

-1 + 1/3= b

-2/3= b

Finally, the line is y= 1/3x -2/3 and the graph of this line is shown in the attached image.

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