What is a negative rational number times a positive integer?
A) A negative integer
B) A positive rational number
C) A negative rational number
D) An irrational number

Converting -4 to polar form gives [tex]-4=4\exp(i\pi)[/tex].

Then the 4th roots of -4 would be the numbers

[tex]4^{1/4}\exp\left(i\dfrac{\pi+2k\pi}4\right)[/tex]

where k is taken from {0, 1, 2, 3}.

So we have

[tex]z_1=4^{1/4}\exp\left(\dfrac{i\pi}4\right)=\sqrt2\left(\cos\dfrac\pi4+i\sin\dfrac\pi4\right)=1+i[/tex]

[tex]z_2=\sqrt2\left(\cos\dfrac{3\pi}4+i\sin\dfrac{3\pi}4\right)=-1+i[/tex]

[tex]z_3=\sqrt2\left(\cos\dfrac{5\pi}4+i\sin\dfrac{5\pi}4\right)=-1-i[/tex]

[tex]z_4=\sqrt2\left(\cos\dfrac{7\pi}4+i\sin\dfrac{7\pi}4\right)=1-i[/tex]

Answer:

The expressión that represents the length:

a = 2w + 1

a = length of the rectangle

w = width of the rectangle

Answer:

Yep

Step-by-step explanation:

Hfbdjdjdkdjdjkeied

Answer:

$54.65 profit per seat

Step-by-step explanation:

150(185) + 35(185)(.8) = 27,750 + 5,180 = 32,930 - 22,000 = 10,930

10,930/200 = $54.65 profit per seat

Answer:

$54.65

Step-by-step explanation:

First, we find the total amount made. This is easy:

(150 x 185) + (35 x .8(185)) =

27750 + 5180 =

32930

We then subtract the $22000, so the company makes a profit of 10930. There are 200 seats, so the profit made per seat is $54.65

Answer:

-16128

Step-by-step explanation:

This expression can be calculated by algebraic means, whose process is described below:

1) [tex](-28)^{3}+(12)^{3}+(16)^{3}[/tex] Given.

2) [tex](-12-16)^{3} + (12)^{3}+(16)^{3}[/tex] Definition of addition.

3) [tex](-12)^{3} + 3\cdot (-12)^{2}\cdot (-16)+3\cdot (-12)\cdot (-16)^{2}+(-16)^{3}+(12)^{3}+(16)^{3}[/tex] Cubic perfect binomial.

4) [tex](12)^{3}+[(-1)\cdot (12)]^{3}+(16)^{3} + [(-1)\cdot (16)]^{3}+3 \cdot (-12)^{2}\cdot (-16) + 3\cdot (-12)\cdot (-16)^{2}[/tex] Commutative property/[tex](-x)\cdot y = -x\cdot y[/tex]

5) [tex](12)^{3} + (-1)^{3}\cdot (12)^{3} + 16^{3} +(-1)^{3}\cdot (16)^{3} + (-3)\cdot [(-12)^{2}\cdot (16) +(-16)^{2}\cdot (12)][/tex] Distributive property/[tex](-x)\cdot y = -x\cdot y[/tex]/[tex]x^{n}\cdot y^{n} = (x\cdot y)^{n}[/tex]

6) [tex](12)^{3} + [-(12)^{3}]+(16)^{3} + [-(16)^{3}]+ (-3)\cdot [(-12)^{2}\cdot (16)+(-16)^{2}\cdot (12)][/tex] [tex](-x)\cdot y = -x\cdot y[/tex]

7) [tex](-3)\cdot [(-12)^{2}\cdot (16) + (-16)^{2}\cdot (12)][/tex] Existence of the additive inverse/Modulative property for addition.

8) [tex](-3) \cdot [(12)^{2}\cdot (16)+(16^{2})\cdot (12)][/tex] [tex]x^{n}\cdot y^{n} = (x\cdot y)^{n}[/tex]/[tex](-x)\cdot (-y) = x\cdot y[/tex]

9) [tex](-3)\cdot (12)\cdot (16)\cdot (12+16)[/tex] Distributive property.

10) [tex]-16128[/tex]     [tex](-x)\cdot y = -x\cdot y[/tex]/Definition of sum/Definition of multiplication/Result

Answer:

  3 1/2 hours

Step-by-step explanation:

This is a problem in units conversion. We want to get from bags to hours by way of minutes per bag. One bag takes an effort of 2/3 person·minute, so we need to divide the total effort by the number of persons and convert minutes to hours.

  (1575 bags)×(2/3 person·min/bag)/(5 person)/(60 min/h)

  = (1575)(2/3)(1/5)(1/60) h = 3.5

It will take the 5 of them about 3 1/2 hours to prepare 1575 bags.

Answer:

3 1/2

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

I just got it correct on a.p.e.x :)

The solution to the equation [tex]\log_5(2x - 3) = 2[/tex] is x = 14

The equation is given as:

[tex]\log_5(2x - 3) = 2[/tex]

Convert the equation to an exponential equation

2x - 3 = 5^2

Evaluate the exponent

2x - 3 = 25

Add 3 to both sides

2x = 28

Divide both sides by 2

x = 14

Hence, the solution to the equation [tex]\log_5(2x - 3) = 2[/tex] is x = 14

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Answer:

co-ordinates are (-3,7) and (5,7)

or

(-3,-5) and (5,-5)

length of diagonal=10 units

Step-by-step explanation:

[tex]length=\sqrt{(5+3)^2+(1-1)^2} =\sqrt{64} =8\\slope ~of~length=\frac{1-1}{5+3} =0\\\\length ~of~rectangle~is~parallel~to~x-axis\\ width~ is~ parallel ~to~y- axis~and~is~6~units~away~from~length.\\other co-ordinates ~of~rectangle are~(-3,1+6)~and ~(5,1+6)~or~(-3,7)~and~(5,7)\\and~other~co-ordinates~are~(-3,1-6)~and~(5,1-6)~or~(-3,-5)~and~(5,-5)[/tex]

length of diagonal

d=\sqrt{8^2+6^2} =\sqrt{64+36} =\sqrt{100} =10 ~units\\or\\d=\sqrt{(5+3)^2+(1-7)^2} =\sqrt{64+36} =\sqrt{100} =10~units.

Answer:

See attached image for the sum computed using wolfram alpha, raw value is: 49382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382715160

Answer:

Step-by-step explanation:

First, i divide all terms by 4

sequence is 1,11,111,1111,....,1111...1111 (with 2000 digits)

[tex]u_1=1\\\\u_2=11=10+1=\dfrac{10^2-1}{9}\\\\u_3=111=100+10+1=\dfrac{10^3-1}{9}\\\\u_4=1111=1000+100+10+1=\dfrac{10^4-1}{9}\\....\\u_n=\dfrac{10^n-1}{9}\\\\\\\displaystyle \sum_{i=1}^n\ u_1 =\dfrac{10^1-1}{9}+\dfrac{10^2-1}{9}+\dfrac{10^3-1}{9}+...+\dfrac{10^n-1}{9}\\=\dfrac{1}{9} *(10+10^2+10^3+....+10^n+1-1-(1+1+1+1...+1)\ )\\\\=\dfrac{1}{9}*( \frac{10^{n+1}-1}{9} -(n+1)\ )[/tex]

[tex]\boxed{4+44+444+....+444...4=\dfrac{4}{9}*( \dfrac{10^{2001}-1}{9} -2001\ )}\\\\\\\approx{4,9382716049382716049382716049383*10^{1999} }[/tex]

Answer:

Hello,

[tex]\begin{bmatrix}\dfrac{-1}{5} &0\\\dfrac{-1}{10}&\dfrac{1}{4}\end{bmatrix}[/tex]

Step-by-step explanation:

See jointed file

The inverse of the matrix A is

[tex]A = \left[\begin{array}{cc}-5&-2\\0&4\end{array}\right][/tex]

A matrix is a set of numbers arranges in rows and columns such that it form a rectangular array.

We have,

[tex]A = \left[\begin{array}{cc}-5&0\\-2&4\end{array}\right][/tex]

The matrix A is a square matrix and its determinant is not zero.

So the inverse exist.

The inverse of matrix A.

We will change the rows into columns and columns into rows.

So,

[tex]A = \left[\begin{array}{cc}-5&-2\\0&4\end{array}\right][/tex]

Thus,

The inverse of the matrix A is given above.

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Answer:

The correct answer is B.

Step-by-step explanation:The entrance fee ($18) and the cost per ball ($0.08B) added together should equal greater or equal to $75 in order to receive $10 off.

Answer:

£24.26 (rounded to 2dp) or full answ £24.255

Step-by-step explanation:

find 1% of 22.05= 0.2205

0.2205*10=2.205(10%)

add this to the 90%(£22.05+2.025)= 24.255

                                                          =24.26(rounded to 2dp)

The price of the lamp before the reduction will be £24.5.

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

To Calculate the percent of a number , divide the number by whole number and multiply by 100.

Given that;

The sale price of the lamp = £22.05

This is a 10% reduction of the normal price.

Now,

Let the price of the lamp before the reduction = x

So, We can formulate;

⇒ x - (10% of x) = £22.05

⇒ x - 10x/100 = £22.05

⇒ (100x - 10x)/100 = £22.05

⇒ 90x / 100 = £22.05

⇒ 90x = £22.05 x 100

⇒ 90x = £2205

⇒ x = £2205/90

⇒ x = £24.5

Thus, The price of the lamp before the reduction will be £24.5.

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9514 1404 393

Answer:

  A.  x = ±2

Step-by-step explanation:

Add 14, then take the square root.

  x^2 -14 +14 = -10 +14

  x^2 = 4

  x = ±√4

  x = ±2

Answer:

A

Step-by-step explanation:

X^2-14=-10

X^2=14-10

X^2=4

√X2=√4

X=±2

Step-by-step explanation:

it was helpful to you

always be happy in your life㋛︎㋛︎☺︎︎☺︎︎☺︎︎

[tex] {x}^{2} + 7x \\ x(x + 7) \\ \\ \\ 6 + 9x \\ 3(2 + 3x) \\ \\ 6 {y}^{2} - 9xy \\ 3x(2y - 3x)[/tex]

Answer:

x is 3

Step-by-step explanation:

[tex]{ \bf{U _{2} - U _{1} = U _{3} -U _{2} }}[/tex]

[tex]{ \tt{3x - (x + 2) = (4x + 1) - 3x}} \\ { \tt{2x - 2 = x + 1}} \\ { \tt{x = 3}}[/tex]

Answer:

value of x is 6

Step-by-step explanation:

got it right on edgenuit

Answer:

{(1, 2), (3, 2), (5, 7)}

Step-by-step explanation:

A function has a one to one correspondence

Each x can go to only 1 y value

{(1, 2), (3, 2), (5, 7)} function

{(3, 5), (-1, 7), (3, 9)} 3 goes to more than 1 y value

{(1, 2), (1, 4), (1, 6)} 1 goes to more than 1 y value

Answer:

[tex]\huge \boxed{ \{(1, 2), (3, 2), (5, 7)\} }[/tex]

Step-by-step explanation:

[tex]\sf A \ function \ is \ a \ relation \ if \ each \ x \ value \ is \ for \ each \ y \ value.[/tex]

[tex]\{(1, 2), (3, 2), (5, 7)\} \ \sf represents \ a \ function.[/tex]

[tex]\{(3, 5), (-1, 7), (3, 9)\} \ \sf does \ not \ represent \ a \ function.[/tex]

[tex]\{(1, 2), (1, 4), (1, 6)\} \ \sf does \ not \ represent \ a \ function.[/tex]

Answer:

x^2-12x+31

Step-by-step explanation:

Standard form of the quadratic equation (x-6)^2-5 is x^2-12x+36-5=x^2-12x+31

Answer:

f(x) = 8(1/2)^x.

Step-by-step explanation:

According to the graph, there is a point at (0, 8) and (1, 4).

That means that when x = 0, y = 8.

8 = a(b)^0

1a = 8

a = 8

That means that a = 8, and when x = 1, y = 4.

4 = 8(b)^1

4 = 8b

8b = 4

b = 4/8

b = 1/2

So, f(x) = 8(1/2)^x.

Hope this helps!

Answer:

36

Step-by-step explanation:

you know the number based on the sequence

the values increase in the form of x+2

e.g. 4-1=3

      9-4=5

      16-9=7

      25-16=9

you can see the number adds 2 for every increased number

and by following this sequence you will get the number 36

Answer:

by the square of 1, 2 ,3 the sequence has been made

Step-by-step explanation:

1 for 1²

4 for 2²

9 for 3²

16 for 4²

25 for 5²

so the later one will be 36 for 6²

so the answer is 36 thats all

Answer:

24 square units

Step-by-step explanation:

Use the formula for area of a parallelogram to solve.  The base is 6 units, and the height is 4 units.

A = bh

A = (6)(4)

A = 24 square units

The area of the parallelogram is 24 square units.

Answer:

C = 4 memory cards.

Step-by-step explanation:

256 × 4 = 1024

1024 + 105 = 1129 GB

She needs 4 memory cards.

Nancy needs to buy 4 memory cards.

Given that Nancy needs at least 1000 gigabytes of storage to take pictures and videos on her upcoming vacation, and she checks and finds that she has 105 GB available on her phone, and she plans on buying additional memory cards to get the rest of the storage she needs, and the cheapest memory cards she can find each hold 256 GB and cost $ 10, and she wants to spend as little money as possible and still get the storage she needs, to determine how many memory cards to buy, the following calculation must be performed:

So if Nancy buys 3 cards she will still be short on gigabytes. Therefore, she must buy 4 memory cards.

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Answer:

I think the answer is both

Answer

hope this helps

Answer:

Sector

Step-by-step explanation:

A sector of a circle is the portion of circle enclosed by two radii and arc

Answer:

A.Line

Step-by-step explanation:

The locus of points in a plane equidistant between (-5, -6) and (-5, 7) is describe by the Line. so option A is correct.

A line segment is a straight line with finite length, and thus, have to endpoints(points on either ends).

We know that the graph of x = 5 is the vertical line through 5 on the x-axis. Two points on this line are (-5, -6) and (-5, 7).

We form a horizontal line through (0,1) and (1,1). This is the locus of points equidistant between (-5, -6) and (-5, 7)

We have parallel lines like this, the locus of points equidistant from the two lines is always one single line, and it's the middle line as described above.

This applies to diagonal parallel lines as well, and vertical parallel lines.

Hence, The locus of points in a plane equidistant between (-5, -6) and (-5, 7) is describe by the Line. so option A is correct.

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Answer:

1st option is decreased 2nd is increased

Step-by-step explanation:

Because you add a liquid to dilute a solution, it makes the solution weaker (less concentrated) you also added more liquid which would increase the volume

Answer:

decreased; increased

Step-by-step explanation:

when you dilute something you make it less concentrated by adding something else (usually water i think). so the concentration decreases while the volume increases

Answer:

Step-by-step explanation:

The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known the angle opposite to the third side is given. The distance between A and B is 85.6 yds.

The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known the angle opposite to the third side is given. It is given by the formula,

[tex]c =\sqrt{a^2 + b^2 -2ab\cdot Cos\theta}[/tex]

where

c is the third side of the triangle

a and b are the other two sides of the triangle,

and θ is the angle opposite to the third side, therefore, opposite to side c.

The three points A, B, and C will form a triangle. Therefore, using the law of cosine the measure of the third side AB can be written as,

[tex]AB =\sqrt{(AC)^2 + (BC)^2 -2(AC)(BC)\cdot \cos(51.2^o)}\\\\AB =\sqrt{(80)^2 + (104)^2 -2(80)(104)\cdot \cos(51.2^o)}\\\\AB = \sqrt{6400+10816-16640\cos51.2^o}\\\\AB = \sqrt{7328.4}\\\\AB=85.6\rm\ yd[/tex]

Hence, the distance between A and B is 85.6 yds.

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